http://2012.igem.org/wiki/index.php?title=Special:Contributions/Ksk_89&feed=atom&limit=50&target=Ksk_89&year=&month=2012.igem.org - User contributions [en]2020-02-26T13:43:53ZFrom 2012.igem.orgMediaWiki 1.16.0http://2012.igem.org/Team:Colombia/Human/EssayTeam:Colombia/Human/Essay2012-10-27T04:04:54Z<p>Ksk 89: /* Geneticized future: the gene dream and the gene nightmare */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
''Note'': If by any chance you, the reader, knows about genetics history and basic Mendelian laws, you may be bored by the first couple of sections, so just '''jump''' straight to ''The Human Genome Project and the gene as a cultural icon'' section's '''fourth paragraph'''!<br />
<br />
= '''Essay: The Impact of Genetic Technologies on Society'''=<br />
<br />
The generation of offspring may be the only way of “genetic-self” preservation for years to come. As ephemeral beings, it’s only natural for humans to become concerned about heritage as a means to prolong their legacy on Earth. In this context, genetics emerges as the science in charge of explaining the inheritance of characteristics from parents to the next generation. This essay will try to explore the several phases of genetics in history: how it has moulded society from its very beginnings, defined important aspects of our everyday lives, and how it may revolutionize the future of the human species.<br />
<br />
== From practical genetics to Mendel [[#References|[1] ]] ==<br />
<br />
As mentioned earlier, genetics is not a new concept. The idea of offspring acquiring traits from their parents should have become evident to the first human civilizations. What’s more, during humanity’s process towards a sedentary lifestyle, phenotypic advantages of some crops or domestic animals over others stimulated the idea of selective breeding, probably one of the first genetic notions. This initiative, also known as practical genetics, resulted in the careful controlling of the mating of the “better”, more productive individuals, while getting rid of the “worst”. Thus, genetics begins as a necessity for the forging of towns and villages, through the increasing of production efficiency, in order to maintain larger social associations. <br />
<br />
The first notions of the possible heritage material came from history’s early philosophers, such as [http://en.wikipedia.org/wiki/Hippocrates Hippocrates] and [http://en.wikipedia.org/wiki/Aristotle Aristotle]. They both agreed that the heritable traits were carried in semen, where, either the semen from both parents (for Hippocrates) or the interference of the mother’s blood with the father’s semen (for Aristotle), were finally mixed into a whole new individual who would carry characteristics from both. Even though the fall of the Greek civilization and the advent of the Roman Empire and the Middle Ages slowed down science for more than a thousand years, practical geneticists, namely farmers and stockbreeders, had already achieved important advances. First, the realization that some stable varieties nearly always bred true, with their offspring having the same characteristics as their parents. Second, that it was sometimes possible to mate parents from different varieties to form [http://en.wikipedia.org/wiki/Hybrid_(biology) hybrids]; and third, that even stable varieties occasionally produced offspring different from either parent.<br />
<br />
Practical genetics, however, was purely empirical, and society had yet to discover any laws of inheritance, that is, until [http://en.wikipedia.org/wiki/Gregor_Mendel Gregor Mendel]’s experiments (XIX century). In accordance with Hippocrates’s conjectures, Mendel described heritable traits as physical substances (genes) that retained their identity in hybrids, never blending together. Differing from Aristotle, Mendel confirmed the importance of both parents towards the generation of an offspring’s traits, where each organism, while having two copies per gene (each from one parent), produces gametes carrying one gene copy for each trait. Another of Mendel’s discoveries was that a gene form ([http://en.wikipedia.org/wiki/Allele allele]) may be [http://en.wikipedia.org/wiki/Dominance_(genetics) dominant over another (recessive)], and that different alleles would be sorted out to sperm and eggs [http://en.wikipedia.org/wiki/Mendelian_inheritance randomly and independently], where all combinations of alleles are equally likely. Even though ignored at first, the rediscovery of Mendel’s work, together with the emerging [http://en.wikipedia.org/wiki/Cytology cytology], [http://en.wikipedia.org/wiki/Cytogenetics cytogenetics], and advances in [http://en.wikipedia.org/wiki/Microscopy microscopy], enabled men to locate these genes in [http://en.wikipedia.org/wiki/Chromosome chromosomes], map them, and analyze their patterns of inheritance.<br />
<br />
== The Human Genome Project and the gene as a cultural icon ==<br />
<br />
Throughout the next two hundred years, scientists delved deeper into the basic Mendelian laws. [http://en.wikipedia.org/wiki/Gene Genes] were known to exist and found to be packaged in chromosomes, however, the exact composition of genes and how they work was still an enigma [[#References|[1] ]]. Biological models such as the rod shaped bacterium ''Escherichia coli'', and the fruit fly ''Drosophila melanogaster'', enabled science to describe what is now known as the [http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology central dogma of molecular biology]. This theory states that genes are a compilation of a four letter code in the [http://en.wikipedia.org/wiki/DNA DNA molecule], that they are read and transcribed into another code called [http://en.wikipedia.org/wiki/Messenger_RNA messenger RNA], and finally interpreted and translated into a [http://en.wikipedia.org/wiki/Protein protein] (biological effector) by the combined interaction of [http://en.wikipedia.org/wiki/Transfer_RNA transfer RNA] and [http://en.wikipedia.org/wiki/Ribosome ribosomes]. Furthermore, the notion of genes as the unchanging units of heredity was found to be wrong, as they may be, and constantly are, altered by [http://en.wikipedia.org/wiki/Mutation mutations]. In summary, the genetic code carries the information necessary to build a living being, from a bacterium to a fungus, a chimpanzee or a human. <br />
Research in gene sequencing and its association to a particular biological function were the first steps towards [http://en.wikipedia.org/wiki/Genetic_engineering gene engineering], where scientists discovered ways of transforming organisms with [http://en.wikipedia.org/wiki/Transgene transgenes] (genetic information coming from another species). Pharmaceutical industries and other large companies, encouraged by the possibility of using this information to revolutionize industrial and medical market, accelerated genetics evolution by funding its research.<br />
<br />
In this context, the realization of a [http://en.wikipedia.org/wiki/Human_Genome_Project Human Genome Project (HGP)] was the next natural step to make. The HGP refers to an international 13 year effort (finished in 2003) whose goals were: the identification of the approximate 20,000 genes in the human DNA, the determination of the sequence of the 3 billion base pairs (letter code) that make up human DNA, the storage of this information in databases, the improvement of tools for sequence analysis, the transferral of related technologies to the private sector, and the addressing of the the ethical, legal, and social issues that may arise from the its discoveries [[#References|[2] ]].<br />
<br />
Since differences in genetic coding are, in principle, what makes an individual unique among members of its own species, the HGP inspired enormous symbolical expectancies in the general public. This could be because certain achievements, such as the first lunar landing, atomic fission, and in this case the determination of the human genome sequence ultimately change how humans think of themselves [[#References|[3] ]]. Determination of the internal genetic scaffold around which every human life is moulded, and how this has been handed to us from our ancestors, is crucial towards the understanding of how humans have evolved, revealing just how similar or different we are to each other and to other species: what is it exactly that makes us humans.<br />
<br />
Advances in genetic comprehension made way for the geneticization of society, “an ongoing process by which priority is given to differences between individuals based on their DNA codes, with most disorders, behaviours, and physiological variations [...] structured as, at least in part, hereditary” [[#References|[4] ]]. Thus, the development of genetics as a science has progressively influenced genetic knowledge and technology in particular areas of society and culture. Influence that manifests itself directly by the application of gene testing; and indirectly through new concepts of health, disease [[#References|[5] ]], and politics. Dunn and Dobzhansky [[#References|[6] ]] sustain that in the uniqueness of each individual, that is, that everyone of us is different to anybody that has existed before and probably different than anyone who will exist, lies the fundamental base for ethics and democracy. Studies in Western society show diverse references to DNA, genes, and genetics –be it film, television, news reports, comic books, ads or cartoons; in addition to the media’s allusions to the idea that the essence of man, his true self, is in some way or another found in his genes [[#References|[5] ]], [[#References|[7] ]]. <br />
<br />
Medicine, too, is currently undergoing an extraordinary transition from its initial morphological and phenotypic orientation towards a molecular and genotypic one, promoting the importance of prognosis and prediction [[#References|[8] ]]. Thus, public health is suffering a massive change on disease conception, whereas pre and post–natal gene therapy to diminish susceptibilities to some disorders, and personalized drug prescriptions as treatment are no longer ideas, but possibilities.<br />
<br />
== Geneticized future: the gene dream and the gene nightmare ==<br />
<br />
Molecular geneticist Peter Little’s book [[#References|[9] ]] portrays the life of two very different individuals living the gene dream and the gene nightmare, respectively, in the same geneticized future. The former illustrates a world where “disease and suffering were an echo of the past” [[#References|[9] ]]: where prenatal DNA characteristics (disease susceptibilities and even personality issues) of fertilized embryos may be screened for the selection of the desired baby to be implanted via in vitro fertilization; where DNA may be tested for drug-response indicators so as to ensure future drug treatment perfectly matching the patient’s genetic profile. A future where severe burns may be completely healed or dismemberments entirely re-grown as a result of stem cell research; where personality disorders such as attention-deficit or alcohol abuse are treated with combinations of cell receptor regulators. A reality where many infectious diseases have been taken care of through appropriate drug targeting, where cancer is no more and neurodegenerative ailments such as [http://en.wikipedia.org/wiki/Alzheimer's_disease Alzheimer's disease] and [http://en.wikipedia.org/wiki/Huntington's_disease Huntington’s chorea] may be treated.<br />
<br />
In the gene nightmare, however, “disease and suffering were the results of nature and malign human influence”: where uncontrolled births, prone to high probability susceptibility to disease may deny an individual from eligibility to state medical insurance; where education is limited to those with a minimum genetically defined IQ. A future where people may become preventively imprisoned for displaying criminal predisposition; where DNA differences may be used as an object to racism and discrimination. A reality where humans may be declared genetically unsuitable for reproduction (eugenics), and where ethnic weapons, targeting specific gene markers, may annihilate complete human populations.<br />
Even though many of these ideals and curses are unlikely to happen, scientists are aware of the social outcomes that genetic research may inspire. As a matter of fact, “race” has been found not to have a strong “scientific support”, since it reflects just a few continuous traits determined by a small fraction of our genes. Conversely, genome studies should foster compassion, not only because our gene pool is extremely mixed, but because in the understanding of the genotype’s correspondence to the phenotype is the demonstration that everyone carries at least some deleterious alleles3. [http://en.wikipedia.org/wiki/Nazism Nazism], however, is sufficient proof that mankind's stupidity.<br />
<br />
Despite the huge amount of genetic data available to the general public, we strongly believe society lacks some crucial information about genes. Contemporary ideas suggest that we as individuals are product of our genes; however, this is not entirely true. Our genetic code indeed possesses the information necessary for every physiological process that we will carry on during our lifetime; nevertheless, society seems to be unaware of gene regulation and its explicit importance in defining an individual. In understanding that genes + environment = you, lies the life uncertainty that frees us from a definite destiny, highlighting the significance behind every decision we make. <br />
<br />
The greatest impact of genetics on society I believe lies within the very concept of manipulation, and synthetic biology stands as one of the major steps forward into life manipulation and organism programmed design. History has driven us in a way where the human essence rises from nature and spirituality. However, we are unavoidably getting to a point where human reason may finally impose over the laws of nature: where the discrimination of what is good or evil, beautiful or ugly, the ethic and the aesthetic, and the significance of life itself lies in our very own hands. Genetics promises great power, probably the one of the greatest mankind will ever experience, and with power comes the responsibility of choosing wisely.<br />
<br />
“''With great power comes great responsibility''” <br />
– Benjamin Parker ([http://en.wikipedia.org/wiki/Uncle_Ben Uncle Ben] from Spiderman)<br />
<br />
== References ==<br />
<br />
#Stubbe, H. History of genetics, from prehistoric times to the rediscovery of Mendel's laws (M.I.T. Press, 1972).<br />
#Oak Ridge National Laboratory. (2009).<br />
#Pääbo, S. The Human Genome and Our View of Ourselves. Science 291, 1219-1220 (2001).<br />
#Lippman, A. Prenatal genetic testing and screening: constructing needs and reinforcing inequities. American Journal of Law and Medicine 17, 15-50 (1991).<br />
#ten Have, H. Genetics and culture: the geneticization thesis. Medicine, Health Care and Philosophy 4, 295-304 (2001).<br />
#Dunn, L. & Dobzhansky, T. Heredity, Race, and Society (Pinguin Books, Inc., New York, 1946).<br />
#Gordijn, B. & Dekkers, W. Genetics and its impact on society, healthcare and medicine. Medicine, Health Care and Philosophy 9, 1-2 (2006).<br />
#Brand, A., Brand, H. & Schulte, T. The impact of genetics and genomics on public health. European Journal of Human Genetics 16, 5-13 (2008).<br />
#Little, P. Genetic Destinies (Oxford University Press, Oxford, 2002).<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/EssayTeam:Colombia/Human/Essay2012-10-27T04:04:32Z<p>Ksk 89: /* Geneticized future: the gene dream and the gene nightmare */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
''Note'': If by any chance you, the reader, knows about genetics history and basic Mendelian laws, you may be bored by the first couple of sections, so just '''jump''' straight to ''The Human Genome Project and the gene as a cultural icon'' section's '''fourth paragraph'''!<br />
<br />
= '''Essay: The Impact of Genetic Technologies on Society'''=<br />
<br />
The generation of offspring may be the only way of “genetic-self” preservation for years to come. As ephemeral beings, it’s only natural for humans to become concerned about heritage as a means to prolong their legacy on Earth. In this context, genetics emerges as the science in charge of explaining the inheritance of characteristics from parents to the next generation. This essay will try to explore the several phases of genetics in history: how it has moulded society from its very beginnings, defined important aspects of our everyday lives, and how it may revolutionize the future of the human species.<br />
<br />
== From practical genetics to Mendel [[#References|[1] ]] ==<br />
<br />
As mentioned earlier, genetics is not a new concept. The idea of offspring acquiring traits from their parents should have become evident to the first human civilizations. What’s more, during humanity’s process towards a sedentary lifestyle, phenotypic advantages of some crops or domestic animals over others stimulated the idea of selective breeding, probably one of the first genetic notions. This initiative, also known as practical genetics, resulted in the careful controlling of the mating of the “better”, more productive individuals, while getting rid of the “worst”. Thus, genetics begins as a necessity for the forging of towns and villages, through the increasing of production efficiency, in order to maintain larger social associations. <br />
<br />
The first notions of the possible heritage material came from history’s early philosophers, such as [http://en.wikipedia.org/wiki/Hippocrates Hippocrates] and [http://en.wikipedia.org/wiki/Aristotle Aristotle]. They both agreed that the heritable traits were carried in semen, where, either the semen from both parents (for Hippocrates) or the interference of the mother’s blood with the father’s semen (for Aristotle), were finally mixed into a whole new individual who would carry characteristics from both. Even though the fall of the Greek civilization and the advent of the Roman Empire and the Middle Ages slowed down science for more than a thousand years, practical geneticists, namely farmers and stockbreeders, had already achieved important advances. First, the realization that some stable varieties nearly always bred true, with their offspring having the same characteristics as their parents. Second, that it was sometimes possible to mate parents from different varieties to form [http://en.wikipedia.org/wiki/Hybrid_(biology) hybrids]; and third, that even stable varieties occasionally produced offspring different from either parent.<br />
<br />
Practical genetics, however, was purely empirical, and society had yet to discover any laws of inheritance, that is, until [http://en.wikipedia.org/wiki/Gregor_Mendel Gregor Mendel]’s experiments (XIX century). In accordance with Hippocrates’s conjectures, Mendel described heritable traits as physical substances (genes) that retained their identity in hybrids, never blending together. Differing from Aristotle, Mendel confirmed the importance of both parents towards the generation of an offspring’s traits, where each organism, while having two copies per gene (each from one parent), produces gametes carrying one gene copy for each trait. Another of Mendel’s discoveries was that a gene form ([http://en.wikipedia.org/wiki/Allele allele]) may be [http://en.wikipedia.org/wiki/Dominance_(genetics) dominant over another (recessive)], and that different alleles would be sorted out to sperm and eggs [http://en.wikipedia.org/wiki/Mendelian_inheritance randomly and independently], where all combinations of alleles are equally likely. Even though ignored at first, the rediscovery of Mendel’s work, together with the emerging [http://en.wikipedia.org/wiki/Cytology cytology], [http://en.wikipedia.org/wiki/Cytogenetics cytogenetics], and advances in [http://en.wikipedia.org/wiki/Microscopy microscopy], enabled men to locate these genes in [http://en.wikipedia.org/wiki/Chromosome chromosomes], map them, and analyze their patterns of inheritance.<br />
<br />
== The Human Genome Project and the gene as a cultural icon ==<br />
<br />
Throughout the next two hundred years, scientists delved deeper into the basic Mendelian laws. [http://en.wikipedia.org/wiki/Gene Genes] were known to exist and found to be packaged in chromosomes, however, the exact composition of genes and how they work was still an enigma [[#References|[1] ]]. Biological models such as the rod shaped bacterium ''Escherichia coli'', and the fruit fly ''Drosophila melanogaster'', enabled science to describe what is now known as the [http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology central dogma of molecular biology]. This theory states that genes are a compilation of a four letter code in the [http://en.wikipedia.org/wiki/DNA DNA molecule], that they are read and transcribed into another code called [http://en.wikipedia.org/wiki/Messenger_RNA messenger RNA], and finally interpreted and translated into a [http://en.wikipedia.org/wiki/Protein protein] (biological effector) by the combined interaction of [http://en.wikipedia.org/wiki/Transfer_RNA transfer RNA] and [http://en.wikipedia.org/wiki/Ribosome ribosomes]. Furthermore, the notion of genes as the unchanging units of heredity was found to be wrong, as they may be, and constantly are, altered by [http://en.wikipedia.org/wiki/Mutation mutations]. In summary, the genetic code carries the information necessary to build a living being, from a bacterium to a fungus, a chimpanzee or a human. <br />
Research in gene sequencing and its association to a particular biological function were the first steps towards [http://en.wikipedia.org/wiki/Genetic_engineering gene engineering], where scientists discovered ways of transforming organisms with [http://en.wikipedia.org/wiki/Transgene transgenes] (genetic information coming from another species). Pharmaceutical industries and other large companies, encouraged by the possibility of using this information to revolutionize industrial and medical market, accelerated genetics evolution by funding its research.<br />
<br />
In this context, the realization of a [http://en.wikipedia.org/wiki/Human_Genome_Project Human Genome Project (HGP)] was the next natural step to make. The HGP refers to an international 13 year effort (finished in 2003) whose goals were: the identification of the approximate 20,000 genes in the human DNA, the determination of the sequence of the 3 billion base pairs (letter code) that make up human DNA, the storage of this information in databases, the improvement of tools for sequence analysis, the transferral of related technologies to the private sector, and the addressing of the the ethical, legal, and social issues that may arise from the its discoveries [[#References|[2] ]].<br />
<br />
Since differences in genetic coding are, in principle, what makes an individual unique among members of its own species, the HGP inspired enormous symbolical expectancies in the general public. This could be because certain achievements, such as the first lunar landing, atomic fission, and in this case the determination of the human genome sequence ultimately change how humans think of themselves [[#References|[3] ]]. Determination of the internal genetic scaffold around which every human life is moulded, and how this has been handed to us from our ancestors, is crucial towards the understanding of how humans have evolved, revealing just how similar or different we are to each other and to other species: what is it exactly that makes us humans.<br />
<br />
Advances in genetic comprehension made way for the geneticization of society, “an ongoing process by which priority is given to differences between individuals based on their DNA codes, with most disorders, behaviours, and physiological variations [...] structured as, at least in part, hereditary” [[#References|[4] ]]. Thus, the development of genetics as a science has progressively influenced genetic knowledge and technology in particular areas of society and culture. Influence that manifests itself directly by the application of gene testing; and indirectly through new concepts of health, disease [[#References|[5] ]], and politics. Dunn and Dobzhansky [[#References|[6] ]] sustain that in the uniqueness of each individual, that is, that everyone of us is different to anybody that has existed before and probably different than anyone who will exist, lies the fundamental base for ethics and democracy. Studies in Western society show diverse references to DNA, genes, and genetics –be it film, television, news reports, comic books, ads or cartoons; in addition to the media’s allusions to the idea that the essence of man, his true self, is in some way or another found in his genes [[#References|[5] ]], [[#References|[7] ]]. <br />
<br />
Medicine, too, is currently undergoing an extraordinary transition from its initial morphological and phenotypic orientation towards a molecular and genotypic one, promoting the importance of prognosis and prediction [[#References|[8] ]]. Thus, public health is suffering a massive change on disease conception, whereas pre and post–natal gene therapy to diminish susceptibilities to some disorders, and personalized drug prescriptions as treatment are no longer ideas, but possibilities.<br />
<br />
== Geneticized future: the gene dream and the gene nightmare ==<br />
<br />
Molecular geneticist Peter Little’s book [[#References|[9] ]] portrays the life of two very different individuals living the gene dream and the gene nightmare, respectively, in the same geneticized future. The former illustrates a world where “disease and suffering were an echo of the past” [[#References|[9] ]]: where prenatal DNA characteristics (disease susceptibilities and even personality issues) of fertilized embryos may be screened for the selection of the desired baby to be implanted via in vitro fertilization; where DNA may be tested for drug-response indicators so as to ensure future drug treatment perfectly matching the patient’s genetic profile. A future where severe burns may be completely healed or dismemberments entirely re-grown as a result of stem cell research; where personality disorders such as attention-deficit or alcohol abuse are treated with combinations of cell receptor regulators. A reality where many infectious diseases have been taken care of through appropriate drug targeting, where cancer is no more and neurodegenerative ailments such as [http://en.wikipedia.org/wiki/Alzheimer's_disease Alzheimer's disease] and [http://en.wikipedia.org/wiki/Huntington's_disease Huntington’s chorea] may be treated.<br />
<br />
In the gene nightmare, however, “disease and suffering were the results of nature and malign human influence”: where uncontrolled births, prone to high probability susceptibility to disease may deny an individual from eligibility to state medical insurance; where education is limited to those with a minimum genetically defined IQ. A future where people may become preventively imprisoned for displaying criminal predisposition; where DNA differences may be used as an object to racism and discrimination. A reality where humans may be declared genetically unsuitable for reproduction (eugenics), and where ethnic weapons, targeting specific gene markers, may annihilate complete human populations.<br />
Even though many of these ideals and curses are unlikely to happen, scientists are aware of the social outcomes that genetic research may inspire. As a matter of fact, “race” has been found not to have a strong “scientific support”, since it reflects just a few continuous traits determined by a small fraction of our genes. Conversely, genome studies should foster compassion, not only because our gene pool is extremely mixed, but because in the understanding of the genotype’s correspondence to the phenotype is the demonstration that everyone carries at least some deleterious alleles3. [http://en.wikipedia.org/wiki/Nazism Nazism], however, is sufficient proof that mankind's stupidity.<br />
<br />
Despite the huge amount of genetic data available to the general public, we strongly believe society lacks some crucial information about genes. Contemporary ideas suggest that we as individuals are product of our genes; however, this is not entirely true. Our genetic code indeed possesses the information necessary for every physiological process that we will carry on during our lifetime; nevertheless, society seems to be unaware of gene regulation and its explicit importance in defining an individual. In understanding that genes + environment = you, lies the life uncertainty that frees us from a definite destiny, highlighting the significance behind every decision we make. <br />
<br />
The greatest impact of genetics on society I believe lies within the very concept of manipulation, and synthetic biology stands as one of the major steps forward into life manipulation and organism programmed design. History has driven us in a way where the human essence rises from nature and spirituality. However, we are unavoidably getting to a point where human reason may finally impose over the laws of nature: where the discrimination of what is good or evil, beautiful or ugly, the ethic and the aesthetic, and the significance of life itself lies in our very own hands. Genetics promises great power, probably the one of the greatest mankind will ever experience, and with power comes the responsibility of choosing wisely.<br />
<br />
“''With great power comes great responsibility''” <br />
– Benjamin Parker (Uncle Ben from Spiderman)<br />
<br />
== References ==<br />
<br />
#Stubbe, H. History of genetics, from prehistoric times to the rediscovery of Mendel's laws (M.I.T. Press, 1972).<br />
#Oak Ridge National Laboratory. (2009).<br />
#Pääbo, S. The Human Genome and Our View of Ourselves. Science 291, 1219-1220 (2001).<br />
#Lippman, A. Prenatal genetic testing and screening: constructing needs and reinforcing inequities. American Journal of Law and Medicine 17, 15-50 (1991).<br />
#ten Have, H. Genetics and culture: the geneticization thesis. Medicine, Health Care and Philosophy 4, 295-304 (2001).<br />
#Dunn, L. & Dobzhansky, T. Heredity, Race, and Society (Pinguin Books, Inc., New York, 1946).<br />
#Gordijn, B. & Dekkers, W. Genetics and its impact on society, healthcare and medicine. Medicine, Health Care and Philosophy 9, 1-2 (2006).<br />
#Brand, A., Brand, H. & Schulte, T. The impact of genetics and genomics on public health. European Journal of Human Genetics 16, 5-13 (2008).<br />
#Little, P. Genetic Destinies (Oxford University Press, Oxford, 2002).<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/EssayTeam:Colombia/Human/Essay2012-10-27T04:04:08Z<p>Ksk 89: /* Geneticized future: the gene dream and the gene nightmare */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
''Note'': If by any chance you, the reader, knows about genetics history and basic Mendelian laws, you may be bored by the first couple of sections, so just '''jump''' straight to ''The Human Genome Project and the gene as a cultural icon'' section's '''fourth paragraph'''!<br />
<br />
= '''Essay: The Impact of Genetic Technologies on Society'''=<br />
<br />
The generation of offspring may be the only way of “genetic-self” preservation for years to come. As ephemeral beings, it’s only natural for humans to become concerned about heritage as a means to prolong their legacy on Earth. In this context, genetics emerges as the science in charge of explaining the inheritance of characteristics from parents to the next generation. This essay will try to explore the several phases of genetics in history: how it has moulded society from its very beginnings, defined important aspects of our everyday lives, and how it may revolutionize the future of the human species.<br />
<br />
== From practical genetics to Mendel [[#References|[1] ]] ==<br />
<br />
As mentioned earlier, genetics is not a new concept. The idea of offspring acquiring traits from their parents should have become evident to the first human civilizations. What’s more, during humanity’s process towards a sedentary lifestyle, phenotypic advantages of some crops or domestic animals over others stimulated the idea of selective breeding, probably one of the first genetic notions. This initiative, also known as practical genetics, resulted in the careful controlling of the mating of the “better”, more productive individuals, while getting rid of the “worst”. Thus, genetics begins as a necessity for the forging of towns and villages, through the increasing of production efficiency, in order to maintain larger social associations. <br />
<br />
The first notions of the possible heritage material came from history’s early philosophers, such as [http://en.wikipedia.org/wiki/Hippocrates Hippocrates] and [http://en.wikipedia.org/wiki/Aristotle Aristotle]. They both agreed that the heritable traits were carried in semen, where, either the semen from both parents (for Hippocrates) or the interference of the mother’s blood with the father’s semen (for Aristotle), were finally mixed into a whole new individual who would carry characteristics from both. Even though the fall of the Greek civilization and the advent of the Roman Empire and the Middle Ages slowed down science for more than a thousand years, practical geneticists, namely farmers and stockbreeders, had already achieved important advances. First, the realization that some stable varieties nearly always bred true, with their offspring having the same characteristics as their parents. Second, that it was sometimes possible to mate parents from different varieties to form [http://en.wikipedia.org/wiki/Hybrid_(biology) hybrids]; and third, that even stable varieties occasionally produced offspring different from either parent.<br />
<br />
Practical genetics, however, was purely empirical, and society had yet to discover any laws of inheritance, that is, until [http://en.wikipedia.org/wiki/Gregor_Mendel Gregor Mendel]’s experiments (XIX century). In accordance with Hippocrates’s conjectures, Mendel described heritable traits as physical substances (genes) that retained their identity in hybrids, never blending together. Differing from Aristotle, Mendel confirmed the importance of both parents towards the generation of an offspring’s traits, where each organism, while having two copies per gene (each from one parent), produces gametes carrying one gene copy for each trait. Another of Mendel’s discoveries was that a gene form ([http://en.wikipedia.org/wiki/Allele allele]) may be [http://en.wikipedia.org/wiki/Dominance_(genetics) dominant over another (recessive)], and that different alleles would be sorted out to sperm and eggs [http://en.wikipedia.org/wiki/Mendelian_inheritance randomly and independently], where all combinations of alleles are equally likely. Even though ignored at first, the rediscovery of Mendel’s work, together with the emerging [http://en.wikipedia.org/wiki/Cytology cytology], [http://en.wikipedia.org/wiki/Cytogenetics cytogenetics], and advances in [http://en.wikipedia.org/wiki/Microscopy microscopy], enabled men to locate these genes in [http://en.wikipedia.org/wiki/Chromosome chromosomes], map them, and analyze their patterns of inheritance.<br />
<br />
== The Human Genome Project and the gene as a cultural icon ==<br />
<br />
Throughout the next two hundred years, scientists delved deeper into the basic Mendelian laws. [http://en.wikipedia.org/wiki/Gene Genes] were known to exist and found to be packaged in chromosomes, however, the exact composition of genes and how they work was still an enigma [[#References|[1] ]]. Biological models such as the rod shaped bacterium ''Escherichia coli'', and the fruit fly ''Drosophila melanogaster'', enabled science to describe what is now known as the [http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology central dogma of molecular biology]. This theory states that genes are a compilation of a four letter code in the [http://en.wikipedia.org/wiki/DNA DNA molecule], that they are read and transcribed into another code called [http://en.wikipedia.org/wiki/Messenger_RNA messenger RNA], and finally interpreted and translated into a [http://en.wikipedia.org/wiki/Protein protein] (biological effector) by the combined interaction of [http://en.wikipedia.org/wiki/Transfer_RNA transfer RNA] and [http://en.wikipedia.org/wiki/Ribosome ribosomes]. Furthermore, the notion of genes as the unchanging units of heredity was found to be wrong, as they may be, and constantly are, altered by [http://en.wikipedia.org/wiki/Mutation mutations]. In summary, the genetic code carries the information necessary to build a living being, from a bacterium to a fungus, a chimpanzee or a human. <br />
Research in gene sequencing and its association to a particular biological function were the first steps towards [http://en.wikipedia.org/wiki/Genetic_engineering gene engineering], where scientists discovered ways of transforming organisms with [http://en.wikipedia.org/wiki/Transgene transgenes] (genetic information coming from another species). Pharmaceutical industries and other large companies, encouraged by the possibility of using this information to revolutionize industrial and medical market, accelerated genetics evolution by funding its research.<br />
<br />
In this context, the realization of a [http://en.wikipedia.org/wiki/Human_Genome_Project Human Genome Project (HGP)] was the next natural step to make. The HGP refers to an international 13 year effort (finished in 2003) whose goals were: the identification of the approximate 20,000 genes in the human DNA, the determination of the sequence of the 3 billion base pairs (letter code) that make up human DNA, the storage of this information in databases, the improvement of tools for sequence analysis, the transferral of related technologies to the private sector, and the addressing of the the ethical, legal, and social issues that may arise from the its discoveries [[#References|[2] ]].<br />
<br />
Since differences in genetic coding are, in principle, what makes an individual unique among members of its own species, the HGP inspired enormous symbolical expectancies in the general public. This could be because certain achievements, such as the first lunar landing, atomic fission, and in this case the determination of the human genome sequence ultimately change how humans think of themselves [[#References|[3] ]]. Determination of the internal genetic scaffold around which every human life is moulded, and how this has been handed to us from our ancestors, is crucial towards the understanding of how humans have evolved, revealing just how similar or different we are to each other and to other species: what is it exactly that makes us humans.<br />
<br />
Advances in genetic comprehension made way for the geneticization of society, “an ongoing process by which priority is given to differences between individuals based on their DNA codes, with most disorders, behaviours, and physiological variations [...] structured as, at least in part, hereditary” [[#References|[4] ]]. Thus, the development of genetics as a science has progressively influenced genetic knowledge and technology in particular areas of society and culture. Influence that manifests itself directly by the application of gene testing; and indirectly through new concepts of health, disease [[#References|[5] ]], and politics. Dunn and Dobzhansky [[#References|[6] ]] sustain that in the uniqueness of each individual, that is, that everyone of us is different to anybody that has existed before and probably different than anyone who will exist, lies the fundamental base for ethics and democracy. Studies in Western society show diverse references to DNA, genes, and genetics –be it film, television, news reports, comic books, ads or cartoons; in addition to the media’s allusions to the idea that the essence of man, his true self, is in some way or another found in his genes [[#References|[5] ]], [[#References|[7] ]]. <br />
<br />
Medicine, too, is currently undergoing an extraordinary transition from its initial morphological and phenotypic orientation towards a molecular and genotypic one, promoting the importance of prognosis and prediction [[#References|[8] ]]. Thus, public health is suffering a massive change on disease conception, whereas pre and post–natal gene therapy to diminish susceptibilities to some disorders, and personalized drug prescriptions as treatment are no longer ideas, but possibilities.<br />
<br />
== Geneticized future: the gene dream and the gene nightmare ==<br />
<br />
Molecular geneticist Peter Little’s book [[#References|[9] ]] portrays the life of two very different individuals living the gene dream and the gene nightmare, respectively, in the same geneticized future. The former illustrates a world where “disease and suffering were an echo of the past” [[#References|[9] ]]: where prenatal DNA characteristics (disease susceptibilities and even personality issues) of fertilized embryos may be screened for the selection of the desired baby to be implanted via in vitro fertilization; where DNA may be tested for drug-response indicators so as to ensure future drug treatment perfectly matching the patient’s genetic profile. A future where severe burns may be completely healed or dismemberments entirely re-grown as a result of stem cell research; where personality disorders such as attention-deficit or alcohol abuse are treated with combinations of cell receptor regulators. A reality where many infectious diseases have been taken care of through appropriate drug targeting, where cancer is no more and neurodegenerative ailments such as [http://en.wikipedia.org/wiki/Alzheimer's_disease Alzheimer's disease] and [http://en.wikipedia.org/wiki/Huntington's_disease Huntington’s chorea] may be treated.<br />
<br />
In the gene nightmare, however, “disease and suffering were the results of nature and malign human influence”: where uncontrolled births, prone to high probability susceptibility to disease may deny an individual from eligibility to state medical insurance; where education is limited to those with a minimum genetically defined IQ. A future where people may become preventively imprisoned for displaying criminal predisposition; where DNA differences may be used as an object to racism and discrimination. A reality where humans may be declared genetically unsuitable for reproduction (eugenics), and where ethnic weapons, targeting specific gene markers, may annihilate complete human populations.<br />
Even though many of these ideals and curses are unlikely to happen, scientists are aware of the social outcomes that genetic research may inspire. As a matter of fact, “race” has been found not to have a strong “scientific support”, since it reflects just a few continuous traits determined by a small fraction of our genes. Conversely, genome studies should foster compassion, not only because our gene pool is extremely mixed, but because in the understanding of the genotype’s correspondence to the phenotype is the demonstration that everyone carries at least some deleterious alleles3. [http://en.wikipedia.org/wiki/Nazism Nazism], however, is sufficient proof that mankind's stupidity.<br />
<br />
Despite the huge amount of genetic data available to the general public, we strongly believe society lacks some crucial information about genes. Contemporary ideas suggest that we as individuals are product of our genes; however, this is not entirely true. Our genetic code indeed possesses the information necessary for every physiological process that we will carry on during our lifetime; nevertheless, society seems to be unaware of gene regulation and its explicit importance in defining an individual. In understanding that genes + environment = you, lies the life uncertainty that frees us from a definite destiny, highlighting the significance behind every decision we make. <br />
<br />
The greatest impact of genetics on society I believe lies within the very concept of manipulation. Synthetic biology stands as one of the major steps forward into life manipulation and organism programmed design. History has driven us in a way where the human essence rises from nature and spirituality. However, we are unavoidably getting to a point where human reason may finally impose over the laws of nature: where the discrimination of what is good or evil, beautiful or ugly, the ethic and the aesthetic, and the significance of life itself lies in our very own hands. Genetics promises great power, probably the one of the greatest mankind will ever experience, and with power comes the responsibility of choosing wisely.<br />
<br />
“''With great power comes great responsibility''” <br />
– Benjamin Parker (Uncle Ben from Spiderman)<br />
<br />
== References ==<br />
<br />
#Stubbe, H. History of genetics, from prehistoric times to the rediscovery of Mendel's laws (M.I.T. Press, 1972).<br />
#Oak Ridge National Laboratory. (2009).<br />
#Pääbo, S. The Human Genome and Our View of Ourselves. Science 291, 1219-1220 (2001).<br />
#Lippman, A. Prenatal genetic testing and screening: constructing needs and reinforcing inequities. American Journal of Law and Medicine 17, 15-50 (1991).<br />
#ten Have, H. Genetics and culture: the geneticization thesis. Medicine, Health Care and Philosophy 4, 295-304 (2001).<br />
#Dunn, L. & Dobzhansky, T. Heredity, Race, and Society (Pinguin Books, Inc., New York, 1946).<br />
#Gordijn, B. & Dekkers, W. Genetics and its impact on society, healthcare and medicine. Medicine, Health Care and Philosophy 9, 1-2 (2006).<br />
#Brand, A., Brand, H. & Schulte, T. The impact of genetics and genomics on public health. European Journal of Human Genetics 16, 5-13 (2008).<br />
#Little, P. Genetic Destinies (Oxford University Press, Oxford, 2002).<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/EssayTeam:Colombia/Human/Essay2012-10-27T04:03:01Z<p>Ksk 89: /* Geneticized future: the gene dream and the gene nightmare */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
''Note'': If by any chance you, the reader, knows about genetics history and basic Mendelian laws, you may be bored by the first couple of sections, so just '''jump''' straight to ''The Human Genome Project and the gene as a cultural icon'' section's '''fourth paragraph'''!<br />
<br />
= '''Essay: The Impact of Genetic Technologies on Society'''=<br />
<br />
The generation of offspring may be the only way of “genetic-self” preservation for years to come. As ephemeral beings, it’s only natural for humans to become concerned about heritage as a means to prolong their legacy on Earth. In this context, genetics emerges as the science in charge of explaining the inheritance of characteristics from parents to the next generation. This essay will try to explore the several phases of genetics in history: how it has moulded society from its very beginnings, defined important aspects of our everyday lives, and how it may revolutionize the future of the human species.<br />
<br />
== From practical genetics to Mendel [[#References|[1] ]] ==<br />
<br />
As mentioned earlier, genetics is not a new concept. The idea of offspring acquiring traits from their parents should have become evident to the first human civilizations. What’s more, during humanity’s process towards a sedentary lifestyle, phenotypic advantages of some crops or domestic animals over others stimulated the idea of selective breeding, probably one of the first genetic notions. This initiative, also known as practical genetics, resulted in the careful controlling of the mating of the “better”, more productive individuals, while getting rid of the “worst”. Thus, genetics begins as a necessity for the forging of towns and villages, through the increasing of production efficiency, in order to maintain larger social associations. <br />
<br />
The first notions of the possible heritage material came from history’s early philosophers, such as [http://en.wikipedia.org/wiki/Hippocrates Hippocrates] and [http://en.wikipedia.org/wiki/Aristotle Aristotle]. They both agreed that the heritable traits were carried in semen, where, either the semen from both parents (for Hippocrates) or the interference of the mother’s blood with the father’s semen (for Aristotle), were finally mixed into a whole new individual who would carry characteristics from both. Even though the fall of the Greek civilization and the advent of the Roman Empire and the Middle Ages slowed down science for more than a thousand years, practical geneticists, namely farmers and stockbreeders, had already achieved important advances. First, the realization that some stable varieties nearly always bred true, with their offspring having the same characteristics as their parents. Second, that it was sometimes possible to mate parents from different varieties to form [http://en.wikipedia.org/wiki/Hybrid_(biology) hybrids]; and third, that even stable varieties occasionally produced offspring different from either parent.<br />
<br />
Practical genetics, however, was purely empirical, and society had yet to discover any laws of inheritance, that is, until [http://en.wikipedia.org/wiki/Gregor_Mendel Gregor Mendel]’s experiments (XIX century). In accordance with Hippocrates’s conjectures, Mendel described heritable traits as physical substances (genes) that retained their identity in hybrids, never blending together. Differing from Aristotle, Mendel confirmed the importance of both parents towards the generation of an offspring’s traits, where each organism, while having two copies per gene (each from one parent), produces gametes carrying one gene copy for each trait. Another of Mendel’s discoveries was that a gene form ([http://en.wikipedia.org/wiki/Allele allele]) may be [http://en.wikipedia.org/wiki/Dominance_(genetics) dominant over another (recessive)], and that different alleles would be sorted out to sperm and eggs [http://en.wikipedia.org/wiki/Mendelian_inheritance randomly and independently], where all combinations of alleles are equally likely. Even though ignored at first, the rediscovery of Mendel’s work, together with the emerging [http://en.wikipedia.org/wiki/Cytology cytology], [http://en.wikipedia.org/wiki/Cytogenetics cytogenetics], and advances in [http://en.wikipedia.org/wiki/Microscopy microscopy], enabled men to locate these genes in [http://en.wikipedia.org/wiki/Chromosome chromosomes], map them, and analyze their patterns of inheritance.<br />
<br />
== The Human Genome Project and the gene as a cultural icon ==<br />
<br />
Throughout the next two hundred years, scientists delved deeper into the basic Mendelian laws. [http://en.wikipedia.org/wiki/Gene Genes] were known to exist and found to be packaged in chromosomes, however, the exact composition of genes and how they work was still an enigma [[#References|[1] ]]. Biological models such as the rod shaped bacterium ''Escherichia coli'', and the fruit fly ''Drosophila melanogaster'', enabled science to describe what is now known as the [http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology central dogma of molecular biology]. This theory states that genes are a compilation of a four letter code in the [http://en.wikipedia.org/wiki/DNA DNA molecule], that they are read and transcribed into another code called [http://en.wikipedia.org/wiki/Messenger_RNA messenger RNA], and finally interpreted and translated into a [http://en.wikipedia.org/wiki/Protein protein] (biological effector) by the combined interaction of [http://en.wikipedia.org/wiki/Transfer_RNA transfer RNA] and [http://en.wikipedia.org/wiki/Ribosome ribosomes]. Furthermore, the notion of genes as the unchanging units of heredity was found to be wrong, as they may be, and constantly are, altered by [http://en.wikipedia.org/wiki/Mutation mutations]. In summary, the genetic code carries the information necessary to build a living being, from a bacterium to a fungus, a chimpanzee or a human. <br />
Research in gene sequencing and its association to a particular biological function were the first steps towards [http://en.wikipedia.org/wiki/Genetic_engineering gene engineering], where scientists discovered ways of transforming organisms with [http://en.wikipedia.org/wiki/Transgene transgenes] (genetic information coming from another species). Pharmaceutical industries and other large companies, encouraged by the possibility of using this information to revolutionize industrial and medical market, accelerated genetics evolution by funding its research.<br />
<br />
In this context, the realization of a [http://en.wikipedia.org/wiki/Human_Genome_Project Human Genome Project (HGP)] was the next natural step to make. The HGP refers to an international 13 year effort (finished in 2003) whose goals were: the identification of the approximate 20,000 genes in the human DNA, the determination of the sequence of the 3 billion base pairs (letter code) that make up human DNA, the storage of this information in databases, the improvement of tools for sequence analysis, the transferral of related technologies to the private sector, and the addressing of the the ethical, legal, and social issues that may arise from the its discoveries [[#References|[2] ]].<br />
<br />
Since differences in genetic coding are, in principle, what makes an individual unique among members of its own species, the HGP inspired enormous symbolical expectancies in the general public. This could be because certain achievements, such as the first lunar landing, atomic fission, and in this case the determination of the human genome sequence ultimately change how humans think of themselves [[#References|[3] ]]. Determination of the internal genetic scaffold around which every human life is moulded, and how this has been handed to us from our ancestors, is crucial towards the understanding of how humans have evolved, revealing just how similar or different we are to each other and to other species: what is it exactly that makes us humans.<br />
<br />
Advances in genetic comprehension made way for the geneticization of society, “an ongoing process by which priority is given to differences between individuals based on their DNA codes, with most disorders, behaviours, and physiological variations [...] structured as, at least in part, hereditary” [[#References|[4] ]]. Thus, the development of genetics as a science has progressively influenced genetic knowledge and technology in particular areas of society and culture. Influence that manifests itself directly by the application of gene testing; and indirectly through new concepts of health, disease [[#References|[5] ]], and politics. Dunn and Dobzhansky [[#References|[6] ]] sustain that in the uniqueness of each individual, that is, that everyone of us is different to anybody that has existed before and probably different than anyone who will exist, lies the fundamental base for ethics and democracy. Studies in Western society show diverse references to DNA, genes, and genetics –be it film, television, news reports, comic books, ads or cartoons; in addition to the media’s allusions to the idea that the essence of man, his true self, is in some way or another found in his genes [[#References|[5] ]], [[#References|[7] ]]. <br />
<br />
Medicine, too, is currently undergoing an extraordinary transition from its initial morphological and phenotypic orientation towards a molecular and genotypic one, promoting the importance of prognosis and prediction [[#References|[8] ]]. Thus, public health is suffering a massive change on disease conception, whereas pre and post–natal gene therapy to diminish susceptibilities to some disorders, and personalized drug prescriptions as treatment are no longer ideas, but possibilities.<br />
<br />
== Geneticized future: the gene dream and the gene nightmare ==<br />
<br />
Molecular geneticist Peter Little’s book [[#References|[9] ]] portrays the life of two very different individuals living the gene dream and the gene nightmare, respectively, in the same geneticized future. The former illustrates a world where “disease and suffering were an echo of the past” [[#References|[9] ]]: where prenatal DNA characteristics (disease susceptibilities and even personality issues) of fertilized embryos may be screened for the selection of the desired baby to be implanted via in vitro fertilization; where DNA may be tested for drug-response indicators so as to ensure future drug treatment perfectly matching the patient’s genetic profile. A future where severe burns may be completely healed or dismemberments entirely re-grown as a result of stem cell research; where personality disorders such as attention-deficit or alcohol abuse are treated with combinations of cell receptor regulators. A reality where many infectious diseases have been taken care of through appropriate drug targeting, where cancer is no more and neurodegenerative ailments such as [http://en.wikipedia.org/wiki/Alzheimer's_disease Alzheimer's disease] and [http://en.wikipedia.org/wiki/Huntington's_disease Huntington’s chorea] may be treated.<br />
<br />
In the gene nightmare, however, “disease and suffering were the results of nature and malign human influence”: where uncontrolled births, prone to high probability susceptibility to disease may deny an individual from eligibility to state medical insurance; where education is limited to those with a minimum genetically defined IQ. A future where people may become preventively imprisoned for displaying criminal predisposition; where DNA differences may be used as an object to racism and discrimination. A reality where humans may be declared genetically unsuitable for reproduction (eugenics), and where ethnic weapons, targeting specific gene markers, may annihilate complete human populations.<br />
Even though many of these ideals and curses are unlikely to happen, scientists are aware of the social outcomes that genetic research may inspire. As a matter of fact, “race” has been found not to have a strong “scientific support”, since it reflects just a few continuous traits determined by a small fraction of our genes. Conversely, genome studies should foster compassion, not only because our gene pool is extremely mixed, but because in the understanding of the genotype’s correspondence to the phenotype is the demonstration that everyone carries at least some deleterious alleles3. [http://en.wikipedia.org/wiki/Nazism Nazism], however, is sufficient proof that mankind's stupidity.<br />
<br />
Despite the huge amount of genetic data available to the general public, we strongly believe society lacks some crucial information about genes. Contemporary ideas suggest that we as individuals are product of our genes; however, this is not entirely true. Our genetic code indeed possesses the information necessary for every physiological process that we will carry on during our lifetime; nevertheless, society seems to be unaware of gene regulation and its explicit importance in defining an individual. In understanding that genes + environment = you, lies the life uncertainty that frees us from a definite destiny, highlighting the significance behind every decision we make. <br />
<br />
The greatest impact of genetics on society I believe lies within the very concept of manipulation. History has driven us in a way where the human essence rises from nature and spirituality. However, we are unavoidably getting to a point where human reason may finally impose over the laws of nature: where the discrimination of what is good or evil, beautiful or ugly, the ethic and the aesthetic, and the significance of life itself lies in our very own hands. Genetics promises great power, probably the one of the greatest mankind will ever experience, and with power comes the responsibility of choosing wisely.<br />
<br />
“''With great power comes great responsibility''” <br />
– Benjamin Parker (Uncle Ben from Spiderman)<br />
<br />
== References ==<br />
<br />
#Stubbe, H. History of genetics, from prehistoric times to the rediscovery of Mendel's laws (M.I.T. Press, 1972).<br />
#Oak Ridge National Laboratory. (2009).<br />
#Pääbo, S. The Human Genome and Our View of Ourselves. Science 291, 1219-1220 (2001).<br />
#Lippman, A. Prenatal genetic testing and screening: constructing needs and reinforcing inequities. American Journal of Law and Medicine 17, 15-50 (1991).<br />
#ten Have, H. Genetics and culture: the geneticization thesis. Medicine, Health Care and Philosophy 4, 295-304 (2001).<br />
#Dunn, L. & Dobzhansky, T. Heredity, Race, and Society (Pinguin Books, Inc., New York, 1946).<br />
#Gordijn, B. & Dekkers, W. Genetics and its impact on society, healthcare and medicine. Medicine, Health Care and Philosophy 9, 1-2 (2006).<br />
#Brand, A., Brand, H. & Schulte, T. The impact of genetics and genomics on public health. European Journal of Human Genetics 16, 5-13 (2008).<br />
#Little, P. Genetic Destinies (Oxford University Press, Oxford, 2002).<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/EssayTeam:Colombia/Human/Essay2012-10-27T04:02:44Z<p>Ksk 89: /* Geneticized future: the gene dream and the gene nightmare */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
''Note'': If by any chance you, the reader, knows about genetics history and basic Mendelian laws, you may be bored by the first couple of sections, so just '''jump''' straight to ''The Human Genome Project and the gene as a cultural icon'' section's '''fourth paragraph'''!<br />
<br />
= '''Essay: The Impact of Genetic Technologies on Society'''=<br />
<br />
The generation of offspring may be the only way of “genetic-self” preservation for years to come. As ephemeral beings, it’s only natural for humans to become concerned about heritage as a means to prolong their legacy on Earth. In this context, genetics emerges as the science in charge of explaining the inheritance of characteristics from parents to the next generation. This essay will try to explore the several phases of genetics in history: how it has moulded society from its very beginnings, defined important aspects of our everyday lives, and how it may revolutionize the future of the human species.<br />
<br />
== From practical genetics to Mendel [[#References|[1] ]] ==<br />
<br />
As mentioned earlier, genetics is not a new concept. The idea of offspring acquiring traits from their parents should have become evident to the first human civilizations. What’s more, during humanity’s process towards a sedentary lifestyle, phenotypic advantages of some crops or domestic animals over others stimulated the idea of selective breeding, probably one of the first genetic notions. This initiative, also known as practical genetics, resulted in the careful controlling of the mating of the “better”, more productive individuals, while getting rid of the “worst”. Thus, genetics begins as a necessity for the forging of towns and villages, through the increasing of production efficiency, in order to maintain larger social associations. <br />
<br />
The first notions of the possible heritage material came from history’s early philosophers, such as [http://en.wikipedia.org/wiki/Hippocrates Hippocrates] and [http://en.wikipedia.org/wiki/Aristotle Aristotle]. They both agreed that the heritable traits were carried in semen, where, either the semen from both parents (for Hippocrates) or the interference of the mother’s blood with the father’s semen (for Aristotle), were finally mixed into a whole new individual who would carry characteristics from both. Even though the fall of the Greek civilization and the advent of the Roman Empire and the Middle Ages slowed down science for more than a thousand years, practical geneticists, namely farmers and stockbreeders, had already achieved important advances. First, the realization that some stable varieties nearly always bred true, with their offspring having the same characteristics as their parents. Second, that it was sometimes possible to mate parents from different varieties to form [http://en.wikipedia.org/wiki/Hybrid_(biology) hybrids]; and third, that even stable varieties occasionally produced offspring different from either parent.<br />
<br />
Practical genetics, however, was purely empirical, and society had yet to discover any laws of inheritance, that is, until [http://en.wikipedia.org/wiki/Gregor_Mendel Gregor Mendel]’s experiments (XIX century). In accordance with Hippocrates’s conjectures, Mendel described heritable traits as physical substances (genes) that retained their identity in hybrids, never blending together. Differing from Aristotle, Mendel confirmed the importance of both parents towards the generation of an offspring’s traits, where each organism, while having two copies per gene (each from one parent), produces gametes carrying one gene copy for each trait. Another of Mendel’s discoveries was that a gene form ([http://en.wikipedia.org/wiki/Allele allele]) may be [http://en.wikipedia.org/wiki/Dominance_(genetics) dominant over another (recessive)], and that different alleles would be sorted out to sperm and eggs [http://en.wikipedia.org/wiki/Mendelian_inheritance randomly and independently], where all combinations of alleles are equally likely. Even though ignored at first, the rediscovery of Mendel’s work, together with the emerging [http://en.wikipedia.org/wiki/Cytology cytology], [http://en.wikipedia.org/wiki/Cytogenetics cytogenetics], and advances in [http://en.wikipedia.org/wiki/Microscopy microscopy], enabled men to locate these genes in [http://en.wikipedia.org/wiki/Chromosome chromosomes], map them, and analyze their patterns of inheritance.<br />
<br />
== The Human Genome Project and the gene as a cultural icon ==<br />
<br />
Throughout the next two hundred years, scientists delved deeper into the basic Mendelian laws. [http://en.wikipedia.org/wiki/Gene Genes] were known to exist and found to be packaged in chromosomes, however, the exact composition of genes and how they work was still an enigma [[#References|[1] ]]. Biological models such as the rod shaped bacterium ''Escherichia coli'', and the fruit fly ''Drosophila melanogaster'', enabled science to describe what is now known as the [http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology central dogma of molecular biology]. This theory states that genes are a compilation of a four letter code in the [http://en.wikipedia.org/wiki/DNA DNA molecule], that they are read and transcribed into another code called [http://en.wikipedia.org/wiki/Messenger_RNA messenger RNA], and finally interpreted and translated into a [http://en.wikipedia.org/wiki/Protein protein] (biological effector) by the combined interaction of [http://en.wikipedia.org/wiki/Transfer_RNA transfer RNA] and [http://en.wikipedia.org/wiki/Ribosome ribosomes]. Furthermore, the notion of genes as the unchanging units of heredity was found to be wrong, as they may be, and constantly are, altered by [http://en.wikipedia.org/wiki/Mutation mutations]. In summary, the genetic code carries the information necessary to build a living being, from a bacterium to a fungus, a chimpanzee or a human. <br />
Research in gene sequencing and its association to a particular biological function were the first steps towards [http://en.wikipedia.org/wiki/Genetic_engineering gene engineering], where scientists discovered ways of transforming organisms with [http://en.wikipedia.org/wiki/Transgene transgenes] (genetic information coming from another species). Pharmaceutical industries and other large companies, encouraged by the possibility of using this information to revolutionize industrial and medical market, accelerated genetics evolution by funding its research.<br />
<br />
In this context, the realization of a [http://en.wikipedia.org/wiki/Human_Genome_Project Human Genome Project (HGP)] was the next natural step to make. The HGP refers to an international 13 year effort (finished in 2003) whose goals were: the identification of the approximate 20,000 genes in the human DNA, the determination of the sequence of the 3 billion base pairs (letter code) that make up human DNA, the storage of this information in databases, the improvement of tools for sequence analysis, the transferral of related technologies to the private sector, and the addressing of the the ethical, legal, and social issues that may arise from the its discoveries [[#References|[2] ]].<br />
<br />
Since differences in genetic coding are, in principle, what makes an individual unique among members of its own species, the HGP inspired enormous symbolical expectancies in the general public. This could be because certain achievements, such as the first lunar landing, atomic fission, and in this case the determination of the human genome sequence ultimately change how humans think of themselves [[#References|[3] ]]. Determination of the internal genetic scaffold around which every human life is moulded, and how this has been handed to us from our ancestors, is crucial towards the understanding of how humans have evolved, revealing just how similar or different we are to each other and to other species: what is it exactly that makes us humans.<br />
<br />
Advances in genetic comprehension made way for the geneticization of society, “an ongoing process by which priority is given to differences between individuals based on their DNA codes, with most disorders, behaviours, and physiological variations [...] structured as, at least in part, hereditary” [[#References|[4] ]]. Thus, the development of genetics as a science has progressively influenced genetic knowledge and technology in particular areas of society and culture. Influence that manifests itself directly by the application of gene testing; and indirectly through new concepts of health, disease [[#References|[5] ]], and politics. Dunn and Dobzhansky [[#References|[6] ]] sustain that in the uniqueness of each individual, that is, that everyone of us is different to anybody that has existed before and probably different than anyone who will exist, lies the fundamental base for ethics and democracy. Studies in Western society show diverse references to DNA, genes, and genetics –be it film, television, news reports, comic books, ads or cartoons; in addition to the media’s allusions to the idea that the essence of man, his true self, is in some way or another found in his genes [[#References|[5] ]], [[#References|[7] ]]. <br />
<br />
Medicine, too, is currently undergoing an extraordinary transition from its initial morphological and phenotypic orientation towards a molecular and genotypic one, promoting the importance of prognosis and prediction [[#References|[8] ]]. Thus, public health is suffering a massive change on disease conception, whereas pre and post–natal gene therapy to diminish susceptibilities to some disorders, and personalized drug prescriptions as treatment are no longer ideas, but possibilities.<br />
<br />
== Geneticized future: the gene dream and the gene nightmare ==<br />
<br />
Molecular geneticist Peter Little’s book [[#References|[9] ]] portrays the life of two very different individuals living the gene dream and the gene nightmare, respectively, in the same geneticized future. The former illustrates a world where “disease and suffering were an echo of the past” [[#References|[9] ]]: where prenatal DNA characteristics (disease susceptibilities and even personality issues) of fertilized embryos may be screened for the selection of the desired baby to be implanted via in vitro fertilization; where DNA may be tested for drug-response indicators so as to ensure future drug treatment perfectly matching the patient’s genetic profile. A future where severe burns may be completely healed or dismemberments entirely re-grown as a result of stem cell research; where personality disorders such as attention-deficit or alcohol abuse are treated with combinations of cell receptor regulators. A reality where many infectious diseases have been taken care of through appropriate drug targeting, where cancer is no more and neurodegenerative ailments such as [http://en.wikipedia.org/wiki/Alzheimer's_disease Alzheimer's disease] and [http://en.wikipedia.org/wiki/Huntington's_disease Huntington’s chorea] may be treated.<br />
<br />
In the gene nightmare, however, “disease and suffering were the results of nature and malign human influence”: where uncontrolled births, prone to high probability susceptibility to disease may deny an individual from eligibility to state medical insurance; where education is limited to those with a minimum genetically defined IQ. A future where people may become preventively imprisoned for displaying criminal predisposition; where DNA differences may be used as an object to racism and discrimination. A reality where humans may be declared genetically unsuitable for reproduction (eugenics), and where ethnic weapons, targeting specific gene markers, may annihilate complete human populations.<br />
Even though many of these ideals and curses are unlikely to happen, scientists are aware of the social outcomes that genetic research may inspire. As a matter of fact, “race” has been found not to have a strong “scientific support”, since it reflects just a few continuous traits determined by a small fraction of our genes. Conversely, genome studies should foster compassion, not only because our gene pool is extremely mixed, but because in the understanding of the genotype’s correspondence to the phenotype is the demonstration that everyone carries at least some deleterious alleles3. [http://en.wikipedia.org/wiki/Nazism Nazism], however, is sufficient proof that mankind's stupidity.<br />
<br />
Despite the huge amount of genetic data available to the general public, we strongly believe society lacks some crucial information about genes. Contemporary ideas suggest that we as individuals are product of our genes; however, this is not entirely true. Our genetic code indeed possesses the information necessary for every physiological process that we will carry on during our lifetime; nevertheless, society seems to be unaware of gene regulation and its explicit importance in defining an individual. In understanding that genes + environment = you, lies the life uncertainty that frees us from a definite destiny, highlighting the significance behind every decision we make. <br />
<br />
The greatest impact of genetics on society I believe lies within the very concept of manipulation. History has driven us in a way where the human essence rises from nature and spirituality. However, we are unavoidably getting to a point where human reason may finally impose over the laws of nature: where the discrimination of what is good or evil, beautiful or ugly, the ethic and the aesthetic, and the significance of life itself lies in our very own hands. Genetics promises great power, probably the one of the greatest mankind will ever experience, and with power comes the responsibility of choosing wisely.<br />
<br />
-“''With great power comes great responsibility''” <br />
– Benjamin Parker (Uncle Ben from Spiderman)<br />
<br />
== References ==<br />
<br />
#Stubbe, H. History of genetics, from prehistoric times to the rediscovery of Mendel's laws (M.I.T. Press, 1972).<br />
#Oak Ridge National Laboratory. (2009).<br />
#Pääbo, S. The Human Genome and Our View of Ourselves. Science 291, 1219-1220 (2001).<br />
#Lippman, A. Prenatal genetic testing and screening: constructing needs and reinforcing inequities. American Journal of Law and Medicine 17, 15-50 (1991).<br />
#ten Have, H. Genetics and culture: the geneticization thesis. Medicine, Health Care and Philosophy 4, 295-304 (2001).<br />
#Dunn, L. & Dobzhansky, T. Heredity, Race, and Society (Pinguin Books, Inc., New York, 1946).<br />
#Gordijn, B. & Dekkers, W. Genetics and its impact on society, healthcare and medicine. Medicine, Health Care and Philosophy 9, 1-2 (2006).<br />
#Brand, A., Brand, H. & Schulte, T. The impact of genetics and genomics on public health. European Journal of Human Genetics 16, 5-13 (2008).<br />
#Little, P. Genetic Destinies (Oxford University Press, Oxford, 2002).<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/EssayTeam:Colombia/Human/Essay2012-10-27T04:01:31Z<p>Ksk 89: /* The Human Genome Project and the gene as a cultural icon */</p>
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<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
''Note'': If by any chance you, the reader, knows about genetics history and basic Mendelian laws, you may be bored by the first couple of sections, so just '''jump''' straight to ''The Human Genome Project and the gene as a cultural icon'' section's '''fourth paragraph'''!<br />
<br />
= '''Essay: The Impact of Genetic Technologies on Society'''=<br />
<br />
The generation of offspring may be the only way of “genetic-self” preservation for years to come. As ephemeral beings, it’s only natural for humans to become concerned about heritage as a means to prolong their legacy on Earth. In this context, genetics emerges as the science in charge of explaining the inheritance of characteristics from parents to the next generation. This essay will try to explore the several phases of genetics in history: how it has moulded society from its very beginnings, defined important aspects of our everyday lives, and how it may revolutionize the future of the human species.<br />
<br />
== From practical genetics to Mendel [[#References|[1] ]] ==<br />
<br />
As mentioned earlier, genetics is not a new concept. The idea of offspring acquiring traits from their parents should have become evident to the first human civilizations. What’s more, during humanity’s process towards a sedentary lifestyle, phenotypic advantages of some crops or domestic animals over others stimulated the idea of selective breeding, probably one of the first genetic notions. This initiative, also known as practical genetics, resulted in the careful controlling of the mating of the “better”, more productive individuals, while getting rid of the “worst”. Thus, genetics begins as a necessity for the forging of towns and villages, through the increasing of production efficiency, in order to maintain larger social associations. <br />
<br />
The first notions of the possible heritage material came from history’s early philosophers, such as [http://en.wikipedia.org/wiki/Hippocrates Hippocrates] and [http://en.wikipedia.org/wiki/Aristotle Aristotle]. They both agreed that the heritable traits were carried in semen, where, either the semen from both parents (for Hippocrates) or the interference of the mother’s blood with the father’s semen (for Aristotle), were finally mixed into a whole new individual who would carry characteristics from both. Even though the fall of the Greek civilization and the advent of the Roman Empire and the Middle Ages slowed down science for more than a thousand years, practical geneticists, namely farmers and stockbreeders, had already achieved important advances. First, the realization that some stable varieties nearly always bred true, with their offspring having the same characteristics as their parents. Second, that it was sometimes possible to mate parents from different varieties to form [http://en.wikipedia.org/wiki/Hybrid_(biology) hybrids]; and third, that even stable varieties occasionally produced offspring different from either parent.<br />
<br />
Practical genetics, however, was purely empirical, and society had yet to discover any laws of inheritance, that is, until [http://en.wikipedia.org/wiki/Gregor_Mendel Gregor Mendel]’s experiments (XIX century). In accordance with Hippocrates’s conjectures, Mendel described heritable traits as physical substances (genes) that retained their identity in hybrids, never blending together. Differing from Aristotle, Mendel confirmed the importance of both parents towards the generation of an offspring’s traits, where each organism, while having two copies per gene (each from one parent), produces gametes carrying one gene copy for each trait. Another of Mendel’s discoveries was that a gene form ([http://en.wikipedia.org/wiki/Allele allele]) may be [http://en.wikipedia.org/wiki/Dominance_(genetics) dominant over another (recessive)], and that different alleles would be sorted out to sperm and eggs [http://en.wikipedia.org/wiki/Mendelian_inheritance randomly and independently], where all combinations of alleles are equally likely. Even though ignored at first, the rediscovery of Mendel’s work, together with the emerging [http://en.wikipedia.org/wiki/Cytology cytology], [http://en.wikipedia.org/wiki/Cytogenetics cytogenetics], and advances in [http://en.wikipedia.org/wiki/Microscopy microscopy], enabled men to locate these genes in [http://en.wikipedia.org/wiki/Chromosome chromosomes], map them, and analyze their patterns of inheritance.<br />
<br />
== The Human Genome Project and the gene as a cultural icon ==<br />
<br />
Throughout the next two hundred years, scientists delved deeper into the basic Mendelian laws. [http://en.wikipedia.org/wiki/Gene Genes] were known to exist and found to be packaged in chromosomes, however, the exact composition of genes and how they work was still an enigma [[#References|[1] ]]. Biological models such as the rod shaped bacterium ''Escherichia coli'', and the fruit fly ''Drosophila melanogaster'', enabled science to describe what is now known as the [http://en.wikipedia.org/wiki/Central_dogma_of_molecular_biology central dogma of molecular biology]. This theory states that genes are a compilation of a four letter code in the [http://en.wikipedia.org/wiki/DNA DNA molecule], that they are read and transcribed into another code called [http://en.wikipedia.org/wiki/Messenger_RNA messenger RNA], and finally interpreted and translated into a [http://en.wikipedia.org/wiki/Protein protein] (biological effector) by the combined interaction of [http://en.wikipedia.org/wiki/Transfer_RNA transfer RNA] and [http://en.wikipedia.org/wiki/Ribosome ribosomes]. Furthermore, the notion of genes as the unchanging units of heredity was found to be wrong, as they may be, and constantly are, altered by [http://en.wikipedia.org/wiki/Mutation mutations]. In summary, the genetic code carries the information necessary to build a living being, from a bacterium to a fungus, a chimpanzee or a human. <br />
Research in gene sequencing and its association to a particular biological function were the first steps towards [http://en.wikipedia.org/wiki/Genetic_engineering gene engineering], where scientists discovered ways of transforming organisms with [http://en.wikipedia.org/wiki/Transgene transgenes] (genetic information coming from another species). Pharmaceutical industries and other large companies, encouraged by the possibility of using this information to revolutionize industrial and medical market, accelerated genetics evolution by funding its research.<br />
<br />
In this context, the realization of a [http://en.wikipedia.org/wiki/Human_Genome_Project Human Genome Project (HGP)] was the next natural step to make. The HGP refers to an international 13 year effort (finished in 2003) whose goals were: the identification of the approximate 20,000 genes in the human DNA, the determination of the sequence of the 3 billion base pairs (letter code) that make up human DNA, the storage of this information in databases, the improvement of tools for sequence analysis, the transferral of related technologies to the private sector, and the addressing of the the ethical, legal, and social issues that may arise from the its discoveries [[#References|[2] ]].<br />
<br />
Since differences in genetic coding are, in principle, what makes an individual unique among members of its own species, the HGP inspired enormous symbolical expectancies in the general public. This could be because certain achievements, such as the first lunar landing, atomic fission, and in this case the determination of the human genome sequence ultimately change how humans think of themselves [[#References|[3] ]]. Determination of the internal genetic scaffold around which every human life is moulded, and how this has been handed to us from our ancestors, is crucial towards the understanding of how humans have evolved, revealing just how similar or different we are to each other and to other species: what is it exactly that makes us humans.<br />
<br />
Advances in genetic comprehension made way for the geneticization of society, “an ongoing process by which priority is given to differences between individuals based on their DNA codes, with most disorders, behaviours, and physiological variations [...] structured as, at least in part, hereditary” [[#References|[4] ]]. Thus, the development of genetics as a science has progressively influenced genetic knowledge and technology in particular areas of society and culture. Influence that manifests itself directly by the application of gene testing; and indirectly through new concepts of health, disease [[#References|[5] ]], and politics. Dunn and Dobzhansky [[#References|[6] ]] sustain that in the uniqueness of each individual, that is, that everyone of us is different to anybody that has existed before and probably different than anyone who will exist, lies the fundamental base for ethics and democracy. Studies in Western society show diverse references to DNA, genes, and genetics –be it film, television, news reports, comic books, ads or cartoons; in addition to the media’s allusions to the idea that the essence of man, his true self, is in some way or another found in his genes [[#References|[5] ]], [[#References|[7] ]]. <br />
<br />
Medicine, too, is currently undergoing an extraordinary transition from its initial morphological and phenotypic orientation towards a molecular and genotypic one, promoting the importance of prognosis and prediction [[#References|[8] ]]. Thus, public health is suffering a massive change on disease conception, whereas pre and post–natal gene therapy to diminish susceptibilities to some disorders, and personalized drug prescriptions as treatment are no longer ideas, but possibilities.<br />
<br />
== Geneticized future: the gene dream and the gene nightmare ==<br />
<br />
Molecular geneticist Peter Little’s book [[#References|[9] ]] portrays the life of two very different individuals living the gene dream and the gene nightmare, respectively, in the same geneticized future. The former illustrates a world where “disease and suffering were an echo of the past” [[#References|[9] ]]: where prenatal DNA characteristics (disease susceptibilities and even personality issues) of fertilized embryos may be screened for the selection of the desired baby to be implanted via in vitro fertilization; where DNA may be tested for drug-response indicators so as to ensure future drug treatment perfectly matching the patient’s genetic profile. A future where severe burns may be completely healed or dismemberments entirely re-grown as a result of stem cell research; where personality disorders such as attention-deficit or alcohol abuse are treated with combinations of cell receptor regulators. A reality where many infectious diseases have been taken care of through appropriate drug targeting, where cancer is no more and neurodegenerative ailments such as [http://en.wikipedia.org/wiki/Alzheimer's_disease Alzheimer's disease] and [http://en.wikipedia.org/wiki/Huntington's_disease Huntington’s chorea] may be treated.<br />
<br />
In the gene nightmare, however, “disease and suffering were the results of nature and malign human influence”: where uncontrolled births, prone to high probability susceptibility to disease may deny an individual from eligibility to state medical insurance; where education is limited to those with a minimum genetically defined IQ. A future where people may become preventively imprisoned for displaying criminal predisposition; where DNA differences may be used as an object to racism and discrimination. A reality where humans may be declared genetically unsuitable for reproduction (eugenics), and where ethnic weapons, targeting specific gene markers, may annihilate complete human populations.<br />
Even though many of these ideals and curses are unlikely to happen, scientists are aware of the social outcomes that genetic research may inspire. As a matter of fact, “race” has been found not to have a strong “scientific support”, since it reflects just a few continuous traits determined by a small fraction of our genes. Conversely, genome studies should foster compassion, not only because our gene pool is extremely mixed, but because in the understanding of the genotype’s correspondence to the phenotype is the demonstration that everyone carries at least some deleterious alleles3. [http://en.wikipedia.org/wiki/Nazism Nazism], however, is sufficient proof that mankind's stupidity.<br />
<br />
Despite the huge amount of genetic data available to the general public, we strongly believe society lacks some crucial information about genes. Contemporary ideas suggest that we as individuals are product of our genes; however, this is not entirely true. Our genetic code indeed possesses the information necessary for every physiological process that we will carry on during our lifetime; nevertheless, society seems to be unaware of gene regulation and its explicit importance in defining an individual. In understanding that genes + environment = you, lies the life uncertainty that frees us from a definite destiny, highlighting the significance behind every decision we make. <br />
<br />
The greatest impact of genetics on society I believe lies within the very concept of manipulation. History has driven us in a way where the human essence rises from nature and spirituality. However, we are unavoidably getting to a point where human reason may finally impose over the laws of nature: where the discrimination of what is good or evil, beautiful or ugly, the ethic and the aesthetic, and the significance of life itself lies in our very own hands. Genetics promises great power, probably the one of the greatest mankind will ever experience, and with power comes the responsibility of choosing wisely.<br />
<br />
== References ==<br />
<br />
#Stubbe, H. History of genetics, from prehistoric times to the rediscovery of Mendel's laws (M.I.T. Press, 1972).<br />
#Oak Ridge National Laboratory. (2009).<br />
#Pääbo, S. The Human Genome and Our View of Ourselves. Science 291, 1219-1220 (2001).<br />
#Lippman, A. Prenatal genetic testing and screening: constructing needs and reinforcing inequities. American Journal of Law and Medicine 17, 15-50 (1991).<br />
#ten Have, H. Genetics and culture: the geneticization thesis. Medicine, Health Care and Philosophy 4, 295-304 (2001).<br />
#Dunn, L. & Dobzhansky, T. Heredity, Race, and Society (Pinguin Books, Inc., New York, 1946).<br />
#Gordijn, B. & Dekkers, W. Genetics and its impact on society, healthcare and medicine. Medicine, Health Care and Philosophy 9, 1-2 (2006).<br />
#Brand, A., Brand, H. & Schulte, T. The impact of genetics and genomics on public health. European Journal of Human Genetics 16, 5-13 (2008).<br />
#Little, P. Genetic Destinies (Oxford University Press, Oxford, 2002).<br />
<br />
</div></div>Ksk 89http://2012.igem.org/File:Elcheck.jpgFile:Elcheck.jpg2012-10-27T03:59:49Z<p>Ksk 89: uploaded a new version of &quot;File:Elcheck.jpg&quot;</p>
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<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:59:33Z<p>Ksk 89: /* Implementation Model scripting check */</p>
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{{http://2012.igem.org/User:Tabima}}<br />
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<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|500px|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -1000*R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
The model works as expected. When chitin (fungi) is present, the persister and activated cell count decay to give rise to stimulated cells. Once these surpass the ''Anot'' 3500 threshold, the leaf drops and the fungi count goes to zero. The activated cell plot presents two distinct distributions, a first one of exponential decay (when R is present)and a second one (when the fungus dies). The second one shows an initial rise to steady state and then another decay due to cell death.<br />
<br />
=== Model Usage ===<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''. Using the above code, we can probe for different ''Anot'' values and check the minimum ''B'' number that effectively eliminates fungi. We then, plot valid ''Anot'' against their minimum ''B'' values. In this way, we may fit a distribution to this data and then calulate the nomber of bacteria we need for the experimentally obtained ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:55:15Z<p>Ksk 89: /* Model Usage */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|500px|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
The model works as expected. When chitin (fungi) is present, the persister and activated cell count decay to give rise to stimulated cells. Once these surpass the ''Anot'' 3500 threshold, the leaf drops and the fungi count goes to zero. The activated cell plot presents two distinct distributions, a first one of exponential decay (when R is present)and a second one (when the fungus dies). The second one shows an initial rise to steady state and then another decay due to cell death.<br />
<br />
=== Model Usage ===<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''. Using the above code, we can probe for different ''Anot'' values and check the minimum ''B'' number that effectively eliminates fungi. We then, plot valid ''Anot'' against their minimum ''B'' values. In this way, we may fit a distribution to this data and then calulate the nomber of bacteria we need for the experimentally obtained ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:55:05Z<p>Ksk 89: /* Model Results */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|500px|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
The model works as expected. When chitin (fungi) is present, the persister and activated cell count decay to give rise to stimulated cells. Once these surpass the ''Anot'' 3500 threshold, the leaf drops and the fungi count goes to zero. The activated cell plot presents two distinct distributions, a first one of exponential decay (when R is present)and a second one (when the fungus dies). The second one shows an initial rise to steady state and then another decay due to cell death.<br />
<br />
== Model Usage ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''. Using the above code, we can probe for different ''Anot'' values and check the minimum ''B'' number that effectively eliminates fungi. We then, plot valid ''Anot'' against their minimum ''B'' values. In this way, we may fit a distribution to this data and then calulate the nomber of bacteria we need for the experimentally obtained ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:41:20Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|500px|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
The model works as expected. When chitin (fungi) is present, the persister and activated cell count decay to give rise to stimulated cells. Once these surpass the ''Anot'' 3500 threshold, the leaf drops and the fungi count goes to zero. The activated cell plot presents two distinct distributions, a first one of exponential decay (when R is present)and a second one (when the fungus dies). The second one shows an initial rise to steady state and then another decay due to cell death.<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/File:Elcheck.jpgFile:Elcheck.jpg2012-10-27T03:30:08Z<p>Ksk 89: uploaded a new version of &quot;File:Elcheck.jpg&quot;</p>
<hr />
<div></div>Ksk 89http://2012.igem.org/File:Elcheck.jpgFile:Elcheck.jpg2012-10-27T03:28:27Z<p>Ksk 89: uploaded a new version of &quot;File:Elcheck.jpg&quot;</p>
<hr />
<div></div>Ksk 89http://2012.igem.org/File:Elcheck.jpgFile:Elcheck.jpg2012-10-27T03:27:19Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:26:36Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px]]<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:25:33Z<p>Ksk 89: /* Model Results */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:dzekocheck.jpg|center|700px]]<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:22:36Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:dzekocheck.jpg|center|700px]]<br />
<br />
=== Model Results ===<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/File:Dzekocheck.jpgFile:Dzekocheck.jpg2012-10-27T02:31:01Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:30:52Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:dzekocheck.jpg]]<br />
<br />
=== Model Results ===<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:29:55Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
=== Model Results ===<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:28:05Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:26:12Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
[[File:figurarnots.png|center|500px]]<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:25:28Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/File:Ecochecks.pngFile:Ecochecks.png2012-10-27T02:24:55Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:23:39Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:ecochecks.png]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:22:49Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:ecocheck.png|thumb|center|700px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:22:21Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:ecocheck.png|center|thumb|700px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/File:Ecocheck.pngFile:Ecocheck.png2012-10-27T02:21:59Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:21:43Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
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<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:ecocheck.png|center|700px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Human/SynthEthicsTeam:Colombia/Human/SynthEthics2012-10-27T02:19:21Z<p>Ksk 89: /* Participation in the Sabana University's First Philosophy and Biosciences Workshop */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''SynthEthics - A Phylosophical Debate''' =<br />
<br />
== Introduction ==<br />
<br />
Emerging technologies must not forget to have a clear bioethical stand, and synthetic biology should be no different. Advances in this field may open the door to engineering living systems in a similar way we design new dishwashers, computers or spaceships, and may certainly improve our life quality. However, we are talking about the same engineering has created sophisticated weapons, tanks, and the atomic bomb: synthetic biology could be used for good or bad. Even though we may expect huge benefits from it, there are risks. One major concrete concern refers to the possibility of purposely designing pathogenic strains as a tool for bioterrorism. What was fiction a decade ago, namely the creation of a target population specific pathogen, may aid from advances in tumor specific therapies and recent improvements in DNA synthesis and become a real weapon for xenophobism. To address all these issues, different bodies, agents and organizations have started lively discussions and actions against the potential risks of synthetic biology (discussed on the [http://syntheticbiology.org/SB2.0/Biosecurity_and_Biosafety.html internet site] of the US synthetic biology. Both in the US and in the EU several forums for discussion and documents regarding Biosafety have appeared ([http://www.jcvi.org/research/synthetic-genomics-report/ JCVI Synthetic Genomics - Options for Governance]; [http://www.rathenau.nl/en.html Rathenau Institut]; [http://openwetware.org/wiki/Synthetic_Society/Community_Organization_and_Culture OpenWetWare]). In the case of the EU, some research projects have been funded to analyze the impact and safety problems of Synthetic Biology in Europe ([http://www.synbiosafe.eu SYNBIOSAFE]; [http://www2.spi.pt/synbiology/ SYNBIOLOGY]) (Serrano, 2007). In this way, the success of synthetic biology will depend on its capacity to surpass traditional engineering, blending the best features of natural systems with artificial designs that are extensible, comprehensible, user-friendly, ethical, and most importantly implement stated specifications to fulfill user goals (Andrianantoandro et al., 2006).<br />
<br />
== Participation in the Sabana University's First Philosophy and Biosciences Workshop ==<br />
<br />
[[File:simbolito.jpg|center]]<br />
<br />
As an attempt to spread the principles of synthetic biology into diverse social populations, we accepted an invitation from the [http://www.unisabana.edu.co/ Sabana University] located in Chía, Colombia to the [http://www.unisabana.edu.co/nc/la-sabana/campus-20/noticia/articulo/primer-workshop-filosofia-y-biociencias-facultad-de-filosofia-y-ciencias-humanas/ first philosophy and biosciences workshop] (11, 12, and 13th of June). The main focus of this event was to address the concepts of “complexity and emergency” from both stand points, as well as to generate very much forgotten dialogues between philosophers and scientists. The main guests ranged from local representatives of the scientific community, to expert philosophers from Spain and Poland. Some of these special guests were [http://investigacion.us.es/sisius/sis_showpub.php?idpers=1210 Prof. Juan Arana], an expert in Philosophy and Contemporary Culture from the Universidad De Sevilla in Spain, [http://201.234.78.173:8081/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000268186 Dr. Fernando Lizcano], an Endocrinnology specialist from Universidad de la Sabana, Colombia, [http://www.unav.es/adi/servlet/Cv2.ara?personid=33807&pagina=8962&action=ver_pagina&cambia_idioma=2 Prof. José Murillo], an subdirector of the Anthropology and Ethics Institute of the Universidad de Navarra, Spain, among others.<br />
<br />
<br />
[[File:build.png|thumb|300px|'''Read more''' in [[#References|Elowitz & Lim, 2010 [2] ]]]]For this particular audience, we elaborated a different style of lecture, based in a presentation given by Stanford’s [http://en.wikipedia.org/wiki/Drew_Endy Prof. Drew Endy] during a [http://events.embo.org/12-synthetic-biology/ synthetic biology EMBO workshop] in Buenos Aires, Argentina last April. We skipped the basic biology and molecular biology sections of our usual formula, and decided to focus into the technical, scientific, and social ambitions of synthetic biology. We discussed how the scientific perspective to an emergent technology may be different from the general public political ones, and how interdisciplinary projects together with philosophy may strengthen bioethical initiatives. As always, we followed with a short overview of our project aims and methods. As a means to address the main topics of the workshop, our main point was extracted from the words of Caltech’s [http://en.wikipedia.org/wiki/Michael_Elowitz Michael Elowitz] (Elowitz & Lim, 2010): “''Build life to understand it''”. We proposed synthetic biology as an alternative to understand life and what makes us human, and purposely used expressions such as “create life” or “produce organisms” in order to generate philosophical debates regarding our way to address complexity. We proposed the idea that synthetic biology may stand as a vanguard discipline in the way in which we think about life. Instead of limiting biology’s concern with past and present life forms, synthetic biology may be making an important step forwards into thinking about the organisms that may be. We also stated how the gap between engineering and biology is rapidly shortening, and discussed if philosophy and science may merge again in the future in a similar way. If you are interested in the lecture and the debate click [https://www.dropbox.com/s/xc7o0howmg4lubu/unisabana.mp3 here]! (Sorry, spanish only!).<br />
<br />
<br />
[[File:lastMan.jpg|thumb|left|180px]]After our presentation at the workshop, we were given about 30 minutes for questions and debate. There were two main concerns from our audience. The first one questioned synthetic biology feasibility from a biosecurity and bioethical point of view. Since biological causality is nonlinear, that is, since biological events are generally regulated by many others (e.g., because of the cascade properties of intracellular signaling a single change of a signaling protein may have different cellular consequences), Prof. Arana claimed that genetic modifications would be very difficult to perfectly restrict. He stated how things may go out of control and we may end up as [http://en.wikipedia.org/wiki/Johann_Wolfgang_von_Goethe Goethe]'s proverbial “[http://en.wikipedia.org/wiki/The_Sorcerer's_Apprentice_(Dukas) Aorcerer’s Apprentice]”. Additionally, taking into account the high globalization of the current age, he quoted [http://en.wikipedia.org/wiki/J._Robert_Oppenheimer Oppenheimer] and stated that every technologically feasible idea ends up being constructed, and warned us about the danger of proof of concept explorations. Dr. Fernando Lizcano, M.D., based his opinion in a paragraph of [http://en.wikipedia.org/wiki/Francis_Fukuyama Francis Fukuyama]’s book [http://en.wikipedia.org/wiki/The_End_of_History_and_the_Last_Man The End of History and the Last Man], claiming that any particular political and economic interest may be justified by the right person. He claimed that President Obama changed the bioethical committee and searched important Universities for people who would agree with his views. Whether or not this is true in this particular case, it is certainly feasible.<br />
<br />
<br />
[[File:elowitz.jpg|thumb|300px| The Sorcerer's Apprentice. Illustration from around 1882 by S. Barth for the original Goethe's Poem]]On the other hand, Prof. José Murillo focused in a more existential aspect of synthetic biology. Our use of controversial expressions earlier teased Prof. Murillo as expected, and he strongly defended how life may not be produced or built, but instead transformed. The reason behind this is the fact that synthetic biology relies on “ingredients” generated by biological processes. He believes that to “build” life is not the only way to understand it, and that the concept of producing life is ambiguous and obscures the reality of life itself. He proposed that one main difference between human generated machines and “biological machines” is that the whole purpose of the former is to accomplish a specific objective. This is their whole meaning of existence. Quoting [http://en.wikipedia.org/wiki/Aristotle Aristotle], life is generated by motion, and a living being is produced only when it sets itself in motion. In this way, machines are not their own movement; they limit themselves to defined functions. Living beings, however, must first function for themselves before being able to ''do'' things. Finally, he questioned the practicality of living beings as engineering scaffolds and we were once again accused of hubris, doing this for the purpose of controlling life instead of pursuing specific advantages of this technology.<br />
<br />
<br />
Regarding Prof. Arana’s input, we believe he is right to a certain extent. Although it is true biological systems are chaotic in nature, and that it is true it is very difficult to assure complete understanding of our design’s, this is the exact reason why iGEM HQ has a biosafety requirement. Additionally, this highlights the importance of making mathematical models in order to predict design behaviors and possible glitches. On the other hand, even though it is true that the construction of any feasible technology will not be stopped by particular interests, this doesn’t necessarily mean every conceivable piece of machinery will actually be built. Dr. Fernando Lizcano’s opinion was very important for us since it is possible that political interests may interfere with bioethical initiatives. However, it is important to understand that there are some very well conceived ethical stand points within the scientific community (e.g., regarding stem cell research or climate engineering). This means that even if some crazy idea is accepted by a government decision, the scientific community will not just stand aside. It is also true that there are many instances where gray areas may be found, and this highlights the importance of spreading synthetic biology into pop culture so people may make informed decisions. This was one of our main motivations for the organization of our [http://2012.igem.org/Team:Colombia/Human/Research Research in Colombia forum].<br />
<br />
[[File:Foro iGELA.jpg|center|700px]]<br />
<br />
Prof. José Murillo's opinion was particularly interesting. It showed us that strong preconceptions may be present even within high academic contexts. To us, Prof. Murillo believes life to be a kind of higher state of being, rather than the coincidence of certain physical conditions. His statements opened our eyes to other kinds of conceptual criticisms and convinced us of the need for healthy legislative and educational campaigns for synthetic biology. This, we believe, is one of the main reasons why Human Practices must be carried out with great effort.<br />
<br />
<br />
From this activity, we realized how new technologies change how people think about themselves. This encouraged us to make the decision of [http://2012.igem.org/Team:Colombia/Human/Social:_Schools extending our outreach not only to students but coffee growers], since they would be the people directly affected by our technology. We realized we had to be very careful as to how to express ourselves, and how our actions could heavily influence the lifestyle of others. With this in mind, we decided to investigate how the emergence of genetics and genetically oriented technologies has impacted society. We thought that by doing this, we would be able to improve our perspective into how to approach different social groups, as well as to understand our responsibility as scientists. For this matter, we developed a [http://2012.igem.org/Team:Colombia/Human/Essay short essay] that summarizes our findings.<br />
<br />
= References =<br />
<br />
#Andrianantoandro, E., Basu, S., Karig, D. K., & Weiss, R. (2006). Synthetic biology: new engineering rules for an emerging discipline. Molecular systems biology, 2, 2006.0028. doi:10.1038/msb4100073<br />
#Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a<br />
#Serrano, L. (2007). Synthetic biology: promises and challenges. Molecular systems biology, 3(158), 158. doi:10.1038/msb4100202<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/SynthEthicsTeam:Colombia/Human/SynthEthics2012-10-27T02:18:32Z<p>Ksk 89: /* Participation in the Sabana University's First Philosophy and Biosciences Workshop */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''SynthEthics - A Phylosophical Debate''' =<br />
<br />
== Introduction ==<br />
<br />
Emerging technologies must not forget to have a clear bioethical stand, and synthetic biology should be no different. Advances in this field may open the door to engineering living systems in a similar way we design new dishwashers, computers or spaceships, and may certainly improve our life quality. However, we are talking about the same engineering has created sophisticated weapons, tanks, and the atomic bomb: synthetic biology could be used for good or bad. Even though we may expect huge benefits from it, there are risks. One major concrete concern refers to the possibility of purposely designing pathogenic strains as a tool for bioterrorism. What was fiction a decade ago, namely the creation of a target population specific pathogen, may aid from advances in tumor specific therapies and recent improvements in DNA synthesis and become a real weapon for xenophobism. To address all these issues, different bodies, agents and organizations have started lively discussions and actions against the potential risks of synthetic biology (discussed on the [http://syntheticbiology.org/SB2.0/Biosecurity_and_Biosafety.html internet site] of the US synthetic biology. Both in the US and in the EU several forums for discussion and documents regarding Biosafety have appeared ([http://www.jcvi.org/research/synthetic-genomics-report/ JCVI Synthetic Genomics - Options for Governance]; [http://www.rathenau.nl/en.html Rathenau Institut]; [http://openwetware.org/wiki/Synthetic_Society/Community_Organization_and_Culture OpenWetWare]). In the case of the EU, some research projects have been funded to analyze the impact and safety problems of Synthetic Biology in Europe ([http://www.synbiosafe.eu SYNBIOSAFE]; [http://www2.spi.pt/synbiology/ SYNBIOLOGY]) (Serrano, 2007). In this way, the success of synthetic biology will depend on its capacity to surpass traditional engineering, blending the best features of natural systems with artificial designs that are extensible, comprehensible, user-friendly, ethical, and most importantly implement stated specifications to fulfill user goals (Andrianantoandro et al., 2006).<br />
<br />
== Participation in the Sabana University's First Philosophy and Biosciences Workshop ==<br />
<br />
[[File:simbolito.jpg|center]]<br />
<br />
As an attempt to spread the principles of synthetic biology into diverse social populations, we accepted an invitation from the [http://www.unisabana.edu.co/ Sabana University] located in Chía, Colombia to the [http://www.unisabana.edu.co/nc/la-sabana/campus-20/noticia/articulo/primer-workshop-filosofia-y-biociencias-facultad-de-filosofia-y-ciencias-humanas/ first philosophy and biosciences workshop] (11, 12, and 13th of June). The main focus of this event was to address the concepts of “complexity and emergency” from both stand points, as well as to generate very much forgotten dialogues between philosophers and scientists. The main guests ranged from local representatives of the scientific community, to expert philosophers from Spain and Poland. Some of these special guests were [http://investigacion.us.es/sisius/sis_showpub.php?idpers=1210 Prof. Juan Arana], an expert in Philosophy and Contemporary Culture from the Universidad De Sevilla in Spain, [http://201.234.78.173:8081/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000268186 Dr. Fernando Lizcano], an Endocrinnology specialist from Universidad de la Sabana, Colombia, [http://www.unav.es/adi/servlet/Cv2.ara?personid=33807&pagina=8962&action=ver_pagina&cambia_idioma=2 Prof. José Murillo], an subdirector of the Anthropology and Ethics Institute of the Universidad de Navarra, Spain, among others.<br />
<br />
<br />
[[File:build.png|thumb|300px|'''Read more''' in [[#References|Elowitz & Lim, 2010 [2] ]]]]For this particular audience, we elaborated a different style of lecture, based in a presentation given by Stanford’s [http://en.wikipedia.org/wiki/Drew_Endy Prof. Drew Endy] during a [http://events.embo.org/12-synthetic-biology/ synthetic biology EMBO workshop] in Buenos Aires, Argentina last April. We skipped the basic biology and molecular biology sections of our usual formula, and decided to focus into the technical, scientific, and social ambitions of synthetic biology. We discussed how the scientific perspective to an emergent technology may be different from the general public political ones, and how interdisciplinary projects together with philosophy may strengthen bioethical initiatives. As always, we followed with a short overview of our project aims and methods. As a means to address the main topics of the workshop, our main point was extracted from the words of Caltech’s [http://en.wikipedia.org/wiki/Michael_Elowitz Michael Elowitz] (Elowitz & Lim, 2010): “''Build life to understand it''”. We proposed synthetic biology as an alternative to understand life and what makes us human, and purposely used expressions such as “create life” or “produce organisms” in order to generate philosophical debates regarding our way to address complexity. We proposed the idea that synthetic biology may stand as a vanguard discipline in the way in which we think about life. Instead of limiting biology’s concern with past and present life forms, synthetic biology may be making an important step forwards into thinking about the organisms that may be. We also stated how the gap between engineering and biology is rapidly shortening, and discussed if philosophy and science may merge again in the future in a similar way. If you are interested in the lecture and the debate click [https://www.dropbox.com/s/xc7o0howmg4lubu/unisabana.mp3 here]! (Sorry, spanish only!).<br />
<br />
<br />
[[File:lastMan.jpg|thumb|left|180px]]After our presentation at the workshop, we were given about 30 minutes for questions and debate. There were two main concerns from our audience. The first one questioned synthetic biology feasibility from a biosecurity and bioethical point of view. Since biological causality is nonlinear, that is, since biological events are generally regulated by many others (e.g., because of the cascade properties of intracellular signaling a single change of a signaling protein may have different cellular consequences), Prof. Arana claimed that genetic modifications would be very difficult to perfectly restrict. He stated how things may go out of control and we may end up as [http://en.wikipedia.org/wiki/Johann_Wolfgang_von_Goethe Goethe]'s proverbial “[http://en.wikipedia.org/wiki/The_Sorcerer's_Apprentice_(Dukas) Aorcerer’s Apprentice]”. Additionally, taking into account the high globalization of the current age, he quoted [http://en.wikipedia.org/wiki/J._Robert_Oppenheimer Oppenheimer] and stated that every technologically feasible idea ends up being constructed, and warned us about the danger of proof of concept explorations. Dr. Fernando Lizcano, M.D., based his opinion in a paragraph of [http://en.wikipedia.org/wiki/Francis_Fukuyama Francis Fukuyama]’s book [http://en.wikipedia.org/wiki/The_End_of_History_and_the_Last_Man The End of History and the Last Man], claiming that any particular political and economic interest may be justified by the right person. He claimed that President Obama changed the bioethical committee and searched important Universities for people who would agree with his views. Whether or not this is true in this particular case, it is certainly feasible.<br />
<br />
<br />
[[File:elowitz.jpg|thumb|300px|Illustration from around 1882 by S. Barth for the original Goethe's Poem]]On the other hand, Prof. José Murillo focused in a more existential aspect of synthetic biology. Our use of controversial expressions earlier teased Prof. Murillo as expected, and he strongly defended how life may not be produced or built, but instead transformed. The reason behind this is the fact that synthetic biology relies on “ingredients” generated by biological processes. He believes that to “build” life is not the only way to understand it, and that the concept of producing life is ambiguous and obscures the reality of life itself. He proposed that one main difference between human generated machines and “biological machines” is that the whole purpose of the former is to accomplish a specific objective. This is their whole meaning of existence. Quoting [http://en.wikipedia.org/wiki/Aristotle Aristotle], life is generated by motion, and a living being is produced only when it sets itself in motion. In this way, machines are not their own movement; they limit themselves to defined functions. Living beings, however, must first function for themselves before being able to ''do'' things. Finally, he questioned the practicality of living beings as engineering scaffolds and we were once again accused of hubris, doing this for the purpose of controlling life instead of pursuing specific advantages of this technology.<br />
<br />
<br />
Regarding Prof. Arana’s input, we believe he is right to a certain extent. Although it is true biological systems are chaotic in nature, and that it is true it is very difficult to assure complete understanding of our design’s, this is the exact reason why iGEM HQ has a biosafety requirement. Additionally, this highlights the importance of making mathematical models in order to predict design behaviors and possible glitches. On the other hand, even though it is true that the construction of any feasible technology will not be stopped by particular interests, this doesn’t necessarily mean every conceivable piece of machinery will actually be built. Dr. Fernando Lizcano’s opinion was very important for us since it is possible that political interests may interfere with bioethical initiatives. However, it is important to understand that there are some very well conceived ethical stand points within the scientific community (e.g., regarding stem cell research or climate engineering). This means that even if some crazy idea is accepted by a government decision, the scientific community will not just stand aside. It is also true that there are many instances where gray areas may be found, and this highlights the importance of spreading synthetic biology into pop culture so people may make informed decisions. This was one of our main motivations for the organization of our [http://2012.igem.org/Team:Colombia/Human/Research Research in Colombia forum].<br />
<br />
[[File:Foro iGELA.jpg|center|700px]]<br />
<br />
Prof. José Murillo's opinion was particularly interesting. It showed us that strong preconceptions may be present even within high academic contexts. To us, Prof. Murillo believes life to be a kind of higher state of being, rather than the coincidence of certain physical conditions. His statements opened our eyes to other kinds of conceptual criticisms and convinced us of the need for healthy legislative and educational campaigns for synthetic biology. This, we believe, is one of the main reasons why Human Practices must be carried out with great effort.<br />
<br />
<br />
From this activity, we realized how new technologies change how people think about themselves. This encouraged us to make the decision of [http://2012.igem.org/Team:Colombia/Human/Social:_Schools extending our outreach not only to students but coffee growers], since they would be the people directly affected by our technology. We realized we had to be very careful as to how to express ourselves, and how our actions could heavily influence the lifestyle of others. With this in mind, we decided to investigate how the emergence of genetics and genetically oriented technologies has impacted society. We thought that by doing this, we would be able to improve our perspective into how to approach different social groups, as well as to understand our responsibility as scientists. For this matter, we developed a [http://2012.igem.org/Team:Colombia/Human/Essay short essay] that summarizes our findings.<br />
<br />
= References =<br />
<br />
#Andrianantoandro, E., Basu, S., Karig, D. K., & Weiss, R. (2006). Synthetic biology: new engineering rules for an emerging discipline. Molecular systems biology, 2, 2006.0028. doi:10.1038/msb4100073<br />
#Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a<br />
#Serrano, L. (2007). Synthetic biology: promises and challenges. Molecular systems biology, 3(158), 158. doi:10.1038/msb4100202<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Human/SynthEthicsTeam:Colombia/Human/SynthEthics2012-10-27T02:18:01Z<p>Ksk 89: /* Participation in the Sabana University's First Philosophy and Biosciences Workshop */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''SynthEthics - A Phylosophical Debate''' =<br />
<br />
== Introduction ==<br />
<br />
Emerging technologies must not forget to have a clear bioethical stand, and synthetic biology should be no different. Advances in this field may open the door to engineering living systems in a similar way we design new dishwashers, computers or spaceships, and may certainly improve our life quality. However, we are talking about the same engineering has created sophisticated weapons, tanks, and the atomic bomb: synthetic biology could be used for good or bad. Even though we may expect huge benefits from it, there are risks. One major concrete concern refers to the possibility of purposely designing pathogenic strains as a tool for bioterrorism. What was fiction a decade ago, namely the creation of a target population specific pathogen, may aid from advances in tumor specific therapies and recent improvements in DNA synthesis and become a real weapon for xenophobism. To address all these issues, different bodies, agents and organizations have started lively discussions and actions against the potential risks of synthetic biology (discussed on the [http://syntheticbiology.org/SB2.0/Biosecurity_and_Biosafety.html internet site] of the US synthetic biology. Both in the US and in the EU several forums for discussion and documents regarding Biosafety have appeared ([http://www.jcvi.org/research/synthetic-genomics-report/ JCVI Synthetic Genomics - Options for Governance]; [http://www.rathenau.nl/en.html Rathenau Institut]; [http://openwetware.org/wiki/Synthetic_Society/Community_Organization_and_Culture OpenWetWare]). In the case of the EU, some research projects have been funded to analyze the impact and safety problems of Synthetic Biology in Europe ([http://www.synbiosafe.eu SYNBIOSAFE]; [http://www2.spi.pt/synbiology/ SYNBIOLOGY]) (Serrano, 2007). In this way, the success of synthetic biology will depend on its capacity to surpass traditional engineering, blending the best features of natural systems with artificial designs that are extensible, comprehensible, user-friendly, ethical, and most importantly implement stated specifications to fulfill user goals (Andrianantoandro et al., 2006).<br />
<br />
== Participation in the Sabana University's First Philosophy and Biosciences Workshop ==<br />
<br />
[[File:simbolito.jpg|center]]<br />
<br />
As an attempt to spread the principles of synthetic biology into diverse social populations, we accepted an invitation from the [http://www.unisabana.edu.co/ Sabana University] located in Chía, Colombia to the [http://www.unisabana.edu.co/nc/la-sabana/campus-20/noticia/articulo/primer-workshop-filosofia-y-biociencias-facultad-de-filosofia-y-ciencias-humanas/ first philosophy and biosciences workshop] (11, 12, and 13th of June). The main focus of this event was to address the concepts of “complexity and emergency” from both stand points, as well as to generate very much forgotten dialogues between philosophers and scientists. The main guests ranged from local representatives of the scientific community, to expert philosophers from Spain and Poland. Some of these special guests were [http://investigacion.us.es/sisius/sis_showpub.php?idpers=1210 Prof. Juan Arana], an expert in Philosophy and Contemporary Culture from the Universidad De Sevilla in Spain, [http://201.234.78.173:8081/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000268186 Dr. Fernando Lizcano], an Endocrinnology specialist from Universidad de la Sabana, Colombia, [http://www.unav.es/adi/servlet/Cv2.ara?personid=33807&pagina=8962&action=ver_pagina&cambia_idioma=2 Prof. José Murillo], an subdirector of the Anthropology and Ethics Institute of the Universidad de Navarra, Spain, among others.<br />
<br />
<br />
[[File:build.png|thumb|300px|'''Read more''' in [[#References|Elowitz & Lim, 2010 [2] ]]]]For this particular audience, we elaborated a different style of lecture, based in a presentation given by Stanford’s [http://en.wikipedia.org/wiki/Drew_Endy Prof. Drew Endy] during a [http://events.embo.org/12-synthetic-biology/ synthetic biology EMBO workshop] in Buenos Aires, Argentina last April. We skipped the basic biology and molecular biology sections of our usual formula, and decided to focus into the technical, scientific, and social ambitions of synthetic biology. We discussed how the scientific perspective to an emergent technology may be different from the general public political ones, and how interdisciplinary projects together with philosophy may strengthen bioethical initiatives. As always, we followed with a short overview of our project aims and methods. As a means to address the main topics of the workshop, our main point was extracted from the words of Caltech’s [http://en.wikipedia.org/wiki/Michael_Elowitz Michael Elowitz] (Elowitz & Lim, 2010): “''Build life to understand it''”. We proposed synthetic biology as an alternative to understand life and what makes us human, and purposely used expressions such as “create life” or “produce organisms” in order to generate philosophical debates regarding our way to address complexity. We proposed the idea that synthetic biology may stand as a vanguard discipline in the way in which we think about life. Instead of limiting biology’s concern with past and present life forms, synthetic biology may be making an important step forwards into thinking about the organisms that may be. We also stated how the gap between engineering and biology is rapidly shortening, and discussed if philosophy and science may merge again in the future in a similar way. If you are interested in the lecture and the debate click [https://www.dropbox.com/s/xc7o0howmg4lubu/unisabana.mp3 here]! (Sorry, spanish only!).<br />
<br />
<br />
[[File:lastMan.jpg|thumb|left|180px]]After our presentation at the workshop, we were given about 30 minutes for questions and debate. There were two main concerns from our audience. The first one questioned synthetic biology feasibility from a biosecurity and bioethical point of view. Since biological causality is nonlinear, that is, since biological events are generally regulated by many others (e.g., because of the cascade properties of intracellular signaling a single change of a signaling protein may have different cellular consequences), Prof. Arana claimed that genetic modifications would be very difficult to perfectly restrict. He stated how things may go out of control and we may end up as [http://en.wikipedia.org/wiki/Johann_Wolfgang_von_Goethe Goethe]'s proverbial “[http://en.wikipedia.org/wiki/The_Sorcerer's_Apprentice_(Dukas) sorcerer’s apprentice]”. Additionally, taking into account the high globalization of the current age, he quoted [http://en.wikipedia.org/wiki/J._Robert_Oppenheimer Oppenheimer] and stated that every technologically feasible idea ends up being constructed, and warned us about the danger of proof of concept explorations. Dr. Fernando Lizcano, M.D., based his opinion in a paragraph of [http://en.wikipedia.org/wiki/Francis_Fukuyama Francis Fukuyama]’s book [http://en.wikipedia.org/wiki/The_End_of_History_and_the_Last_Man The End of History and the Last Man], claiming that any particular political and economic interest may be justified by the right person. He claimed that President Obama changed the bioethical committee and searched important Universities for people who would agree with his views. Whether or not this is true in this particular case, it is certainly feasible.<br />
<br />
<br />
[[File:elowitz.jpg|thumb|300px|Illustration from around 1882 by S. Barth for the original Goethe's Poem]]On the other hand, Prof. José Murillo focused in a more existential aspect of synthetic biology. Our use of controversial expressions earlier teased Prof. Murillo as expected, and he strongly defended how life may not be produced or built, but instead transformed. The reason behind this is the fact that synthetic biology relies on “ingredients” generated by biological processes. He believes that to “build” life is not the only way to understand it, and that the concept of producing life is ambiguous and obscures the reality of life itself. He proposed that one main difference between human generated machines and “biological machines” is that the whole purpose of the former is to accomplish a specific objective. This is their whole meaning of existence. Quoting [http://en.wikipedia.org/wiki/Aristotle Aristotle], life is generated by motion, and a living being is produced only when it sets itself in motion. In this way, machines are not their own movement; they limit themselves to defined functions. Living beings, however, must first function for themselves before being able to ''do'' things. Finally, he questioned the practicality of living beings as engineering scaffolds and we were once again accused of hubris, doing this for the purpose of controlling life instead of pursuing specific advantages of this technology.<br />
<br />
<br />
Regarding Prof. Arana’s input, we believe he is right to a certain extent. Although it is true biological systems are chaotic in nature, and that it is true it is very difficult to assure complete understanding of our design’s, this is the exact reason why iGEM HQ has a biosafety requirement. Additionally, this highlights the importance of making mathematical models in order to predict design behaviors and possible glitches. On the other hand, even though it is true that the construction of any feasible technology will not be stopped by particular interests, this doesn’t necessarily mean every conceivable piece of machinery will actually be built. Dr. Fernando Lizcano’s opinion was very important for us since it is possible that political interests may interfere with bioethical initiatives. However, it is important to understand that there are some very well conceived ethical stand points within the scientific community (e.g., regarding stem cell research or climate engineering). This means that even if some crazy idea is accepted by a government decision, the scientific community will not just stand aside. It is also true that there are many instances where gray areas may be found, and this highlights the importance of spreading synthetic biology into pop culture so people may make informed decisions. This was one of our main motivations for the organization of our [http://2012.igem.org/Team:Colombia/Human/Research Research in Colombia forum].<br />
<br />
[[File:Foro iGELA.jpg|center|700px]]<br />
<br />
Prof. José Murillo's opinion was particularly interesting. It showed us that strong preconceptions may be present even within high academic contexts. To us, Prof. Murillo believes life to be a kind of higher state of being, rather than the coincidence of certain physical conditions. His statements opened our eyes to other kinds of conceptual criticisms and convinced us of the need for healthy legislative and educational campaigns for synthetic biology. This, we believe, is one of the main reasons why Human Practices must be carried out with great effort.<br />
<br />
<br />
From this activity, we realized how new technologies change how people think about themselves. This encouraged us to make the decision of [http://2012.igem.org/Team:Colombia/Human/Social:_Schools extending our outreach not only to students but coffee growers], since they would be the people directly affected by our technology. We realized we had to be very careful as to how to express ourselves, and how our actions could heavily influence the lifestyle of others. With this in mind, we decided to investigate how the emergence of genetics and genetically oriented technologies has impacted society. We thought that by doing this, we would be able to improve our perspective into how to approach different social groups, as well as to understand our responsibility as scientists. For this matter, we developed a [http://2012.igem.org/Team:Colombia/Human/Essay short essay] that summarizes our findings.<br />
<br />
= References =<br />
<br />
#Andrianantoandro, E., Basu, S., Karig, D. K., & Weiss, R. (2006). Synthetic biology: new engineering rules for an emerging discipline. Molecular systems biology, 2, 2006.0028. doi:10.1038/msb4100073<br />
#Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a<br />
#Serrano, L. (2007). Synthetic biology: promises and challenges. Molecular systems biology, 3(158), 158. doi:10.1038/msb4100202<br />
<br />
</div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:16:15Z<p>Ksk 89: /* Implementation Model scripting check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:08:12Z<p>Ksk 89: /* Implementation Model check */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:04:01Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model check ===<br />
<br />
awklvhbawv<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T02:03:17Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model check ===<br />
<br />
awklvhbawv<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:54:28Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
=== Implementation Model check ===<br />
<br />
awklvhbawv<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:52:00Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:47:27Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 (Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results.<br />
<br />
[[File:leafcount.png|center|500px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/File:Leafcount.pngFile:Leafcount.png2012-10-27T01:46:58Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:46:43Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 (Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results.<br />
<br />
[[File:leafcount.png|center]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:30:39Z<p>Ksk 89: /* References */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Ksk 89http://2012.igem.org/File:Figurarnot.pngFile:Figurarnot.png2012-10-27T01:29:56Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:29:41Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390<br />
Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:28:11Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot|center|500px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390<br />
Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:18:21Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390<br />
Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a</div>Ksk 89http://2012.igem.org/File:Figuraalfa.pngFile:Figuraalfa.png2012-10-27T01:17:40Z<p>Ksk 89: </p>
<hr />
<div></div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:15:46Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png]]<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390<br />
Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:10:57Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
-''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004).<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390<br />
Elowitz, M., & Lim, W. A. (2010). Build life to understand it. Nature, 468(7326), 889–90. doi:10.1038/468889a</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T01:10:32Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
-''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004).</div>Ksk 89http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T00:57:12Z<p>Ksk 89: /* Inferences from the Molecular Mathematical Model */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|center]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.</div>Ksk 89