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Team:WHU-China/Project/MicrobiotaModel
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<h1>The Human Gut Microbiota Regulation by <i>E.coslim</i> and Mathematical Modeling</h1> | <h1>The Human Gut Microbiota Regulation by <i>E.coslim</i> and Mathematical Modeling</h1> | ||
<p> | <p> | ||
| - | + | As it has been mentioned, manipulating the number of Firmicutes and Bacteriodetes might be an effective method to achieve 'a slim glutton'. So the following content is about to provide a theoretical base for the whole project. </p><p> | |
| - | + | We assume that resources S (glucose) and R (fatty acid) are perfectly substitutable for both populations x1 (Firmicutes) and x2 (Bacteriodetes). We simplify this situation as an exploitative competition in a chemostat, and the ODEs are: </p><p> | |
| - | + | <center><img src="https://static.igem.org/mediawiki/2012/d/d3/Microbiota_Fml_1.png" width="584" height="236" hspace="2" vspace="1" border="2" align="top" /></center> | |
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| - | + | 1. S(t) and R(t): concentrations of glucose and fatty acid </p><p> | |
| + | 2. xi: biomass of the competing populations at time t </p><p> | ||
| + | 3. S0 and R0: concentrations of resource S and R in the feed bottle </p><p> | ||
| + | 4. D: dilution rate </p><p> | ||
| + | [The specific death rates of the microorganisms are assumed to be insignificant compared to this dilution rate D] </p><p> | ||
| + | 5.Si and Ri: the rate of conversion of nutrient S to biomass of population xi </p><p> | ||
| + | [if the conversion of nutrient to biomass is proportional to the amount of nutrient consumed, the consumption rate of resource S per unit of competitor xi is denoted <img src="https://static.igem.org/mediawiki/2012/a/ab/Microbiota_let_1.png" width="142" height="81" hspace="2" vspace="1" border="2" align="top" /> where ξi is the respective growth yield constant] </p><p> | ||
| + | 6. Gi: the rate of conversion of nutrient to biomass of population xi </p><p> | ||
| + | [Since perfectly substitutable resources are alternate sources of the same essential nutrient, the rate of conversion of nutrient to biomass of population xi is made up of a contribution from the consumption of resource S as well as R: <img src="https://static.igem.org/mediawiki/2012/b/bf/Microbiota_let_2.png" width="474" height="54" hspace="2" vspace="1" border="2" align="top" /> </p><p> | ||
| + | Here we choose </p><p> | ||
| + | |||
| + | <center><img src="https://static.igem.org/mediawiki/2012/6/6b/Microbiota_Fml_2.png" width="737" height="93" hspace="2" vspace="1" border="2" align="top" />;</center> | ||
| + | And let </p><p> | ||
| + | |||
| + | <center><img src="https://static.igem.org/mediawiki/2012/7/7f/Microbiota_Fml_3.png" width="432" height="69" hspace="2" vspace="1" border="2" align="top" />;</center> | ||
| + | |||
| + | They denote the maximal growth rate of population xi on resource S(R) when none of the other resource is available. </p><p> | ||
<h2>PART I</h2> | <h2>PART I</h2> | ||
<p> | <p> | ||
| - | + | A model is built to describe a quantitative relationship between Firmicutes and Bacteriodetes in people's intestines who are overweight. </p><p> | |
| - | + | Parameters mSi(mSi) can be assigned values to Firmicutes and Bacteriodetes so as to simulate the ability to utilize glucose and fatty acid. If their ability to use nutrient are given as follow: </p><p> | |
| - | <center><table border=1 bordercolor=# | + | <center><table border=1 bordercolor=#999999 cellpadding="10"> |
| - | <tr><td align=center> | + | <tr><td align=center> </td><td align=center> Firmicutes </td><td align=center> Bacteriodetes </td></tr> |
| - | <tr><td align=center>Glucose | + | <tr><td align=center> Glucose </td><td align=center> +++ (mS1) </td><td align=center> ++(mS2) </td></tr> |
| - | <tr><td align=center>Fatty acid</td><td align=center>+ (mR1) | + | <tr><td align=center> Fatty acid </td><td align=center> + (mR1) </td><td align=center> ++(mR2) </td></tr> |
</table></center> | </table></center> | ||
| - | + | Then we can set mS1=2.25, mR1=0.5, mS2=2.1, mR2=2.1. In order to make easier ODEs, we set S0=R0=D=1 and <img src="https://static.igem.org/mediawiki/2012/c/ce/Microbiota_let_3.png" width="93" height="73" hspace="2" vspace="1" border="2" align="top" />. </p><p> | |
| - | + | ||
| - | + | <center><img src="https://static.igem.org/mediawiki/2012/d/de/Microbiota_Fig_1.png" width="527" height="327" hspace="2" vspace="1" border="2" align="top" /></center> </p><p> | |
| + | |||
| + | In this situation, the ratio N(Firmicutes)/N(Bacteriodetes) is rather high, usually achieving a value 8.0, and each of their absolute number, or concentration, is stable. </p><p> | ||
<h2>PART II</h2> | <h2>PART II</h2> | ||
<p> | <p> | ||
| - | + | We try to add a Genetic Engineered Bacterium(GEB) into system. This ideal type of bacterium consumes glucose as well as fatty acid, thus makes itself a competitor to Firmicutes and Bacteriodetes. While it is reproducing in intestines, the competition among these three types of bacteria makes the number change gradually. At last, we hope to achieve a lower ratio of Firmicutes/Bacteriodetes. </p><p> | |
| + | |||
| + | The key point is to find out how competitive our GEB should be. In other words, we have to point out its ability to consume glucose and fatty acid---to study new parameters <img src="https://static.igem.org/mediawiki/2012/f/fd/Microbiota_let_4.png" width="122" height="65" hspace="2" vspace="1" border="2" align="top" />. For example, if mS3＞mS1, then we conclude that GEB has stronger ability to consume glucose than Firmicutes. We try to find out an appropriate pair of <img src="https://static.igem.org/mediawiki/2012/f/fd/Microbiota_let_4.png" width="122" height="65" hspace="2" vspace="1" border="2" align="top" />. </p><p> | ||
| + | |||
| + | 1. (2.5, 2.1) </p><p> | ||
| + | |||
| + | <center><table border=1 bordercolor=#999999 cellpadding="10"> | ||
| + | <tr><td align=center> </td><td align=center> Firmicutes </td><td align=center> Bacteriodetes</td><td align=center>GEB</td></tr> | ||
| + | <tr><td align=center> Glucose </td><td align=center> +++ (mS1) </td><td align=center> ++(mS2) </td><td align=center>++++(mS3)</td></tr> | ||
| + | <tr><td align=center> Fatty acid </td><td align=center> + (mR1) </td><td align=center> ++(mR2) </td><td align=center>++(mR3)</td></tr> | ||
| + | </table></center></p><p> | ||
| + | |||
| + | <center><img src="https://static.igem.org/mediawiki/2012/4/45/Microbiota_Fig_2.png" width="527" height="327" hspace="2" vspace="1" border="2" align="top" /></center> | ||
| + | |||
| + | 1'. (2.1,2.5) </p><p> | ||
| - | + | <center><table border=1 bordercolor=#999999 cellpadding="10"> | |
| + | <tr><td align=center> </td><td align=center> Firmicutes </td><td align=center> Bacteriodetes</td><td align=center>GEB</td></tr> | ||
| + | <tr><td align=center> Glucose </td><td align=center> +++ (mS1) </td><td align=center> ++(mS2) </td><td align=center>++(mS3)</td></tr> | ||
| + | <tr><td align=center> Fatty acid </td><td align=center> + (mR1) </td><td align=center> ++(mR2) </td><td align=center>+++(mR3)</td></tr> | ||
| + | </table></center></p><p> | ||
| - | + | <center><img src="https://static.igem.org/mediawiki/2012/5/5a/Microbiota_Fig_2-.png" width="549" height="347" hspace="2" vspace="1" border="2" align="top" /></center> | |
| - | + | ||
| - | + | ||
| - | + | 1 and 1' show that GEB are so competitive that others die out. </p><p> | |
| - | |||
| - | |||
| - | |||
| - | + | 2. (2.1,0.4) </p><p> | |
| - | 1 | + | <center><table border=1 bordercolor=#999999 cellpadding="10"> |
| + | <tr><td align=center> </td><td align=center> Firmicutes </td><td align=center> Bacteriodetes</td><td align=center>GEB</td></tr> | ||
| + | <tr><td align=center> Glucose </td><td align=center> +++ (mS1) </td><td align=center> ++(mS2) </td><td align=center>++(mS3)</td></tr> | ||
| + | <tr><td align=center> Fatty acid </td><td align=center> + (mR1) </td><td align=center> ++(mR2) </td><td align=center>＜+(mR3)</td></tr> | ||
| + | </table></center></p><p> | ||
| + | <center><img src="https://static.igem.org/mediawiki/2012/6/69/Microbiota_Fig_3.png" width="547" height="368" hspace="2" vspace="1" border="2" align="top" /></center> | ||
| - | + | GEB is too weak to survive. </p><p> | |
| - | + | ||
| - | + | ||
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| - | + | 3. (2.1,2.11) </p><p> | |
| + | <center><table border=1 bordercolor=#999999 cellpadding="10"> | ||
| + | <tr><td align=center> </td><td align=center> Firmicutes </td><td align=center> Bacteriodetes</td><td align=center>GEB</td></tr> | ||
| + | <tr><td align=center> Glucose </td><td align=center> +++ (mS1) </td><td align=center> ++(mS2) </td><td align=center>++(mS3)</td></tr> | ||
| + | <tr><td align=center> Fatty acid </td><td align=center> + (mR1) </td><td align=center> ++(mR2) </td><td align=center>++(mR3)</td></tr> | ||
| + | </table></center></p><p> | ||
| - | + | <center><img src="https://static.igem.org/mediawiki/2012/b/b7/Microbiota_Fig_4.png" width="556" height="352" hspace="2" vspace="1" border="2" align="top" /></center> | |
| - | + | ||
| - | + | ||
| - | |||
| + | 4. (2.25,0.5) </p><p> | ||
| - | + | <center><table border=1 bordercolor=#999999 cellpadding="10"> | |
| - | Glucose | + | <tr><td align=center> </td><td align=center> Firmicutes </td><td align=center> Bacteriodetes</td><td align=center>GEB</td></tr> |
| - | Fatty acid | + | <tr><td align=center> Glucose </td><td align=center> +++ (mS1) </td><td align=center> ++(mS2) </td><td align=center>+++(mS3)</td></tr> |
| + | <tr><td align=center> Fatty acid </td><td align=center> + (mR1) </td><td align=center> ++(mR2) </td><td align=center>+(mR3)</td></tr> | ||
| + | </table></center></p><p> | ||
| - | + | <center><img src="https://static.igem.org/mediawiki/2012/d/da/Microbiota_Fig_5.png" width="572" height="362" hspace="2" vspace="1" border="2" align="top" /></center> | |
| - | + | In this situation N(firmicutes)/N(bacteriodetes)<8.0 is obvious. We successfully finished our task of finding a pair of <img src="https://static.igem.org/mediawiki/2012/f/fd/Microbiota_let_4.png" width="122" height="65" hspace="2" vspace="1" border="2" align="top" />=(2.25,0.5), and this kind of GEB is exactly what we hope to build. </p> | |
</html> | </html> | ||
Latest revision as of 12:11, 24 September 2012
The Human Gut Microbiota Regulation by E.coslim and Mathematical Modeling
As it has been mentioned, manipulating the number of Firmicutes and Bacteriodetes might be an effective method to achieve 'a slim glutton'. So the following content is about to provide a theoretical base for the whole project.
We assume that resources S (glucose) and R (fatty acid) are perfectly substitutable for both populations x1 (Firmicutes) and x2 (Bacteriodetes). We simplify this situation as an exploitative competition in a chemostat, and the ODEs are:
2. xi: biomass of the competing populations at time t
3. S0 and R0: concentrations of resource S and R in the feed bottle
4. D: dilution rate
[The specific death rates of the microorganisms are assumed to be insignificant compared to this dilution rate D]
5.Si and Ri: the rate of conversion of nutrient S to biomass of population xi
[if the conversion of nutrient to biomass is proportional to the amount of nutrient consumed, the consumption rate of resource S per unit of competitor xi is denoted 
where ξi is the respective growth yield constant]
6. Gi: the rate of conversion of nutrient to biomass of population xi
[Since perfectly substitutable resources are alternate sources of the same essential nutrient, the rate of conversion of nutrient to biomass of population xi is made up of a contribution from the consumption of resource S as well as R: 
Here we choose
;
;
PART I
A model is built to describe a quantitative relationship between Firmicutes and Bacteriodetes in people's intestines who are overweight.
Parameters mSi(mSi) can be assigned values to Firmicutes and Bacteriodetes so as to simulate the ability to utilize glucose and fatty acid. If their ability to use nutrient are given as follow:
| Firmicutes | Bacteriodetes | |
| Glucose | +++ (mS1) | ++(mS2) |
| Fatty acid | + (mR1) | ++(mR2) |
.
In this situation, the ratio N(Firmicutes)/N(Bacteriodetes) is rather high, usually achieving a value 8.0, and each of their absolute number, or concentration, is stable.
PART II
We try to add a Genetic Engineered Bacterium(GEB) into system. This ideal type of bacterium consumes glucose as well as fatty acid, thus makes itself a competitor to Firmicutes and Bacteriodetes. While it is reproducing in intestines, the competition among these three types of bacteria makes the number change gradually. At last, we hope to achieve a lower ratio of Firmicutes/Bacteriodetes.
The key point is to find out how competitive our GEB should be. In other words, we have to point out its ability to consume glucose and fatty acid---to study new parameters 
. For example, if mS3＞mS1, then we conclude that GEB has stronger ability to consume glucose than Firmicutes. We try to find out an appropriate pair of .
1. (2.5, 2.1)
| Firmicutes | Bacteriodetes | GEB | |
| Glucose | +++ (mS1) | ++(mS2) | ++++(mS3) |
| Fatty acid | + (mR1) | ++(mR2) | ++(mR3) |
| Firmicutes | Bacteriodetes | GEB | |
| Glucose | +++ (mS1) | ++(mS2) | ++(mS3) |
| Fatty acid | + (mR1) | ++(mR2) | +++(mR3) |
2. (2.1,0.4)
| Firmicutes | Bacteriodetes | GEB | |
| Glucose | +++ (mS1) | ++(mS2) | ++(mS3) |
| Fatty acid | + (mR1) | ++(mR2) | ＜+(mR3) |
3. (2.1,2.11)
| Firmicutes | Bacteriodetes | GEB | |
| Glucose | +++ (mS1) | ++(mS2) | ++(mS3) |
| Fatty acid | + (mR1) | ++(mR2) | ++(mR3) |
| Firmicutes | Bacteriodetes | GEB | |
| Glucose | +++ (mS1) | ++(mS2) | +++(mS3) |
| Fatty acid | + (mR1) | ++(mR2) | +(mR3) |
=(2.25,0.5), and this kind of GEB is exactly what we hope to build.
