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| - | <h1>Modelling</h1> | + | <h1>Context and Objectives</h1> |
| | <div class="contenuTexte"> | | <div class="contenuTexte"> |
| | <div style="float:left;width:680px;margin-left:20px;"> | | <div style="float:left;width:680px;margin-left:20px;"> |
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| - | An interesting question when you are more biologist than mathematician (too many complicated equations!!!). And most of our team members are biologists/biochemists… Thus, we tried to explain modelling and our model in a comprehensive way for everyone.<br/><br/>
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| | <br/><br/> | | <br/><br/> |
| - | <span style="margin-top:150px;margin-left:100px; font-size:20px;">This is our Biological Modelling for Dummies ! </span> | + | Every year industries spend billions of dollars to get rid of the biofilms which develop in their installations. Indeed biofims are reponsible for :<br/><br/> |
| - | </div> | + | <li>Food spoilage or poisoning in the food industry<br/> |
| - | <img src="https://static.igem.org/mediawiki/2012/8/82/Dummies.jpg" width="250" style="float:right;margin-right:20px;"/><br/> | + | <li>Pathogens' persistence and dispersal in health industry<br/> |
| - | <div style="clear:both"></div> | + | <li>Corrosion and diameter reduction of pipelines<br/><br/> |
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| | + | At the moment, industries have some solutions at their disposal to limit the biofilm development but they have generaly an environmental impact and/or an important cost.<br/><br/> |
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| | + | Thus, we develop a new generation of solution against biofilms in industry, which allows to reduce : <br/><br/> |
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| - | <br/><br/> | + | <li>The use of harmful chemical reagents in cleaning processes<br/> |
| | + | <li>The cleaning costs for industrialists<br/> |
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| - | <div><center><b><big>Click on the title to show/hide the text.</big></b></center></div>
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| - | <h2>What is modelling ?</h2>
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| - | <div class="wrapper">
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| - | <div class="contenuTexte">
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| - | <h3>Definitions</h3>
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| - | <br>
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| - | A <b>model</b> is a symbolic representation of an object’s or phenomenon’s aspects in the real world.<br/>
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| - | <br/>
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| - | <center>“<i>All models are false. Some are useful.</i>” Georges Box</center> <br/>
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| - | <br/>
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| - | <b>Modelling</b> is the process that allows the development of a model. It’s taking into account [1]:<br/>
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| - | <ul>
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| - | <li>The phenomenon to represent </li>
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| - | <li>A specific formal system (equation, diagram..)</li>
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| - | <li>Objectives (what we want to do with the model)</li>
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| - | <li>Data (for variables) and knowledge (relation between variables) available or accessible by experimentation or observation</li>
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| - | </ul>
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| - | <br><br>
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| - | The <b>tasks</b> to obtain and use the model depend on the biological situation and the formal system chosen. Nevertheless, it must:<br/>
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| - | <ul>
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| - | <li>Have a formalization work, which is the model writing </li>
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| - | <li>Manipulate the model in the formal system to describe its properties (theoretical main behaviour independently on the values of the parameters)</li>
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| - | <li>Establish relationships with other representations (computer program, graph function)</li>
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| - | <li>Interpret and compare different representations obtained in the formal world with the biological reality (often that reality is seen through experimental data)</li>
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| - | </ul>
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| - | <br/>
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| - | <div style="font-size:12px">
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| - | <b>References: </b><br>
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| - | <ul>
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| - | <li> [1] Alain Pavé, <i>Modélisation en biologie et en écologie</i>, Aléas, 1994
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| - | </ul>
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| - | <br>
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| | </div> | | </div> |
| - | </div>
| + | <div> |
| | + | <img src="https://static.igem.org/mediawiki/2012/b/bf/Biofilm1.jpg" width="250" style="margin-left:20px;"/><br/><br/> |
| | + | <img src="https://static.igem.org/mediawiki/2012/b/bb/Biofilm2.jpg" width="250" style="margin-left:20px;"/><br/> |
| | </div> | | </div> |
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| - | <h2>Biological System description</h2>
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| - | <div class="wrapper">
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| - | <div class="contenuTexte">
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| - | <h3>Situation</h3>
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| - | <br>
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| - | After the destruction of the biofilm by “Biofilm Killer” bacteria, we want to have the choice to either create a surfactant or establish a positive biofilm, both to prevent the recolonization of the surface by deleterious organisms. The toggle switch is done by environmental conditions : two inducers can be added to select one behaviour or another.<br>
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| - | <div class="petitSsTitre">Biological system to model</div>
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| - | For this, we have created the following construction, with a double regulation:<br>
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| - | <center><img src="https://static.igem.org/mediawiki/2012/d/d6/2%29_biological_system.png" width = 450px/></center><br>
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| - | <center><small>Figure 1: The construction of the biological model, with the following elements: 2 promoters (P<i>xyl</i> and P<i>lac</i>), 2 repressors (LacI and XylR proteins) <br>and 2 inducers (IPTG and Xylose), and also <i>sfp</i> and <i>abrB</i> genes for Sfp and AbrB proteins.</i></small></center><br>
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| - | <br>
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| - | This system is a gene-regulatory network, where two different states are possible:<br>
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| - | <ul>
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| - | <li><b>Formation of a naturally toxic bio-surfactant through <i>sfp</i> gene</b>, which has antimicrobial properties that prevents the recolonization of the surface. The surfactant used is surfactin, whose production is activated by the <i>sfp</i> gene. This is the <b>COAT</b> option.</li>
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| - | <li><b>Establishment of a positive biofilm</b> by the inhibition of the main biofilm repressor gene <i>abrB</i>. This is the <b>STICK</b> option.</li>
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| - | </ul>
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| - | <br>
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| - | <center><img src="https://static.igem.org/mediawiki/2012/a/a5/2%29_constructs.png" width=450px/></center><br>
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| - | <center><small>Figure 2: The two possible states, surfactant formation for the top operon or biofilm formation for the bottom construction</small></center><br>
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| - | LacI and XylR proteins are called repressors. They bind to their respective promoters (P<i>lac</i> and P<i>xyl</i>), thus preventing RNA polymerase binding. So proteins under the inactivated promoter are not produced. <br> There are also two inducers in the system, <b>IPTG</b> (isopropyl β-D-1-thiogalactopyranoside) and <b>Xylose</b> (monosaccharide of the aldopentose type). In the absence of these inducers, both constructions are inhibited. If only one of them is present, the corresponding inhibition disappears and the associated construction is expressed.<br>
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| - | <br>
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| - | <div style="display:inline-block;margin-right:20px;text-align:center" >
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| - | <iframe frameborder="0" width="430" height="280" src="http://www.dailymotion.com/embed/video/xttbqi"></iframe><br /><a href="http://www.dailymotion.com/video/xttbqi_xylose-induction_tech" target="_blank">Xylose Induction</a>
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| | </div> | | </div> |
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| - | <div style="display:inline-block;text-align:center;float:right;"> | + | <br/><br/> |
| - | <iframe style="display:inline-block" frameborder="0" width="430" height="280" src="http://www.dailymotion.com/embed/video/xttbr9"></iframe><br /><a href="http://www.dailymotion.com/video/xttbr9_iptg-induction_tech" target="_blank">IPTG Induction</a>
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| - | </div>
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| - | <br><br> | + | <div><center><b><big>Click on the title to show/hide the text.</big></b></center></div> |
| - | For example, in the presence of Xylose, XylR proteins will form an enzymatic complex with their Xylose sugar. Thus, the inhibition of P<i>xyl</i> caused by XylR binding will disappear, resulting in an enhanced production of Sfp, AbrB and LacI proteins. Sfp production induces surfactin production, and AbrB production involves the repression of the formation of the biofilm. Eventually, LacI production will inhibit XylR production, <b>so there will be stabilisation of P<i>xyl</i> activation.</b><br>
| + | |
| - | In opposition, in the presence of IPTG, LacI proteins will bind to their ligand, and P<i>lac</i> promoter will be free. So XylR proteins will be overproduced, limiting Sfp and AbrB productions. Thus, there will be no surfactin in the environment, biofilm formation can begin.<br>
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| - | <br>
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| - | <div class="petitSsTitre">Aim of the model:</div>
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| - | <br>
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| - | With this model, we pursue two main objectives : <br>
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| - | <ul>
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| - | <li>1) verify the design of the biological system, to be sure that the toggle switch is functional,
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| - | <li>2) predict the behaviour of this biological system depending on the presence of inducers to give usage guidelines for its industrialization</ul><br>
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| - |
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| - | <b>However...</b><br><br>
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| - | We are working in a <i>Bacillus subtilis</i> strain and some parameters such as XylR values on binding/unbinding kinetics to both inducer and promoter or production rate from P<i>xyl</i> promoter cannot be found in the literature and most of the existing values come from an <i>E. coli</i> strain rather than <i>B. subtilis</i>.
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| - | Furthermore, we are finishing the biological system construction and its characterization is underway. Parameters will be measured very soon.<br>
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| - | <br>
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| - | Because of this lack of information, we will create a theoretical model in order to characterize the global behavior of the system.<br>
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| - | <br>
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| - | Moreover, as we are mainly biologists in the team, we thought interesting to explain how we can easily obtain a mathematical model from a biological system. <br>
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| - | </div>
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| - | </div>
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| - | <h2>Biological modelling for dummies !</h2> | + | <h2><strong>PROJECT STRATEGY</strong> </h2> |
| | <div class="wrapper"> | | <div class="wrapper"> |
| | <div class="contenuTexte"> | | <div class="contenuTexte"> |
| - | | + | <div style="float:left;width:680px;margin-left:20px;"> |
| - | <br> | + | <br/> |
| - | | + | Our solution is based on engineered bacterial "torpedos" capable of infiltrating, destroying biofilms (<strong>KILL</strong>) and protecting the cleaned surfaces by either a surfactant coating (<strong>COAT</strong> option), or by establishment of a positive biofilm (<strong> STICK </strong> option).<br/> |
| - | <h3>Basic knowledge</h3>
| + | |
| - | <br>
| + | |
| - | We want to transform the biological system into mathematical equations in order to be able to determine the quantity of inducers (input) needed to obtain a particular behavior (output).<br>
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| - | | + | |
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| - | <center><img src="https://static.igem.org/mediawiki/2012/2/27/3%29_Black_Box.png" border="1"width=550px/></center>
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| - | <center>Figure 3: The black box model: <br>there will be the STICK or COAT option depending on the inducers concentration</center><br>
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| - | <br>
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| - | | + | |
| - | <div class="petitSsTitre">Ordinary differential equation (ODE)</div>
| + | |
| - | <ul>
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| - | <li>mathematical equation
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| - | <li>format: <img style="margin-left:20px;" src="https://static.igem.org/mediawiki/2012/4/42/3%29_EDO.png" width=10%/>
| + | |
| - | <li>explanation: used in biology and physics to represent the growth or evolution of a quantity dx (i.e. population or concentration) proportional to the population size/effective concentration x during a period of time t
| + | |
| - | <li>x is called a variable
| + | |
| - | </ul>
| + | |
| - | <br><br> | + | |
| - | <h3>Elements of the model</h3>
| + | |
| - | <br>
| + | |
| - | <div class="petitSsTitre">First list of variables</div>
| + | |
| - | We want to have the concentration of LacI and XylR as output depending of the inducers concentrations input. We know that the repressors can bind either to their promoter (P<i>lac</i> and P<i>xyl</i> respectively) or to their inducer (IPTG and xylose). Thus, first of all, we have the following variables in the system:<br><br>
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| - | <br>
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| - | <center><img src="https://static.igem.org/mediawiki/2012/5/50/3%29_element_1.png" width=400px/></center>
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| - | <center>Figure 4: The model variables at first glimpse</center><br>
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| - | <br>
| + | |
| - | <div class="petitSsTitre">Binding and unbinding kinetics</div>
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| - | We decided to analyze the relation between repressors, promoters and inducers depending on the law of mass action. It is a branch of chemical kinetics, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances. These substances will bind with an association kinetic k and unbind with a dissociation kinetic km. </br><br>
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| - | <div style="display:inline-block;text-align:center;margin-top:60px">
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| - | <iframe frameborder="0" width="430" height="250" src="http://www.dailymotion.com/embed/video/xttbop"></iframe>
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| - | <br />
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| - | <a href="http://www.dailymotion.com/video/xttbop_binding-and-unbinding-kinetic_tech" target="_blank">Binding and unbinding kinetic</a> <br>
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| - | </div>
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| - | <div style="display:inline-block;text-align:center;float:right">
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| - | <img src="https://static.igem.org/mediawiki/2012/1/1b/3%29_binding_and_unbinding.png" width=400px/>
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| | <br/> | | <br/> |
| - | Figure 5: Binding and unbinding kinetics in the model
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| | </div> | | </div> |
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| - | <br> | + | <center><img src="https://static.igem.org/mediawiki/2012/c/cb/ModelBs.jpg" width = 450px/></center><br/> |
| - | <div style="clear:both;"></div> | + | <div style="clear:both"></div><br/> |
| - | <br>It is working either for LacI binding to its P<i>lac</i> promoter than for XylR to P<i>xyl</i> and also the inducers and LacI and XylR. This binding creates a new complex.<br><br> | + | |
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| - | <center><img src="https://static.igem.org/mediawiki/2012/3/32/3%29_element_2.png" width=450px/></center> | + | This tunneling activity of <i>Bacillus subtilis</i> swimmer cells enables to : |
| - | <center>Figure 6: The model variables</center><br> | + | <li>Facilitate the delivery of the active substances within the biofilm.</li> |
| | + | <li>Destroy the inacessible biofilms in pipes.</li><br/> |
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| | + | Moreover <i>Bacillus</i> strains are non pathogenic and do not cause equipment deteroriation by corrosion. |
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| - | <h3>Equations of the model</h3> | + | To sum up, this biocide-alternative strategy provides a money-saving and an environementally friendly solution for the control of unwanted biofilm.<br/><br/> |
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| - | <br>Now, we can find the equations, based on the behavior of each element. There will be 3 types of equations, each of them related to the nature of the variable, i.e. a promoter, an inducer or a repressor.<br>
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| - | <div class="petitSsTitre">Promoters</div>
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| - | As described above, there are two promoters, P<i>lac</i> and P<i>xyl</i>, and each of them can be free (with no repressor binds on it) or occupied (with the corresponding repressor associated).
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| - | <br>Thanks to the law of mass action and binding and unbinding kinetics, we obtain the equations like this:<br><br>
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| - | <div style="display:inline-block;text-align:center;">
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| - | <iframe frameborder="0" width="430" height="250" src="http://www.dailymotion.com/embed/video/xttbtn"></iframe><br /><a href="http://www.dailymotion.com/video/xttbtn_plac-equation_tech" target="_blank">Plac Equation</a>
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| | </div> | | </div> |
| - | | + | </div> |
| - | <div style="display:inline-block;text-align:center;float:right"> | + | |
| - | So the equations for the promoters are this:<br><br>
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| - | <img src="https://static.igem.org/mediawiki/2012/8/87/3%29_equations_promoters.png" width=430px/><br/>
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| - | Figure 7: Promoters' equations<br>
| + | |
| | </div> | | </div> |
| - | <div style="clear:both"></div>
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| - | <br/>
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| - | <div class="petitSsTitre">Inducers</div>
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| - | With the same method based on law of mass action and binding/unbinding kinetic, we obtain the inducers' equations.<br/><br/>
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| - | <div style="display:inline-block;text-align:center"> | + | <h2><strong> KILL : DESTROY BIOFILM </strong></h2> |
| - | <iframe frameborder="0" width="430" height="250" src="http://www.dailymotion.com/embed/video/xttbsf"></iframe><br /><a href="http://www.dailymotion.com/video/xttbsf_inducer-equation_tech" target="_blank">Inducer Equation</a> | + | |
| - | </div>
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| - | <div style="display:inline-block;text-align:center;float:right;margin-top:30px">
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| - | <img src="https://static.igem.org/mediawiki/2012/c/cb/3%29_equations_inducers.png" width=430px/><br/>
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| - | Figure 8: Inducers' equations<br/>
| + | |
| - | </div>
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| - | <div style="clear:both"></div>
| + | |
| - | <br>
| + | |
| - | <div class="petitSsTitre">Repressors</div>
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| - | Now, for the repressors, the method is quite similar as before. However, we have to take into account that the proteins have a degradation rate (δ) depending on their nature and the environment. The quantity of protein produced at each time depends on the promoter under control (α). <br><br>
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| - | | + | |
| - | <center>
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| - | <iframe frameborder="0" width="480" height="270" src="http://www.dailymotion.com/embed/video/xtuc6t?logo=0"></iframe><br /><a href="http://www.dailymotion.com/video/xtuc6t_lacinequation_tech" target="_blank">LacI Equation</a> </center>
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| - | | + | |
| - | <br><br>
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| - | We obtain XylR's equation exactly as LacI's. <br><br>
| + | |
| - | | + | |
| - | <center><img src="https://static.igem.org/mediawiki/2012/c/c8/3%29_LacI_and_XylR_equations.png" width = 90%/></center>
| + | |
| - | <center>Figure 9: The repressors equations <br></center><br><br>
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| - | | + | |
| - | | + | |
| - | <h3>Parameters of the model</h3>
| + | |
| - | <br>
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| - | For this model, we need at least 12 parameters that characterize the variables and their relationship between each other.
| + | |
| - | The available values have been measure mainly in <i>E. coli</i> strain.
| + | |
| - | <br><br>
| + | |
| - | <center>
| + | |
| - | <table>
| + | |
| - | <tr>
| + | |
| - | <th>Name</th>
| + | |
| - | <th>Description</th>
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| - | <th>Unit</th>
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| - | <th>Value</th>
| + | |
| - | <th>Reference</th>
| + | |
| - | </tr>
| + | |
| - | | + | |
| - | <tr>
| + | |
| - | <td>Prod_Plac</td>
| + | |
| - | <td>Production rate from <i>Plac</i> promoter</td>
| + | |
| - | <td>mol.s-1</td>
| + | |
| - | <td>1.66E23</td>
| + | |
| - | <td>1</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>Prod_Pxyl</td>
| + | |
| - | <td>Production rate from <i>Pxyl</i> promoter</td>
| + | |
| - | <td>mol.s-1</td>
| + | |
| - | <td>***</td>
| + | |
| - | <td>**</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>k1</td>
| + | |
| - | <td>binding kinetic of LacI and IPTG</td>
| + | |
| - | <td>mol-1.s-1</td>
| + | |
| - | <td>1.2E5</td>
| + | |
| - | <td>2</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>km1</td>
| + | |
| - | <td>unbinding kinetic of LacI_IPTG</td>
| + | |
| - | <td>s-1</td>
| + | |
| - | <td>2.1E-1</td>
| + | |
| - | <td>2</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>k2</td>
| + | |
| - | <td>binding kinetic of XylR and Xylose</td>
| + | |
| - | <td>mol-1.s-1</td>
| + | |
| - | <td>***</td>
| + | |
| - | <td>**</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>km2</td>
| + | |
| - | <td>unbinding kinetic of XylR_Xylose</td>
| + | |
| - | <td>s-1</td>
| + | |
| - | <td>***</td>
| + | |
| - | <td>**</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>k3</td>
| + | |
| - | <td>binding kinetic of LacI and <i>Plac</i></td>
| + | |
| - | <td>mol-1.s-1</td>
| + | |
| - | <td>5.1E6</td>
| + | |
| - | <td>2</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>km3</td>
| + | |
| - | <td>unbinding kinetic of <i>PlacO</i></td>
| + | |
| - | <td>s-1</td>
| + | |
| - | <td>3.7E-2</td>
| + | |
| - | <td>2</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>k4</td>
| + | |
| - | <td>binding kinetic of XylR and <i>Plac</i></td>
| + | |
| - | <td>mol-1.s-1</td>
| + | |
| - | <td>***</td>
| + | |
| - | <td>**</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>km4</td>
| + | |
| - | <td>unbinding kinetic of XylR and <i>PlacO</i></td>
| + | |
| - | <td>s-1</td>
| + | |
| - | <td>***</td>
| + | |
| - | <td>**</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>δ_LacI</td>
| + | |
| - | <td>degradation rate of LacI</td>
| + | |
| - | <td>s-1</td>
| + | |
| - | <td></td>
| + | |
| - | <td>3</td>
| + | |
| - | </tr>
| + | |
| - | <tr>
| + | |
| - | <td>δ_XylR</td>
| + | |
| - | <td>degradation rate of XylR</td>
| + | |
| - | <td>s-1</td>
| + | |
| - | <td>***</td>
| + | |
| - | <td>**</td>
| + | |
| - | </tr>
| + | |
| - | </table><br>
| + | |
| - | Model parameters. <small>*** for no value and ** for no reference</small>
| + | |
| - | </center>
| + | |
| - | | + | |
| - | <br><br>
| + | |
| - | <h3>Hypotheses</h3>
| + | |
| - | <br>
| + | |
| - | The following hypotheses have been made for this model.
| + | |
| - | <ul>
| + | |
| - | <li>we just need LacI concentration for surfactant production and not Sfp and AbrB concentration because there is a proportional link between them. If there are LacI proteins produced, there will be also Sfp and AbrB proteins.
| + | |
| - | <li>we assumed that there will be no degradation of IPTG due to its high stability[4] and no metabolism of Xylose in our condition[5].
| + | |
| - | <li>we are aware of LacI[6] and XylR[7] dimerisation as fundamental functional unit but they are not taken into account in this model.
| + | |
| - | </ul>
| + | |
| - | <br>
| + | |
| - | | + | |
| - | <div style="font-size:12px">
| + | |
| - | <b>References:</b><br>
| + | |
| - | <ul>
| + | |
| - | <li> [1] Nature. 2000 Jan 20;403(6767):335-8.<i> A synthetic oscillatory network of transcriptional regulators.</i> Elowitz MB, Leibler S.
| + | |
| - | <li> [2] Xu H.,Moraitis M., Reedstrom R. J., Matthews K. S. 1998. <i>Kinetic and thermodynamic studies of purine repressor binding to corepressor and operator DNA.</i> J. Biol. Chem. 273:8958–8964.
| + | |
| - | <li> [3] Tuttle et al. <i>Model-Driven Designs of an Oscillating Gene Network.</i>, Biophys J 89(6):3873-3883, 2005
| + | |
| - | <li> [4] Herzenberg, L.A., <i>Studies on the induction of beta-galactosidase in a cryptic strain of Escherichia coli.</i> Biochim. Biophys. Acta, 31, 525 (1959)
| + | |
| - | <li> [5] http://bsubcyc.org/BSUB/NEW-IMAGE?type=PATHWAY&object=XYLCAT-PWY
| + | |
| - | <li> [6] Ramot, R. et al, <i>Lactose Repressor Experimental Folding Landscape: Fundamental Functional Unit and Tetramer Folding Mechanisms</i>. Biochemistry (2012)
| + | |
| - | <li> [7] Song S., Park C. <i>Organization and regulation of the D-xylose operons in Escherichia coli K-12: XylR acts as a transcriptional activator.</i> J Bacteriol. 1997 Nov;179(22):7025-32.
| + | |
| - | </ul>
| + | |
| - | </div>
| + | |
| - | | + | |
| - | </div>
| + | |
| - | </div>
| + | |
| - | <h2>Results</h2>
| + | |
| | <div class="wrapper"> | | <div class="wrapper"> |
| - | <div class="contenuTexte"> | + | <div class="contenuTexte"> |
| | | | |
| - | <br>
| |
| - | <div class="petitSsTitre">Expected results</div>
| |
| - | Finally, we translated the biological system into mathematical equations. As we can see, there is a lot of paramaters for the binding and unbinding kinetics, degradation rates and productions from promoters. However, values for only a few of them are available. This is why we needed to simulate the behaviour of our system. <br>
| |
| - | We want to have an overproduction of XylR in the presence of IPTG, for the STICK option. And an overproduction of LacI when there is xylose in the environment, for the COAT option. <br>
| |
| - |
| |
| - | According to the above theoretical model, we should generate the expected toggle switch (figure below), using the appropriate values for all parameters.<br><br>
| |
| - |
| |
| - |
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/e/e6/4%29_COAT.png" width=300px/>
| |
| - | <img style="margin-left:50px;" src="https://static.igem.org/mediawiki/2012/5/51/4%29_Stick.png" width=300px/></center><br>
| |
| - | <center>Figure 10: Expected results of the model</center><br>
| |
| - |
| |
| - | <div id="pageContent">
| |
| - | <h1>Modelling</h1>
| |
| - | <div class="contenuTexte">
| |
| - | <div style="float:left;width:680px;margin-left:20px;">
| |
| | <br/> | | <br/> |
| - | <br/> | + | <strong> LYSOSTAPHIN</strong> part <a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_K802000" target="_blank"><font color="#664499"><b> BBa_K802000</b></font></a> <br/><br/> |
| - | An interesting question when you are more biologist than mathematician (too many complicated equations!!!). And most of our team members are biologists/biochemists… Thus, we tried to explain modelling and our model in a comprehensive way for everyone.<br/><br/>
| + | |
| - | <br/><br/>
| + | |
| - | <span style="margin-top:150px;margin-left:100px; font-size:20px;">This is our Biological Modelling for Dummies ! </span>
| + | |
| - | </div>
| + | |
| - | <img src="https://static.igem.org/mediawiki/2012/8/82/Dummies.jpg" width="250" style="float:right;margin-right:20px;"/><br/>
| + | |
| - | <div style="clear:both"></div> | + | |
| | | | |
| - | | + | <center><img src="https://static.igem.org/mediawiki/2012/f/f3/Lyso.jpg" width = 650px/></center><br/> |
| - | | + | |
| - | <br/><br/>
| + | |
| - | | + | |
| - | <div><center><b><big>Click on the title to show/hide the text.</big></b></center></div>
| + | |
| - | | + | |
| - | | + | |
| - | <h2>What is modelling ?</h2>
| + | |
| - | <div class="wrapper">
| + | |
| - | <div class="contenuTexte">
| + | |
| - | | + | |
| - | <h3>Definitions</h3>
| + | |
| - | <br>
| + | |
| - | A <b>model</b> is a symbolic representation of an object’s or phenomenon’s aspects in the real world.<br/>
| + | |
| | <br/> | | <br/> |
| - | <center>“<i>All models are false. Some are useful.</i>” Georges Box</center> <br/> | + | <center><img src="https://static.igem.org/mediawiki/2012/4/44/Lysostaphin.jpg" width = 650px/></center><br/> |
| | <br/> | | <br/> |
| - | <b>Modelling</b> is the process that allows the development of a model. It’s taking into account [1]:<br/> | + | <strong> DISPERSIN</strong> part <a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_K802001" target="_blank"><font color="#664499"><b> BBa_K802001</b></font></a> <br/><br/> |
| - | <ul> | + | |
| - | <li>The phenomenon to represent </li> | + | |
| | | | |
| - | <li>A specific formal system (equation, diagram..)</li> | + | <center><img src="https://static.igem.org/mediawiki/2012/e/e9/Dispersin.jpg" width = 650px/></center><br/><br/> |
| | | | |
| - | <li>Objectives (what we want to do with the model)</li> | + | <strong> COMBINED EFFECT</strong> <br/><br/> |
| | | | |
| - | <li>Data (for variables) and knowledge (relation between variables) available or accessible by experimentation or observation</li> | + | <center><img src="https://static.igem.org/mediawiki/2012/8/81/Combined.png" width = 650px/></center><br/> |
| - | </ul> | + | |
| - | <br><br>
| + | |
| | | | |
| - | The <b>tasks</b> to obtain and use the model depend on the biological situation and the formal system chosen. Nevertheless, it must:<br/>
| |
| - | <ul>
| |
| - | <li>Have a formalization work, which is the model writing </li>
| |
| - |
| |
| - | <li>Manipulate the model in the formal system to describe its properties (theoretical main behaviour independently on the values of the parameters)</li>
| |
| - |
| |
| - | <li>Establish relationships with other representations (computer program, graph function)</li>
| |
| - |
| |
| - | <li>Interpret and compare different representations obtained in the formal world with the biological reality (often that reality is seen through experimental data)</li>
| |
| - |
| |
| - | </ul>
| |
| - | <br/>
| |
| - | <div style="font-size:12px">
| |
| - | <b>References: </b><br>
| |
| - | <ul>
| |
| - | <li> [1] Alain Pavé, <i>Modélisation en biologie et en écologie</i>, Aléas, 1994
| |
| - | </ul>
| |
| - | <br>
| |
| | </div> | | </div> |
| - | </div>
| |
| | </div> | | </div> |
| | | | |
| - | <h2>Biological System description</h2> | + | <h2><strong> COAT or STICK : AVOID NEW BIOFILM FORMATION </strong></h2> |
| | <div class="wrapper"> | | <div class="wrapper"> |
| | <div class="contenuTexte"> | | <div class="contenuTexte"> |
| - | <h3>Situation</h3>
| |
| - | <br>
| |
| - | After the destruction of the biofilm by “Biofilm Killer” bacteria, we want to have the choice to either create a surfactant or establish a positive biofilm, both to prevent the recolonization of the surface by deleterious organisms. The toggle switch is done by environmental conditions : two inducers can be added to select one behaviour or another.<br>
| |
| | | | |
| - | <div class="petitSsTitre">Biological system to model</div>
| |
| - | For this, we have created the following construction, with a double regulation:<br>
| |
| - | <br>
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/d/d6/2%29_biological_system.png" width = 450px/></center><br>
| |
| - | <center><small>Figure 1: The construction of the biological model, with the following elements: 2 promoters (P<i>xyl</i> and P<i>lac</i>), 2 repressors (LacI and XylR proteins) <br>and 2 inducers (IPTG and Xylose), and also <i>sfp</i> and <i>abrB</i> genes for Sfp and AbrB proteins.</i></small></center><br>
| |
| - | <br>
| |
| - |
| |
| - | This system is a gene-regulatory network, where two different states are possible:<br>
| |
| - | <ul>
| |
| - | <li><b>Formation of a naturally toxic bio-surfactant through <i>sfp</i> gene</b>, which has antimicrobial properties that prevents the recolonization of the surface. The surfactant used is surfactin, whose production is activated by the <i>sfp</i> gene. This is the <b>COAT</b> option.</li>
| |
| - |
| |
| - | <li><b>Establishment of a positive biofilm</b> by the inhibition of the main biofilm repressor gene <i>abrB</i>. This is the <b>STICK</b> option.</li>
| |
| - | </ul>
| |
| - | <br>
| |
| - |
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/a/a5/2%29_constructs.png" width=450px/></center><br>
| |
| - | <center><small>Figure 2: The two possible states, surfactant formation for the top operon or biofilm formation for the bottom construction</small></center><br>
| |
| - |
| |
| - |
| |
| - |
| |
| - | LacI and XylR proteins are called repressors. They bind to their respective promoters (P<i>lac</i> and P<i>xyl</i>), thus preventing RNA polymerase binding. So proteins under the inactivated promoter are not produced. <br> There are also two inducers in the system, <b>IPTG</b> (isopropyl β-D-1-thiogalactopyranoside) and <b>Xylose</b> (monosaccharide of the aldopentose type). In the absence of these inducers, both constructions are inhibited. If only one of them is present, the corresponding inhibition disappears and the associated construction is expressed.<br>
| |
| - | <br>
| |
| - | <div style="display:inline-block;margin-right:20px;text-align:center" >
| |
| - | <iframe frameborder="0" width="430" height="280" src="http://www.dailymotion.com/embed/video/xttbqi"></iframe><br /><a href="http://www.dailymotion.com/video/xttbqi_xylose-induction_tech" target="_blank">Xylose Induction</a>
| |
| - | </div>
| |
| - |
| |
| - | <div style="display:inline-block;text-align:center;float:right;">
| |
| - | <iframe style="display:inline-block" frameborder="0" width="430" height="280" src="http://www.dailymotion.com/embed/video/xttbr9"></iframe><br /><a href="http://www.dailymotion.com/video/xttbr9_iptg-induction_tech" target="_blank">IPTG Induction</a>
| |
| - | </div>
| |
| - |
| |
| - | <br><br>
| |
| - | For example, in the presence of Xylose, XylR proteins will form an enzymatic complex with their Xylose sugar. Thus, the inhibition of P<i>xyl</i> caused by XylR binding will disappear, resulting in an enhanced production of Sfp, AbrB and LacI proteins. Sfp production induces surfactin production, and AbrB production involves the repression of the formation of the biofilm. Eventually, LacI production will inhibit XylR production, <b>so there will be stabilisation of P<i>xyl</i> activation.</b><br>
| |
| - | In opposition, in the presence of IPTG, LacI proteins will bind to their ligand, and P<i>lac</i> promoter will be free. So XylR proteins will be overproduced, limiting Sfp and AbrB productions. Thus, there will be no surfactin in the environment, biofilm formation can begin.<br>
| |
| - | <br>
| |
| - |
| |
| - | <div class="petitSsTitre">Aim of the model:</div>
| |
| - |
| |
| - | <br>
| |
| - | With this model, we pursue two main objectives : <br>
| |
| - | <ul>
| |
| - | <li>1) verify the design of the biological system, to be sure that the toggle switch is functional,
| |
| - | <li>2) predict the behaviour of this biological system depending on the presence of inducers to give usage guidelines for its industrialization</ul><br>
| |
| - |
| |
| - | <b>However...</b><br><br>
| |
| - | We are working in a <i>Bacillus subtilis</i> strain and some parameters such as XylR values on binding/unbinding kinetics to both inducer and promoter or production rate from P<i>xyl</i> promoter cannot be found in the literature and most of the existing values come from an <i>E. coli</i> strain rather than <i>B. subtilis</i>.
| |
| - | Furthermore, we are finishing the biological system construction and its characterization is underway. Parameters will be measured very soon.<br>
| |
| - | <br>
| |
| - | Because of this lack of information, we will create a theoretical model in order to characterize the global behavior of the system.<br>
| |
| - | <br>
| |
| - | Moreover, as we are mainly biologists in the team, we thought interesting to explain how we can easily obtain a mathematical model from a biological system. <br>
| |
| - |
| |
| - |
| |
| - | </div>
| |
| - | </div>
| |
| - |
| |
| - | <h2>Biological modelling for dummies !</h2>
| |
| - | <div class="wrapper">
| |
| - | <div class="contenuTexte">
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <h3>Basic knowledge</h3>
| |
| - | <br>
| |
| - | We want to transform the biological system into mathematical equations in order to be able to determine the quantity of inducers (input) needed to obtain a particular behavior (output).<br>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <br>
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/2/27/3%29_Black_Box.png" border="1"width=550px/></center>
| |
| - | <center>Figure 3: The black box model: <br>there will be the STICK or COAT option depending on the inducers concentration</center><br>
| |
| - | <br>
| |
| - |
| |
| - | <div class="petitSsTitre">Ordinary differential equation (ODE)</div>
| |
| - | <ul>
| |
| - | <li>mathematical equation
| |
| - | <li>format: <img style="margin-left:20px;" src="https://static.igem.org/mediawiki/2012/4/42/3%29_EDO.png" width=10%/>
| |
| - | <li>explanation: used in biology and physics to represent the growth or evolution of a quantity dx (i.e. population or concentration) proportional to the population size/effective concentration x during a period of time t
| |
| - | <li>x is called a variable
| |
| - | </ul>
| |
| - | <br><br>
| |
| - | <h3>Elements of the model</h3>
| |
| - | <br>
| |
| - | <div class="petitSsTitre">First list of variables</div>
| |
| - | We want to have the concentration of LacI and XylR as output depending of the inducers concentrations input. We know that the repressors can bind either to their promoter (P<i>lac</i> and P<i>xyl</i> respectively) or to their inducer (IPTG and xylose). Thus, first of all, we have the following variables in the system:<br><br>
| |
| - | <br>
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/5/50/3%29_element_1.png" width=400px/></center>
| |
| - | <center>Figure 4: The model variables at first glimpse</center><br>
| |
| - | <br>
| |
| - | <div class="petitSsTitre">Binding and unbinding kinetics</div>
| |
| - | We decided to analyze the relation between repressors, promoters and inducers depending on the law of mass action. It is a branch of chemical kinetics, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances. These substances will bind with an association kinetic k and unbind with a dissociation kinetic km. </br><br>
| |
| - |
| |
| - | <div style="display:inline-block;text-align:center;margin-top:60px">
| |
| - | <iframe frameborder="0" width="430" height="250" src="http://www.dailymotion.com/embed/video/xttbop"></iframe>
| |
| - | <br />
| |
| - | <a href="http://www.dailymotion.com/video/xttbop_binding-and-unbinding-kinetic_tech" target="_blank">Binding and unbinding kinetic</a> <br>
| |
| - | </div>
| |
| - |
| |
| - | <div style="display:inline-block;text-align:center;float:right">
| |
| - | <img src="https://static.igem.org/mediawiki/2012/1/1b/3%29_binding_and_unbinding.png" width=400px/>
| |
| | <br/> | | <br/> |
| - | Figure 5: Binding and unbinding kinetics in the model
| + | <strong> SURFACTIN + BIOFILM</strong> part <a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_K802009" target="_blank"><font color="#664499"><b> BBa_K802009</b></font></a><br/><br/> |
| - | </div> | + | |
| | | | |
| | + | <center><img src="https://static.igem.org/mediawiki/2012/3/31/Coatstick.jpg" width = 650px/></center><br/> |
| | <br> | | <br> |
| - | <div style="clear:both;"></div> | + | <strong> AVOID NEW BIOFILM FORMATION</strong> <br/><br/> |
| - | <br>It is working either for LacI binding to its P<i>lac</i> promoter than for XylR to P<i>xyl</i> and also the inducers and LacI and XylR. This binding creates a new complex.<br><br> | + | <strong> NEW RESULTS </strong> <br/><br/> |
| | | | |
| - | <center><img src="https://static.igem.org/mediawiki/2012/3/32/3%29_element_2.png" width=450px/></center> | + | <center><img src="https://static.igem.org/mediawiki/2012/2/2e/Combined2.jpg" width = 650px/></center><br/> |
| - | <center>Figure 6: The model variables</center><br>
| + | |
| | | | |
| - |
| |
| - | <h3>Equations of the model</h3>
| |
| - |
| |
| - | <br>Now, we can find the equations, based on the behavior of each element. There will be 3 types of equations, each of them related to the nature of the variable, i.e. a promoter, an inducer or a repressor.<br>
| |
| - |
| |
| - | <div class="petitSsTitre">Promoters</div>
| |
| - | As described above, there are two promoters, P<i>lac</i> and P<i>xyl</i>, and each of them can be free (with no repressor binds on it) or occupied (with the corresponding repressor associated).
| |
| - |
| |
| - | <br>Thanks to the law of mass action and binding and unbinding kinetics, we obtain the equations like this:<br><br>
| |
| - |
| |
| - | <div style="display:inline-block;text-align:center;">
| |
| - | <iframe frameborder="0" width="430" height="250" src="http://www.dailymotion.com/embed/video/xttbtn"></iframe><br /><a href="http://www.dailymotion.com/video/xttbtn_plac-equation_tech" target="_blank">Plac Equation</a>
| |
| | </div> | | </div> |
| - |
| |
| - | <div style="display:inline-block;text-align:center;float:right">
| |
| - | So the equations for the promoters are this:<br><br>
| |
| - |
| |
| - | <img src="https://static.igem.org/mediawiki/2012/8/87/3%29_equations_promoters.png" width=430px/><br/>
| |
| - | Figure 7: Promoters' equations<br>
| |
| | </div> | | </div> |
| - | <div style="clear:both"></div>
| |
| - | <br/>
| |
| - | <div class="petitSsTitre">Inducers</div>
| |
| - | With the same method based on law of mass action and binding/unbinding kinetic, we obtain the inducers' equations.<br/><br/>
| |
| | | | |
| - | <div style="display:inline-block;text-align:center">
| |
| - | <iframe frameborder="0" width="430" height="250" src="http://www.dailymotion.com/embed/video/xttbsf"></iframe><br /><a href="http://www.dailymotion.com/video/xttbsf_inducer-equation_tech" target="_blank">Inducer Equation</a>
| |
| - | </div>
| |
| | | | |
| - | <div style="display:inline-block;text-align:center;float:right;margin-top:30px">
| |
| - | <img src="https://static.igem.org/mediawiki/2012/c/cb/3%29_equations_inducers.png" width=430px/><br/>
| |
| - | Figure 8: Inducers' equations<br/>
| |
| - | </div>
| |
| - | <div style="clear:both"></div>
| |
| - | <br>
| |
| - | <div class="petitSsTitre">Repressors</div>
| |
| - | Now, for the repressors, the method is quite similar as before. However, we have to take into account that the proteins have a degradation rate (δ) depending on their nature and the environment. The quantity of protein produced at each time depends on the promoter under control (α). <br><br>
| |
| - |
| |
| - | <center>
| |
| - | <iframe frameborder="0" width="480" height="270" src="http://www.dailymotion.com/embed/video/xtuc6t?logo=0"></iframe><br /><a href="http://www.dailymotion.com/video/xtuc6t_lacinequation_tech" target="_blank">LacI Equation</a> </center>
| |
| - |
| |
| - | <br><br>
| |
| - | We obtain XylR's equation exactly as LacI's. <br><br>
| |
| - |
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/c/c8/3%29_LacI_and_XylR_equations.png" width = 90%/></center>
| |
| - | <center>Figure 9: The repressors equations <br></center><br><br>
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| - |
| |
| - |
| |
| - | <h3>Parameters of the model</h3>
| |
| - | <br>
| |
| - | For this model, we need at least 12 parameters that characterize the variables and their relationship between each other.
| |
| - | The available values have been measure mainly in <i>E. coli</i> strain.
| |
| - | <br><br>
| |
| - | <center>
| |
| - | <table>
| |
| - | <tr>
| |
| - | <th>Name</th>
| |
| - | <th>Description</th>
| |
| - | <th>Unit</th>
| |
| - | <th>Value</th>
| |
| - | <th>Reference</th>
| |
| - | </tr>
| |
| - |
| |
| - | <tr>
| |
| - | <td>Prod_Plac</td>
| |
| - | <td>Production rate from <i>Plac</i> promoter</td>
| |
| - | <td>mol.s-1</td>
| |
| - | <td>1.66E23</td>
| |
| - | <td>1</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>Prod_Pxyl</td>
| |
| - | <td>Production rate from <i>Pxyl</i> promoter</td>
| |
| - | <td>mol.s-1</td>
| |
| - | <td>***</td>
| |
| - | <td>**</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>k1</td>
| |
| - | <td>binding kinetic of LacI and IPTG</td>
| |
| - | <td>mol-1.s-1</td>
| |
| - | <td>1.2E5</td>
| |
| - | <td>2</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>km1</td>
| |
| - | <td>unbinding kinetic of LacI_IPTG</td>
| |
| - | <td>s-1</td>
| |
| - | <td>2.1E-1</td>
| |
| - | <td>2</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>k2</td>
| |
| - | <td>binding kinetic of XylR and Xylose</td>
| |
| - | <td>mol-1.s-1</td>
| |
| - | <td>***</td>
| |
| - | <td>**</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>km2</td>
| |
| - | <td>unbinding kinetic of XylR_Xylose</td>
| |
| - | <td>s-1</td>
| |
| - | <td>***</td>
| |
| - | <td>**</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>k3</td>
| |
| - | <td>binding kinetic of LacI and <i>Plac</i></td>
| |
| - | <td>mol-1.s-1</td>
| |
| - | <td>5.1E6</td>
| |
| - | <td>2</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>km3</td>
| |
| - | <td>unbinding kinetic of <i>PlacO</i></td>
| |
| - | <td>s-1</td>
| |
| - | <td>3.7E-2</td>
| |
| - | <td>2</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>k4</td>
| |
| - | <td>binding kinetic of XylR and <i>Plac</i></td>
| |
| - | <td>mol-1.s-1</td>
| |
| - | <td>***</td>
| |
| - | <td>**</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>km4</td>
| |
| - | <td>unbinding kinetic of XylR and <i>PlacO</i></td>
| |
| - | <td>s-1</td>
| |
| - | <td>***</td>
| |
| - | <td>**</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>δ_LacI</td>
| |
| - | <td>degradation rate of LacI</td>
| |
| - | <td>s-1</td>
| |
| - | <td></td>
| |
| - | <td>3</td>
| |
| - | </tr>
| |
| - | <tr>
| |
| - | <td>δ_XylR</td>
| |
| - | <td>degradation rate of XylR</td>
| |
| - | <td>s-1</td>
| |
| - | <td>***</td>
| |
| - | <td>**</td>
| |
| - | </tr>
| |
| - | </table><br>
| |
| - | Model parameters. <small>*** for no value and ** for no reference</small>
| |
| - | </center>
| |
| - |
| |
| - | <br><br>
| |
| - | <h3>Hypotheses</h3>
| |
| - | <br>
| |
| - | The following hypotheses have been made for this model.
| |
| - | <ul>
| |
| - | <li>we just need LacI concentration for surfactant production and not Sfp and AbrB concentration because there is a proportional link between them. If there are LacI proteins produced, there will be also Sfp and AbrB proteins.
| |
| - | <li>we assumed that there will be no degradation of IPTG due to its high stability[4] and no metabolism of Xylose in our condition[5].
| |
| - | <li>we are aware of LacI[6] and XylR[7] dimerisation as fundamental functional unit but they are not taken into account in this model.
| |
| - | </ul>
| |
| - | <br>
| |
| - |
| |
| - | <div style="font-size:12px">
| |
| - | <b>References:</b><br>
| |
| - | <ul>
| |
| - | <li> [1] Nature. 2000 Jan 20;403(6767):335-8.<i> A synthetic oscillatory network of transcriptional regulators.</i> Elowitz MB, Leibler S.
| |
| - | <li> [2] Xu H.,Moraitis M., Reedstrom R. J., Matthews K. S. 1998. <i>Kinetic and thermodynamic studies of purine repressor binding to corepressor and operator DNA.</i> J. Biol. Chem. 273:8958–8964.
| |
| - | <li> [3] Tuttle et al. <i>Model-Driven Designs of an Oscillating Gene Network.</i>, Biophys J 89(6):3873-3883, 2005
| |
| - | <li> [4] Herzenberg, L.A., <i>Studies on the induction of beta-galactosidase in a cryptic strain of Escherichia coli.</i> Biochim. Biophys. Acta, 31, 525 (1959)
| |
| - | <li> [5] http://bsubcyc.org/BSUB/NEW-IMAGE?type=PATHWAY&object=XYLCAT-PWY
| |
| - | <li> [6] Ramot, R. et al, <i>Lactose Repressor Experimental Folding Landscape: Fundamental Functional Unit and Tetramer Folding Mechanisms</i>. Biochemistry (2012)
| |
| - | <li> [7] Song S., Park C. <i>Organization and regulation of the D-xylose operons in Escherichia coli K-12: XylR acts as a transcriptional activator.</i> J Bacteriol. 1997 Nov;179(22):7025-32.
| |
| - | </ul>
| |
| - | </div>
| |
| - |
| |
| - | </div>
| |
| - | </div>
| |
| - | <h2>Results</h2>
| |
| - | <div class="wrapper">
| |
| - | <div class="contenuTexte">
| |
| - |
| |
| - | <br>
| |
| - | <div class="petitSsTitre">Expected results</div>
| |
| - | Finally, we translated the biological system into mathematical equations. As we can see, there is a lot of paramaters for the binding and unbinding kinetics, degradation rates and productions from promoters. However, values for only a few of them are available. This is why we needed to simulate the behaviour of our system. <br>
| |
| - | We want to have an overproduction of XylR in the presence of IPTG, for the STICK option. And an overproduction of LacI when there is xylose in the environment, for the COAT option. <br>
| |
| - |
| |
| - | According to the above theoretical model, we should generate the expected toggle switch (figure below), using the appropriate values for all parameters.<br><br>
| |
| - |
| |
| - |
| |
| - | <center><img src="https://static.igem.org/mediawiki/2012/e/e6/4%29_COAT.png" width=300px/>
| |
| - | <img style="margin-left:50px;" src="https://static.igem.org/mediawiki/2012/5/51/4%29_Stick.png" width=300px/></center><br>
| |
| - | <center>Figure 10: Expected results of the model</center><br>
| |
| - |
| |
| - |
| |
| - |
| |
| - |
| |
| - | <div class="petitSsTitre">Experimentations</div>
| |
| - | So far, we can consider the values for the P<i>lac</i> promoter, LacI and IPTG that have been measured in <i>E. coli</i> to apply to our <i>B. subtilis</i> model. We have performed experiments with the P<i>xyl</i>, xylose and XylR to evaluate whether this promoter can be modelled using similar values. When this step is performed, our model will allow us to determine two important concentration limits: <br>
| |
| - | <ul>
| |
| - | <li>1) the lowest IPTG concentration for the induction of the COAT option
| |
| - | <li>2) the lowest xylose concentration for the induction of the STICK option.
| |
| - | </ul>
| |
| - | <br>
| |
| - |
| |
| - | <br><br>
| |
| - | We also thought of a way to obtain binding and unbinding kinetics of the proteins. Some methods such as Isothermal titration calorimetry (ITC) permit to determine the thermodynamic parameters of interactions in solution
| |
| - |
| |
| - |
| |
| - | </div>
| |
| - | </div>
| |
| - | </div>
| |
| - | </div>
| |
| - |
| |
| - |
| |
| - | <div class="petitSsTitre">Experimentations</div>
| |
| - | So far, we can consider the values for the P<i>lac</i> promoter, LacI and IPTG that have been measured in <i>E. coli</i> to apply to our <i>B. subtilis</i> model. We have performed experiments with the P<i>xyl</i>, xylose and XylR to evaluate whether this promoter can be modelled using similar values. When this step is performed, our model will allow us to determine two important concentration limits: <br>
| |
| - | <ul>
| |
| - | <li>1) the lowest IPTG concentration for the induction of the COAT option
| |
| - | <li>2) the lowest xylose concentration for the induction of the STICK option.
| |
| - | </ul>
| |
| - | <br>
| |
| | | | |
| - | <br><br>
| |
| - | We also thought of a way to obtain binding and unbinding kinetics of the proteins. Some methods such as Isothermal titration calorimetry (ITC) permit to determine the thermodynamic parameters of interactions in solution
| |
| | | | |
| | | | |
"
