Team:TU Delft-Leiden/Modeling

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<h2> Modeling Overview</h2>
<h2> Modeling Overview</h2>
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<p>We developed models for each of the three different modules of our project: the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli">conductive curli module</a>, the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET">extracellular electron transport (EET) module</a> and the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine">landmine detection module</a>. <br>
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For the conductive curli module, we wanted to know if a conductive path between two electrodes of a chip filled with curli growing <i> E. coli </i> arise at a certain point in time. We also wanted to make quantitative predictions about the resistance between the two electrodes of our system in time. <br>
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For the EET module, our goal was to investigate the carbon metabolism providing the electrons for the EET module. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Gadget">gadget section</a> of our wiki. Furthermore, in our modeling of the assembly of the EET complex, we wanted to predict how many EET complexes are formed under different initial conditions. We focused, in addition to the assembly mechanism, also on the apparent reduced cell viability.<br>
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For the landmine module, we tried to find a model which would be able to reproduce the response curves of both the landmine promoters, as found in [1]. <br>
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For the EET and landmine modules, we used deterministic modeling. For the curli module, we used a stochastic modeling approach, and considered the system at the gene, cell and colony level. At the colony levvel, we employed <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#PercolationTheory">percolation theory</a> in order to predict if a conductive path between the two electrodes arise at a certain point in time and to predict at which time this happens. Our application of percolation theory to describe the formation of a conductive biological network represents a novel approach that has not been used in the literature before.
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</p>
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<p> We modeled all three different modules our project consists of, namely the landmine module, the Extracellular Electron Transport (EET) module and the conductive curli module. In order to achieve this, we had to use all kinds of different modeling methods.</p>
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<br>
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<p>
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We used Matlab for most of the calculations; the scripts we made can be found in the <a href="/Team:TU_Delft-Leiden/Modeling/CodeRepository">Code Repository</a>. We had great interactions with the Life Science and Microfluidics departments, which for the conductive curli module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/curli/integration">here</a>, for the EET module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET/integration">here</a> and for the landmine detection module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/landmine/integration">here</a>.  
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</p>
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          <a href="/Team:TU_Delft-Leiden/Modeling/Landmine">
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        <a href="/Team:TU_Delft-Leiden/Modeling/Curli">
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          <p>Landmine Module</p>
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        <p>Curli Module</p>
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          </a>
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        </a>
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              <ul>
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          <ul>
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                    <li>
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Gene">
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine#simplemodel">
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                     <p>Gene Level Modeling</p>
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                     <p>Simple Binding Model </p>
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                     </a>
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine#coopbinding">
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                     <p>Cooperative Binding Model</p>
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                    <li>
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Cell">
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                     <p>Cell Level Modeling</p>
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                    <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Colony">
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                    <p>Colony Level Modeling</p>
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                              <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Reflection">
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                              <p>Critical reflection on our model</p>
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                              </a>
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                              </li>
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           <a href="/Team:TU_Delft-Leiden/Modeling/EET">
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                    </li>
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              </ul>
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           <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET">
           <p>EET Module</p>
           <p>EET Module</p>
           </a>
           </a>
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                     <a href="/Team:TU_Delft-Leiden/Modeling/EET/FBA">
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/FBA">
                     <p> Flux Balance Analysis of the EET Module</p>
                     <p> Flux Balance Analysis of the EET Module</p>
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                     <a href="/Team:TU_Delft-Leiden/Modeling/EET/Deterministic">  
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/Deterministic">  
                     <p> Deterministic Model of EET Complex Assembly</p>
                     <p> Deterministic Model of EET Complex Assembly</p>
                     </a>
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         </ul>
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          <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine">
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          <p>Landmine Module</p>
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          </a>
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        <a href="/Team:TU_Delft-Leiden/Modeling/Curli">
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        <p>Curli Module</p>
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          <ul>
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                     <a href="/Team:TU_Delft-Leiden/Modeling/Curli#Gene Level">
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                     <p>Gene Level Modeling</p>
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine#simplemodel">
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                     <p>Simple Binding Model </p>
                     </a>
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              </li>
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine#coopbinding">
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                    <li>
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                     <p>Cooperative Binding Model</p>
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                     <a href="/Team:TU_Delft-Leiden/Modeling/Curli#Cell Level">
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                     <p>Cell Level Modeling</p>
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                     <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine#experimentaldata">
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                    <p>Fitting to Experimental Data</p>
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                    </a>
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          </ul>
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                    <a href="/Team:TU_Delft-Leiden/Modeling/Curli#Colony Level">
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                    <p>Colony Level Modeling</p>
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                    </a>
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          <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/interactions">
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          <p>Interaction with Life Science and Microfluidics</p>
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                    </li>
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          </a>
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                    <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/curli/integration">
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                    <p>Curli Module </p>
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                    </a>
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              </li>
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                    <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET/integration">
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                    <p>EET Module </p>
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                    </a>
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              </li>
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                <li>
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                    <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/landmine/integration">
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                    <p>Landmine Module </p>
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                    </a>
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              </li>
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          </ul>
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           <a href="/Team:TU_Delft-Leiden/Modeling/Techniques">
           <a href="/Team:TU_Delft-Leiden/Modeling/Techniques">
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          <a href="/Team:TU_Delft-Leiden/Modeling/CodeRepository">
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          <p>Code Repository</p>
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          </a>
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</div>
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<h3>Landmine Module </h3>
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<h3> References </h3>
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<p>
 
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An important part of our iGEM project is a promoter sensitive to DNT/TNT. We will use two promoters that are sensitive to DNT/TNT, namely <i>ybiJ</i> and <i>ybiFB2A1</i>, in our project. Of these promoters, not much is known other than the fact that they have a DNT/TNT-dependent response curve . Our goal was to find a model which would be able to reproduce the response curves of both promoters. To achieve this, we constructed two different models, both using <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#DeterministicTheory">deterministic modeling methods</a>. One model is based on a simple binding model of DNT to the promoter, the other is based on cooperative binding of DNT to the promoter.
 
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When based on the simple binding model, fits of promoter activation with respect to DNT concentration to the experimental data of [1] did not yield good results. However, when the fits were based on the cooperative binding model, we were able to match the experimental data in [1] really well, see figure 1.
 
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</p>
 
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<figure>
 
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<img src="https://static.igem.org/mediawiki/2014/5/59/TUDelft_2014_model_fit_tnt_promoters_coop.png" width="100%" width="100%" height="100%">
 
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<figcaption>
 
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Figure 1: Fits of the promoter activation model described by cooperative promoter activation to the data of [1]. The left panel shows the fit for the jbiJ promoter, the right panel the fit for the yqjFB2A1 promoter. For comparison, also the fits described by the simple binding model are displayed.
 
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</figcaption>
 
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</figure>
 
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<h3>EET Module </h3>
 
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<h4> Flux Balance Analysis </h4>
 
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<p>
 
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In the wet lab, we integrated the Extracellular Electron Transport (EET) module of <i>S. oneidensis</i> into <i>E. coli</i> <font color="red">[reference]</font>. For the modeling of the EET module, we wanted at first to gain insight in the consequences of the integration of the EET module into <i>E. coli</i>. To achieve this, we simulated the cell metabolism of <i>E. coli</i> including the EET module using the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#FBATheory">Flux Balance Analysis (FBA) method</a>. <br>
 
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Our goal was to investigate the carbon metabolism providing the electrons for the EET module <font color="red">[reference]</font>. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor <font color="red">[reference]</font>.
 
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From the FBA method, we conclude that in aerobic conditions the cell does not use the EET pathway, but oxygen gets reduced instead, as it is a stronger oxidizing agent. However, in anaerobic growth the cell does use the EET pathway to export electrons out of the cell. When the cell is grown on glucose, the growth rate will be higher than when the cell is grown on D-lactate. <br>
 
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We also conclude that in an experimental setting the EET pathway has a higher chance of being used when the cells are grown on D-lactate as the EET pathway is necessary in order for the cells to grow, while when grown on glucose and the EET pathway is turned off (represented by \(0 \ mmol \ (gDW)^{-1} \ hr^{-1}\) (per gram dry weight per hour) maximum EET flux) growth is still possible, see figure 2. From Flux Variability Analysis (FVA) we conclude that for maximum growth for each specific combination of carbon source uptake flux and maximum EET flux, only one possible EET flux is possible for both growth on glucose and growth on D-lactate, namely the EET flux shown in figure 2.
 
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</p>
 
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<figure>
 
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<img src="https://static.igem.org/mediawiki/2014/9/9b/TUDelft_2014_Phase_plane%28anaerobe%29_opt_growth_v2.png" width="100%" height="100%">
 
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<figcaption>
 
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Figure 2: Above: Phenotypic phase planes for growth rate, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for growth. The left panel display growth on glucose, the right panel growth on D-lactate. Green means a low growth rate, yellow means a high growth rate. Regions indicated by I correspond to no growth, regions indicated by II correspond to carbon source-limited growth, regions indicated by III correspond to carbon source-limited and maximum EET flux-limited growth. Below: Phenotypic phase planes for EET flux, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for growth. The left panel display growth on glucose, the right panel growth on lactate. Green means a low EET flux, yellow means a high EET flux. Regions indicated by I correspond to no EET flux (and no growth), regions indicated by II correspond to carbon source-limited EET flux, and regions indicated by III correspond to maximum EET flux-limited EET flux.
 
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<br>
 
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As performing the FBA method while maximizing the EET flux yielded no growth, we wondered if there are pathways possible that would yield growth. So, we performed FVA, the results can be found in figure 3. From this figure, we conclude that when maximizing the EET flux, there are pathways possible that yield growth, as the figure displays the difference between the optimized maximum value and the optimized minimum value of growth. We see that this value is not equal to zero everywhere in the figure, thus there are multiple pathways possible when maximizing EET flux that all yield different values for growth. Note that the EET flux is 2.8 times higher and 2 times higher in comparison to maximizing for growth rate, for glucose and D-lactate as a carbon source, respectively.
 
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</p>
 
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<figure>
 
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<img src="https://static.igem.org/mediawiki/2014/0/04/TUDelft_2014_Growth_diff_phase_plane%28anaerobe%29_opt_EET_v2.png" width="100%" height="100%">
 
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<figcaption>
 
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Figure 3: Above: Phenotypic phase plane for EET flux, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for EET flux. The left panel display growth on glucose, the right panel growth on D-lactate. Green means a low EET flux, yellow means a high EET flux. Regions indicated by I correspond to no EET flux, regions indicated by II correspond to carbon source-limited EET flux, and regions indicated by III correspond to maximum EET flux-limited EET flux. Below: Phenotypic phase planes for growth rate, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for EET flux. The left panel display growth on glucose, the right panel growth on D-lactate. Both panels give the difference between the optimized maximum value and the optimized minimum value of growth. Green means a low growth rate, yellow means a high growth rate. Regions indicated by I correspond to no growth, regions indicated by II correspond to carbon source-limited EET flux, and regions indicated by III correspond to carbon source-limited and maximum EET flux-limited growth.
 
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</figure>
 
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<p>
 
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From figures 2 and 3 we conclude that there are different regions in which the cell can operate. In an experimental setting, it can be investigated in which region the cell actually operates and if it maximizes its growth rate or its EET flux. To be able to do this, the experimental observed pathway has to be compared to the possible pathways when maximizing the EET flux and to the pathway when maximizing the growth rate. From these regions, it can be deduced if the experimentally observed EET flux and growth rate are carbon source limited or limited by the maximum possible EET flux. <br>
 
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Finally, we investigated an extended model of <i>E. coli</i> metabolism. This model contains, in contrast to the previously used core model, L-lactate as a metabolite. Using the extended model, we found that for glucose and D-lactate as carbon sources, the maximized growth rate agreed quite well to the previous analysis's using the core model. Using L-lactate as a carbon source, we conclude that a steady state solution in which <i>E. coli</i> can grow on L-lactate and use the EET pathway is not possible. A possible way to obtain information about the EET flux when the cells are not in steady state as observed by Goldbeck <i>et al.</i> [2], would be by the use of dynamic flux balance analysis (dFBA), which can also model the dynamics of a system before it reaches steady state [3].
 
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<h4>Deterministic Model of EET Complex Assembly</h4>
 
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<p>
 
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The EET module consists of three proteins: MtrA, a cytochrome on the inside of the outer membrane, MtrB, a β-barrel protein located in the outer membrane, and MtrC, another cytochrome, located on the cell surface. This complex enables the cell to transport electrons from the cytoplasm of the cell to the extracellular environment. <br>
 
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The assembly of the trans-membrane EET complex depends on many factors other than transcriptional and translational control, as it requires a large amount of post-translational modifications. We set up a simplified model of this assembly process, largely based on section 1.3 of the thesis of Jensen [4]. With the use of <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#DeterministicTheory">deterministic modeling methods</a>, our goal is to predict how many EET complexes are formed under different initial conditions. <br>
 
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In our modeling of the assembly of the EET complex, in addition to the assembly mechanism, we also focus on the apparent reduced cell viability. Jensen [4] proposes two possible explanations for this: the formation of cytosolic aggregates and reduced membrane integrity due to the high amount of trans-membrane protein complexes.
 
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We constructed two different models, one based on an extensive model of EET complex assembly, which we based upon the work of Jensen [4], the other based on a very much simplified model of EET complex assembly, which includes only the most fundamental reactions of the assembly process. <br>
 
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From the extensive model, we concluded that the amount of δ-ALA (and therefore heme) is rate limiting and not the amount of available binding sites. We therefore predict that adding extra δ-ALA to the cells will increase the amount of EET complexes, see figure 4. This effect is also observed by Jensen [4].
 
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<img src="https://static.igem.org/mediawiki/2014/5/54/TUDelft_2014_EETvsdALA.png" width="100%" height="100%">
 
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Figure 4: The final concentration of EET complexes as a function of the initial concentration of δ-ALA.
 
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Although the extensive model proved to be valuable in the investigation of the mechanism which assembles the EET pathway, it is not suitable for the quantitative prediction of the amount of EET complexes. The most important reason for this is the large number of unknown parameters. Therefore we decided not to aim at enhancing this model, and rather set up a more simplified model.
 
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To sidestep the difficulties experienced with the extensive model of the assembly of the EET complex, we reduced the system to a bare minimum. For this simplified model, we only included the production of MtrCAB, the formation of cytosolic aggregates and the assembly of the EET complex. <br>
 
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The simplified model does not represent all the actual mechanisms of the EET complex assembly process that happens in nature, but it is able to match the experimental data of Goldbeck <i>et al.</i> [2], see figure 5. A maximum at low promoter strength is clearly visible. This corroborates the statement in [2] that maximum promoter strength does not result in maximum EET concentration due to reduced cell viability. </p>
 
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<figure>
 
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<img src="https://static.igem.org/mediawiki/2014/7/76/TUDelft_2014_EETvsk1.png" width="100%" height="100%">
 
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Figure 5: A plot of the end concentration of EET versus promoter strength using the parameters in table 3. The red circles correspond to the data points shown in figure 4a of Goldbeck et al. [2].
 
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This is a confirmation that our assumptions concerning cell viability might be correct. Therefore, we conclude that reduced cell viability because of the implementation of the EET pathway is the consequence of three molecular processes, namely firstly, the amount of EET complexes reduces the transcription and translation of the MtrA proteins due to reduced membrane integrity, secondly, the forming of MtrCAB aggregates and thirdly, the clogging of the secretion system transporting the MtrCAB complexes.
 
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<h3>Curli Module </h3>
 
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<p>
 
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<font color="red">still has to be written</font>
 
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</p>
 
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<h3>References </h3>
 
<p>
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[1] S. Yagur-Kroll, S. Belkin <i>et al.</i>, “<i>Escherichia Coli</i> bioreporters for the detection of 2,4-dinitrotoluene and 2,4,6-trinitrotoluene”, Appl. Microbiol. Biotechnol. 98, 885-895, 2014.  
[1] S. Yagur-Kroll, S. Belkin <i>et al.</i>, “<i>Escherichia Coli</i> bioreporters for the detection of 2,4-dinitrotoluene and 2,4,6-trinitrotoluene”, Appl. Microbiol. Biotechnol. 98, 885-895, 2014.  
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[2] C.P. Goldbeck, H.M. Jensen <i>et al.</i>, “Tuning Promoter Strengths for Improved Synthesis and Function of Electron Conduits in <i>Escherichia coli</i>”, ACS Synth. Biol. 2, 150-159, 2013.
 
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[3] R. Mahadevan, J.S. Edwards & F.J. Doyle, “Dynamic Flux Balanace Analysis of Diauxic Growth in <i>Escherichia coli</i>”, Biophys. J. 83, 1331-1340, 2002.
 
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[4] H.M. Jensen, “Engineering <i>Escherichia coli</i> for molecularly defined electron transfer to metal oxides and electrodes”, PhD Thesis Chemistry UC Berkeley, 2013.
 
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Latest revision as of 23:44, 17 October 2014


Modeling Overview

We developed models for each of the three different modules of our project: the conductive curli module, the extracellular electron transport (EET) module and the landmine detection module.
For the conductive curli module, we wanted to know if a conductive path between two electrodes of a chip filled with curli growing E. coli arise at a certain point in time. We also wanted to make quantitative predictions about the resistance between the two electrodes of our system in time.
For the EET module, our goal was to investigate the carbon metabolism providing the electrons for the EET module. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the gadget section of our wiki. Furthermore, in our modeling of the assembly of the EET complex, we wanted to predict how many EET complexes are formed under different initial conditions. We focused, in addition to the assembly mechanism, also on the apparent reduced cell viability.
For the landmine module, we tried to find a model which would be able to reproduce the response curves of both the landmine promoters, as found in [1].
For the EET and landmine modules, we used deterministic modeling. For the curli module, we used a stochastic modeling approach, and considered the system at the gene, cell and colony level. At the colony levvel, we employed percolation theory in order to predict if a conductive path between the two electrodes arise at a certain point in time and to predict at which time this happens. Our application of percolation theory to describe the formation of a conductive biological network represents a novel approach that has not been used in the literature before.


We used Matlab for most of the calculations; the scripts we made can be found in the Code Repository. We had great interactions with the Life Science and Microfluidics departments, which for the conductive curli module can be read here, for the EET module can be read here and for the landmine detection module can be read here.

Contents

References

[1] S. Yagur-Kroll, S. Belkin et al., “Escherichia Coli bioreporters for the detection of 2,4-dinitrotoluene and 2,4,6-trinitrotoluene”, Appl. Microbiol. Biotechnol. 98, 885-895, 2014.

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