Team:Bielefeld-CeBiTec/Results/Modelling/erster/test/123

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<h1>Modelling</h1>
 
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<h2>Abstract</h2>
 
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Different modelling approaches were used to identify enzymatic bottlenecks in the isobutanol production pathways and to predict the formation of the desired product in a given time. First of all we created a map of all metabolic reactions which are part of our project (figure 1). This network not only provides a good overview, it also serves as the basic tool for further considerations. Due to the huge amount of components it does not seem feasible to create a computational model for all reactions at once. Therefore we started our modelling work by carrying out a stochiometric analysis. It reveals that 42 electrons are needed for the production of one isobutanol molecule from CO<sub>2</sub>. As for the isobutanol production pathway, dynamic modeling was carried out, in the course of which bottlenecks could be identified. An increase in expression von ilvD and kivD could increase the isobutanol production after four hours by 100%. Finally we prepared the extension of the existing model to predict the effect of specific carbon dioxide fixing reactions.
 
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<a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Results/Modelling"> Modelling </a>
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<h2>Introduction</h2>
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Mathematical modelling is crucial to understand complex biological systems (<a href="#schaber2009">Schaber et al., 2009</a>). The analysis of isolated biological components hass been supplemented by a systems biology approach in over ten years (<a href="#chuang2010">Chuang et al., 2010</a>). Mathematical modelling is used to combine biological results (<a href="#kherlopian2008">Kherlopian et al., 2008</a>). Modeling is also a way to achieve results without carrying out experiments in a laboratory. The behaviour of a system can be simulated to get results, which cannot be derived from simply looking at the given system (<a href="#schaber2009">Schaber et al., 2009</a>).
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The most important aim of any modelling approach is the reduction of complexity. As the given biological reality is often diverse and variable, it is important to identify the major rules and principles, which can describe a system.
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<h2>Our aims</h2>
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<li>Visualization of the complete meatoblic network </li>
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<li>Relating electron input to product output </li>
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<li>Relating electron input to carbon dioxide fixation </li>
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<li>The identification of bottlenecks in the isobutanol production pathway </li>
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<li>Prediction of maximal isobutanol production over the time</li>
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<h2>Stoichiometric analysis</h2>
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Stoichiometric analysis are useful to get information about the maximal output of a system. In this project the numer of electrons moving into the system limits the amount of product, which could be synhetized in the cells. Therefore the stoichiometric relations of all substances involved in our complex reaction network were calculated (figure 1). The calculation starts with the electrons, which are transportet into the system by mediators. We calculated the resulting production of intracellular molecules based on our map of the metabolic system (figure 1). The results are listed below.
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      <a href="https://static.igem.org/mediawiki/2014/5/53/Bielefeld-CeBiTec_14-10-14_complete_metabolic_system.jpg" target="_blank"><img src="https://static.igem.org/mediawiki/2014/5/53/Bielefeld-CeBiTec_14-10-14_complete_metabolic_system.jpg" width="750px"></a><br>
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<b>Figure 1</b>: Complete metabolic network of reactions involved in our project. </font>
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The theoretical electron costs of different molecules is listed in table 1. All calculations are based on our pathway map. According to our pathway map there are 42 electrons needed for the production of one molecule isobutanol, if CO<sub>2</sub> is used as sole carbon source. Our calculation does not involve the house keeping metabolism of <i>E. coli</i>, which consumes lots of energy for the survival of the cell. The true number of consumed electrons per produced isobutanol molecule is therefore much higher. The applied electric power can be converted into a number of electrons by the following equation: 1 A = 1 C * s<sup>-1</sup> = 6.2415065 * 10<sup>18</sup> electrons.
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<b>Table1:</b> This table shows the theoretical electron cost of different intracellular molecules. The electron cost is the number of electrons which are needed for the synthesis of this metabolite. The intermediates are substances which are needed for the production of the final product. There costs are included in the final value for each substance.
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<table width="100%" border="1" cellpadding="5" style="background-color:transparent">
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<tr>
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<th>Substance</th>
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<th>Intermediates</th>
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<th>Number of electrons</th>
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<tr> <td>FADH<sub>2<sub></td>  <td>-</td>  <td>2</td></tr>
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<tr> <td>NADH+H<sup>+</sup></td>  <td>-</td>  <td>2</td></tr>
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<tr> <td>ATP</td>  <td>-</td>  <td>1</td></tr>
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<tr> <td>Triosephosphate</td>  <td>9 ATP + 6 NADH</td> <td>21</td></tr>
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<tr> <td>CO<sub>2</sub> fixation</td>  <td>-</td>  <td>7</td></tr>
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<tr> <td>Pyruvate</td> <td>Triosephosphate</td> <td>19</td></tr>
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<tr> <td>Isobutanol</td> <td>2x Pyruvate</td> <td>42</td></tr>
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</table>
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<h2> Dynamic modelling </h2>
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After the stoichiometric analysis of the system we designed a dynamic model containing kinetic equations for the metabolite concentrations. It allows the identification of metabolic or enzymatic bottlenecks. This is our major aim. We could even use this information in the next step to modify constructs e.g. exchange an RBS or a promotor sequence. This could improve the different enzyme concentrations for upcoming experiments in the laboratory. Furthermore it was our target to predict the production of isobutanol per substrate in a given time. Our model predicts the isobutanol production in a carbon dioxide fixing cell. To achieve our aims we reduced the complex system shown in figure 1 to the version shown in figure 2. This metabolic network was suitable for our dynamic modelling approach.
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      <a href="https://static.igem.org/mediawiki/2014/b/ba/Bielefeld-CeBiTec_14-10-14_reduced_metabolic_system.jpg" target="_blank"><img src="https://static.igem.org/mediawiki/2014/b/ba/Bielefeld-CeBiTec_14-10-14_reduced_metabolic_system.jpg" width="750px"></a><br>
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<b>Figure 2</b>: Reduced metabolic network of reactions which were selected for modelling. </font>
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<h3>Dynamic modelling of the isobutanol production pathway</h3>
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The modelling work on the <a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Project/Isobutanol/GeneticalApproach">isobutanol pathway</a> is based on publications about the isobutanol production pathway <a href="#atsumi2008">(Atsumi et al., 2008</a> and <a href="#atsumi2010"> Atsumi et al., 2010)</a>. We started our work on the isobutanol production pathway by collecting the appropriated kinetic parameters. They were used for the development of a  system of differential equations. As for the choice of the kinetics used, we stick to Michaelis-Menten kinetics. This was published as the best approach, if reaction kinetics are not known (<a href="#breitling2008">Breitling et al., 2008</a>; <a href="#chubukov2014">Chubukov et al., 2014</a>). Additionally kcat and KM values were collected from databases like <a href=“http://www.genome.jp/kegg/“>KEGG</a>, <a href=“http://biocyc.org/“>biocyc</a> and <a href=“http://www.brenda-enzymes.org/“>BRENDA </a>(table 2). Missing values had to be estimated. The starting concentrations for different metabolites were also taken from the literature and from different databases (table 3). <br>
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We decided to use only the forward reactions from pyruvate to isobutanol for different reasons. First it is necessary to get the maximal product concentration, second the reactions are neary irreversibel due to the decarboxylation steps and third there are only a few information on the back reactions available.
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<b>Table2:</b> This table shows all enzymatic parameters which were used for our dynamic model.
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<th>Enzyme</th>
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<th>k<sub>cat</sub></th>
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<th>Reference</th>
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<td>AlsS</td> <td>121</td> <td>13.6</td> <td><a href="#atsumi2009">Atsumi et al., 2009</a></td>
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<td>IlvC</td> <td>2.2</td> <td>0.25</td> <td><a href="#tyagi2005">Tyagi et al., 2005</a></td>
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<td>IlvD</td> <td>10 (estimated)</td> <td>1.5</td> <td><a href="#flint1993">Flint et al., 1993</a></td>
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<td>KivD</td> <td>20 (estimated)</td> <td>5 (estimated)</td> <td><a href="#werther2008">Werther et al., 2008</a>; <a href="#gorcke2007">Gorcke et al., 2007</a></td>
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<td>AdhA</td> <td>6.6</td> <td>9.1</td> <td><a href="#atsumi2010">Atsumi et al., 2010</a></td>
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<b>Table3:</b> This table shows all metabolite concentrations which were used for our first model. The metabolite concentration was set to zero, if no published value was available.
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<td>Pyruvate</td> <td>10</td> <td><a href="#yang2000">Yang et al., 2000</a></td>
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<td>Isobutyraldehyde</td> <td>0.6</td> <td></td>
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We implemented the system of differential equations (figure 3) in matlab (<a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Results/Modelling/sourcecode">source code</a>). The predicted changing of the metabolic concentration over the time is shown in figures 4-7. The amount of expressed proteins could differ depending on the distance of the coding sequence downstream of the promotor. The coding sequences for the involved enzymes are located downstream of a common promotor. Therefore we decided to set the enzyme concentration for the first enzyme to 1 and decrease in steps of 0.1 (<a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Results/Modelling/sourcecode">source code</a>). These different values were tried to identify appropiate concentrations for each enzyme. The results of this dynamic modelling approach could be transfered to the laboratory by using promotors of different strength.
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      <a href="https://static.igem.org/mediawiki/2014/7/7e/Bielefeld-CeBiTec_14_10_16_dgls.png" target="_blank"><img src="https://static.igem.org/mediawiki/2014/7/7e/Bielefeld-CeBiTec_14_10_16_dgls.png" width="750px"></a><br>
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<b>Figure 3</b>: Differential equations for the dynamic modelling of the isobutanol production. </font>
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<b>Figure 4</b>: Predicted changes in metabolic concentration over time. </font>
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      <a href="https://static.igem.org/mediawiki/2014/1/1e/Bielefeld-CeBiTec_14-10-16_without_improvement_zoom_in.png"> <img src="https://static.igem.org/mediawiki/2014/1/1e/Bielefeld-CeBiTec_14-10-16_without_improvement_zoom_in.png" width="750px"></a><br>
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<b>Figure 5</b>: Predicted changes in metabolic concentration over time. The development in the first minutes is shown by zooming into the figure 4. </font>
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      <a href="https://static.igem.org/mediawiki/2014/8/83/Bielefeld-CeBiTec_14-10-16_improved_enzyme_concentrations.jpg"><img src="https://static.igem.org/mediawiki/2014/8/83/Bielefeld-CeBiTec_14-10-16_improved_enzyme_concentrations.jpg" width="750px"></a><br>
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<b>Figure 4</b>: Predicted changes in metabolic concentration in an improved system over time. The concentration of IlvD and KivD was increased by factor 3 and 4 respectively. </font>
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      <a href="https://static.igem.org/mediawiki/2014/7/75/Bielefeld-CeBiTec_14-10-16_improved_zoom_in.png
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" target="_blank"><img src="https://static.igem.org/mediawiki/2014/7/75/Bielefeld-CeBiTec_14-10-16_improved_zoom_in.png
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<b>Figure 7</b>: Predicted changes in metabolic concentration in an improved system over time. The concentration of IlvD and KivD was increased by factor 3 and 4 respectively. </font>
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Our modelling results indicated that the concentration of two enzymes are limiting the isobutanol production. They are <a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Project/Isobutanol/GeneticalApproach">IlvD</a> and <a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Project/Isobutanol/GeneticalApproach">KivD</a>. An experimentell verification of this effect is the next logical step. This enzymatic bottleneck could be removed by overexpression of the corresponding coding sequences (<a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Project/Isobutanol/GeneticalApproach"><i>ilvD</i></a> and <a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Project/Isobutanol/GeneticalApproach"><i>kivD</i></a>). One way to achieve this is the integration of a strong promotor upstream of theire coding sequences. It could be a possibility to improve our isobutanol production.
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As shown in figure 4 the isobutanol concentration reaches 2mM after four hours. In the improved system the concentration of isobutanol after four hours is nearly doubled.
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<h2>Conclusion</h2>
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The complete metabolic network of our project is visualized in figure 1. Stoichiometric caculations revealed the number of electrons which is in theory need for the production of a desired substance. There are 42 electrons required for the synthesis of one molecule isobutanol. The fixation of one carbon dioxide molecule would cost seven electrons. We were able to identify a putative enzymatic bottleneck in the isobutanol production pathway. An increased amount of IlvD and KivD could improve the isobutanol production. Additionally the production of isobutanol from pyruvate can be predicted. The next and very important step would be the validation of these prediction by experimental approaches.
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<h2>Outlook: addition of carbon dioxide fixing reactions</h2>
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The next step would be the addition of specific carbon fixing reactions and the pathway leading to pyruvate to the existing dynamic model. Therefore we collected k<sub>cat</sub> and K<sub>M</sub> values for nearly all relevant steps (table 4). They were could be used to formulate additional differential equations, which describe these additional reactions.
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<b>Table4:</b> This table shows all k<sub>cat</sub> and K<sub>M</sub> values of enzymes involved in CO<sub>2</sub>-fixation and the pathway leading to pyruvate.
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<td>PrkA</td>         <td>72.6</td> <td>0.09</td> <td><a href="#wadano1998">Wadano et al., 1998</a>,<a href="#kobayashi2003">Kobayashi et al., 2003</a></td>
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<td>RubisCO</td> <td>20 (estimated)</td> <td>0.02 (estimated)</td> <td><a href="#lan1991">Lan and Mott, 1991</a>,<a href="#sage2002">Sage, 2002</a></td>
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<td>Pgk</td> <td>480</td> <td>1 (estimated)</td> <td><a href="#fifis1978">Fifis and Scopes., 1978</a></td>
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<td>GapA</td> <td>-</td> <td>0.5</td> <td><a href="#zhao1995">Zhao et al., 1995</a></td>
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<td>GpmA</td> <td>490 (in <i>S.cerevisiae</i>)</td> <td>0.15</td> <td><a href="#fraser1999">Fraser et al., 1999</a>,<a href="#white1992">White and Fothergil-Gilmore, 1992</a></td>
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<td>Eno</td> <td>17600</td> <td>0.1</td> <td><a href="#spring1972">Spring and Wold, 1972</a>, <a href="#albe1990">Albe et al., 1990</a></td>
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</tr>
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<tr>
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<td>PykF</td> <td>3.2</td> <td>0.3 (estimated)</td> <td><a href="#oria2005">Oria-Hernandez et al., 2005</a></td>
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</tr>
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</table>
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<br><br>
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</div>
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Using all these information the combination of two parts of our project would be possible. The carbon dioxide fixation pathway could be checked for enzymatic bottlenecks. It would be possible to predict the isobutanol production from fixed carbon dioxide.
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<br><br>
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  <div id="text">
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  <h6>References</h6>
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Atsumi, Shota, Tung-Yun Wu, Eva-Maria Eckl, Sarah D. Hawkins, Thomas Buelter, und James C. Liao. „Engineering the isobutanol biosynthetic pathway in Escherichia coli by comparison of three aldehyde reductase/alcohol dehydrogenase genes“. <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2802489/">Applied Microbiology and Biotechnology</a> 85, no. 3 (2010): 651–57.
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