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

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<a href="https://2014.igem.org/Team:Bielefeld-CeBiTec/Results/Modelling"> Modelling </a>
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<h1>Modelling</h1>
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<h2>Abstract</h2>
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We used these modelling approaches to identiy bottlenecks in the constructed pathways and to predict the formation of 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 is a usefull tool to give a first overview. Due to the huge amount of components it seems not like to create a computational model for all of these reactions at once. Therefor we started our modelling work by carrying out a stochiometric analysis. Afterwards we started a break down of the project in different parts. Dynamic modelling by creating kinetic equiations was carried out for the isobutanol production pathway. This was done to identify bottlenecks. Finally we extended the existing model by adding some of the carbon dioxide fixing reactions.
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<h2>Introduction</h2>
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Mathematical modelling is essentiell to understand complex biological systems (<a href="#schaber2009">Schaber et al., 2009</a>). The analysis of isolated biological components is supplemented by a systems biology approach since ten years ago (<a href="#chuang2010">Chuang et al., 2010</a>). Mathematical modelling is used to combine biological results (Kherlopian et al., 2008). Modelling is also a way to gain 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 (Klipp et al., 2009).
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The most important aim of any modelling approach is the reduction of complexity. The given biological reality is often very divers and variable. Therefor it is important to identify the major rules and principles which can describe a system.
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Our aims were
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<ul>
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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 isobutanol production. </li>
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<h2>Stoichiometric analysis</h2>
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We calculated the stoichiometric relations of all substances involved in our complex reaction network (figure 1). The calculation starts with the electrons. They are transported 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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      <font size="2" style="text-align:left;">
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<b>Figure 1</b>: Complete metabolic network of reactions which describes 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. The housekeeping metabolism of <i>E. coli</i> is ignored.
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In theory and 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 number of consumed electrons per produced isobutanol molecule is therefor 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 electrons<sup>.
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<b>Table1:</b> This table shows the theoretical electron costs of different intracellular molecules. The electron costs is the number of electrons which are needed for the synthesis of this metabolite.
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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>Number of electrons</th>
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<tr> <td>FADH<sub>2<sub></td>  <td>2</td></tr>
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<tr> <td>NADH+H<sup>+</sup></td>  <td>2</td></tr>
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<tr> <td>ATP</td>  <td>1</td></tr>
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<tr> <td>Triosephosphate</td> <td>21</td></tr>
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<tr> <td>CO<sub>2</sub> fixation</td> <td>7</td></tr>
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<tr> <td>Pyruvate</td> <td>19</td></tr>
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<tr> <td>Isobutanol</td> <td>42</td></tr>
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</table>
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<br><br>
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<h2> Dynamic modelling </h2>
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After the stochiometric analasis of the system we decided to use a dynamic model with kinetic equiations. It allows the identification of bottlenecks. This is our major aim. At least we would like to identify bottlenecks. Maybe we could even use this information in the next step to modify constructs e.g. exchange a RBS or a promotor sequence. This could be nessesary to optimize the different enzyme concentrations. Beside that it was our aim to predict the production of isobutanol. An improvement of this model could predict the isobutanol production in a carbon dioxide fixing cell.
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To achiev our aims we broke down the complex system shwon in figure 1. It was was reduced to the system shown in figure 2. This reduced version was suitable for modelling.
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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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      <font size="2" style="text-align:left;">
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<b>Figure 2</b>: Reduced metabolic network of reactions which were selected for modelling. </font>
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<h3>Isobutanol production pathway</h3>
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We started our modelling work on the isobutanol pathway by reading publications about the isobutanol production pathway <a href="#atsumi2008">(Atsumi et al., 2008</a> and <a href="#atsumi2010"> Atsumi et al., 2010)</a>. Doing that we colleted a lot of information. The first modelling approach was a system of differential equations using Michealis-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>). All needed V<sub>max</sub> and K<sub>M</sub> values were colleted from the literature and 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 were replaced by estimations.
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<b>Table2:</b> This table shows all enzymatic parameters which were used for our first model.
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<th>Enzyme</th>
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<th>V<sub>max</sub></th>
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<th>K<sub>M</sub> [mM]</th>
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<th>Reference</th>
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<td>AlsS</td> <td></td> <td>13.6</td> <td><a href="#atsumi2008">Atsumi et al., 2008</a></td>
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<td>IlvC</td> <td></td> <td></td> <td></td>
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<td>IlvD</td> <td></td> <td></td> <td></td>
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<td>KivD</td> <td></td> <td></td> <td></td>
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<td>AdhA</td> <td></td> <td>385.1</td> <td><a href="#atsumi2010">Atsumi et al., 2010</a></td>
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The starting concentrations for different metabolites were also taken from the literature and from different databases (table 3).
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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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<table width="100%" border="1" cellpadding="5" style="background-color:transparent">
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<th>Metabolite</th>
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<th>Concentration [mM]</th>
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<th>Reference</th>
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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>2-Acetolactate</td> <td>-</td> <td>-</td>
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<td>2,3-Dihydroxyisovalerate</td> <td>-</td> <td>-</td>
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<td>2-Ketoisovalerate</td> <td>-</td> <td>-</td>
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<td>Isobutyraldehyde</td> <td>0.6</td> <td></td>
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<td>Isobutanol</td> <td>variable</td> <td>-</td>
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We implemented the system of differential equations in matlab (link to source code) and created first results (fig. 3).
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      <a href="https://static.igem.org/mediawiki/2014/6/6b/Bielefeld-CeBiTec_14-10-14_modelling_1.png" target="_blank"><img src="https://static.igem.org/mediawiki/2014/6/6b/Bielefeld-CeBiTec_14-10-14_modelling_1.png" width="750px"></a><br>
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<b>Figure 3</b>: Predicted changes in metabolic concentration over time. </font>
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To improve our prediction we decided to switch from V<sub>max</sub> and K<sub>M</sub> to k<sub>cat</sub> and the amount of the different enzymes (table 4). The amount of expressed proteins could differ depending on the distance of the coding sequence downstream of the promotor. Different values can be used to simulate the usage of promotors of different strength. This approach also allows the modelling of different growth states. The growth is represented by an increase in the amount of enzyme.
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<b>Table4:</b> This table shows all k<sub>cat</sub> values which were used for modelling of the isobutanol production pathway. k<sub>cat</sub> was set to 10, if no published value was available.
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<th>Enzyme</th>
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<th>k<sub>cat</sub></th>
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<td>AlsS</td> <td>121</td> <td><a href="#atsumi2008">Atsumi et al., 2008</a></td>
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<td>IlvC</td> <td></td> <td></td>
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<td>IlvD</td> <td></td> <td></td>
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<td>KivD</td> <td></td> <td></td>
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<td>AdhA</td> <td>0.9</td> <td><a href="#atsumi2010">Atsumi et al., 2010</a></td>
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The modelling results indicated that the concentration of IlvD is limiting the isobutanol production. An experimentell verification of this hind is the next logical step. This bottleneck could be removed by overexpression of the corresponding coding sequence. One way to achieve this is the integration of a strong promotor and RBS upstream of this coding sequence. Due to a lack of time we were not able to follow up this lead. It could be a great possibility to improve our isobutanol production.
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<h3>Carbon dioxide fixing reacions</h3>
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The next model improvement was the addition of some of the carbon fixing reactions and the pathway leading to pyruvate. We collected k<sub>cat</sub> and K<sub>M<sub> values for nearly all relevant steps (table 5). They were used for differential equiations which describe these additional reactions.
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<b>Table5:</b> This table shows all kcat values of enzymes involved in CO2-fixation and the pathway leading to pyruvate.
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<th>Enzyme</th>
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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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<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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  <h6>References</h6>
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<li id="atsumi2008">
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<div class="element" style="margin_10px 10px 10px 10px; padding:10px 10px 10px 10px">
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Atsumi, Shota, Taizo Hanai, und James C. Liao. „Non-Fermentative Pathways for Synthesis of Branched-Chain Higher Alcohols as Biofuels“. <a href="http://www.nature.com/nature/journal/v451/n7174/full/nature06450.html">Nature</a> 451, Nr. 7174 (3. Januar 2008): 86–89. doi:10.1038/nature06450.
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<li id="atsumi2010">
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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, Nr. 3 (Januar 2010): 651–57. doi:10.1007/s00253-009-2085-6.
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Yang, Y. T., G. N. Bennett, und K. Y. San. „The Effects of Feed and Intracellular Pyruvate Levels on the Redistribution of Metabolic Fluxes in Escherichia Coli“. <a href="http://bioc.rice.edu/bennetlab/references/ref40-sdarticle.pdf">Metabolic Engineering</a> 3, Nr. 2 (April 2001): 115–23. doi:10.1006/mben.2000.0166.
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<li id="wadamo1998">
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Wadano, Akira, Keisuke Nishikawa, Tomohiro Hirahashi, Ryohei Satoh, und Toshio Iwaki. „Reaction Mechanism of Phosphoribulokinase from a Cyanobacterium, Synechococcus PCC7942“. <a href="http://link.springer.com/article/10.1023%2FA%3A1005979801741">Photosynthesis Research</a> 56, Nr. 1 (1. April 1998): 27–33. doi:10.1023/A:1005979801741.
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Kobayashi, Daisuke, Masahiro Tamoi, Toshio Iwaki, Shigeru Shigeoka, und Akira Wadano. „Molecular Characterization and Redox Regulation of Phosphoribulokinase from the Cyanobacterium Synechococcus Sp. PCC 7942“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/12668773/">Plant & Cell Physiology</a> 44, Nr. 3 (März 2003): 269–76.
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Latest revision as of 19:10, 16 October 2014


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