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Overview

rMFC

CO₂ Fixation

Isobutanol

Biosafety

Modeling

Parts

Data Page

Achievements

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Modelling

Abstract

We used the following modelling approaches to identify bottlenecks in the constructed pathways and to predict the formation of a 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. Afterwards we divided our project into different parts. As for the isobutanol production pathway, dynamic modeling was carried out, in the course of which bottlenecks could be identified.Finally we extended the existing model by adding specific carbon dioxide fixing reactions.

Introduction

Mathematical modelling is crucial to understand complex biological systems (Schaber et al., 2009). The analysis of isolated biological components hass been supplemented by a systems biology approach in over ten years (Chuang et al., 2010). Mathematical modelling is used to combine biological results (Kherlopian et al., 2008). 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 (Schaber et al., 2009). 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.

Our aims

Visualization of the complete meatoblic network
Relating electron input to product output
Relating electron input to carbon dioxide fixation
The identification of bottlenecks in the isobutanol production pathway
Prediction of isobutanol production

Stoichiometric analysis

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.

Figure 1: Complete metabolic network of reactions involved in our project.

The theoretical electron costs of different molecules is listed in table 1. All calculations are based on our pathway map. In theory and according to our pathway map there are 42 electrons needed for the production of one molecule isobutanol if CO₂ is used as sole carbon source. Our calculation does not involve the house keeping metabolism of E. coli which consumes lots of energy for the survival of the cell. The 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^-1 = 6.2415065 * 10¹⁸ electrons.

Table1: 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. Nevertheless the calculation of the electron cost was done for a de novo synthesis from carbon dioxide.

Substance	Intermediates	Number of electrons
FADH₂	-	2
NADH+H⁺	-	2
ATP	-	1
Triosephosphate	9 ATP + 6 NADH	21
CO₂ fixation	-	7
Pyruvate	Triosephosphate	19
Isobutanol	2x Pyruvate	42

Dynamic modelling

After the stoichiometric analysis of the system we decided to use a dynamic model with kinetic equations for the metabolite concentrations. It allows the identification of metabolic or enzymatical bottlenecks. This is our major aim. At least we would like to identify them. 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 necessary to optimize the different enzyme concentrations. Beside that it was our aim to predict the production of isobutanol per substrate. An improvement of this model could predict the isobutanol production in a carbon dioxide fixing cell. To achieve our aims we broke down the complex system shown in figure 1. It was reduced to the system shown in figure 2. This reduced version was suitable for modelling.

Figure 2: Reduced metabolic network of reactions which were selected for modelling.

Isobutanol production pathway

We started our modelling work on the isobutanol pathway by reading publications about the isobutanol production pathway (Atsumi et al., 2008 and Atsumi et al., 2010). Doing that we collected 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 (Breitling et al., 2008; Chubukov et al., 2014). All needed k_cat and K_M values were collected from the literature and from databases like KEGG, biocyc and BRENDA (table 2). Missing values were replaced by estimations. The starting concentrations for different metabolites were also taken from the literature and from different databases (table 3).

Table2: This table shows all enzymatic parameters which were used for our first model.

Enzyme	k_cat	K_M [mM]	Reference
AlsS	121	13.6	Atsumi et al., 2009
IlvC	2.2	0.25	Tyagi et al., 2005
IlvD	10 (estimated)	1.5	Flint et al., 1993
KivD	20 (estimated)	5 (estimated)	Werther et al., 2008; Gorcke et al., 2007
AdhA	6.6	9.1	Atsumi et al., 2010

Table3: 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.

Metabolite	Concentration [mM]	Reference
Pyruvate	10	Yang et al., 2000
2-Acetolactate	-	-
2,3-Dihydroxyisovalerate	-	-
2-Ketoisovalerate	-	-
Isobutyraldehyde	0.6
Isobutanol	variable	-

We implemented the system of differential equations (figure 3) in matlab (source code) and created first results. The predicted changing of the metabolic concentration over the time is shown in figure 4.

Figure 4: Differential equations for the dynamic modelling of the isobutanol production.

Figure 4: Predicted changes in metabolic concentration over time.

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. Our modelling results indicated that the concentration of IlvC 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.

Carbon dioxide fixing reactions

The next model improvement was the addition of some of the carbon fixing reactions and the pathway leading to pyruvate. We collected k_cat and K_M values for nearly all relevant steps (table 4). They were used for differential equations which describe these additional reactions.

Table4: This table shows all k_cat and K_M values of enzymes involved in CO₂-fixation and the pathway leading to pyruvate.

Enzyme	k_cat	K_M [mM]	Reference
PrkA	72.6	0.09	Wadano et al., 1998,Kobayashi et al., 2003
RubisCO	20 (estimated)	0.02 (estimated)	Lan and Mott, 1991,Sage, 2002
Pgk	480	1 (estimated)	Fifis and Scopes., 1978
GapA	-	0.5	Zhao et al., 1995
GpmA	490 (in S.cerevisiae)	0.15	Fraser et al., 1999,White and Fothergil-Gilmore, 1992
Eno	17600	0.1	Spring and Wold, 1972, Albe et al., 1990
PykF	3.2	0.3 (estimated)	Oria-Hernandez et al., 2005

Conclusion and summary

We were able to achieve most our aims. 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 needed for the synthesis of one molecule isobutanol. The fixation of one carbon dioxide molecule would cost 7 electrons. We were able to identify a putative bottleneck in the isobutanol production pathway. This needs to be verified by experiments. The production of isobutanol from pyruvate can be predicted. The next and very important step would be the verification of these prediction by experimental approaches.

References

Atsumi, Shota, Taizo Hanai, und James C. Liao. „Non-Fermentative Pathways for Synthesis of Branched-Chain Higher Alcohols as Biofuels“. Nature 451, no. 7174 (2008): 86–89.
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“. Applied Microbiology and Biotechnology 85, no. 3 (2010): 651–57.
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“. Metabolic Engineering 3, no. 2 (2001): 115–23.
Wadano, Akira, Keisuke Nishikawa, Tomohiro Hirahashi, Ryohei Satoh, und Toshio Iwaki. „Reaction Mechanism of Phosphoribulokinase from a Cyanobacterium, Synechococcus PCC7942“. Photosynthesis Research 56, no. 1 (1998): 27–33.
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“. Plant & Cell Physiology 44, no. 3 (2003): 269–76.
Lan, Yun, und Keith A. Mott. „Determination of Apparent Km Values for Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase (Rubisco) Activase Using the Spectrophotometric Assay of Rubisco Activity“. Plant Physiology 95, Nr. 2 (1991): 604–9.
Sage, Rowan F. „Variation in the K(cat) of Rubisco in C(3) and C(4) Plants and Some Implications for Photosynthetic Performance at High and Low Temperature“. Journal of Experimental Botany 53, no. 369 (2002): 609–20.
Fifis, T., und R. K. Scopes. „Purification of 3-Phosphoglycerate Kinase from Diverse Sources by Affinity Elution Chromatography“. The Biochemical Journal 175, no. 1 (1978): 311–19.
Zhao G, Halbur T, Pankratz DC. Colonization of oropharynx and nasal cavity of CDCD pigs by a nontoxigenic strain of Pasteurella multocida type D. J Swine Health Prod 1995;3(3):113-115.
Fraser, H. I., M. Kvaratskhelia, und M. F. White. „The Two Analogous Phosphoglycerate Mutases of Escherichia Coli“. FEBS Letters 455, no. 3 (1999): 344–48.
White, Malcolm F., und Linda A. Fothergill-Gilmore. „Development of a Mutagenesis, Expression and Purification System for Yeast Phosphoglycerate Mutase“. European Journal of Biochemistry 207, no. 2 (1992): 709–14.
Spring, Thomas G., und Finn Wold. „The Purification and Characterization of Escherichia Coli Enolase“. Journal of Biological Chemistry 246, no. 22 (1971): 6797–6802.
Albe, Kathy R., Margaret H. Butler, und Barbara E. Wright. „Cellular concentrations of enzymes and their substrates“. Journal of Theoretical Biology 143, no. 2 (1990): 163–95.
Oria-Hernández, Jesús, Nallely Cabrera, Ruy Pérez-Montfort, und Leticia Ramírez-Silva. „Pyruvate Kinase Revisited: The Activating Effect of K+“. The Journal of Biological Chemistry 280, no. 45 (2005): 37924–29.
Breitling, Rainer, David Gilbert, Monika Heiner, und Richard Orton. „A Structured Approach for the Engineering of Biochemical Network Models, Illustrated for Signalling Pathways“. Briefings in Bioinformatics 9, no. 5 (2008): 404–21.
Chubukov, Victor, Luca Gerosa, Karl Kochanowski, und Uwe Sauer. „Coordination of Microbial Metabolism“. Nature Reviews Microbiology 12, no. 5 (Mai 2014): 327–40.
Schaber, J., W. Liebermeister, und E. Klipp. „Nested Uncertainties in Biochemical Models“. IET Systems Biology 3, no. 1 (2009): 1–9.
Chuang, Han-Yu, Matan Hofree, und Trey Ideker. „A Decade of Systems Biology“. Annual Review of Cell and Developmental Biology 26 (2010): 721–44.
Kherlopian, Armen R., Ting Song, Qi Duan, Mathew A. Neimark, Ming J. Po, John K. Gohagan, und Andrew F. Laine. „A Review of Imaging Techniques for Systems Biology“. BMC Systems Biology 2, no. 1 (12. August 2008): 74.
Tyagi, R., Lee, Y.-T., Guddat, L.W., and Duggleby, R.G. (2005). Probing the mechanism of the bifunctional enzyme ketol-acid reductoisomerase by site-directed mutagenesis of the active site. FEBS J. 272, 593–602.
Atsumi, S., Li, Z., and Liao, J.C. (2009). Acetolactate Synthase from Bacillus subtilis Serves as a 2-Ketoisovalerate Decarboxylase for Isobutanol Biosynthesis in Escherichia coli. Appl Environ Microbiol 75, 6306–6311.
Flint, D.H., Emptage, M.H., Finnegan, M.G., Fu, W., and Johnson, M.K. (1993). The role and properties of the iron-sulfur cluster in Escherichia coli dihydroxy-acid dehydratase. J. Biol. Chem. 268, 14732–14742.
Gocke, D., Nguyen, C.L., Pohl, M., Stillger, T., Walter, L., and Müller, M. (2007). Branched-Chain Keto Acid Decarboxylase from Lactococcus lactis (KdcA), a Valuable Thiamine Diphosphate-Dependent Enzyme for Asymmetric CC Bond Formation. Adv. Synth. Catal. 349, 1425–1435.
Werther, T., Spinka, M., Tittmann, K., Schütz, A., Golbik, R., Mrestani-Klaus, C., Hübner, G., and König, S. (2008). Amino Acids Allosterically Regulate the Thiamine Diphosphate-dependent α-Keto Acid Decarboxylase from Mycobacterium tuberculosis. J. Biol. Chem. 283, 5344–5354.

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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.
+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, no. 1 (1998): 27–33.
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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.
+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, no. 3 (2003): 269–76.
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-Lan, Yun, und Keith A. Mott. „Determination of Apparent Km Values for Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase (Rubisco) Activase Using the Spectrophotometric Assay of Rubisco Activity“. <a href="http://www.plantphysiol.org/content/95/2/604.abstract">Plant Physiology</a> 95, Nr. 2 (2. Januar 1991): 604–9. doi:10.1104/pp.95.2.604.
+Lan, Yun, und Keith A. Mott. „Determination of Apparent Km Values for Ribulose 1,5-Bisphosphate Carboxylase/Oxygenase (Rubisco) Activase Using the Spectrophotometric Assay of Rubisco Activity“. <a href="http://www.plantphysiol.org/content/95/2/604.abstract">Plant Physiology</a> 95, Nr. 2 (1991): 604–9.
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-Sage, Rowan F. „Variation in the K(cat) of Rubisco in C(3) and C(4) Plants and Some Implications for Photosynthetic Performance at High and Low Temperature“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/11886880">Journal of Experimental Botany</a> 53, Nr. 369 (April 2002): 609–20.
+Sage, Rowan F. „Variation in the K(cat) of Rubisco in C(3) and C(4) Plants and Some Implications for Photosynthetic Performance at High and Low Temperature“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/11886880">Journal of Experimental Botany</a> 53, no. 369 (2002): 609–20.
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-Fifis, T., und R. K. Scopes. „Purification of 3-Phosphoglycerate Kinase from Diverse Sources by Affinity Elution Chromatography“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/?term=fifis+1978">The Biochemical Journal</a> 175, Nr. 1 (1. Oktober 1978): 311–19.
+Fifis, T., und R. K. Scopes. „Purification of 3-Phosphoglycerate Kinase from Diverse Sources by Affinity Elution Chromatography“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/?term=fifis+1978">The Biochemical Journal</a> 175, no. 1 (1978): 311–19.
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-Fraser, H. I., M. Kvaratskhelia, und M. F. White. „The Two Analogous Phosphoglycerate Mutases of Escherichia Coli“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/10437801">FEBS Letters</a> 455, Nr. 3 (23. Juli 1999): 344–48.
+Fraser, H. I., M. Kvaratskhelia, und M. F. White. „The Two Analogous Phosphoglycerate Mutases of Escherichia Coli“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/10437801">FEBS Letters</a> 455, no. 3 (1999): 344–48.
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-White, Malcolm F., und Linda A. Fothergill-Gilmore. „Development of a Mutagenesis, Expression and Purification System for Yeast Phosphoglycerate Mutase“. <a href="http://onlinelibrary.wiley.com/doi/10.1111/j.1432-1033.1992.tb17099.x/pdf">European Journal of Biochemistry</a> 207, Nr. 2 (1. Juli 1992): 709–14. doi:10.1111/j.1432-1033.1992.tb17099.x.
+White, Malcolm F., und Linda A. Fothergill-Gilmore. „Development of a Mutagenesis, Expression and Purification System for Yeast Phosphoglycerate Mutase“. <a href="http://onlinelibrary.wiley.com/doi/10.1111/j.1432-1033.1992.tb17099.x/pdf">European Journal of Biochemistry</a> 207, no. 2 (1992): 709–14.
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-Spring, Thomas G., und Finn Wold. „The Purification and Characterization of Escherichia Coli Enolase“. <a href="http://www.jbc.org/content/246/22/6797.long">Journal of Biological Chemistry</a> 246, Nr. 22 (25. November 1971): 6797–6802.
+Spring, Thomas G., und Finn Wold. „The Purification and Characterization of Escherichia Coli Enolase“. <a href="http://www.jbc.org/content/246/22/6797.long">Journal of Biological Chemistry</a> 246, no. 22 (1971): 6797–6802.
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-Albe, Kathy R., Margaret H. Butler, und Barbara E. Wright. „Cellular concentrations of enzymes and their substrates“. <a href="http://www.sciencedirect.com/science/article/pii/S0022519305802668">Journal of Theoretical Biology</a> 143, Nr. 2 (22. März 1990): 163–95. doi:10.1016/S0022-5193(05)80266-8.
+Albe, Kathy R., Margaret H. Butler, und Barbara E. Wright. „Cellular concentrations of enzymes and their substrates“. <a href="http://www.sciencedirect.com/science/article/pii/S0022519305802668">Journal of Theoretical Biology</a> 143, no. 2 (1990): 163–95.
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-Oria-Hernández, Jesús, Nallely Cabrera, Ruy Pérez-Montfort, und Leticia Ramírez-Silva. „Pyruvate Kinase Revisited: The Activating Effect of K+“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/16147999">The Journal of Biological Chemistry</a> 280, Nr. 45 (11. November 2005): 37924–29. doi:10.1074/jbc.M508490200.
+Oria-Hernández, Jesús, Nallely Cabrera, Ruy Pérez-Montfort, und Leticia Ramírez-Silva. „Pyruvate Kinase Revisited: The Activating Effect of K+“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/16147999">The Journal of Biological Chemistry</a> 280, no. 45 (2005): 37924–29.
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-Breitling, Rainer, David Gilbert, Monika Heiner, und Richard Orton. „A Structured Approach for the Engineering of Biochemical Network Models, Illustrated for Signalling Pathways“. <a href="http://bib.oxfordjournals.org/content/9/5/404.short">Briefings in Bioinformatics</a> 9, Nr. 5 (9. Januar 2008): 404–21. doi:10.1093/bib/bbn026.
+Breitling, Rainer, David Gilbert, Monika Heiner, und Richard Orton. „A Structured Approach for the Engineering of Biochemical Network Models, Illustrated for Signalling Pathways“. <a href="http://bib.oxfordjournals.org/content/9/5/404.short">Briefings in Bioinformatics</a> 9, no. 5 (2008): 404–21.
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-Chubukov, Victor, Luca Gerosa, Karl Kochanowski, und Uwe Sauer. „Coordination of Microbial Metabolism“. <a href="http://www.nature.com/nrmicro/journal/v12/n5/abs/nrmicro3238.html">Nature Reviews Microbiology</a> 12, Nr. 5 (Mai 2014): 327–40. doi:10.1038/nrmicro3238.
+Chubukov, Victor, Luca Gerosa, Karl Kochanowski, und Uwe Sauer. „Coordination of Microbial Metabolism“. <a href="http://www.nature.com/nrmicro/journal/v12/n5/abs/nrmicro3238.html">Nature Reviews Microbiology</a> 12, no. 5 (Mai 2014): 327–40.
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-Schaber, J., W. Liebermeister, und E. Klipp. „Nested Uncertainties in Biochemical Models“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/19154080">IET Systems Biology</a> 3, Nr. 1 (Januar 2009): 1–9. doi:10.1049/iet-syb:20070042.
+Schaber, J., W. Liebermeister, und E. Klipp. „Nested Uncertainties in Biochemical Models“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/19154080">IET Systems Biology</a> 3, no. 1 (2009): 1–9.
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-Chuang, Han-Yu, Matan Hofree, und Trey Ideker. „A Decade of Systems Biology“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/20604711">Annual Review of Cell and Developmental Biology</a> 26 (2010): 721–44. doi:10.1146/annurev-cellbio-100109-104122.
+Chuang, Han-Yu, Matan Hofree, und Trey Ideker. „A Decade of Systems Biology“. <a href="http://www.ncbi.nlm.nih.gov/pubmed/20604711">Annual Review of Cell and Developmental Biology</a> 26 (2010): 721–44.
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-Kherlopian, Armen R., Ting Song, Qi Duan, Mathew A. Neimark, Ming J. Po, John K. Gohagan, und Andrew F. Laine. „A Review of Imaging Techniques for Systems Biology“. <a href="http://www.biomedcentral.com/1752-0509/2/74">BMC Systems Biology</a> 2, Nr. 1 (12. August 2008): 74. doi:10.1186/1752-0509-2-74.
+Kherlopian, Armen R., Ting Song, Qi Duan, Mathew A. Neimark, Ming J. Po, John K. Gohagan, und Andrew F. Laine. „A Review of Imaging Techniques for Systems Biology“. <a href="http://www.biomedcentral.com/1752-0509/2/74">BMC Systems Biology</a> 2, no. 1 (12. August 2008): 74.
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Team:Bielefeld-CeBiTec/Results/Modelling/erster/test/123