Stoichiometric analysis

Stoichiometric analysis is useful to get information about the maximal output of a system. In this project the number of electrons moving into the system limits the amount of the product which could be synthetized 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 transported into the system by mediators. We calculated the resulting production of intracellular molecules based on our map of the metabolic network (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. 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 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^-1 = 6.2415065 * 10¹⁸ electrons.

Dynamic modeling

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, the major aim of our modeling approach. This information might then be used in the next step to modify constructs e.g. exchange an RBS or a promotor sequence. This could help to balance the different enzyme concentrations in upcoming experiments in the laboratory, it was our goal 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 modeling approach.

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

The modeling work on the isobutanol pathway is based on publications about the isobutanol production pathway (Atsumi et al., 2008 and Atsumi et al., 2010). We started our work on the isobutanol production pathway by collecting the appropriate kinetic parameters. They were used for the development of a system of differential equations. Concerning the choice of the kinetics used, we stuck to Michaelis-Menten kinetics as this was published as the best approach if reaction kinetics are not known (Breitling et al., 2008; Chubukov et al., 2014). Additionally k_cat and K_M values were collected from databases like KEGG, biocyc and BRENDA (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).
We decided to use only the forward reactions from pyruvate to isobutanol for different reasons. First of all, it is necessary to get the maximal product concentration, secondly the reactions are nearly irreversible due to the decarboxylation steps and thirdly there is only few information on the back reactions available.

Figure 3: Examples of differential equations for the dynamic modeling of the isobutanol production.

Figure 4: Predicted changes in metabolic concentration over time.

Figure 5: Predicted changes in metabolic concentration over time. The development in the first minutes is shown by zooming into the Figure 4.

Figure 6: Predicted changes in metabolic concentration in an improved system over time. The concentration of KivD and AdhA was increased by factors 3 and 4, respectively.

Figure 7: Predicted changes in metabolic concentration in an improved system over time. The concentration of KivD and AdhA was increased by factor 3 and 4 respectively. The development in the first minutes is shown by zooming into the Figure 6.

Conclusion

Outlook: addition of carbon dioxide fixing reactions

The next step would be the addition of specific carbon fixing reactions and the pathway leading to pyruvate in the existing dynamic model. Therefore we collected k_cat and K_M values for nearly all relevant steps (Table 4). They can be used to formulate additional differential equations which describe these additional reactions.

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 CC 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.