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 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. 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. 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 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 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 (Breitling et al., 2008; Chubukov et al., 2014). Additionally kcat and KM 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 neary irreversible due to the decarboxylation steps and thirdly there is only a few information on the back reactions available.

Figure 3: 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 IlvD and KivD was increased by factors 3 and 4, respectively.

Figure 7: 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.

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 could be used to formulate additional differential equations which describe these additional reactions.

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