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

The complete metabolic network of our project is visualized in Figure 1. Stoichiometric calculations 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 KivD and AdhA 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 predictions by experimental approaches.

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.

Using 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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