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

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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 kcat and KM 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 kcat KM [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 kcat and KM values for nearly all relevant steps (table 4). They were used for differential equations which describe these additional reactions.



Table4: This table shows all kcat and KM values of enzymes involved in CO2-fixation and the pathway leading to pyruvate.
Enzyme kcat KM [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.


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