Modeling the propane pathway
Introduction
Propane is a commonly used, convenient and clean-burning fuel, currently produced from non-renewable sources. Our project is about producing propane in bacteria, paving way for its sustainable production from renewable biomass. Ultimately, the pathway could be transferred to cyanobacteria, producing propane from CO2 and solar energy.
In our mathematical model our goal is to grasp the important concepts underlying the experiments made in the lab, and to see how those concepts could help us produce more propane. By having a better understanding of the ideas that govern our project, we could see the influence of each compound in the reaction pathway and have a basis to make decisions that would have a long term impact in our results.
Materials and methods: Building the model / our pathway
We built a model of our propane pathway based on Michaelis-Menten enzyme kinetics. It is a basic way to model enzyme reactions that assumes that the change that enzyme causes is faster than the binding of the enzyme and releasing of the substrate.
--picture of pathway somewhere here--
Not all enzyme reactions in our pathway happen the same way, and thus they need to be modeled with various different ways. For more specific information about how each enzyme reaction is modeled and about the constants involved see our page of enzyme kinetics.
Because of time restrictions we couldn't measure how much enzymes there are in our cells. This is why in modeling we had to use estimated values, namely 1e-6 mol/l, for all the enzyme concentrations.
For modeling this propane pathway we used Copasi and Matlab.
Results and implications
Here text about our results in all subcategories:
Car-activation
One of the enzymes in our pathway, Car, needs activation before it can function. To further understand how this affects the function of this enzyme we modeled the reactions governing the activation. To summarize the results: in most scenarios our Car is mostly in its active form so we have assumed that it is all activated in following calculations.
Bottlenecks: Comparing enzyme rates
To know which are the rate limiting steps in our pathway, we compared the rates of the enzyme reactions. This was done by calculating the reaction speeds with different substrate concentrations. The reactions are explained in depth here and the estimated Michaelis-Menten rate equations tell us directly the reaction speeds. We implemented the code to plot these with Matlab, it is available here(<- download link).
FadB2 reaction is reversible in our model but for this we approximated it as irreversible. This yields better results for it than in reality.
The results shown above tell us that FadB2 is a really bad enzyme and quite a large bottleneck in our reaction. This find caused us to change it to Hdb; an enzyme with same function and reportedly better performance.
The plot also shows us that Ado isn't a good one either. To ease Ado-bottleneck, we put the construct containing it to the backbone that had higher copy number.
Car isn’t the best enzyme in our pathway, and unfortunately we couldn’t do anything to make it’s performance better because it was in different construct than Ado. We had ordered our constructs before we knew the bottleneck results and because of time restrictions we had to cope with what we had, but based on the obtained results we can deduce a better ordering of constructs than we now have. To the higher copy number backbone we should put as many of the slowest enzymes as possible.
We could also confirm these results by checking the fluxes through reactions and running parameter scan for different enzymes with Copasi (download link for the file here). After identifying one bottleneck this way we removed that enzyme from our model of the reaction pathway and repeated the calculations.
After getting these results we performed the bottleneck analysis again out of curiosity with relative enzyme amounts. When before we had all the enzyme concentrations to be 1e-6 mol/l, now we scaled them to correspond to the different copy numbers of different backbones. We had put Car-construct into pSB6A1 (ORI: pMB1, copynumber: 15-20) and Ado-construct into pCDFDuet-1 (ORI: CloDF13, copynumber: 20-40). Based on this we approximated that there is about 1.5 times more of those enzymes that are in Ado construct. It is good to remember that we don’t have real information how much there are enzymes in the cell so the actual values might not be right. Despite that this approach gives us a good idea of how one could improve the pathway in the future.
Sensitivity analysis
We performed sensitivity analysis of our model to see the robustness of different parameters in our model. We performed this analysis with the aid of Copasi, which has a ready task for it. Further, we performed this analysis based on both parameters/(constants? is it better said like that?) and initial concentrations.
--pic of parameter results--
These results confirm what we already knew of our pathway: the main bottlenecks. We could improve propane production by finding substitutive enzymes with better kinetic constants and performances.
--pic of concentration results--
The other results show that not very surprisingly the concentration of NADP and NADPH (among the known bottleneck concentrations, this could be said better) affect a lot our propane production. To improve this in future, one could add mechanisms of creating these in the cell in higher amounts.
Time course
From time course analysis we can have some kind of idea how much propane our system is able to produce. We performed this analysis with Copasi. Since we knew from the bottleneck analysis that FadB2 should be changed to Hdb, we considered only the latter in our Copasi file. Also we had different amounts of enzymes based on which backbone they were. For Car we knew from our previous analysis that the reaction reaches equilibrium quite fast and then 90-100% of it was active, so we could just put it’s value as constant, as for all other enzymes too.
With step length of 1 minute and total time 100 min, we got for propane concentration 6.8e-07 mol/l, see the picture below.
--pic here--
It is good to remember that this doesn’t tell us the exact value of propane produced, rather just an idea of the order of magnitude. We don’t know the amount of enzymes in our cell so we had to estimate it. Also, our model has some simplifications that very possibly affect the outcome.
The predicted amount of propane produced isn't very high. To produce propane more efficiently in the future, we would need to greatly improve the performance of our pathway. This could be done by taking a look into bottlenecks of our pathway and other limiting factors such as NADH and NADPH.
Discussion
No perfect model of reactions; irreversibility and other assumptions.
Guesses on enzyme concentrations (no effect on bottlenecs, time course yes).
More accuracy if we could have measured all the constants ourselves.
Not taking into account what happens in the cell outside of our pathway.
