Team:SDU-Denmark/Tour32

Modelling

Revealing the bits behind the simulation

An introduction
The projects aims to optimize the conditions present in our cells to maximize the production of rubber. Two pathways aid the conversion of glucose to the substrates of the prenyltransferase: the glycolysis and the MEP pathway. The glycolysis is heavily regulated and changes to this pathway will be diminished and overridden by the cell. However, overexpressing rate-limiting steps in the MEP pathway should allow for a faster conversion of substrates; thereby pulling the pyruvate out of the glycolysis and speeding up the overall rate of conversion.

The obvious questions that follow upon such a deduction are: Which steps in the MEP pathway are rate limiting? And what will happen to overall production economy if we speed up the pathway?

The answers to these questions indicate which steps in the MEP pathway would be most effective to manipulate.

The model
The model consists of four different velocity terms, depending on the reaction. The four terms are:

• Ordinary uni-uni reaction
• Ordinary bi-bi reaction
• Reversible bi-bi reaction
• Substrate inhibitory bi-bi reaction

All of the terms are given by their respective Michaelis-Menten velocity term.
Change in the concentration is given by the the ingoing terms subtracted the outgoing terms:

This allows a system of equations to be build with one differential equation for each step in the pathway.

The solution to the system is found using K_cat and K_m, which are constants related directly to a given enzyme and to substrate and product concentrations, respectively. Both can be established experimentally, and we found them in the literature. From these equations and constants, the maximum speed of each enzyme relative to the substrate(s) concentration, can then be determined.

Results
We're interested in the largest slope (velocity) of the curve, here we see that the increase in slope stops after a certain increase in the starting velocity. A rate limiting step! Rate limiting steps: Articles have shown the reaction catalysed by dxs to be the rate limiting step, and we asked the question: If we were to manipulate this step, which step would then be rate limiting? Simulating reaction kinetics often leads to stiff systems, and this is no exception. Traditional methods of solving differential equations therefore did not suffice, and MATLAB’s ODE15s, which is an L-stable solver, was used.

Simulations showed that the next rate limiting step would occur after an improvement in rate of conversion of 12 percent, and that this new rate limiting step was the reaction catalysed by IspG, as seen below. This result is worth keeping in mind when deciding on the design of the plasmids. Namely, if there was time to spare, then cloning IspG into the system might have further enhanced its functionality.

Repeating the simulation with the increased velocities (i.e. post-modifying of Dxs and IspG), it is seen that IspF catalysed the third rate limiting step. IspF would thus be an enzyme of interest, if the system was to be further improved.

Economy:
Here we see how much dxs reacts to B1 vitamin. As it's reversible, it stops producing B1 vitamin faster, than the cell can use it, which is indicated by the horizontal line. But still what we throw exponentially more and more out as a function of the speed of the pathway. The second question posed concerned the economy of the system. That is, does the increase in velocity through the pathway result in increased product, or does the substrates exit the pathway at an unintended point. Based on the literature, intermediates after the reaction catalysed by IspD pass directly through the pathway, while there exists a reversible exit to vitamin B1 from DXP.

It has been implicitly established that the increase in velocity through the pathway does not exclusively represent an increased exit to vitamin B1. Otherwise, there would be no increase in product, at all. So, the question is (in plain English) how much, exactly, can we increase the speed of the pathway before it starts leaking - before the amount diverted to the exit surpasses the increase in amount of product. This can be seen on the plot below.

It is noticeable that the increase in speed leads to an increase in the B1 vitamin producing term. At increases up to 100 percent, the exit term is unproblematic, while it seems at increases above 200% that the reaction would become uneconomical, as growth of this term is exponential. However, this is not of concern, as such increases in speed through the pathway are far higher than what we hope to achieve.

In conclusion, the simulations showed the rate limiting steps to be the reactions catalysed by Dxs, IspG, and IspF. Furthermore, the outflow of the pathway was shown to have little effect at increases in velocity up to 100 percent, while additional increases in velocity would be less effective.