Team:Imperial College London/Drylab/Enzyme/Simulations

Simulation 1: The Generic Graph

This simulation shows the standard enzyme kinetics graph. Concentrations of product, enzyme, substrate, and enzyme-substrate complex over time are shown. Comparisons between the standard enzyme kinetic graph with and without Michaelis-Menten kinetics are made.

In this simulation, all parameters are arbitrary. K1 = 100000, K2 = 1000 and K3 = 0.1. This makes K_M = 0.01. Furthermore, [E₀] = 0.01 and [S₀] = 0.1. The values of K1, K2 and K3 are proportional to their kinetic values [1], while the values of E₀ and S₀ are chosen to ensure a clear graph.

The above simulation shows that the Enzyme-Substrate complex is at a steady state.

There is a decrease in substrate concentration, accompanied by a rise in product concentration. As all the substrate is used up, there will be no more products formed. There is, however, a time delay before significant product formation starts. This time delay occurs as the enzymatic conversion of substrate to product takes some time.

After this time delay, the concentration of ES complex will gradually drop to 0, while the concentration of enzyme will correspondingly return to initial values.

In our case where the enzyme concentration is much smaller than the Km value, there is not much difference in the rate of formation of product when we compare the graphs obtained with the Michaelis-Menten assumption, and the graphs obtained when not making this assumption. This shows that our assumptions of Michaelis-Menten kinetics is valid.

Keeping the parameters the same as above, we perform a simulation of the first few moments of the enzymatic reaction. We can observe the transition state of the standard reaction that we would have missed otherwise. Here, the enzyme concentration will decrease to zero due to the formation of enzyme-substrate complex, and there is a corresponding decrease in substrate concentration by an equal amount. There is no rise in product concentration within this short initial period, as the enzymatic conversion of substrate to product takes some time.