Decomposition of enzyme kinetics system with fast and slow variables in suicide substrate problem

In this paper an example of cooperative phenomenon, in which the substrate is known as suicide substrate, because it binds to the active enzyme as a substrate, inactivates because enzyme turns it into an inhibitor and provides an irreversible reaction is considered. In this case the substrate “commits suicide”. The aim of the work is to apply the method of integral manifolds to the reduction of the system of kinetics of suicide substrate. Work describes in detail the rationale for the decomposition algorithm of the enzyme kinetics problem for dynamical systems with fast and slow variables and the construction of integral manifolds for such systems, this article presents the results of applying the above methods to systems of the suicide substrate kinetics and compares solutions for four equations graphically. Comparisons of solutions for four equations are given graphically, the graphs are created using Microsoft Excel.