Mathematical modeling for enzyme inhibitors with slow and fast subsystems

Abstract

Mathematical modeling for biochemical enzyme inhibitor systems plays an important role in the systems of biology. Studying and analyzing the dynamical behavior for such models often need some techniques to obtain the model reduction. The well-known techniques of model reduction are suggested in order to divide the model equations into slow and fast subsystems. They are quasi steady-state approximation and quasi-equilibrium approximation. These techniques are great mathematical tools for simplifying model equations and identifying some analytical approximate solutions. In this work, we define mathematical models of enzyme inhibitors and suggest the model reduction approaches. We study two models as examples for enzyme inhibitors such as competitive inhibition and uncompetitive inhibition. Obtained results show that the suggested approaches are effective tools to minimize the number of elements and to find analytical approximate solutions. Accordingly, the idea of separating slow and fast equations will be applied for a wide range of complex enzyme inhibitor networks.

Keywords

• mathematical modeling
• enzyme reactions
• slow and fast subsystems
• model reductions