Theoretical Analysis of Pre-Steady State Behaviour of Non-Linear Double Intermediate Enzymatic Reaction (Contemporary Mathematics, 2024)
This paper explores the mathematical modelling of a non-linear double intermediate enzymatic reaction, focusing on its pre-steady state behaviour. Using homotopy perturbation and Taylor's series methods, an approximate analytical solution is derived for the concentrations of substrate, the first enzyme-substrate complex, and the second enzyme-substrate complex. The model is applicable in scenarios where the initial substrate concentration dramatically exceeds that of the enzyme and when they are comparable. Comparisons between analytical and numerical solutions are made, highlighting the efficacy of the proposed model. Additionally, an improved understanding is achieved by comparing results obtained from Matlab simulations with analytical solutions. Moreover, sensitivity analysis on parameters affecting the concentrations is conducted. This mathematical model enhances comprehension of biochemical reactions in living organisms.
Keywords: homotopy perturbation method, Taylor's series method, pre-steady state, double intermediate, non-linear equations