A Semi-analytical Approach for Solving Nonlinear Initial-Value Problem in Michaelis–Menten Enzymatic Reaction Model

The current study examines an earlier mathematical description of the Michaelis–Menten enzymatic reaction (MMER) framework. The synthesis of the complex is found to be directly correlated with the substrate concentration and reaction rate. In this case, the Laplace Adomian Decomposition method (LADM) is implemented to calculate the analytical approximation for the substrate concentrations. Unlike many earlier models that primarily relied on numerical simulation or simplified linear assumptions, this study provides explicit analytical expressions for substrate concentrations. The approach effectively manages the inherent nonlinearity of the governing equations, offering tractable expressions for system behavior. Also, it is applicable to handle the nonlinear terms systematically using the Adomian polynomial, namely the concentration of enzyme and substrate, which impact all concentrations. A contrast between the numerical simulation and the approximate analytical approach is given. Also, it is given in tabular form and graphical illustration; it shows a strong correlation. It offers valuable insights for how critical parameters like rate of reactions impact the concentrations. The findings are expected to have direct relevance to industrial and environmental applications, biofuels, and wastewater treatment.