On mathematical modeling of biochemical reactions

Enzymes are naturally occurring biological catalysts found in living organisms that accelerate biochemical reactions in cellular metabolism. Cells employ various regulatory mechanisms to maintain physiological levels of metabolites. Enzymatic inhibition, notably non-competitive inhibition, is a significant mechanism in cellular metabolism, playing an important role in the regulation of enzymatic activity. Mathematical modeling is crucial in the field of systems biology as it helps to understand and analyze how biochemical enzyme inhibitors bind to their target molecules. These kinds of dynamic mathematical models provide valuable insights and produce accurate results. However, enzymatic reversible inhibitors, which are competitive, uncompetitive and noncompetitive inhibitions, respectively, have a mathematically complex chemical reaction system. Certain techniques are required to make these models more manageable and to reduce the number of relevant parameters. In this study, competitive and uncompetitive inhibitions are first introduced and then a dynamic model for a noncompetitive inhibition reaction is developed and a model reduction technique called the quasi-steady state approximation is used to analyze the dynamic behavior of the model and understand the reaction mechanism. As a result of this study, the reduced system of equations facilitates the analysis of the substrate and inhibitor effect on product formation in competitive, uncompetitive and noncompetitive inhibitors.