A mathematical model for the nonlinear enzymatic reaction process is discussed. An approximate analytical expression of concentrations of substrate, enzyme, and free enzyme-product is obtained using homotopy perturbation method (HPM). The main objective is to propose an analytical solution, which does not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to analyze the effect of different parameters. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation. 1. Introduction The importance of biocatalytic processes and reactions for organic synthesis and the pharmaceutical food and cosmetics industry has been constantly growing during the last few years [1, 2]. From a synthetic point of view, enzymes are highly efficient catalysts for an extremely broad palette of reactions [3]. Enzymes of one type, but from different origins, are specialized for substrates, positions in substrates, and products [4]. Enzyme reactions do not follow the law of mass action directly. The rate of the reaction only increases to a certain extent as the concentration of substrate increases. The maximum reaction rate is reached at high substrate concentration due to enzyme saturation. This is in contrast to the law of mass action that states that the reaction rate increases as the concentration of substrate increases [5]. Various simplified analytical models have been developed over the last 20 years. In brief, the analysis involves the construction and solution of reaction/diffusion differential equations, resulting in the development of approximate analytical expressions for [6, 7] nonlinear enzyme catalyzed reaction processes. The simplest model that explains the kinetic behaviour of enzyme reactions is the classic 1913 model of Michaelis and Menten [8] which is widely used in biochemistry for many types of enzymes. The Michaelis-Menten model is based on the assumption that the enzyme binds the substrate to form an intermediate complex which then dissociates to form the final product and release the enzyme in its original form. The schematic representation of this two-step process is given by where , , and are constant parameters associated with the rates of the reaction. Note that it is generally assumed that the second step of the reaction equation (1) is irreversible. In reality, this is not always the case. Typically, reaction rates are measured under the condition that the product is continually removed, which prevents the reverse reaction
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