KINETIC MODELLING OF BIOCHEMICAL REACTIONS USING MATHСAD ANALYTICAL TOOLKIT
Authors: Chalyy K.O. , Kryvenko I.P. , Andriychuk M.D. 
Published: July 2024

Background.  The study of the kinetics of biochemical reactions provides a better understanding of how biological processes occur in living organisms. Understanding the peculiarities of such reactions is important for the development of new technologies, in particular for the production of biologically active substances and for the synthesis of drugs. A powerful tool for solving problems in biochemical reaction kinetics is mathematical modelling, which can be carried out using computer mathematical systems, in particular the MATHCAD analytical toolkit.
Aim: to substantiate the feasibility and effectiveness of using the MATHCAD analytical toolkit to solve problems of kinetic modelling of biochemical reactions in pharmaceutical research, and to review the capabilities of MATHCAD for computer modelling in pharmacy.
Materials and methods. In the context of studying the rate of enzymatic reactions and developing models, such as the Michaelis-Menten model, to describe reactions in which enzymes catalyze the transformation of substrates, the use of a computer mathematical system (CMS) is considered. CMS is a software package and environment for performing mathematical computations, modelling and visualization. The possibilities of using the MATHCAD system to create mathematical models of biochemical reactions based on kinetic equations are demonstrated. This involves the creation of differential equations describing changes in reagent concentrations over time. These equations were solved using numerical methods in MATHCAD. In addition, the results obtained are visualized using 3D graphics in MATHCAD. The stages of using the MATHCAD analytical toolkit in the kinetic modelling of biochemical reactions have been determined.
Results. The use of MATHCAD in the kinetic modelling of biochemical reactions is effective for the study of: (1) the kinetics of enzymatic reactions, e.g. reactions in which an enzyme catalyzes the conversion of a substrate into a product; (2) biochemical reactions that take place in reaction vessels in which reagents mix and interact; (3) modelling of reactions in reaction vessels based on the solution of differential equations of reaction kinetics; (4) the effect of inhibitors or activators on enzymatic reactions; (5) scenarios of interaction of reagents to determine changes in the kinetics of reactions that occur when different active substances are introduced; (6) kinetics of biochemical reactions in cases where reactions are accompanied by diffusion of reagents through membranes or other semi-permeable barriers; (7) modelling the effect of diffusion processes on the kinetics of biochemical reactions; (8) models describing the kinetics of decomposition of substances, for example the decomposition of biologically active compounds in the body or in the environment; (9) predicting the effect of changes in the conditions of the reaction medium (temperature, pH, concentration of reagents) on the kinetics of biochemical reactions.
It is substantiated that model descriptions of the kinetics of biochemical reactions are important for forming an understanding of the functions of biological systems, including metabolism, enzymatic reactions, and other physiological phenomena. Tools have been used to visualize the modelling results in the form of three-dimensional MATHCAD graphics, which improves the understanding of the reaction mechanism and allows a more thorough analysis of its kinetics.
Conclusion. MATHCAD provides an optimized environment for kinetic modelling of biochemical reactions through its ergonomic interface. Particular advantages are the ability to work with symbolic expressions and to use a wide range of built-in functions and tools for exploring mathematical models and visualizing results. The obtained results may be important both for further scientific pharmaceutical research and for implementation in the training of future Masters of Pharmacy in the discipline of "Computer Modelling in Pharmacy" in higher medical education institutions.