Approximate analytic solution of a simple system of kinetic equations describing the enzymatic synthesis of nucleic acids.

Macroscopic kinetic models describing the process of polymerase chain reaction (PCR) are currently solved only by numerical methods, which hampers the development of effective software algorithms for processing the results of the reaction. This paper considers the application of the homotopy perturbation method for obtaining approximate analytical solution of the simplest system of enzymatic kinetic equations describing the synthesis of nucleic acid molecules during PCR. The resulting approximate analytic solution with high accuracy reproduces the results of a numerical solution of the system in a wide range of ratios of enzyme and substrate concentrations both for the case of a large excess of the substrate over the enzyme and vice versa.

Alternative solution of the simplest model of enzymatic synthesis of nucleic acids by homotopy perturbation method.

Development of methods for obtaining approximate analytical solutions of nonlinear differential equations and their systems is a rapidly developing field of mathematical physics. Earlier, an approximate solution of the simplest system of kinetic enzymatic equations for calculating dynamics of complementary strands of nucleic acids was obtained. In this study, we consider an alternative approach to selecting the basic linear approximation of the used method, which makes it possible to obtain more accurate analytical solutions of the set problem.