The polymerase chain reaction model analyzed by the homotopy perturbation method

• Published in: Journal of mathematical chemistry Vol. 57; no. 4; pp. 971 - 985
• Main Authors: Fedorov, Alexey Alexandrovich, Berdnikov, Alexander S., Kurochkin, Vladimir E.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2019; Springer Nature B.V
• Subjects: Chemical synthesis; Chemistry; Chemistry and Materials Science; Data processing; Deoxyribonucleic acid; DNA; Enzymes; Math. Applications in Chemistry; Mathematical models; Nucleotides; Operators; Organic chemistry; Original Paper; Perturbation methods; Physical Chemistry; Polymerase chain reaction; Qualitative analysis; Quantitative analysis; Substrates; Theoretical and Computational Chemistry; 92C45; 93C15; Polymerase chain reaction model; Approximate analytical solution; Homotopy perturbation method; Enzyme kinetics; 80A30
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-018-00998-8

Polymerase chain reaction (PCR) is an enzyme controlled cyclic synthesis of copies of DNA molecules starting from a given template in the media containing free nucleotides, specific enzyme and some other chemicals. In some cases the standard methods of PCR data processing can lead to a significant error of the DNA template quantification. To develop more advanced data processing methods it is necessary to obtain an analytical expression that would establish the relationship between the reaction parameters. This paper demonstrates how to use the homotopy perturbation method (HPM) to obtain approximate analytical solutions of the proposed PCR model. Although a typical PCR model is rather complex and does not allow the researcher to get some strict analytical solutions, HPM allows producing approximate analytical solutions suitable for subsequent qualitative and quantitative analysis. It is shown that these solutions are in a good agreement with the numerical solutions in a wide range of enzyme and substrate concentrations, in particular, for cases of significant substrate or enzyme excess. The analysis of the results produced by different HPM operators The analysis of the results produced by different HPM operators demonstrates that the basic HPM operator should be chosen as close as possible to the initial equations.