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Implicit Analytic Solution of Michaelis-Menten-Monod Kinetics.

ABSTRACT: An analytic solution to enzyme kinetics expressed by the Michaelis-Menten-Monod mathematical framework is presented. The analytic solution describes the implicit problem with the independent variable, normally time, substituted with the concentration of the reaction product. The analytic solution provides the substrate, enzyme, and microbial biomass concentration instantaneously and over all time domains without the use of numerical integration schemes or iterative solvers required to overcome transcendental functions. Experiments of NO₂ ^- nitrification by Candidatus Nitrospira defluvii at temperatures ranging between 10 and 32 °C were used for validation tests with the numerical solution by finite differences and the implicit analytic solution presented here. Results showed that both finite differences and analytic solutions matched the experiments particularly well, with a correlation coefficient greater than 0.99 and residuals smaller than 2.75%.

SUBMITTER: Maggi F

PROVIDER: S-EPMC6640786 | biostudies-literature | 2016 Nov

REPOSITORIES: biostudies-literature

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Implicit Analytic Solution of Michaelis-Menten-Monod Kinetics.

Maggi Federico F la Cecilia Daniele D

ACS omega 20161111 5

An analytic solution to enzyme kinetics expressed by the Michaelis-Menten-Monod mathematical framework is presented. The analytic solution describes the implicit problem with the independent variable, normally time, substituted with the concentration of the reaction product. The analytic solution provides the substrate, enzyme, and microbial biomass concentration instantaneously and over all time domains without the use of numerical integration schemes or iterative solvers required to overcome t ...[more]

PMID: 31457171

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