Analytical solution to the simultaneous Michaelis-Menten and second-order kinetics problem-Reference-Cited by-同舟云学术

Analytical solution to the simultaneous Michaelis-Menten and second-order kinetics problem

Published:2023-11-14 Issue: Volume: Page:
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Author:

Paz Alejandro Perez¹

Affiliation:

1. United Arab Emirates University

Abstract

Abstract An analytic solution is presented for the simultaneous substrate elimination problem that combines Michaelis-Menten (MM) consumption with an irreversible second-order kinetics process.The implicit solution involves logarithm and inverse tangent functions and perfectly agrees with the numerical solution of the differential equation. A solution is also presented for the generalized dynamical problem that simultaneously combines MM kinetics with first and second-order processes.Useful exact expressions such as the half-life and the area under the curve are also derived for these problems.

Publisher

Research Square Platform LLC

Reference28 articles.

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3. Chetan T. Goudar and Jagadeesh R. Sonnad and Ronald G. Duggleby (1999) Parameter estimation using a direct solution of the integrated Michaelis-Menten equation. Biochimica et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology 1429(2): 377-383 https://doi.org/https://doi.org/10.1016/S0167-4838(98)00247-7, A novel method of estimating enzyme kinetic parameters is presented using the Lambert ω function coupled with non-linear regression. Explicit expressions for the substrate and product concentrations in the integrated Michaelis-Menten equation were obtained using the ω function which simplified kinetic parameter estimation as root-solving and numerical integration of the Michaelis-Menten equation were avoided. The ω function was highly accurate in describing the substrate and product concentrations in the integrated Michaelis-Menten equation with an accuracy of the order of 10 −16 when double precision arithmetic was used. Progress curve data from five different experimental systems were used to demonstrate the suitability of the ω function for kinetic parameter estimation. In all cases, the kinetic parameters obtained using the ω function were almost identical to those obtained using the conventional root-solving technique. The availability of highly efficient algorithms makes the computation of ω simpler than root-solving or numerical integration. The accuracy and simplicity of the ω function approach make it an attractive alternative for parameter estimation in enzyme kinetics.

4. Chetan T. Goudar and Steve K. Harris and Michael J. McInerney and Joseph M. Suflita (2004) Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function. Journal of Microbiological Methods 59(3): 317-326 https://doi.org/https://doi.org/10.1016/j.mimet.2004.06.013, We present a simple method for estimating kinetic parameters from progress curve analysis of biologically catalyzed reactions that reduce to forms analogous to the Michaelis –Menten equation. Specifically, the Lambert W function is used to obtain explicit, closed-form solutions to differential rate expressions that describe the dynamics of substrate depletion. The explicit nature of the new solutions greatly simplifies nonlinear estimation of the kinetic parameters since numerical techniques such as the Runge –Kutta and Newton –Raphson methods used to solve the differential and integral forms of the kinetic equations, respectively, are replaced with a simple algebraic expression. The applicability of this approach for estimating Vmax and Km in the Michaelis –Menten equation was verified using a combination of simulated and experimental progress curve data. For simulated data, final estimates of Vmax and Km were close to the actual values of 1 μM/h and 1 μM, respectively, while the standard errors for these parameter estimates were proportional to the error level in the simulated data sets. The method was also applied to hydrogen depletion experiments by mixed cultures of bacteria in activated sludge resulting in Vmax and Km estimates of 6.531 μM/h and 2.136 μM, respectively. The algebraic nature of this solution, coupled with its relatively high accuracy, makes it an attractive candidate for kinetic parameter estimation from progress curve data.

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