Explicit Solutions for Real-time Reversible Inhibition Kinetics using Lambert W Function: Towards Progress Curve Analysis

Authors

  • Geradius Deogratias Chemistry Department, College of Natural and Applied Sciences, University of Dar es Salaam, P.O. Box 35061, Dar es Salaam, Tanzania
  • Makungu Madirisha Chemistry Department, College of Natural and Applied Sciences, University of Dar es Salaam, P.O. Box 35061, Dar es Salaam, Tanzania
  • Fortunatus Jacob Chemistry Department, College of Natural and Applied Sciences, University of Dar es Salaam, P.O. Box 35061, Dar es Salaam, Tanzania

DOI:

https://doi.org/10.4314/tjs.v48i4.15

Abstract

Accurate estimation of kinetic parameters is challenging due to the dynamics and mathematical nature of the chemical systems. This paper presents simple, yet efficient closed-form solutions for the enzymatic conversion of the substrate to the product in real-time derived using the Lambert  W  function. The real values of the Lambert  W  function were calculated from the Lambert package as implemented in MATLAB. The expressions exhibit remarkable robustness in estimating the parameters for randomized data at 1% to 4% variation in noise levels. Furthermore, unlike the initial rates method, the expressions estimate chemical kinetic parameters utilizing a full range of experimental data, thus minimizing the risk of missing information that would be detected at an extended time-span. Thus, the implementation of closed-form solutions presented in this paper for the estimation of kinetic parameters eliminates common pitfalls imposed by the initial rates and double reciprocal methods.

Keywords:  Enzyme, Lambert  W  function, Reversible inhibition, Closed-form solutions

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Published

2022-12-31

Issue

Vol. 48 No. 4 (2022)

Section

Articles