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

Geradius Deogratias, Makungu Madirisha, Fortunatus Jacob


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 function. The real values of the Lambert 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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DOI: http://dx.doi.org/10.4314/tjs.v48i4.15


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