Addressing Sensitivity and Non-Uniqueness in the Determination of Enzyme Kinetic Parameters

M. Lakner and I. Plazl

Abstract
Accurate determination of enzyme kinetic parameters is critical for model-based design and intensification of biocatalytic processes, particularly in microscale systems. While Michaelis-Menten kinetics provides a foundational framework, its extension to reversible, multi-substrate, and inhibited reactions introduces significant challenges in parameter estimation-most notably, parameter sensitivity and non-uniqueness. This study systematically investigates these challenges across three case studies of increasing complexity: (i) mono-substrate Michaelis-Menten kinetics, (ii) reversible enzymatic reactions with four parameters, and (iii) a six-parameter reversible mono-substrate kinetic model with substrate and product inhibition. In the first two cases, we show that vastly different parameter sets can yield nearly indistinguishable model fits to experimental data, exposing the limitations of classical graphical and nonlinear regression methods. In the mono-substrate case based on real experimental data, two parameter sets differing by nearly two orders of magnitude produce virtually identical model outputs, demonstrating practical non-uniqueness even for simple kinetic models. For the six-parameter inhibited system, a theoretical and numerical analysis reveals intrinsic non-uniqueness of the parameter estimation problem, characterized by an in finite family of parameter vectors yielding identical solutions. These results demonstrate that parameter non-uniqueness is not merely a consequence of experimental noise, but a structural property of complex kinetic models, emphasizing the need for more robust and structurally informed modeling approaches in biocatalysis.

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Keywords
enzyme kinetics, kinetic parameter estimation, parameter non-uniqueness