The unique equilibrium’s global exponential asymptotic stability of the irreversible Michaelis–Menten mechanism of enzyme kinetics

2026/07/27 by Benjamin Wacker

paper · doi:10.1007/s10910-026-01817-1

crossref issued 2026/07/27 · crossref published 2026/07/27 · crossref published-online 2026/07/27 · crossref created 2026/07/27 · crossref deposited 2026/07/31 · crossref indexed 2026/07/31 · crossref published-print 2026/08/01

Abstract

Abstract In this work, we investigate the dynamical system of irreversible Michaelis–Menten kinetics in enzyme kinetics. We first summarize some important theoretical results such as non-negativity, boundedness or conservation laws for solutions of the time-continuous dynamical system. As our main contribution regarding this time-continuous setting, we demonstrate that the unique equilibrium state is globally exponentially asymptotically stable by providing a suitable Lyapunov-function. Based on the implicit Eulerian time-stepping method, we propose an explicit reformulation of this time-discretization for the numerical simulation. Our main result for the time-discrete dynamical system is that the unique equilibrium state of the time-discretization is globally exponentially asymptotically stable as well. Conclusively, we illustrate our theoretical findings by numerical experiments.

Citations

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