Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation
Year: 2025
Type: article
Abstract: The application of the standard quasi-steady-state approximation to the Michaelis-Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific biochemical conditions that dictate the validity of the standard quasi-steady-state approximation remains a challenging endeavor. Emerging research suggests that the accuracy of the standard quasi-steady-state approximation improves as the ratio of the initial enzyme concentration, $$e_0$$ e 0 , to the Michaelis constant, $$K_M$$ K M , decreases. In this work, we examine this ratio and its implications for the accuracy and validity of the standard quasi-steady-state approximation as compared to other quasi-steady-state reductions in its proximity. Using standard tools from the analysis of ordinary differential equations, we show that while $$e_0/K_M$$ e 0 / K M provides an indication of the standard quasi-steady-state approximation’s asymptotic accuracy, the standard quasi-steady-state approximation’s predominance relies on a small ratio of $$e_0$$ e 0 to the Van Slyke-Cullen constant, K. Here, we define the predominance of a quasi-steady-state reduction when it offers the highest approximation accuracy among other well-known reductions with overlapping validity conditions. We conclude that the magnitude of $$e_0/K$$ e 0 / K offers the most accurate measure of the validity of the standard quasi-steady-state approximation.
Source: Bulletin of Mathematical Biology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: University of Notre Dame
OpenAlex ID: W4410430387