Srivastava Kashvi, Eilertsen Justin, Booth Victoria, Schnell Santiago
Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA.
Mathematical Reviews, American Mathematical Society, 416 4th Street, Ann Arbor, MI, 48103, USA.
Bull Math Biol. 2025 May 16;87(6):73. doi: 10.1007/s11538-025-01451-z.
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, , to the Michaelis constant, , 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 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 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 offers the most accurate measure of the validity of the standard quasi-steady-state approximation.
将标准准稳态近似应用于米氏反应机制是生化模型简化的一个典型例子，它是利用奇异摄动理论推导出来的。然而，确定决定标准准稳态近似有效性的具体生化条件仍然是一项具有挑战性的工作。新出现的研究表明，随着初始酶浓度与米氏常数的比值降低，标准准稳态近似的准确性会提高。在这项工作中，我们研究了这个比值，以及与附近其他准稳态简化相比，它对标准准稳态近似的准确性和有效性的影响。使用常微分方程分析中的标准工具，我们表明，虽然 给出了标准准稳态近似的渐近准确性的一个指标，但标准准稳态近似的优势依赖于 与范斯莱克 - 卡伦常数K的比值较小。在这里，当一个准稳态简化在其他具有重叠有效性条件的著名简化中提供最高的近似准确性时，我们定义了它的优势。我们得出结论， 的大小提供了标准准稳态近似有效性的最准确度量。
