The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

中文翻译：

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分子浓度随时间变化的广义米氏速率定律

一个多世纪以来，米氏 (MM) 速率定律一直是生化速率过程建模的主导范式，应用于生物化学、生物物理学、细胞生物学、系统生物学和化学工程。MM 速率定律及其修正形式基于这样的假设：相互作用分子复合体的浓度在每个时刻接近平衡（准稳态）的速度比分子浓度变化的速度快得多。然而，这种假设并不总是合理的。在这里，我们放宽了这种准稳态要求，并提出了活性浓度随时间变化的分子相互作用的广义 MM 速率定律。我们针对时变分子浓度的方法称为有效时间延迟方案 (ETS)，基于分子复合物形成中严格估计的时间延迟效应。随着蛋白质-蛋白质和蛋白质-DNA 相互作用模型的显着改进，ETS 提供了一个分析框架来解释和预测丰富的瞬态或节律动态（例如自体调节的细胞适应和昼夜节律蛋白质周转），这超出了准稳态假设。