Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India.
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
J Chem Phys. 2021 Jan 21;154(3):035101. doi: 10.1063/5.0031368.
The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis-Menten equation. The ubiquity of this relation in diverse chemical and biological contexts has recently been rationalized by a graph-theoretic analysis of deterministic reaction networks. Experiments, however, have revealed that "molecular noise"-intrinsic stochasticity at the molecular scale-leads to significant deviations from classical results and to unexpected effects like "molecular memory," i.e., the breakdown of statistical independence between turnover events. Here, we show, through a new method of analysis, that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes. Networks of single enzymes do not admit such transients. The transient yields, asymptotically, to a steady-state in which memory vanishes and hyperbolicity is recovered. We propose new statistical measures, defined in terms of turnover times, to distinguish between the transient and steady-states and apply these to experimental data from a landmark experiment that first observed molecular memory in a single enzyme with multiple binding sites. Our study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.
催化速率与底物浓度之间的双曲线依赖性是酶动力学中的一个经典结果，由著名的米氏方程定量描述。最近，通过对确定性反应网络的图论分析，这种关系在不同的化学和生物背景下得到了广泛的解释。然而，实验表明，“分子噪声”——分子尺度上的固有随机性——导致与经典结果的显著偏差，并产生了意想不到的效应，如“分子记忆”，即周转率事件之间的统计独立性的破坏。在这里，我们通过一种新的分析方法表明，记忆和非双曲线性有一个共同的来源，即在多个酶的随机反应网络中，存在一个最初的、可观察到的、特有的、短暂的过程。单个酶的网络不存在这种瞬态。该瞬态渐近于一个稳态，在该稳态中，记忆消失，双曲线性得到恢复。我们提出了新的统计度量，用周转率来定义，以区分瞬态和稳态，并将这些应用于首次在具有多个结合位点的单个酶中观察到分子记忆的一个标志性实验的实验数据。我们的研究表明，具有多个酶的分子水平上的催化作用总是包含一个非经典的区域，并提供了对如何达到经典极限的深入了解。
