Reactive conformations and non-Markovian reaction kinetics of a Rouse polymer searching for a target in confinement
Reactive conformations and non-Markovian reaction kinetics of a Rouse polymer searching for a target in confinement
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寻找限制目标的劳斯聚合物的反应构象和非马尔可夫反应动力学
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发表时间：
2012
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通讯作者：
Raphaël Voituriez
中科院分区：
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作者：
Thomas Guérin;O. Bénichou;Raphaël Voituriez
我们从理论上研究了一个扩散限制反应物之间的连接到一个劳斯聚合物和一个外部固定的反应位点的限制。本工作完成并超越了先前的研究[Gu'erin，B'enichou和Voituriez，Nat.Chem.4，568（2012）]，该研究表明在反应的非常瞬间聚合物构象的分布在反应动力学中起关键作用，并且其确定使得能够在理论中包括非马尔可夫效应。在这里，我们详细描述了这个非马尔可夫理论，并将其与数值随机模拟和马尔可夫方法，其中反应构象近似平衡。我们建立了以下结果。我们的分析揭示了一个强烈的非马尔可夫制度在一维，其中的马尔可夫和非马尔可夫依赖的反应时间的初始距离是不同的。在这种制度下，反应构象是如此不同的平衡构象，反应时间的马尔可夫表达式可以高估了几个数量级的长链。我们还展示了如何推导出定性标度律的反应时间在一个系统的方式，考虑到不同的行为的单体运动在所有的时间和长度尺度。最后，我们还给出了一个分析描述的聚合物的平均伸长的形状在瞬间的反应，并表明其光谱表现为一个慢的幂律为大波数。
We investigate theoretically a diffusion-limited reaction between a reactant attached to a Rouse polymer and an external fixed reactive site in confinement. The present work completes and goes beyond a previous study [Gu'erin, B'enichou, and Voituriez, Nat. Chem. 4, 568 (2012)] that showed that the distribution of the polymer conformations at the very instant of reaction plays a key role in the reaction kinetics and its determination enables the inclusion of non-Markovian effects in the theory. Here we describe in detail this non-Markovian theory and compare it with numerical stochastic simulations and a Markovian approach, in which the reactive conformations are approximated by equilibrium ones. We establish the following results. Our analysis reveals a strongly non-Markovian regime in one dimension, where the Markovian and non-Markovian dependences of the reaction time on the initial distance are different. In this regime, the reactive conformations are so different from equilibrium conformations that the Markovian expressions of the reaction time can be overestimated by several orders of magnitudes for long chains. We also show how to derive qualitative scaling laws for the reaction time in a systematic way that takes into account the different behaviors of monomer motion at all time and length scales. Finally, we also give an analytical description of the average elongated shape of the polymer at the instant of the reaction and show that its spectrum behaves as a slow power law for large wave numbers.