Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases , National Institutes of Health , Bethesda , Maryland 20892 , United States.
J Phys Chem B. 2018 Dec 13;122(49):11338-11354. doi: 10.1021/acs.jpcb.8b07250. Epub 2018 Oct 4.
A formalism is developed to describe how diffusion alters the kinetics of coupled reversible association-dissociation reactions in the presence of conformational changes that can modify the reactivity. The major difficulty in constructing a general theory is that, even to the lowest order, diffusion can change the structure of the rate equations of chemical kinetics by introducing new reaction channels (i.e., modifies the kinetic scheme). Therefore, the right formalism must be found that allows the influence of diffusion to be described in a concise and elegant way for networks of arbitrary complexity. Our key result is a set of non-Markovian rate equations involving stoichiometric matrices and net reaction rates (fluxes), in which these rates are coupled by a time-dependent pair association flux matrix, whose elements have a simple physical interpretation. Specifically, each element is the probability density that an isolated pair of reactants irreversibly associates at time t via one reaction channel on the condition that it started out with the dissociation products of another (or the same) channel. In the Markovian limit, the coupling of the chemical rates is described by committors (or splitting/capture probabilities). The committor is the probability that an isolated pair of reactants formed by dissociation at one site will irreversibly associate at another site rather than diffuse apart. We illustrate the use of our formalism by considering three reversible reaction schemes: (1) binding to a single site, (2) binding to two inequivalent sites, and (3) binding to a site whose reactivity fluctuates. In the first example, we recover the results published earlier, while in the second one we show that a new reaction channel appears, which directly connects the two bound states. The third example is particularly interesting because all species become coupled and an exchange-type bimolecular reaction appears. In the Markovian limit, some of the diffusion-modified rate constants that describe new transitions become negative, indicating that memory effects cannot be ignored.
我们提出了一种形式体系来描述扩散如何改变在构象变化存在下的偶联可逆结合-解离反应的动力学，这些构象变化可以改变反应性。构建一般理论的主要困难在于，即使在最低阶，扩散也可以通过引入新的反应通道（即改变动力学方案）来改变化学动力学的速率方程结构。因此，必须找到正确的形式体系，以便以简洁优雅的方式描述具有任意复杂度的网络中扩散的影响。我们的关键结果是一组非马尔可夫速率方程，其中涉及化学计量矩阵和净反应速率（通量），其中这些速率通过时间相关的偶联通量矩阵耦合，其元素具有简单的物理解释。具体而言，每个元素都是在时间 t 下通过一个反应通道不可逆地偶联的一对孤立反应物的概率密度，条件是它从另一个（或相同）通道的解离产物开始。在马尔可夫极限下，化学速率的耦合由配分（或分裂/捕获概率）描述。配分是一对由一个位点解离形成的孤立反应物不可逆地在另一个位点偶联的概率，而不是扩散开。我们通过考虑三个可逆反应方案来说明我们形式体系的用途：（1）结合到单个位点，（2）结合到两个不等价的位点，以及（3）结合到反应性波动的位点。在第一个示例中，我们恢复了先前发表的结果，而在第二个示例中，我们表明出现了一个新的反应通道，该通道直接连接两个结合态。第三个示例特别有趣，因为所有物种都耦合，出现了交换型双分子反应。在马尔可夫极限下，描述新跃迁的一些扩散修正的速率常数变为负值，这表明不能忽略记忆效应。
