离散时空中的门控反应
Gated reactions in discrete time and space
摘要：
两个分子反应需要多长时间？如果接触后发生反应，这个问题的答案归结为经典的首次通过时间问题：找出两个分子相遇所需的时间。然而，情况并非总是如此，因为分子在反应和非反应状态之间随机切换。然后，反应被认为是“门控”的内部状态的分子参与，这可能有一个显着的影响动力学。一个统一的，连续时间的方法，门控反应的网络中提出了[物理。127，018301，2021]。在这里，我们建立在最近的进展，并开发一个类似的离散时间版本的理论。类似于连续时间，我们采用更新的方法表明，门控反应时间总是可以表示在相应的非门控的第一次通过和返回时间，从而产生公式的门控反应时间分布的生成函数及其相应的均值和方差。在平均反应时间发散的情况下，我们证明了门控问题的长时间渐近性是从其ungated对应继承的。然而，当分子花费大部分时间不反应时，在终端渐近之前出现较慢的幂律衰减的临时制度。时间的离散化也产生了共振和反共振，这是连续时间图像所不存在的。这些功能说明使用两个案例研究，也表明如何在这里提出的一般方法大大简化了门控反应的分析。
英文摘要：
How much time does it take two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the time it takes the two molecules to meet. However, this is not always the case as molecules switch stochastically between reactive and non-reactive states. The reaction is then said to be "gated" by the internal states of the molecules involved which could have a dramatic influence on kinetics. A unified, continuous-time, approach to gated reactions on networks was presented in [Phys. Rev. Lett. 127, 018301, 2021]. Here, we build on this recent advancement and develop an analogous discrete-time version of the theory. Similar to continuous-time, we employ a renewal approach to show that the gated reaction time can always be expressed in terms of the corresponding ungated first-passage and return times; which yields formulas for the generating function of the gated reaction-time distribution and its corresponding mean and variance. In cases where the mean reaction time diverges, we show that the long-time asymptotics of the gated problem is inherited from its ungated counterpart. However, when molecules spend most of their time non-reactive, an interim regime of slower power-law decay emerges prior to the terminal asymptotics. The discretization of time also gives rise to resonances and anti-resonances, which were absent from the continuous time picture. These features are illustrated using two case studies that also demonstrate how the general approach presented herein greatly simplifies the analysis of gated reactions.
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