论文标题
具有可逆目标结合动力学的多个扩散粒子的首次弥补时间
First-passage times of multiple diffusing particles with reversible target-binding kinetics
论文作者
论文摘要
我们研究了一类扩散控制的反应，该反应是在$ n $颗粒中独立扩散的$ n $颗粒中规定的$ k $ h $ k $同时绑定到目标区域的时间。在不可逆转的目标结合环境中，与目标结合的粒子永远存在于此，反应时间是$ k $ - 到目标的最快第一个快速时间，其分布是众所周知的。反过来，可逆的结合（对于大多数应用来说都是常见的）使理论分析更具挑战性，并大大改变了反应时间的分布。我们开发了一种基于更新的方法来得出反应时间概率密度的近似解决方案。对于广泛的参数，这种近似值非常准确。我们还分析了平均反应时间的依赖性，或等效地，反应率对主要参数，例如$ k $，$ n $以及绑定/解开常数。简要讨论了一些生物物理应用和进一步的观点。
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the irreversible target-binding setting, the particles that bind to the target stay there forever, and the reaction time is the $K$-th fastest first-passage time to the target, whose distribution is well-known. In turn, reversible binding, which is common for most applications, renders theoretical analysis much more challenging and drastically changes the distribution of reaction times. We develop a renewal-based approach to derive an approximate solution for the probability density of the reaction time. This approximation turns out to be remarkably accurate for a broad range of parameters. We also analyze the dependence of the mean reaction time or, equivalently, the inverse reaction rate, on the main parameters such as $K$, $N$, and binding/unbinding constants. Some biophysical applications and further perspectives are briefly discussed.
