Grebenkov Denis S, Kumar Aanjaneya
Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, IP Paris, 91120 Palaiseau, France.
Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India.
J Chem Phys. 2022 Feb 28;156(8):084107. doi: 10.1063/5.0083849.
Certain biochemical reactions can only be triggered after binding a sufficient number of particles to a specific target region such as an enzyme or a protein sensor. We investigate the distribution of the reaction time, i.e., the first instance when all independently diffusing particles are bound to the target. When each particle binds irreversibly, this is equivalent to the first-passage time of the slowest (last) particle. In turn, reversible binding to the target renders the problem much more challenging and drastically changes the distribution of the reaction time. We derive the exact solution of this problem and investigate the short-time and long-time asymptotic behaviors of the reaction time probability density. We also analyze how the mean reaction time depends on the unbinding rate and the number of particles. Our exact and asymptotic solutions are compared to Monte Carlo simulations.
某些生化反应只有在将足够数量的粒子结合到特定目标区域（如酶或蛋白质传感器）后才能触发。我们研究反应时间的分布，即所有独立扩散的粒子首次全部结合到目标上的时刻。当每个粒子不可逆地结合时，这等同于最慢（最后）一个粒子的首次通过时间。反过来，与目标的可逆结合使问题变得更具挑战性，并极大地改变了反应时间的分布。我们推导出了这个问题的精确解，并研究了反应时间概率密度的短时和长时渐近行为。我们还分析了平均反应时间如何依赖于解离速率和粒子数量。我们将精确解和渐近解与蒙特卡罗模拟进行了比较。
