Group of Data Modeling and Computational Biology, IBENS, Ecole Normale Supérieure-PSL, Paris, France.
J Chem Phys. 2020 Apr 7;152(13):134104. doi: 10.1063/5.0002030.
We study here the extreme statistics of Brownian particles escaping from a cusp funnel: the fastest Brownian particles among n follow an ensemble of optimal trajectories located near the shortest path from the source to the target. For the time of such first arrivers, we derive an asymptotic formula that differs from the mean first passage times obtained for classical narrow escape and dire strait. When particles are initially distributed at a given distance from a cusp, the time of the fastest particles depends on the cusp geometry. Therefore, when many particles diffuse around impermeable obstacles, the geometry plays a role in the time it takes to reach a target. In the context of cellular transduction with signaling molecules, having to escape from such cusp-like domains slows down signaling pathways. Consequently, generating multiple copies of the same molecule enables molecular signals to be delivered through crowded environments in sufficient time.
在 n 个布朗粒子中，最快的粒子遵循位于源到目标最短路径附近的最佳轨迹的集合。对于这些第一批到达者的时间，我们推导出一个渐近公式，它与经典狭窄逃逸和困境中得到的平均首次通过时间不同。当粒子最初分布在与尖峰一定距离处时，最快粒子的时间取决于尖峰的几何形状。因此，当许多粒子在不可渗透的障碍物周围扩散时，几何形状在到达目标所需的时间中起着作用。在具有信号分子的细胞转导的背景下，必须从这样的尖峰状区域逃逸会减缓信号通路。因此，产生相同分子的多个副本可以使分子信号在足够的时间内通过拥挤的环境传递。
