Cellular scale decision making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems are computationally challenging due to the complex geometry and the applied boundary conditions together with intrinsically long transients that occur before a particle is captured. This paper reports on a particle-based Kinetic Monte Carlo (KMC) method that provides rapid accurate simulation of arrival statistics for (i) a half-space bounded by a surface with a finite collection of absorbing traps and (ii) the domain exterior to a convex cell again with absorbing traps. We validate our method by replicating classical results and in addition, newly developed boundary homogenization theories and matched asymptotic expansions on capture rates. In the case of non-spherical domains, we describe a new shielding effect in which geometry can play a role in sharpening cellular estimates on the directionality of diffusive sources.

翻译：细胞尺度的决策过程受信号分子动力学及其从源点到细胞表面微小吸收位点的扩散轨迹所调控。扩散捕获问题的计算具有挑战性，原因在于复杂的几何结构、施加的边界条件以及粒子被捕获前固有的长时间瞬态过程。本文报道了一种基于粒子的动力学蒙特卡洛方法，该方法能够快速准确地模拟以下两种情形下粒子到达的统计特性：(i) 以带有有限个吸收陷阱的表面为边界的半空间；(ii) 具有吸收陷阱的凸细胞外部区域。我们通过复现经典结果，并结合新发展的边界均匀化理论及关于捕获速率的匹配渐近展开，验证了本方法的有效性。对于非球形区域，我们描述了一种新的屏蔽效应，其中几何结构可在锐化细胞对扩散源方向性的估计中发挥作用。