Kinetic Monte Carlo methods for three-dimensional diffusive capture problems in exterior domains

TL;DR

This paper introduces a particle-based Kinetic Monte Carlo method for efficiently simulating diffusive capture in complex three-dimensional exterior domains, validated against classical results and new theories, revealing geometry's role in cellular signaling.

Contribution

The paper presents a novel Kinetic Monte Carlo approach for 3D diffusive capture problems in exterior domains, incorporating boundary homogenization and asymptotic expansions.

Findings

Validated the KMC method against classical results.

Developed boundary homogenization theories.

Discovered a shielding effect influencing cellular source estimates.

Abstract

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.