Kinetics of active surface-mediated diffusion in spherically symmetric domains

TL;DR

This paper provides an exact analytical framework for calculating the mean first-passage time of molecules diffusing on and off spherical surfaces, revealing how reaction times can be optimized by adjusting desorption rates.

Contribution

It generalizes previous models to include biased diffusion and multiple targets, offering an integral equation approach and validated approximations for surface-mediated reactions.

Findings

Mean first-passage time can be minimized by tuning desorption rate.

Analytical solutions for biased diffusion in spherical domains.

Validated approximation schemes for practical calculations.

Abstract

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.