Kinetics of Active Surface-Mediated Diffusion in Spherically Symmetric Domains

J.F. Rupprecht , O. Benichou , D.S. Grebenkov , R. Voituriez

Bibtex , URL
Published 01 Jun. 2012
DOI: 10.1007/s10955-012-0496-8
ISSN: 0022-4715


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 B,nichou et al. in (J. Stat. Phys. 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.

This publication is related to:

Stochastic dynamics of reactive and living systems