Diffusion-controlled mean reaction times in biological systems with elliptical symmetry

Abstract

The mean reaction (encounter or absorption) time is calculated in terms of the system size and reaction probability parameters for three-dimensional systems with diffusion-controlled dynamics and in which there is spherical, prolate spheroidal or oblate spheroidal geometry. Analytical and numerical comparisons are made among the three geometries. For completeness, similar results are derived for a two-dimensional elliptically symmetrical system, and the probability of non-absorption (or reaction) is found for a semi-infinite three-dimensional space with prolate or oblate spheroidal symmetry.