Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions.
We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology.
Laboratory of Systems Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA. prustelt@niaid.nih.gov
Thorsten
T
Prüstel
Martin
M
Meier-Schellersheim
D002462:Cell Membrane / Q000737:chemistry*; D004058:Diffusion; D008962:Models, Theoretical; D011336:Probability