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We investigate reversible diffusion-influenced reactions of an isolated pairin two dimensions. To this end, we employ convolution relations that permitderiving the survival probability of the reversible reaction directly in termsof the survival probability of the irreversible reaction. Furthermore, we makeuse of the mean reaction time approximation to write the irreversible survivalprobability in restricted spaces as a single exponential. In this way, weobtain exact and approximative expressions in the time domain for thereversible survival probability for three different two dimensional diffusionspaces: The infinite and restricted plane as well as the surface of a sphere.Our obtained results should prove useful in the context of membrane-boundreversible diffusion-influenced reactions in cell biology.

Reversible diffusion-influenced reactions of an isolated pair on two dimensional surfaces