When a diffusing particle escapes from a spherical cavity through a narrow, not too long tunnel, the escape kinetics is essentially single-exponential. The presence of reversible binding sites on the cavity wall leads to retention of the particle in the system and converts the single-exponential kinetics into bi-exponential. We develop a theory that describes these effects. The theory shows how the delay time and the average number of binding events depend on the geometric and kinetic parameters of the system. To study the effect of the cavity shape, we also analyze the kinetics when the particle escapes from a cylindrical cavity with reversible binding sites.
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