Single-particle survival in parallel gated trapping

Any chemical reaction A+B→C whose progress is modulated by another reaction of the form A⇄A is said to be gated. The gating reaction A⇄A represents a reversible fluctuation from a reactive state A to an unreactive state A not reacting with B. Reversibly blocked chemical reactions, conformational fluctuations in proteins, and reactions occurring within biomembranes or involving biological molecules have all been studied recently in contexts related to gating. This article calculates certain trapping rates and mean survival times in the presence of a single gated trap. Unlike previous methods, the formalism in this paper is based directly on trapping rates and not on Green's functions. The trapping rate formalism leads quite naturally to explicit solutions for some recently developed ('parallel') gating models, solutions that might be quite difficult to derive within a Green"s-function formalism. These solutions give time-dependent rate coefficients for parallel gated chemical reactions.