Single-particle survival in gated trapping

Any chemical reaction A* + B --> C whose progress is modulated by another reaction of the form A* reversible arrow A is said to be gated. The eating reaction A* reversible arrow A represents a reversible fluctuation from a active state A* to an inactive state A that does not react 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 paper gives a unified, general formalism for calculating trapping rates and mean survival times of gated reactions. It also presents and solves some gating models. Although most of its explicit formulas are for problems with a single particle moving in the presence of a single gated, static trap, the method of solution is formally applicable to problems involving several particles and several point traps, even when the gating kinetics are non-Markovian. Those cases give integral equations that cannot be solved in closed form, however. This paper's results also include the bimolecular rate constant for a gated ligand binding to a gated protein.