The theory of diffusion-influenced reactions is extended to cases where the reactivity of the species fluctuates in time (e.g., the accessibility of a binding site of a protein is modulated by a gate). The opening and closing of the gate is assumed to be a stationary Markov process [i.e., it is described by the kinetic scheme (open) a⇄b (closed)]. When the reaction is described by suitable boundary conditions, by solving the appropriate reaction-diffusion equations, it is shown that the stochastically gated association rate constant (kSG) is given by k−1SG=k−1∞ + [a−1 b(a+b)κ̂u(a+b)]−1, where κ̂u(s) is the Laplace transform of the time-dependent rate constant of the ungated problem and k∞ is the corresponding steady-state rate constant. The limits when the relaxation time for gate fluctuations is larger or smaller than the characteristic time for diffusion are considered. The relation to previous work is discussed. The theory is applied to three models: (i) a gated sphere, (ii) a gated disk on an infinite plane (e.g., a channel in a membrane), and (iii) a gated localized axially symmetric reactive site on the surface of a spherical macromolecule.
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Szabó et al. (1982) studied this question.