We study how the kinetics of diffusion-influenced reactions is modified when the reactivity of species fluctuates in time (stochastically gated) with emphasis on the many-particle aspect of the problem. Because of the fact that the dynamics of ligand binding to proteins originally motivated the problem, it is considered in that context. Recently, Zhou and Szabo [J. Phys. Chem. 100, 2597 (1996)] have demonstrated many-particle effects in the problem and found that the kinetics of reaction between a gated protein with a large number of ligands significantly differs from that between a protein and gated ligands. With our approach, the difference between the kinetics of ligand-gated and protein-gated reactions appears formally the same as the difference between the target and trapping problems despite the origin of the corresponding effects and their manifestations are distinctly different. A simple approximate method to treat the many-particle effects is proposed. The theory is applied to a particular two-state gating model. Explicit analytical expressions for the protein survival probability are obtained. We show that (1) for ligand-gated reactions, gating is effectively accounted for by the appropriate reduction of the species reactivity and (2) for protein-gated reactions, the survival probability changes its time behavior from exponential (fast gating) to nonexponential (slow gating). The role of intensity and asymmetry of the gate motion is discussed.