Stochastically gated chemical reactions

This article derives a Smoluchowski theory for the irreversible, diffusion-influenced stochastically gated reaction P*+L* -->empty set (inert) between a protein P* and its ligand L*, with the ligand in excess, [P] much less than [L]. Protein gating P*reversible arrow P (P unreactive) is contrasted with ligand gating L*reversible arrow L (L unreactive). It is shown explicitly, even for non-Markovian gating or a finite number N of ligand molecules (without N-->infinity), that if the reaction and gating kinetics are comparable, ligand-gated reactions always proceed faster than the corresponding protein-gated reactions, The reaction P*+L*-->empty set is mathematically equivalent to the special case n = 0 of P-n*+L*-->Pn+1*+empty set (n = 0, 1, 2,...). The reaction P-n*+L*-->Pn+1*+empty set might, for example, model reactions between an enzymatic protein molecule and its ligands, where the subscript n on P* counts the number of ligands irreversibly processed by the protein. A simple zero-correlation approximation is used to derive and generalize the Zhou-Szabo approximation for protein-gated reactions from P*+L*-->empty set to P-n*+L*-->Pn+1*+empty set. The zero-correlation approximation naturally suggests a variance-reduction technique for simulating gated reactions in a computer.