THEORY AND SIMULATION OF THE TIME-DEPENDENT RATE COEFFICIENTS OF DIFFUSION-INFLUENCED REACTIONS

A general formalism is developed for calculating the time-dependent ra te coefficient k(t) of an irreversible diffusion-influenced reaction. This formalism allows one to treat most factors that affect k(t), incl uding rotational Brownian motion and conformational gating of reactant molecules and orientation constraint for product formation. At long t imes k(t) is shown to have the asymptotic expansion k(infinity)[1 + k( infinity)(pi Dt)(-1/2)/4 pi D + ...] where D is the relative translati onal diffusion constant. An approximate analytical method for calculat ing k(t) is presented. This is based on the approximation that the pro bability density of the reactant pair in the reactive region keeps the equilibrium distribution but with a decreasing amplitude. The rate co efficient then is determined by the Green function in the absence of c hemical reaction, Within the framework of this approximation, two gene ral relations are obtained. The first relation allows the rate coeffic ient for an arbitrary amplitude of the reactivity to be found if the r ate coefficient for one amplitude of the reactivity is is known. The s econd relation allows the rate coefficient in the presence of conforma tional gating to be found from that in the absence of conformational g ating. The ratio k(t)/k(0) is shown to be the survival probability of the reactant pair at time t starting from an initial distribution that is localized in the reactive region. This relation forms the basis of the calculation of k(t) through Brownian dynamic's simulations. Two s imulation procedures involving the propagation of nonreactive trajecto ries initiated only from the reactive region are described and illustr ated on a model system. Both analytical and simulation results demonst rate the accuracy of the equilibrium-distribution approximation method .