COMPETITIVE AND NONCOMPETITIVE REVERSIBLE BINDING PROCESSES

This work treats many-body aspects in an idealized class of reversible binding problems involving a static binding site with many diffusing point particles. In the noncompetitive limit, where no restriction exi sts on the number of simultaneously bound particles, the problem reduc es to reversible aggregation. In the competitive limit, where only one particle may be simultaneously bound, it becomes a model for a pseudo unimolecular reaction. The general formalism for both binding limits i nvolves the exact microscopic hierarchy of diffusion equations for the N-body density functions. In the noncompetitive limit of independent particles, the hierarchy admits an analytical solution which may be vi ewed as a generalization of the Smoluchowski aggregation theory to the (idealized) reversible case. In the competitive limit, the hierarchy enables straightforward derivation of useful identities, determination of the ultimate equilibrium solution, and justification for several a pproximations. In particular, the utility of a density-expansion, shor t-time approximation is investigated. The approximation relies on the ability to solve the hierarchy numerically for a small number of parti cles. This direct-propagation algorithm is described in the numerical section.