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 exists on the number of simultaneously bound particles, the problem reduces to reversible aggregation. In the competitive limit, where only one particle may be simultaneously bound, it becomes a model for a pseudounimolecular reaction. The general formalism for both binding limits involves 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 viewed as a generalization of the Smoluchowski aggregation theory to the (idealized) reversible case. In the competitive limit, the hierarchy enables straightforward derivations of useful identities, determination of the ultimate equilibrium solution, and justification for approximations. In particular, the utility of a density-expansion, short-time approximation is investigated. The approximation relies on the ability to solve the hierarchy numerically for a small number of particles. This direct-propagation algorithm is described in the numerical section.