Competitive reversible binding: A bimolecular boundary condition for the diffusion equation

We simulate one-dimensional competitive reversible binding of many diffusing particles to a single, saturable, static site. The particles are initially randomly distributed, and either one or none is initially bound to the site. The time dependence of the binding probability (site occupancy) is compared with an approximation involving single-particle diffusion with a nonlinear, locally bimolecular, boundary condition representing the mutual site-blocking effect. Our comparison indicates that the approximation is exact in the limit of low site occupancy (infinite particle dilution) and possibly a strict bound otherwise. It also indicates that a reciprocity relation derived earlier for the two initial conditions is exact and that decay to equilibrium is a power law. This contrasts with an exponential decay to equilibrium predicted from a pseudounimolecular kinetic scheme of conventional chemical kinetics, although the equilibrium value of the binding probability agrees with the conventional kinetic/thermodynamic prediction.