Single-occupancy binding in simple bounded and unbounded systems

The number of substrate molecules that can bind to the active site of an enzyme at one time is constrained. This paper develops boundary conditions that correspond to the constraint of single-occupancy binding. Two simple models of substrate molecules diffusing to a single-occupancy site are considered. In the interval model, a fixed number of substrate molecules diffuse in a bounded domain. In the spherical model, a varying number of molecules diffuse in a domain with boundary conditions that model contact with a reservoir containing a large number of substrate molecules. When the diffusive time scale is much shorter than the time scale for entering the single-occupancy site, the dynamics of binding are accurately described by simple approximations.