Theoretical analysis of ligand-binder complex formation: partial equilibrium and incubation time

This report presents a theoretical model of the rate at which complex formation approaches equilibrium in competitive binding systems while ligand concentration varies. Three commonly encountered systems are examined in which binder concentrations (q) are fixed at 0.5/K, 3/K and 50/K, respectively. Our analysis of the incubation time for any particular fraction of reaction completeness shows that longest incubation times occur with the lowest ligand concentrations when q = 0.5/K. However, in systems where q = 3/K and q = 50/K, the longest incubation times correspond not to lowest ligand concentrations but to those approximating the concentration of binder. It is concluded that empirical determination of minimal incubation times for these latter two assay systems should be performed with ligand and binder in approximately equal concentrations.