Ehrlich occupancy time: beyond [Formula: see text] to a complete residence time framework

Drug-target occupancy time-the cumulative duration a target remains bound-critically influences therapeutic efficacy. While Copeland's widely-used residence time ([Formula: see text]) emphasizes dissociation kinetics, it neglects association rates, rebinding events, and drug elimination that affect in vivo outcomes. Returning to Paul Ehrlich's 1913 principle that drugs act only when bound ("Corpora non agunt nisi fixata"), we develop a mathematically rigorous framework defining Ehrlich occupancy time, EOT, as the integral of fractional target occupancy over time. Our approach explicitly incorporates association ([Formula: see text]) and dissociation ([Formula: see text]) kinetics, accounts for rebinding, and extends to systems with drug removal. For drug-receptor closed systems at equilibrium, we prove that relative EOT equals the equilibrium occupancy fraction; under ligand-excess conditions this reduces to [Formula: see text], where [Formula: see text] is the dissociation constant and [Formula: see text] the drug concentration. For induced-fit mechanisms, conformational changes reduce the effective dissociation constant to [Formula: see text] (where [Formula: see text] and [Formula: see text] are forward and reverse isomerization rates), prolonging occupancy through kinetic trapping. Critically, for drug-receptor systems with first-order drug elimination at rate [Formula: see text], we derive rigorous bounds: [Formula: see text], where [Formula: see text] is the total cumulative occupancy time as [Formula: see text], revealing that both binding affinity and elimination rate jointly determine occupancy. This explains why high-affinity drugs can fail clinically if eliminated rapidly, and identifies pharmacokinetic optimization opportunities. We prove Copeland's definition is a special case of Ehrlich occupancy time when rebinding is absent. Our framework provides quantitative tools for optimizing drug design beyond binding affinity and enables improved prediction of in vivo efficacy where pharmacokinetics dominate.