Ehrlich occupancy time: Beyond koff to a complete residence time framework

Abstract

Drug-target occupancy time--the cumulative duration a target remains bound--critically influences therapeutic efficacy. While Copelands widely-used residence time (1/koff) emphasizes dissociation kinetics, it neglects association rates, rebinding events, and drug elimination that affect in vivo outcomes. Returning to Paul Ehrlichs 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 (kon) and dissociation (koff) 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 b0/(Kd +b0), where Kd is the dissociation constant and b0 the drug concentration. For induced-fit mechanisms, conformational changes reduce the effective dissociation constant to [Formula] (where k3 and k4 are forward and reverse isomerization rates), prolonging occupancy through kinetic trapping. Critically, for drug-receptor systems with firstorder drug elimination at rate k3, we derive rigorous bounds: b0/[(b0 + Kd)k3] [≤] EOT{infty} [≤] b0/(Kd {middle dot} k3), where EOT{infty}:= limT[->]{infty} EOT(T) is the total cumulative occupancy time as T[->] {infty}, 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 Copelands 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.