Pharmacodynamic model of slow reversible binding and its applications in pharmacokinetic/pharmacodynamic modeling: review and tutorial

Abstract

Therapeutic responses of most drugs are initiated by the rate and degree of binding to their receptors or targets. The law of mass action describes the rate of drug-receptor complex association (k_on) and dissociation (k_off) where the ratio k_off/k_on is the equilibrium dissociation constant (K_d). Drugs with slow reversible binding (SRB) often demonstrate delayed onset and prolonged pharmacodynamic effects. This report reviews evidence for drugs with SRB features, describes previous pharmacokinetic/pharmacodynamic (PK/PD) modeling efforts of several such drugs, provides a tutorial on the mathematics and properties of SRB models, demonstrates applications of SRB models to additional compounds, and compares PK/PD fittings of SRB with other mechanistic models. We identified and summarized 52 drugs with in vitro-confirmed SRB from a PubMed literature search. Simulations with a SRB model and observed PK/PD profiles showed delayed and prolonged responses and that increasing doses/k_on or decreasing k_off led to greater expected maximum effects and a longer duration of effects. Recession slopes for return of responses to baseline after single doses were nearly linear with an inflection point that approaches a limiting value at larger doses. The SRB model newly captured literature data for the antihypertensive effects of candesartan and antiallergic effects of noberastine. Their PD profiles could also be fitted with indirect response and biophase models with minimal differences. The applicability of SRB models is probably commonplace, but underappreciated, owing to the need for in vitro confirmation of binding kinetics and the similarity of PK/PD profiles to models with other mechanistic determinants.

Keywords: Biophase models; Indirect response models; Mathematical modeling; Pharmacodynamics; Receptor binding kinetics; Slow reversible binding.