The Hill-Langmuir Equation Governs Drug-Target Binding Kinetics for Pulsed Drug Delivery

Receptor occupancy is an important indicator of drug efficacy. Pulsed drug delivery is aimed at accurately determining the dosing time on the basis of the onset rhythm.

Seeking analytical expressions to describe steady-state receptor occupancy and providing the essential principles that must be met when designing pulsed drug delivery.

We use a simplified model that integrates pharmacokinetics and binding kinetics to obtain analytical results.

It was found that a Hill-Langmuir equation can integrate pharmacokinetics and pharmacodynamics and describe receptor occupancy under multiple-dose regimens and pulsed drug delivery without rapid equilibrium assumption. In this equation, the effective dissociation constant is the product of the elimination rate constant, the dosing interval, and the dissociation constant. Thus, the regulation of receptor occupancy by these three parameters has a mutual compensatory function. Regardless of the dosing regimen, the association rate constant mainly controls the rising rate and maximum receptor occupancy, whereas the dissociation rate constant determines the decline rate and maximum receptor occupancy and thus controls the stability of the binding kinetics. The regulation of receptor occupancy by the association and dissociation rate constants is consistent with the classical definition of binding affinity. These results may be useful for drug discovery.

When designing pulsed drug delivery, the elimination rate constant must be greater than the dose frequency. The association rate constant produces a fast effect, whereas the dissociation rate constant produces a slow but sustained effect.