A mathematical formalism to quantify drug-target residence time

Area of Science:

• Pharmacology
• Biophysics
• Mathematical Biology

Background:

• Drug-target residence time (RT) is crucial in binding kinetics but lacks a general theoretical quantification.
• Existing mathematical expressions for RT are limited to specific models like binary ligand-receptor binding and induction-fit.
• A need exists for a broadly applicable mathematical formalism for RT.

Purpose of the Study:

• To propose a general mathematical formalism for calculating drug-target residence time (RT).
• To extend the framework to include relaxation time (RXT) for receptor activation dynamics.
• To provide a unified theoretical basis for RT and RXT in diverse pharmacological contexts.

Main Methods:

• Applied the Law of Mass Action to derive ordinary differential equations (ODEs) for chemical processes.
• Constructed a subsystem by selecting relevant chemical species and omitting global formation.
• Defined RT as 1/k_off, where k_off is the smallest-modulus eigenvalue of the subsystem.

Main Results:

• Derived a general mathematical expression for RT applicable to various pharmacological scenarios.
• Validated the formalism by reproducing known RT expressions for binary ligand-receptor binding and induction-fit models.
• Introduced and defined relaxation time (RXT) within the extended RT framework.

Conclusions:

• The proposed mathematical formalism offers a general approach for quantifying RT and RXT.
• This framework provides a unified mathematical basis for understanding binding kinetics and receptor activation.
• The formalism is expected to benefit diverse pharmacological areas, including PK/PD and enzymology.