A mathematical formalism to quantify drug-target residence time
1Laboratory of Molecular Neuropharmacology and Bioinformatics, Unitat de Bioestadística and Institut de Neurociències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain; Instituto de Salud Carlos III, Centro de Investigación Biomédica en Red de Salud Mental, CIBERSAM, Spain; Unitat de Neurociència Traslacional, Parc Taulí Hospital Universitari, Institut d'Investigació i Innovació Parc Taulí (I3PT), Institut de Neurociències, Universitat Autònoma de Barcelona, Spain.
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View abstract on PubMed
This study introduces a general mathematical framework for quantifying drug-target residence time (RT) and relaxation time (RXT). The novel formalism provides a unified approach applicable to diverse pharmacological systems, including binding kinetics and enzymology.
Area of Science:
- Pharmacology
- Biophysics
- Mathematical Biology
Background:
- Drug-target residence time (RT) is crucial in binding kinetics, yet theoretical quantification remains limited.
- Existing mathematical models for RT are often restricted to simple pharmacological scenarios like binary ligand-receptor interactions or induction-fit models.
Purpose of the Study:
- To propose a general mathematical formalism for calculating drug-target residence time (RT).
- To extend the RT framework by introducing relaxation time (RXT) for receptor activation dynamics.
Main Methods:
- Applying the Law of Mass Action to derive ordinary differential equations (ODEs) for chemical processes.
- Constructing a subsystem by selecting relevant chemical species and omitting global formation processes.
- Defining RT as 1/k_off, where k_off is the smallest-modulus eigenvalue of the subsystem.
Main Results:
- The proposed formalism successfully derives RT expressions for various pharmacological cases.
- Theoretical RT expressions for binary ligand-receptor binding and induction-fit models align with existing literature.
- A novel concept of relaxation time (RXT) is introduced, relating to receptor activation.
Conclusions:
- The developed formalism offers a broadly applicable mathematical framework for RT and RXT.
- This approach provides a unified method for analyzing residence and relaxation times in pharmacological systems.
- The formalism is expected to benefit areas like binding kinetics, pharmacokinetics/pharmacodynamics (PK/PD), and enzymology.