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Rate coefficients, binding probabilities, and related quantities for area reactivity models.

Thorsten Prüstel1, Martin Meier-Schellersheim1

  • 1Laboratory of Systems Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.

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Summary

This study advances the area reactivity model for diffusion-influenced reactions, offering an alternative to classical models. It provides new theoretical insights into receptor-ligand binding dynamics and rate coefficients, validated by simulations.

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Area of Science:

  • Chemical Kinetics
  • Theoretical Chemistry
  • Biophysics

Background:

  • The classical contact reactivity model has limitations in describing diffusion-influenced reactions.
  • An alternative area reactivity model offers a new perspective on receptor-ligand interactions.

Purpose of the Study:

  • To develop the general theory of the area reactivity model for diffusion-influenced reactions.
  • To analyze irreversible and reversible reactions, deriving equations of motion for survival probability.
  • To provide a theoretical framework for comparing experimental data with model predictions.

Main Methods:

  • Generalized Feynman-Kac equation for receptor-ligand pair reactions.
  • Analysis of irreversible and reversible reaction kinetics.
  • Brownian Dynamics simulations for numerical validation.

Main Results:

  • Derived equations of motion for single and many-particle survival probabilities.
  • Identified deficiencies in the classical rate coefficient definition within the area reactivity model.
  • Calculated exact and approximate expressions for the irreversible rate coefficient, showing deviations from classical models.
  • Derived approximate expressions for binding probability and average bound state lifetime.

Conclusions:

  • The area reactivity model provides a robust theoretical framework for diffusion-influenced reactions.
  • The study highlights key differences between area and contact reactivity models.
  • The findings facilitate experimental validation and comparison with theoretical predictions.