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Diffusion-controlled reactions with non-Markovian binding/unbinding kinetics.

Denis S Grebenkov1

  • 1Laboratoire de Physique de la Matière Condensée, CNRS - Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France.

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|June 1, 2023
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Summary
This summary is machine-generated.

This study presents a new theory for reversible diffusion-controlled reactions with generalized binding and unbinding kinetics. It reveals how rare binding or unbinding events can significantly impact reaction dynamics.

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Area of Science:

  • Chemical Kinetics
  • Physical Chemistry
  • Theoretical Chemistry

Background:

  • Diffusion-controlled reactions are fundamental in chemical and biological processes.
  • Conventional models often assume simple exponential kinetics for binding and unbinding events.
  • Generalized kinetics introduce non-Markovian behavior, complicating reaction dynamics.

Purpose of the Study:

  • To develop a theoretical framework for reversible diffusion-controlled reactions with generalized binding/unbinding kinetics.
  • To analyze the impact of non-exponential distributions on reaction dynamics.
  • To elucidate the distinctions between different types of reactivity and boundary conditions.

Main Methods:

  • Development of a theory incorporating generalized binding/unbinding kinetics.
  • Application of renewal techniques and encounter-based approaches.
  • Derivation of spectral expansions for propagator, concentration, and diffusive flux.
  • Analysis of long-time behavior and the effects of heavy-tailed distributions.

Main Results:

  • A generalized Collins-Kimball boundary condition is recovered for exponential distributions.
  • Non-exponential distributions lead to non-Markovian binding or unbinding kinetics.
  • Heavy tails in distributions can cause anomalous rarity of binding/unbinding events.
  • Spectral expansions provide insights into particle concentration and diffusive flux.

Conclusions:

  • The developed theory extends the understanding of diffusion-controlled reactions beyond simple exponential kinetics.
  • Generalized kinetics, particularly with heavy-tailed distributions, introduce significant deviations from conventional models.
  • The study clarifies the relationship between time-dependent reactivity, encounter-dependent reactivity, and memory kernel boundary conditions.