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Rigorous derivation of the long-time asymptotics for reversible binding

Gopich1, Agmon

  • 1Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel.

Physical Review Letters
|October 4, 2000
PubMed
Summary

This study mathematically proves how reversible binding in one dimension approaches equilibrium. Diffusional and many-body effects significantly influence this process, unlike in irreversible reactions.

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Area of Science:

  • Chemical kinetics
  • Statistical mechanics
  • Mathematical modeling

Background:

  • Understanding reaction dynamics is crucial in chemical kinetics.
  • Classical chemical kinetics often simplifies reaction pathways.
  • Long-time behavior of binding reactions requires advanced analytical methods.

Purpose of the Study:

  • To provide a rigorous mathematical proof for the long-time asymptotics of reversible binding in one dimension.
  • To elucidate the role of diffusional and many-body effects in equilibrium dynamics.
  • To contrast the behavior of reversible binding with irreversible reactions.

Main Methods:

  • Iterative solution in Laplace-Fourier space.
  • Asymptotic analysis.
  • Mathematical derivation.

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Main Results:

  • A rigorous proof for the asymptotic power law governing reversible binding.
  • Identification of a concentration-dependent prefactor.
  • Demonstration of dominant roles for diffusional and many-body effects.

Conclusions:

  • Diffusional and many-body effects are critical in shaping the approach to equilibrium for reversible binding.
  • The long-time asymptotics differ significantly from irreversible reactions and classical models.
  • This work provides a fundamental understanding of one-dimensional binding dynamics.