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This study presents a theory for ligand-macromolecule binding kinetics, considering conformational changes. It reveals non-exponential relaxation to equilibrium, a key finding for understanding molecular interactions.

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Area of Science:

  • Biophysics
  • Chemical Kinetics
  • Theoretical Chemistry

Background:

  • Ligand-macromolecule interactions are fundamental in biological processes.
  • Understanding binding kinetics is crucial for drug discovery and molecular biology.
  • Stochastic conformational fluctuations can significantly impact reaction rates.

Purpose of the Study:

  • To develop a theoretical framework for reversible binding kinetics when molecules fluctuate between conformations.
  • To investigate the impact of stochastic fluctuations on reaction-diffusion processes.
  • To derive non-Markovian rate equations and analyze relaxation dynamics.

Main Methods:

  • Development of a theory based on reaction-diffusion equations for pair distribution deviations.
  • Solving an irreversible geminate (two-particle) problem to obtain memory kernels.
  • Analysis of concentration dynamics and relaxation to equilibrium.

Main Results:

  • A theory for approximate but accurate kinetics of reversible binding is established.
  • Non-Markovian rate equations with memory kernels are derived.
  • Relaxation to equilibrium follows a power law, deviating from exponential decay.
  • In the Markovian limit, the theory simplifies to ordinary rate equations with renormalized constants.

Conclusions:

  • Stochastic conformational changes lead to non-exponential binding kinetics.
  • The developed theory provides a more accurate description of complex binding events.
  • Power-law relaxation is a characteristic feature of these systems, differing from simple models.