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Memory effects and oscillations in single-molecule kinetics.

Marcel O Vlad1, Federico Moran, Friedemann W Schneider

  • 1Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.

Proceedings of the National Academy of Sciences of the United States of America
|September 14, 2002
PubMed
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This study introduces a solvable model for single-molecule kinetics, revealing how molecular dynamics and fluctuating rates can cause damped oscillations in fluorescent signals and lead to non-equilibrium behavior.

Area of Science:

  • Chemical Kinetics
  • Single-Molecule Biophysics
  • Statistical Mechanics

Background:

  • Single-molecule kinetics involves transitions between chemical states.
  • Intramolecular fluctuations affect transition rates, making them time-dependent and stochastic.
  • A separability condition simplifies the analysis of fluctuating rate coefficients.

Purpose of the Study:

  • To develop an exactly solvable model for single-molecule kinetics.
  • To investigate the impact of fluctuating rate coefficients on molecular dynamics.
  • To explore the origins of chemical oscillations and non-equilibrium phenomena in single molecules.

Main Methods:

  • Formulation of a local master equation with time-dependent, fluctuating transition rates.
  • Assumption of a separability condition for rate coefficients based on control parameters and process-dependent factors.

Related Experiment Videos

  • Introduction of an intrinsic time scale for calculating experimental observables like fluorescence correlation functions.

    • Main Results:

    • Fluctuating molecular dynamics can induce damped oscillations in fluorescence correlation functions.
    • A renormalized master equation describes the influence of fluctuations using apparent rate coefficients.
    • Apparent rate coefficients may violate detailed balance, even if real coefficients obey it, leading to oscillatory solutions.

    Conclusions:

    • The model provides a framework for understanding complex dynamics in single-molecule systems.
    • Fluctuations and the separability condition are key to observing oscillatory behavior and deviations from detailed balance.
    • This approach offers insights into non-equilibrium chemical processes at the single-molecule level.