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Limiting relaxation times from Markov state models.

Adam Kells1, Alessia Annibale2, Edina Rosta1

  • 1Department of Chemistry, King's College London, SE1 1DB London, United Kingdom.

The Journal of Chemical Physics
|August 24, 2018
PubMed
Summary
This summary is machine-generated.

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This study introduces a method to determine the slowest relaxation time (RT) from molecular simulations, even with limited lagtime data. The approach improves the accuracy of RT calculations, offering a more reliable way to analyze molecular dynamics.

Area of Science:

  • Computational Chemistry
  • Molecular Dynamics
  • Biophysics

Background:

  • Markov state models (MSMs) are crucial for analyzing molecular simulations and extracting timescale information.
  • Determining the slowest relaxation time (RT) often requires convergence across multiple lagtimes, which is not always achievable.
  • Existing methods like hidden Markov models (HMMs) have limitations with biased data and lagtime ambiguity.

Purpose of the Study:

  • To develop a robust method for calculating the slowest relaxation time (RT) in the limit of long lagtimes from molecular simulations.
  • To provide a variational estimate of the optimal RT that improves accuracy.
  • To assess the Markovianity of selected variables for MSM construction.

Main Methods:

  • Utilizing the autocorrelation function of the second eigenvector of the propagator at long lagtimes.

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  • Developing a simple equation relating MSM relaxation time to lagtime with two free parameters.
  • Fitting the derived function to simulation data (analytic, Ala5, ion channel simulations).

    • Main Results:

    • The method accurately describes the behavior of RT as a function of lagtime.
    • The calculated RT improves upon values obtained at the longest accessible lagtime.
    • A secondary parameter indicates the Markovianity of the chosen simulation variable.

    Conclusions:

    • The presented method provides a reliable and variational estimate of the slowest relaxation time (RT).
    • This approach enhances the accuracy of molecular dynamics timescale analysis compared to standard MSMs and HMMs.
    • The method is applicable to biased simulation data, overcoming limitations of HMMs.