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Upper-Order TICA and Fractional Non-Markovian Process to Model Anomalous Dynamic Regimes.

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Area of Science:

  • Computational Chemistry
  • Molecular Dynamics
  • Biophysics

Background:

  • Time-lagged independent component analysis (TICA) and Markov state models (MSM) are established for molecular dynamics.
  • Current methods struggle with approximating transfer operator eigenfunctions and incorporating memory effects.
  • Anomalous dynamics, deviating from standard Markovian behavior, are frequently observed in biomolecules.

Purpose of the Study:

  • To develop enhanced TICA-MSM approaches for improved molecular dynamics analysis.
  • To introduce a fractional non-Markovian process to model anomalous relaxation dynamics.
  • To provide a framework for identifying, quantifying, and treating anomalous dynamics in molecular systems.

Main Methods:

  • Developed a criterion for selecting informative intramolecular distances for TICA.
  • Implemented upper-order TICA for nonlinear basis set construction.
  • Introduced a fractional non-Markovian process using noninteger order time derivatives in the master equation.
  • Applied the theory to benchmark molecular dynamics trajectories of chignolin, villin, and Trp-cage proteins.

Main Results:

  • The proposed methods overcome limitations of linear approximations in TICA.
  • The fractional non-Markovian process effectively describes nonexponential relaxations characteristic of anomalous dynamics.
  • Analysis of chignolin and Trp-cage trajectories revealed the necessity of fractional non-Markovian models for accurate dynamics description.
  • The framework allows distinguishing between Markovian and anomalous dynamic regimes.

Conclusions:

  • The enhanced TICA-MSM framework provides a more accurate description of complex molecular dynamics, especially in anomalous regimes.
  • Fractional non-Markovian processes are crucial for quantitatively understanding protein and peptide dynamics.
  • The developed methods offer a powerful tool for molecular simulation and analysis.