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Adaptive time stepping in biomolecular dynamics.

J Franklin1, S Doniach

  • 1Stanford University, Stanford, California 94305, USA. jfrankli@reed.edu

The Journal of Chemical Physics
|January 6, 2006
PubMed
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This study introduces an adaptive time stepping scheme for molecular dynamics simulations, enabling larger time steps by adjusting integration based on force magnitudes. This method enhances stability and accuracy for simulating slow molecular dynamics, avoiding resonance issues.

Area of Science:

  • Computational Chemistry
  • Molecular Dynamics Simulations
  • Numerical Integration Methods

Background:

  • Traditional molecular dynamics (MD) simulations often face limitations with fixed time steps, especially when integrating the Langevin equation with complex potentials.
  • The presence of strong nonbonded forces and fast bond oscillations necessitates small time steps, compromising the efficient simulation of slow degrees of freedom.
  • Resonance phenomena can occur when time steps are set to half the period of the fastest oscillations, leading to numerical instability.

Purpose of the Study:

  • To present a novel adaptive time stepping scheme for numerically integrating the Langevin equation in molecular dynamics.
  • To demonstrate how this adaptive approach can utilize larger time steps, averaging half the period of the fastest bond oscillations, without sacrificing accuracy for slow dynamics.
  • To provide a mechanism for avoiding the resonance issues traditionally associated with specific time step choices in MD.

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Main Methods:

  • An adaptive time stepping scheme based on the Barth and Schlick extrapolative method (LN) was developed.
  • The scheme employs a slightly more accurate inner integrator to accommodate larger adaptive time steps.
  • The method was tested using simple examples and the bovine pancreatic trypsin inhibitor (BPTI) system, comparing results with short-time integrators and traditional stochastic Verlet methods.

Main Results:

  • The adaptive time step approach successfully reproduces temporal features of the BPTI test system, comparable to short-time integrators.
  • While larger steps cause systematic heating of bonded components, the temporal fluctuations of slow degrees of freedom are accurately captured.
  • Stability is recovered for numerically forced bond oscillations, and performance is compared against fixed-step methods.

Conclusions:

  • The proposed adaptive time stepping scheme offers a viable mechanism to avoid resonance issues in molecular dynamics by dynamically adjusting step sizes.
  • This method theoretically contributes to designing more stable and efficient numerical integration schemes for MD, particularly for systems with significant differences in timescales.
  • The approach is best suited for biomolecular simulations where explicit water is not used and the focus is on slow dynamics, with 'heavy' hydrogen approximations.