A Separating Framework for Increasing the Timestep in Molecular Dynamics

Recent work on our LIN framework for molecular dynamics is described. This separating framework solves the Langevin equations of motion in two steps: linearization and correction. The linearized  equations of motion are solved numerically by an iterative technique whose cost is dominated by sparse-Hessian/vector products; the resulting 'harmonic' solution is then corrected by an implicit integration step, which requires minimization of a nonlinear function. Computational efficiency is achieved by sparse matrix techniques, adaptive timestep selection, and fast minimization.  Applications to the model systems of alanine dipeptide and BPTI demonstrate very similar  trajectories with LIN at moderately large timesteps (15 fs for BPTI and up to 30 fs for the dipeptide) in comparison to traditional MD with much smaller timesteps (0.5 fs). This agreement validates the LIN approach at these timesteps. The net computational gain is modest for BPTI (30% reduction in total time) but is expected to increase with system size. Moreover, examination of the range of validity of the harmonic approximation led also to development of a related method termed LN, which includes LIN's linearization, but not correction, step. LN at a timestep of 5 fs also shows very good agreement with traditional molecular dynamics and already for BPTI gives a speedup factor of 4 (2 for the dipeptide). Speedup will only increase with size, and the new LN variant can be readily implemented in general biomolecular dynamics programs. This unexpected windfall in computational performance illustrates the value of developing novel approaches (e.g., based on normal modes) that might initially appear not practical for macromolecules.

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