Innovative algorithms have been developed during the past decade for simulating Newtonian physics for macromolecules. A major goal is alleviation of the severe requirement that the integration timestep be small enough to resolve the fastest components of the motion and thus guarantee numerical stability. This timestep problem is challenging if strictly faster methods with the same all-atom resolution at small timesteps are sought. Mathematical techniques that have worked well in other multiple-timescale contexts-where the fast motions are rapidly decaying or largely decoupled from others-have nor been successful for biomolecules, where vibrational coupling is strong.

This review examines general issues that limit the timestep and describes available methods (constrained, reduced-variable, implicit, symplectic, multiple-timestep and normal-mode-based schemes). A section compares results of selected integrators for a model dipeptide, assessing physical and numerical performance. Included is our dual timestep method LN, which relies on an approximate  linearization of the equations of motion every t interval (5 fs or less),  the solution for which is obtained by explicit integration at the inner timestep  (e.g., 0.5 fs). LN is computationally competitive, providing 4-5 speedup factors, and results are in good agreement, in comparison to 0.5 fs trajectories.

These collective algorithmic efforts help fill the gap between the time range that can be simulated and the timespans of major biological interest (milliseconds and longer). Still, only a hierarchy of models and methods, along with experimental improvements will ultimately give theoretical modeling the status of partner with experiment.

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