Work on long-timestep integration of biomolecular dynamics is presented, emphasizing the limitations, as well as the success, of various approaches. These approaches include implicit discretization, separation into harmonic and anharmonic motion, and force splitting; some of these techniques are combined with stochastic dynamics. In particular a Langevin/force-splitting approach for biomolecular simulations termed LN (for its origin in a Langevin/normal-modes scheme) is described, suitable for general thermodynamic and sampling questions. LN combines force linearization, stochastic dynamics, and force splitting via extrapolation so that the timestep for updating the slow forces can be increased significantly beyond half the period of the fast motions (i.e., 5 fs). This combination of strategies alleviates the severe stability restriction due to resonance artifacts that apply to symplectic force-splitting methods. The combination of extrapolation and stochastic dynamics in particular, makes possible greater overall speedups (e.g., an order-of-magnitude improvement in computational time over small-timestep reference trajectories) without loss of accuracy. Extensions to sampling problems are natural by this approach.

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