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The internal dynamics of macro-molecular systems is characterized by widelyseparated time scales, ranging from fraction of ps to ns. In ordinary moleculardynamics simulations, the elementary time step dt used to integrate theequation of motion needs to be chosen much smaller of the shortest time scale,in order not to cut-off important physical effects. We show that, in systemsobeying the over-damped Langevin Eq., the fast molecular dynamics which occursat time scales smaller than dt can be analytically integrated out and givesraise to a time-dependent correction to the diffusion coefficient, which werigorously compute. The resulting effective Langevin equation describes byconstruction the same long-time dynamics, but has a lower time resolutionpower, hence it can be integrated using larger time steps dt. We illustrate andvalidate this method by studying the diffusion of a point-particle in aone-dimensional toy-model and the denaturation of a protein.

Molecular Dynamics at Low Time Resolution