  The internal dynamics of macro-molecular systems is characterized by widely
separated time scales, ranging from fraction of ps to ns. In ordinary molecular
dynamics simulations, the elementary time step dt used to integrate the
equation 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 systems
obeying the over-damped Langevin Eq., the fast molecular dynamics which occurs
at time scales smaller than dt can be analytically integrated out and gives
raise to a time-dependent correction to the diffusion coefficient, which we
rigorously compute. The resulting effective Langevin equation describes by
construction the same long-time dynamics, but has a lower time resolution
power, hence it can be integrated using larger time steps dt. We illustrate and
validate this method by studying the diffusion of a point-particle in a
one-dimensional toy-model and the denaturation of a protein.
