  Often gaining insight into the functioning of biomolecular systems requires
to follow their dynamics along a microscopic reaction coordinate (RC) on a
macroscopic time scale, which is beyond the reach of current all atom molecular
dynamics (MD) simulations. A practical approach to this inherently multiscale
problem is to model the system as a fictitious overdamped Brownian particle
that diffuses along the RC in the presence of an effective potential of mean
force (PMF) due to the rest of the system. By employing the recently proposed
FR method [I. Kosztin et al., J. of Chem. Phys. 124, 064106 (2006)], which
requires only a small number of fast nonequilibrium MD simulations of the
system in both forward and time reversed directions along the RC, we
reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end
distance, and (2) that guides the motion of potassium ions through the
gramicidin A channel. In both cases the computed PMFs are found to be in good
agreement with previous results obtained by different methods. Our approach
appears to be about one order of magnitude faster than the other PMF
calculation methods and, in addition, it also provides the position dependent
diffusion coefficient along the RC. Thus, the obtained PMF and diffusion
coefficient can be used in a suitable stochastic model to estimate important
characteristics of the studied systems, e.g., the mean folding time of the
stretched deca-alanine and the mean diffusion time of the potassium ion through
gramicidin A.
