Extended diffusion theory: Recovering dynamics from biased/accelerated molecular simulations

Dynamical properties are of great importance in determining the behavior of syn-thetic and natural molecules, but capturing them by computational methods is a non-trivial task. Very often the time scales of the relevant phenomena are far beyond thetypical time windows accessible by classical Molecular Dynamics (MD) simulations,currently limited to the order of microseconds on standard laboratory workstations.On the other hand, biased and accelerated simulations allow for fast and thoroughexploration of the molecular conformational space, but they lose the dynamic infor-mation. The problem of recovering dynamics from biased/accelerated simulations is avery active field of research, but no totally robust/reliable solutions have been givenyet. In this paper it is shown how the Smoluchowski equation, in the framework ofDiffusion Theory (DT), can be used to bridge this gap, and dynamical properties, inthe form of time correlation functions (TCFs), can be extracted also from such kind ofsimulations. DT is first extended (EDT) to express the mobility tensors entering theSmoluchowski operator in terms of a recently introduced unified and regularizedRotne-Prager-Yamakawa approximation, [P. J. Zuk, E. Wajnryb, K. A. Mizerski,P. Szymczak, J. Fluid. Mech. 2014, 741, R5, 1-13] also involving mixed rotation-trans-lation contributions, and rotation-rotation terms beside the classical translation-translation ones, so far used in DT. Then, the method is applied to recover thedynamics of a nontrivial example of a peptide in explicit water from the first 200 nsof a Replica Exchange Molecular Dynamics simulation, which is a popular computa-tional method that destroys the long time dynamics. EDT dynamics were found tofavorably compare against those coming from a standard MD simulation of the samesystem, requiring a time window of 30 microseconds to converge. This result shows that EDT isa tool of practical value to recover the long time dynamics of systems in diffusiveregimes from biased/accelerated simulations, to be exploited in those cases whendirect evaluation by standard MD is unfeasible.