Efficient sampling in collective coordinate space

Collective motions in biological macromolecules have been shown to be impor tant for function. The most important collective motions occur on slow time scales, which poses a sampling problem in dynamic simulation of biomolecul es. We present a novel method for efficient conformational sampling. The me thod combines the simulation of an ensemble of concurrent trajectories with restraints acting on the ensemble of structures as a whole. Two properties of the ensemble may be restrained: (i) the variance of the ensemble and (i i) the average position of the ensemble. Both properties are defined in a s ubspace of collective coordinate space spanned by an arbitrary number of mo des. We show that weak restraints on the ensemble variance suffice for an i ncrease in sampling efficiency along soft modes by two orders of magnitudes . The resulting trajectories exhibit virtually the same structural quality as trajectories generated by restraint-free-molecular dynamics simulation, as judged by standard structure validation tools. The method is used to pro be the resistance of a structure against conformational changes along colle ctive modes and clearly distinguishes soft from stiff modes. Further applic ations are discussed. (C) 2000 Wiley-Liss, Inc.