Curvilinear all-atom multiscale (CAM) theory of macromolecular dynamics

A method is introduced for simulating long timescale macromolecular structural fluctuations and transitions with atomic-scale detail. The N-atom Liouville equation for the macromolecule/host medium system provides the starting point for the analysis. Order parameters characterizing overall macromolecular architecture are demonstrated to be slowly evolving. For single-stranded macromolecules, a curvilinear coordinate provides a way to introduce the order parameters. Using a multiscale approach, Fokker-Planck equations are derived. A nanocanonical method for constructing the lowest order solution to the Liouville equation and the equivalence of long-time and ensemble averages avoid the tedious bookkeeping needed to preserve the number of degrees of freedom (required in earlier methods). The method overcomes the large energy barriers that plague other approaches for estimating rates of transition between macromolecular conformations. A reduced dynamics is derived for the friction dominated limit. New experimental methods for observing macromolecular dynamics and medical sciences applications are discussed.