Langevin Equations for Macromolecules in Body-Fixed Frames

Molecular Dynamics (MD) simulations using empirical all-atom potentials and explicit solvent molecules result in high-resolution molecular trajectories, but analytical methods are required to decompose the complex results into the essential physiologically relevant motions and their associated timescales. These methods are generally used to analyze trajectories viewed from a body-fixed frame, yet current methods do not make explicit the particular choice of frame, and any coupling between global translation and rotation and internal shape fluctuations is ignored. We present a Langevin equation for systems of interacting particles, based on a previous approach to Langevin mode analysis, in the canonical coordinates of an arbitrary body-fixed frame that accounts for these frame effects and couplings. In addition, the equations of motion allow linearization of the internal dynamics while preserving the three-dimensional structure of the molecule and can be directly simulated once the parameters have been fit to an MD trajectory, serving as a reduced order model of the molecule in an implicit solvent.