Markovian Modeling of Coupled Global and Internal Dynamics in Freely Diffusing Molecules

We present progress on a Langevin formalism for coarse-graining of macromolecules that allows for viscous coupling between global diffusion and internal dynamics as well as an inertial transition between underdamped and overdamped internal motions. Obtaining accurate friction coefficients from observed trajectories is crucial to understanding the significance of both effects, and so the friction must be parameterized in a manner consistent with both types of motion. Meanwhile the intramolecular potential must be consistent with the global symmetry and average properties of the rotational coupling. We use a generalized Einstein Relation for interacting particles with memory to retrieve the long-time Markovian friction from lagged correlations between phase space variables. We discuss numerical instability at long times in systems with free global diffusion and bound internal degrees of freedom, due to saturated internal diffusion, and show a numerically stable route to the friction. We also demonstrate how a harmonic internal potential can be fit to fluctuations in the internal degrees of freedom in a manner consistent with the rotational coupling. We demonstrate accurate reproduction of time correlation functions from a toy simulation of a partially overdamped Markovian trimer. Additionally, our body-fixed formalism allows us to demonstrate that the dynamical features and long-time tail exponents of the internal motion can be modified by coupling with the global diffusion.