In the simulation of protein folding and binding, it is convenient to represent a protein in a body-fixed reference system where global translation and rotation dynamics are opportunely eliminated. The transition from a lab frame to the protein’s body-fixed frame kinematically isolates the protein’s internal fluctuations. However, it also reveals dynamical couplings between those fluctuations and global diffusion. We present a Langevin equation of motion in the body-fixed frame which explicitly quantifies the instantaneous coupling, via inertial and viscous forces, between the molecule’s global diffusion and its internal conformational fluctuations. Couplings due to inertial effects are expected to have little relevance at low Reynolds numbers. Couplings due to viscous forces, however, cannot be dismissed in principle and require careful examination. We hypothesize that these coupling terms could facilitate slow fluctuations necessary for the protein’s function. Our formalism helps to quantify the extent of the global-internal couplings directly from a Molecular Dynamics simulation trajectory, thus identifying the conditions in which each coupling term actively participates in the dynamics. We demonstrate the approach by studying the coupling contributions of some model systems.

Quantifying viscous coupling between global diffusion and conformational dynamics from simulated protein trajectories

ACS Spring 2022

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