Variance of Atomic Coordinates as a Dynamical Metric to Distinguish Proteins and Protein-Protein Interactions in Molecular Dynamics Simulations.

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.