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

In this manuscript, we introduce the Cumulative Variance of Coordinate Fluctuations (CVCF) along atomistic MD trajectories, as a dynamical metric to examine protein dynamics and sampling convergence in MD simulations. Using model 1D and 2D PES, we first show that CVCF, which traces over the fluctuations of protein atoms as a function of sampling coordinate (time in MD simulations), captures both local and global equilibria to distinguish the underlying PES of proteins. For both model PES and protein trajectories, we compare the information content present in CVCF traces with that obtained using other measures proposed in literature to reveal conditions under which a consistent interpretation of data can be obtained. Importantly, we show that independent of convergence to either local or global equilibrium, the values and features of protein CVCF can provide a comparative assessment of the ruggedness and curvature of the underlying PES sampled by proteins along MD trajectories. Trends in CVCF therefore enable us to compare features of the PES across multiple protein systems using MD simulations. We demonstrate some of the attractive features of a CVCF based analysis on multi-microsecond (ms) MD trajectories of structurally homologous ubiquitin family proteins which present a particularly striking example in nature wherein sequence changes and complexation which do not lead to prominent structural changes bring about dramatic functional consequences.