Visualizing correlated motion with HDBSCAN clustering

Correlated motion analysis provides a method for understanding communication between and dynamic similarities of biopolymer residues and domains. The typical equal-time correlation matricesfrequently visualized with pseudo-colorings or heat mapsquickly convey large regions of highly correlated motion but hide more subtle similarities of motion. Here we propose a complementary method for visualizing correlations within proteins (or general biopolymers) that quickly conveys intuition about which residues have a similar dynamic behavior. For grouping residues, we use the recently developed non-parametric clustering algorithm HDBSCAN. Although the method we propose here can be used to group residues using correlation as a similarity matrixthe most straightforward and intuitive methodit can also be used to more generally determine groups of residues which have similar dynamic properties. We term these latter groups Dynamic Domains, as they are based not on spatial closeness but rather closeness in the column space of a correlation matrix. We provide examples of this method across three human proteins of varying size and functionthe Nf-Kappa-Beta essential modulator, the clotting promoter Thrombin and the mismatch repair protein (dimer) complex MutS-alpha. Although the examples presented here are from all-atom molecular dynamics simulations, this visualization technique can also be used on correlations matrices built from any ensembles of conformations from experiment or computation.