Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and Sammon mapping

A direct conformational clustering and mapping approach for peptide conformations based on backbone dihedral angles has been developed and applied to compare conformational sampling of Met-enkephalin using two molecular dynamics (MD) methods. Efficient clustering in dihedrals has been achieved by evaluating all combinations resulting from independent clustering of each dihedral angle distribution, thus resolving all conformational substates. In contrast, Cartesian clustering was unable to accurately distinguish between all substates. Projection of clusters on dihedral principal component (PCA) subspaces did not result in efficient separation of highly populated clusters. However, representation in a nonlinear metric by Sammon mapping was able to separate well the 48 highest populated clusters in just two dimensions. In addition, this approach also allowed us to visualize the transition frequencies between clusters efficiently. Significantly, higher transition frequencies between more distinct conformational substates were found for a recently developed biasing-potential replica exchange MD simulation method allowing faster sampling of possible substates compared to conventional MD simulations. Although the number of theoretically possible clusters grows exponentially with peptide length, in practice, the number of clusters is only limited by the sampling size (typically much smaller), and therefore the method is well suited also for large systems. The approach could be useful to rapidly and accurately evaluate conformational sampling during MD simulations, to compare different sampling strategies and eventually to detect kinetic bottlenecks in folding pathways.