Volume-Scaled Common Nearest Neighbor Clustering Algorithm with Free-Energy Hierarchy

The combination of Markov state modeling (MSM) and molecular dynamics (MD) simulations has been shown in recent years to be a valuable approach to unravel the slow processes of molecular systems with increasing complexity. While the algorithms for intermediate steps in the MSM workflow like featurization and dimensionality reduction have been specifically adapted for MD data sets, conventional clustering methods are generally applied for the discretization step. This work adds to recent efforts to develop specialized density-based clustering algorithms for the Boltzmann-weighted data from MD simulations. We introduce the volume-scaled common nearest neighbor (vs-CNN) clustering that is an adapted version of the common nearest neighbor (CNN) algorithm. A major advantage of the proposed algorithm is that the introduced density-based criterion directly links to a free-energy notion via Boltzmann inversion. Such a free-energy perspective allows for a straightforward hierarchical scheme to identify conformational clusters at different levels of a generally rugged free-energy landscape of complex molecular systems.