Density-based cluster algorithms for the identification of core sets

Abstract

The core-set approach is a discretization method for Markov state models of complex molecular dynamics. Core-sets are disjoint metastable regions in the conformational space, which need to be known prior to the construction of the core-set model. We propose to use density-based cluster algorithms to identify the cores. We compare three different density-based cluster algorithms: the CNN, the DBSCAN and theJarvis-Patrick algorithm. While the core-set models based on the CNN and DBSCAN clustering are well-converged, constructing core-models based on the Jarvis-Patrick clustering cannot be recommended. In a well-converged core-set model, the number of core sets is up to an order of magnitude smaller than the number of states in a conventional Markov state model with comparable approximation error. Moreover, using the density-based clustering one can extend the core-set method to systems which are not strongly metastable. This is important for the practical application of the core-set method because most biologically interesting systems are only marginally metastable. The key point is to perform a hierarchical density-based clustering while monitoring the structure of metric matrix which appears in the core-set method. We test this approach on a molecular-dynamics simulation of a highly exible 14-residue peptide. The resulting core-set models have a high spatial resolution and can distinguish between conformationally similar yet chemically different structures, such as register-shifted hairpin structures.