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 the Jarvis-Patrick algorithm. While the core-set models based on the CNN and DBSCAN clustering are well-converged, constructing core-set 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 the metric matrix which appears in the core-set method. We test this approach on a molecular-dynamics simulation of a highly flexible 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.

Common Nearest Neighbor Clustering—A Benchmark

“…The CNN algorithm successfully processes MD data without prior dimensionality reduction of the dataset [4,24]. It also compares favorably to other density-based cluster algorithms for the analysis of MD data [24].…”

“…We refer to the clusters from such a strict partitioning with outliers, which are interpreted as designating peaks in the underlying probability density, as core sets. In [24], the algorithm has been extended to a hierarchical cluster algorithm.…”

“…It also compares favorably to other density-based cluster algorithms for the analysis of MD data [24]. The CNN algorithm has been used to characterize the molecular ensemble as well as to discretize the molecular state space for the construction of a core-set model of MD [24][25][26][27][28][29].…”

“…(The core sets were identified by common nearest neighbor clustering, where the distance metric was the Euclidean distance in the space spanned by the first two principle components. A preprocessing of the MD dataset by principle component analysis is however not strictly necessary [4,24]). (c) Distance distribution of the distance Met260-Gly290 (highlighted in (b) by orange spheres).…”

“…Yet, one would not like to categorize clusters 3 and 4 as noise points because they represent distinct states (Figure 3), which might be relevant to the function of the molecule. The solution is to apply a hierarchical approach [24]. First, the dataset (Figure 6c) is partitioned into clusters 3 and 4 and a large cluster that combines clusters 1 and 2 ( Figure 6d) using a set of clustering parameters, which represents a very low data-point density, that is, either large R or small N. The large cluster is then partitioned into clusters 1 and 2 by clustering with a parameter set that represents a higher data-point density (Figure 6e), decreasing R and/or increasing N. Reclustering clusters 3 and 4 with these "harsher" parameters partitions these clusters into only noise points, which shows that these clusters do not exhibit any local structure.…”