Overcoming the Heuristic Nature of k-Means Clustering: Identification and Characterization of Binding Modes from...

The accurate and reproducible detection and description of thermodynamic states in computational data is a nontrivial problem, particularly when the number of states is unknown a priori and for large, flexible chemical systems and complexes. To this end, we report a novel clustering protocol that combines high-resolution structural representation, brute-force repeat clustering, and optimization of clustering statistics to reproducibly identify the number of clusters present in a data set (k) for simulated ensembles of butyrylcholinesterase in complex with two previously studied organophosphate inhibitors. Each structure within our simulated ensembles was depicted as a high-dimensionality vector with components defined by specific protein-inhibitor contacts at the chemical group level and the magnitudes of these components defined by their respective extents of pair-wise atomic contact, thus allowing for algorithmic differentiation between varying degrees of interaction. These surface-weighted interaction fingerprints were tabulated for each of over 1 million structures from more than 100 μs of all-atom molecular dynamics simulation per complex and used as the input for repetitive k-means clustering. Minimization of cluster population variance and range afforded accurate and reproducible identification of k, thereby allowing for the characterization of discrete binding modes from molecular simulation data in the form of contact tables that concisely encapsulate the observed intermolecular contact motifs. While the protocol presented herein to determine k and achieve non-heuristic clustering is demonstrated on data from massive atomistic simulation, our approach is generalizable to other data types and clustering algorithms, and is tractable with limited computational resources.