The conformational ensemble of a biomolecule dictates its thermodynamic properties. Molecular dynamics (MD) simulations are used to explore the configurational space of biomolecules, but the extent of data produced necessitates data post-processing to reduce the effective size while retaining pertinent information. Structural clustering of MD trajectory data is a clear solution, however, there is currently no generally accepted protocol for an arbitrary biomolecular system. The most prevalent approach includes three steps: 1. feature selection, 2. unsupervised dimensionality reduction, 3. cluster in reduced space.  Internal coordinates are the dominant feature choice, although they often over-determine the structure and, in some cases, cannot capture structural distinctions. As an alternative approach, we adapt a Gaussian mixture model (GMM) clustering scheme to be applied directly to particle positions. This procedure involves a robust, iterative alignment protocol to remove translational and rotational degrees of freedom and expectation-maximization of the weight, mean and covariance for each cluster. We explore two approximations to the covariance of each cluster: a uniform, independent, spherically symmetric variance and a coupled, spherically symmetric covariance. Toy elastic network models demonstrate GMM on positions correctly differentiates left and right helical structures whereas pairwise distances fail. Application of coupled-variance GMM to extensive MD simulations provided by Shaw and co-workers of the fast-folding NLE-NLE variant villin headpiece (HP35) captures subtle structural fluctuations within highly variable regions during the folding process. This approach can be directly implemented on trajectory data to determine cluster identity and size, even in disordered motion, which enables rigorous evaluation of the conformational ensemble and evaluation of relevant macroscopic attributes.

Structural clustering of biomolecules: Gaussian mixture models applied to particle positions

ACS Spring 2022

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