CATBOSS: Cluster Analysis of Trajectories Based on Segment Splitting

Abstract

Molecular dynamics (MD) simulations are an exceedingly and increasingly potent tool for molecular behavior prediction and analysis. However, the enormous wealth of data generated by these simulations can be difficult to process and render in a human-readable fashion. Cluster analysis is a commonly used way to partition data into structurally distinct states. We present a method that improves on the state of the art by taking advantage of the temporal information of MD trajectories to enable more accurate clustering at a lower memory cost. To date, cluster analysis of MD simulations has generally treated simulation snapshots as a mere collection of independent data points and attempted to separate them into different clusters based on structural similarity. This new method, cluster analysis of trajectories based on segment splitting (CATBOSS), applies density-peak-based clustering to classify trajectory segments learned by change detection. Applying the method to a synthetic toy model as well as four real-life data sets–trajectories of MD simulations of alanine dipeptide and valine dipeptide as well as two fast-folding proteins–we find CATBOSS to be robust and highly performant, yielding natural-looking cluster boundaries and greatly improving clustering resolution. As the classification of points into segments emphasizes density gaps in the data by grouping them close to the state means, CATBOSS applied to the valine dipeptide system is even able to account for a degree of freedom deliberately omitted from the input data set. We also demonstrate the potential utility of CATBOSS in distinguishing metastable states from transition segments as well as promising application to cases where there is little or no advance knowledge of intrinsic coordinates, making for a highly versatile analysis tool.

Size-and-Shape Space Gaussian Mixture Models for Structural Clustering of Molecular Dynamics Trajectories

“…The six-state weighted shape-GMM trained on backbone atoms captures several structural distinctions between unfolded, intermediate, and native states previously suggested by the backbone dihedral clustering schemes for 6- and 12-state models. ,,, For example, the ramacolor plot for this model in Figure C illustrates that states I and II differ in the conformation of Asp3. The helical conformation of Asp3 has previously been shown to distinguish between the native and intermediate states in the 6- and 12-cluster models. , That weighted shape-GMM predicts the native state to be larger in population than the intermediate state is inconsistent with some previous results but consistent with other recent results . A native-like state that is structurally similar to the native state, but differing mainly in the dynamics due to an unlocked and partially unfolded helix 3, has been identified previously and is in line with state IV from weighted shape-GMM. ,,− Alternatively, state V indicates the opposite trend: the N-terminus and helix 1 are highly fluctuating, and there is more stability from residue 17 leading into helix 3, with a slight increase in positional variance again at the C-terminus.…”

“…The six-state weighted shape-GMM trained on backbone atoms captures several structural distinctions between unfolded, intermediate, and native states previously suggested by the backbone dihedral clustering schemes for 6-and 12state models. 7,9,17,48 For example, the ramacolor plot for this model in Figure 4C illustrates that states I and II differ in the conformation of Asp3. The helical conformation of Asp3 has previously been shown to distinguish between the native and intermediate states in the 6-and 12-cluster models.…”

“…Mutations were sought to enhance the folding rate and ultimately yielded a fast-folding double mutant referred to as Nle/Nle (Nlenorleucine) with a measured folding rate of (0.73 ± 0.05 μs) −1 at 300 K . The ∼305 μs all-atom, explicit solvent, MD simulation of the HP35 Nle/Nle mutant from D. E. Shaw Research has been extensively studied and serves as a benchmark system for structural clustering. ,,,− Here, we use this simulation at 360 K to compare and contrast between uniform and weighted shape-GMM, compare weighted shape-GMM clusterings to previous results, and, finally, propose the structural folding mechanism most consistent with the weighted shape-GMM results.…”

“…A six-state model was chosen due to literature precedence and simplicity of comparison (results from a scan of cluster sizes are discussed in Section ). Backbone atoms (C, CA, and N from residues 2 through 34, C from residue 1, and N from residue 35) are selected for the feature set to remain consistent with previous backbone dihedral value clustering methods. , For each covariance approximation, 20 models with different randomly chosen starting conditions were trained, and the model with the largest log likelihood was used for subsequent analysis.…”

“…The inclusion of even all two-body terms yields a feature space that drastically overdetermines the system and hinders the ability to cluster in this space. The possible solutions to the overdetermination problem include the use of a priori knowledge of the system to develop a hypothesis-driven selection of key internal coordinates, segmentation of the trajectory, combination of both kinetic and structural information, and unsupervised dimensionality reduction techniques. We note that applying dimensionality reduction to internal coordinates is nontrivial as projection errors can misconstrue data .…”