More sophisticated is not always better: comparison of similarity measures for unsupervised learning of pathways in biomolecular simulations

TL;DR

This work benchmarks four trajectory similarity measures for unsupervised clustering of protein–ligand unbinding pathways from biased MD simulations. Trajectories are encoded as ligand–protein contact-distance matrices, preprocessed with smoothing, normalization, and PCA, then clustered with Leiden CPM and evaluated against ground-truth pathways in streptavidin-biotin and the A2a receptor system. It finds that Wasserstein and Euclidean distances often outperform more complex metrics like Procrustes and DTW, with Wasserstein showing particular strength when paired with PCA and time normalization, and Euclidean distance remaining robust in complex scenarios; the A2a results corroborate that both E and W can yield meaningful, physically plausible pathway separations and comparable dcTMD free-energy profiles. The study provides practical, scalable guidelines for pathway analysis in biased MD, including parameter choices (γ, preprocessing) and when to prefer simpler distance measures, with implications for efficient pathway discovery and free-energy estimation.

Abstract

Finding process pathways in molecular simulations such as the unbinding paths of small molecule ligands from their binding sites at protein targets in a set of trajectories via unsupervised learning approaches requires the definition of a suitable similarity measure between trajectories. We here evaluate the performance of four such measures with varying degree of sophistication, i.e., Euclidean and Wasserstein distances, Procrustes analysis and dynamical time warping, when analyzing trajectory data from two different biased simulation driving protocols in the form of constant velocity constraint targeted MD and steered MD. In a streptavidin-biotin benchmark system with known ground truth clusters, Wasserstein distances yielded the best clustering performance, closely followed by Euclidean distances, both being the most computationally efficient similarity measures. In a more complex A2a receptor-inhibitor system, however, the simplest measure, i.e., Euclidean distances, was sufficient to reveal meaningful and interpretable clusters.

Figures (16)

• Figure 1: A: Rendering of streptavidin-biotin tetramer. Different biotin unbinding pathways are shown as translucent volumes. Streptavidin is represented as a cartoon. B: Block-ordered similarity matrix of constraint ground truth clusters. C: Distributions of pairwise similarities $s_{i,j}$ for the constraint-pulling streptavidin-biotin test sets A, B, and C across different distance measures.
• Figure 2: Clustering results of the streptavidin-biotin constraint (A) and restraint (B) pulling simulations with defined pulling directions. Left: Sankey diagrams for the highest normalized mutual information (NMI) score results for each measure for sets A (top), B (middle), and C (bottom). Small clusters with five or fewer members are grouped under the "?" label. Right: NMI scores for different similarity measures with different data preprocessing. Gaussian filtering is denoted by $\sigma$, time normalization by $n_t$, and PCA by PC$_{1;4}$, indicating that principal components 1 through 4 were used. The symbol in the squares signifies the $\gamma$ values $Q_2$ ($\circ$), $\langle Q\rangle_{2,3}$ ($\bullet$) and $Q_3$ ($\clubsuit$) used for Leiden clustering resulting in a maximal NMI score. The color of the symbols was adjusted for improved visibility dependent on the underlying field color. The highest NMI scores for each similarity measure are marked with a yellow box.
• Figure 3: Clustering results for the A2a adenosine receptor-inhibitor complex using $\gamma=Q_2$ compared to known clusterig results based on the inverse minimal ligand-lipid distance $1/\delta_\text{lig-lip}$ as a reaction coordinate with microscopically feasible unbinding mechanism. A: Visualization of cluster 1 and 2 as volumes based on inverse ligand lipid distances B: pathwise free energies. C: sankey diagram comparing geometrical path separation results with $1/\delta_\text{lig-lip}$ D: block ordered similarity matrix.
• Figure S1: Distribution of the absolute difference between the similarities calculated from the full trajectories ($s$) and the downsampled trajectories ($s_\text{reduced}$) of the different streptavidine biotine test sets.
• Figure S2: Comparison of the influence of preprocessing on the similarity distribution for streptavidin-biotin constraint simulations sets A, B and C. The similarity measures is given by the label inside the Figure. The data preprocessing is given as color code in the legend.