Divide and Cluster: The DIVINE Framework for Deterministic Top-Down Analysis of Molecular Dynamics Trajectories

Abstract

We present DIVIsive N -ary Ensembles (DIVINE), a deterministic, top-down clustering framework designed for molecular dynamics (MD) trajectories. DIVINE constructs a complete clustering hierarchy by recursively splitting clusters based on n -ary similarity principles, avoiding the need for O(N ² ) pairwise distance matrices. It supports multiple cluster selection criteria, including a weighted variance metric, and deterministic anchor initialization strategies such as NANI (N-ary Natural Initiation), ensuring reproducible and well-balanced partitions. Testing DIVINE up to a 305 μs folding trajectory of the villin headpiece (HP35) revealed that it matched or exceeded the clustering quality of bisecting k -means while reducing runtime and eliminating stochastic variability. Its single-pass design enables efficient exploration of clustering resolutions without repeated executions. By combining scalability, interpretability, and determinism, DIVINE offers a robust and practical alternative to conventional MD clustering methods. DIVINE is publicly available as part of the MDANCE package: https://github.com/mqcomplab/MDANCE .

Figure 1.

DIVINE clustering on a Synthetic 2D Benchmark Dataset. Clustering results are shown for a simple, low-dimensional 2D dataset with clearly separated clusters: ground truth labels (left), k-means NANI (center), and DIVINE using NANI for anchor selection (right). Each color represents a distinct cluster. While both methods broadly recover the true cluster structure, DIVINE achieves better separation and cluster consistency. This illustrative example provides a controlled benchmark for visual comparison but does not reflect the complexity of molecular dynamics data, which typically involve high-dimensionality and conformational noise. As such, we performed a more rigorous validation using a biomolecular system.

Figure 2.

Change in Calinski-Harabasz and Davies-Bouldin indices for HP35 after DIVINE clustering from k = 1 to 30, comparing performance across different cluster selection strategies.

Figure 3.

Change in Calinski-Harabasz and Davies-Bouldin indices for HP35 after DIVINE clustering from k = 1 to 30, comparing performance across different anchor methods.

Figure 4:

Overlaps of best representative structures from the seven clusters of HP35 after performing DIVINE using NANI as anchors and weighted_MSD as cluster selection strategy. Helices 1, 2, and 3 are colored green, cyan, and yellow, respectively.

Figure 4:

Overlaps of best representative structures from the seven clusters of HP35 after performing DIVINE using NANI as anchors and weighted_MSD as cluster selection strategy. Helices 1, 2, and 3 are colored green, cyan, and yellow, respectively.