Revealing the Atomistic Mechanism of Rare Events in Molecular Dynamics

TL;DR

The paper tackles the challenge of interpreting slow, rare conformational transitions in molecular dynamics without relying on predefined collective variables. It introduces AMORE-MD, which uses ISOKANN to learn a smooth membership function $\chi$ that approximates the dominant slow eigenfunction of the backward operator $\mathcal{L}$, yielding a $\chi$-minimum-energy path ($\chi$-MEP) and atomistic saliency via gradient information. Through Müller–Brown, alanine dipeptide, and VGVAPG, the authors show that $\chi$-MEPs representativ e of the slow process and that ensemble-averaged and level-set saliency reveal chemically interpretable mechanisms at atomic resolution. The framework leverages iterative enhanced sampling to cover rare-event regions and improve training stability, providing a general, scalable route to mechanistic insight without explicit CV design. Overall, AMORE-MD connects self-supervised Koopman-based reaction coordinates to concrete atomistic mechanisms, enabling interpretable design and analysis in complex chemical systems.

Abstract

Interpretable reaction coordinates are essential for understanding rare conformational transitions in molecular dynamics. The Atomistic Mechanism Of Rare Events in Molecular Dynamics (AMORE-MD) framework enhances interpretability of deep-learned reaction coordinates by connecting them to atomistic mechanisms, without requiring any a priori knowledge of collective variables, pathways, or endpoints. Here, AMORE-MD employs the ISOKANN algorithm to learn a neural membership function $χ$ representing the dominant slow process, from which transition pathways are reconstructed as minimum-energy paths aligned with the gradient of $χ$, and atomic contributions are quantified through gradient-based sensitivity analysis. Iterative enhanced sampling further enriches transition regions and improves coverage of rare events enabling recovery of known mechanisms and chemically interpretable structural rearrangements at atomic resolution for the Müller-Brown potential, alanine dipeptide, and the elastin-derived hexapeptide VGVAPG.

Figures (4)

• Figure 1: Transition pathways and deep learned gradients in a toy system. The Müller-Brown potential energy landscape is shown as a heatmap of its two coordinates (left). Local minima are shown in cyan, the string MEP in black, and the $\chi$-MEP in blue, initialized from the magenta diamonds. On the right, the gradient of the learned membership function $\chi$ is displayed as downscaled arrows for a subsample of the training data points (colored by their reaction coordinate value). Larger gradient magnitudes highlight the regions of highest $\chi$-sensitivity along the transition barrier.
• Figure 2: Conformational transitions and atomistic sensitivities in alanine dipeptide. The conformational landscape of alanine dipeptide is projected onto the Ramachandran dihedral angles ($\phi$, $\psi$), revealing two dominant metastable states (bottom right). The slowest kinetic mode is learned as a smooth neural membership function $\chi$. The $\chi$-MEP, initialized in the magenta diamonds, is shown in blue and follows the equilibrium distribution (gray), which forms a characteristic tube-like structure around the path. Three representative conformations along the $\chi$-MEP corresponding to $\chi$ values 0.1, 0.5, and 0.95 are displayed above the landscape (left to right). The atomistic contributions to the learned mode are identified via the derived $\chi$-sensitivity measure. This level-set averaged squared norm of the gradient components, $\langle \|\nabla_i \chi\|^2 \rangle_z$, highlights when and where specific atomic movements contribute most to the transition. These contributions are shown as a heatmap (bottom left) and further projected onto the representative structures for interpretability.
• Figure 3: Conformational transitions and atomistic sensitivities in VGVAPG. The conformational landscape of the elastin-mimetic peptide VGVAPG is projected onto the central valine dihedrals $\phi$ and $\psi$ (right). The equilibrium distribution is shown in gray, initial states are marked in magenta, and the $\chi$-MEP states after adaptive sampling are displayed in blue. Multiple transition channels are visible, reflecting the heterogeneous ensemble of conformational pathways. The $\chi$-sensitivity measure $\langle \|\nabla_i \chi\|^2 \rangle_z$ reveals localized atomic regions with high influence on the learned collective mode, with strongest responses for atoms 27, 29, 41, and 43 corresponding to the $\psi$ rotation of Val2 (left). For clarity, representative structures above the plots are shown only for the pathway with the highest stationary density, illustrating the associated backbone rearrangements (see supplementary Movies S2-S5 for all four pathways).
• Figure 4: For Table of Contents Only