SE(3)-Equivariant Graph Mamba Networks for Predicting Temperature-Dependent Protein Conformational Dynamics

Overview

Protein conformational dynamics is the continuous structural transitions proteins undergo during folding, unfolding, and thermal fluctuation, and underlie enzyme catalysis, ligand binding, and the misfolding events implicated in diseases such as Alzheimer's and Parkinson's. Classical molecular dynamics (MD) simulation captures these trajectories with physical accuracy but demands days to weeks of supercomputer time per protein, severely limiting its applicability. Recent AI-based surrogate models have largely employed diffusion transformers, which introduce quadratic O(N²) scaling with sequence length and frequently produce physically inconsistent structures with broken backbone geometry or steric clashes. This project developed GraMO-SE(3) (Graph Mamba Operator with SE(3)-Equivariant Geometric Distillation), a novel generative architecture that predicts continuous protein conformational trajectories at provably linear O(N) complexity. The framework integrates three purpose-designed components: SE(3)-equivariant tensor product message passing enforcing the rotational and translational symmetries all physical protein structures must obey; bidirectional Mamba state-space sequence modeling for long-range residue dependency capture without quadratic attention; and an adaptive rank gating mechanism conditioned on ESM-2 sequence embeddings and simulation temperature, enabling explicit modeling of temperature-dependent flexibility. A velocity field is predicted at each timestep and integrated via 4th-order Runge-Kutta to produce continuous trajectories, with a flow-matching training objective providing direct supervision on per-frame displacements. The model was trained and validated on a structurally diverse sample of proteins from the MDCATH and ATLAS datasets spanning 320K–450K simulation temperatures. Evaluation against held-out MD trajectory frames demonstrated a median Cα RMSD of 2.21 Å and mean TM-score of 0.791, confirming consistent native fold preservation across predicted trajectories. Steric clash analysis showed 99.8% clash-free atomic packing across all predicted frames, and all 15 evaluated proteins maintained stable rollouts across 50 free-integration steps without structural divergence. Predictive accuracy showed near-zero correlation with chain length (r = 0.06), demonstrating generalization across proteins ranging from 64 to 384 residues. Median RMSD improved upon the STAR-MD baseline (2.32 Å). These results demonstrate that SE(3)-equivariant state-space models can generate physically valid protein trajectories at a fraction of the computational cost of MD simulation, with direct implications for studying conformational diseases and accelerating structure-based drug discovery on consumer-grade hardware.

Competition history

• CSEF 2026 Computational Science (Senior Division) · Entry S-07-45

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