Learning Protein-Specific Elastic Interactions for Globally Coupled Protein Dynamics

Proteins function through conformational flexibility and collective motion that a single reference structure does not specify. Molecular dynamics (MD) simulation captures these dynamics but requires long trajectories; learning-based methods that predict covariances from structure avoid this cost, but they couple each residue pair through a single scalar and provide no mechanism from which globally consistent collective motion arises. Elastic network models (ENMs) offer such a mechanism, describing global dynamics through explicit inter-residue interactions, yet they prescribe these interactions with fixed cutoffs and hand-designed rules. We introduce ENMulator, which combines the two: a network maps sequence and structure to protein-specific elastic interactions, which parameterize an elastic network whose Hessian induces a globally coupled, residue-level displacement covariance. A complementary branch predicts residue-wise anisotropic covariances, and a blockwise geodesic congruence calibrates the residue marginals of the elastic covariance toward these predictions while exactly preserving the canonical correlations between residues. On the ATLAS test set, in both covariance and sampled-ensemble evaluation, it improves recovery of covariance geometry, collective modes, and correlated motion over prescribed ENMs and direct covariance predictors, reducing DCCM error by 17% relative to the next-best method, while remaining competitive on residue-wise fluctuations. These results support learned elastic interactions as a principled bridge from a single reference structure to globally coupled protein dynamics without simulation.