CoMoFlow writes proteins' coordinated motions as explicit modes, then steers generated ensembles along them

When generating a protein conformational ensemble, coordinated motion between residues is now written as a set of nameable directions rather than left inside the generative distribution. Earlier flow-matching methods treated each molecular dynamics conformation as an independent training target, so ensemble-level coordinated variation stayed implicit in the learned distribution. On the ATLAS test set, against BBFlow, which is trained from scratch and likewise conditioned only on the equilibrium backbone, DCCM correlation rises from 0.87 to 0.93 and PCA distance falls from 1.33 to 1.21; on the fully held-out set of 100 de novo proteins the two move from 0.83 to 0.89 and from 0.67 to 0.59.

The construction first derives a set of protein-specific collective modes from the equilibrium structure, then has the generator produce conformations according to those modes' coefficients. Each collective mode is parameterized by an equivariant geometric field that gives per-residue rotational and translational components, and masked orthonormalization over valid residues yields an orthonormal basis. Each molecular dynamics conformation is projected onto the modes to obtain coefficients, a Gaussian mixture is fitted to those coefficients under supervision from the projection residual and coefficient-covariance alignment, and at generation a sampled coefficient vector becomes a displacement field fed to SE(3) flow matching through feature conditioning and translational prior recentering.

The coefficients themselves become adjustable knobs: changing one mode's coefficient moves the generated conformation along that mode. Earlier generation could only sample passively, without specifying which direction to move or how far. On ATLAS and de novo proteins, the correlation between prescribed and realized coefficient changes is 0.983 and 0.971, the regression slope 0.864 and 0.797, and the off-target response 0.32 and 0.22; on the ATLAS test set under a budget of 600 generator calls per target, passive sampling reaches 32%/38% of opening/closing targets, and cross-entropy search over the explicit coefficients raises this to 65%/68%.

Evaluation covers 82 ATLAS test proteins and 100 de novo proteins, all with all-atom molecular dynamics trajectories, and the generated object is a backbone conformational ensemble; at inference only the equilibrium structure and residue identities are used, not the test protein's molecular dynamics conformations.

Reconstruction degrades as the reference structure moves further from equilibrium: on ATLAS, DCCM correlation falls from 0.93 with the original reference to 0.88 at Q50 and 0.82 at Q75, while PCA rises from 1.21 to 1.43 and 1.58. Raising the number of collective modes from 8 to 16 yields only small, metric-dependent changes, and the main experiments therefore use 8 modes.