BackFlip-2

A hinge that swings along a single axis and a surface loop that rattles in every direction can share the same root-mean-square fluctuation. RMSF is a scalar: it records how far a residue moves and discards where it goes. The motions that carry protein function are not like that. A lid closing over an active site or a catalytic loop rearranging has a preferred direction, and residues far apart in sequence displace together.

BackFlip-2 predicts both properties directly. Given one equilibrium backbone it returns a 3×3 covariance matrix per residue, whose eigenvectors are the principal directions of fluctuation and whose eigenvalues their amplitudes, plus an N×N matrix of pairwise residue couplings yielding the dynamic cross-correlation matrix. Nothing is sampled: one forward pass replaces the hundreds of conformations an ensemble generator must draw before a dynamical observable converges, and scalar RMSF is the covariance trace.

The model comes from Vsevolod Viliuga and Arne Elofsson at Stockholm University and SciLifeLab with the Gräter group at the Max Planck Institute for Polymer Research, the Heidelberg Institute for Theoretical Studies and Heidelberg University. It generalizes BackFlip-1, the scalar flexibility predictor introduced alongside FliPS and shipped from the same repository, and is a sibling of the group's ensemble generator BBFlow.

#Key Features

• Equivariant covariance head: Each residue's covariance is built as AAᵀ in its local frame and rotated into the global frame by that residue's own rotation, so turning the input structure turns every predicted ellipsoid with it.
• Couplings read off edge embeddings: Pairwise couplings come straight from the backbone encoder's edge features rather than a separate pair-attention module, which keeps the network small while improving accuracy on the coupling task.
• Tolerant of imperfect inputs: Accuracy changes only slightly when the input backbone is noised or replaced by an AlphaFold 2 prediction deviating from the equilibrium state by a median 2.6 Å RMSD.
• Three released checkpoints: Models trained on ATLAS, on mdCATH, and on a joint split, spanning the 300 ns and 500 ns simulation regimes.

#Technical Details

The backbone encoder represents the protein as N rigid-body frames and refines node and edge embeddings through four modified Invariant Point Attention blocks borrowed from AlphaFold 2, with the frame-update step removed so the geometry stays fixed. Node width is 96 and edge width 64; inputs are backbone frames, a one-hot amino-acid type and Cα–Cα distances binned from 0 to 20 Å — no MSA, evolutionary profile, or language-model embedding. The covariance head trains under a log-Frobenius loss, the coupling head under a correlation-matrix-distance loss plus MAE and DCCM terms. Total size is 965K parameters, trained jointly on both tasks for 200 epochs in roughly four GPU hours on one NVIDIA A100.

Training uses ATLAS: three independent 100 ns CHARMM36m molecular dynamics trajectories at 300 K for 1,390 proteins. On the held-out ATLAS test set BackFlip-2 reaches a per-target RMSF correlation of 0.87 at 0.58 Å MAE, against 0.83 for the 1.2B-parameter FlexPert, 0.75 for Pegasus and 0.84 for BackFlip-1; on 100 de novo backbones from RFdiffusion and FrameFlow it reaches 0.78, where the language-model-based predictors fall away. Against DynaProt, which targets the same two observables, it raises DCCM correlation from 0.66 to 0.80 with about a third of the trainable parameters. It stays close to far larger ensemble generators AlphaFlow, BBFlow and BioEmu-1 on covariance metrics while running in under 0.02 s for a 300-residue protein — four to five orders of magnitude faster — and slightly exceeds them on ellipsoid volume overlap, the direct measure of anisotropy.

#Applications

The natural use is dynamics annotation at database scale, roughly 50 proteins per second on one A100, for flagging flexible functional sites, mapping coupling patterns, or screening families for putative allosteric networks. On adenylate kinase it separates apo from holo, predicting higher LID and NMPbind flexibility in the apo form, motion oriented along the closure axis, and strongly anticorrelated LID–NMPbind coupling — the established mechanism, recovered from two static structures. Needing only a structure, it also lets designers check a generated backbone for unintended mobility before synthesis.

#Impact

BackFlip-2 sharpens a division of labour in protein dynamics: when the question is a dynamical descriptor rather than a conformational ensemble, predicting the descriptor directly beats sampling states until it converges. The ablations add that SE(3) equivariance is what makes the directional half of that descriptor learnable at all, since invariant models trained on the same data return near-spherical covariances. Weights, training and inference code are released under the MIT license with a Colab tutorial, alongside the covariance-annotated ATLAS and mdCATH datasets, which inherit ATLAS's non-commercial CC BY-NC 4.0 terms. The authors state the boundary plainly: the descriptors are fitted to 300 ns and 500 ns trajectories and assume approximately Gaussian fluctuations, so sub-microsecond transitions are in scope while millisecond-timescale conformational changes are not.