BA-DDG

A mutation at a protein-protein interface changes binding free energy only insofar as it destabilizes the bound complex more than it destabilizes the two chains on their own; a substitution that hurts both equally should score near zero. Inverse folding models make strong ΔΔG scorers because their sequence log-likelihoods track stability, but the usual recipe compares wild-type and mutant likelihoods under the complex backbone alone, charging the entire likelihood shift to binding and leaving the unbound leg of the thermodynamic cycle unaccounted for.

Boltzmann Alignment is the correction. The Boltzmann distribution ties free energy to the probability of a conformation; that conformational distribution is intractable, so Bayes' theorem is used to flip p(structure | sequence) into p(sequence | structure) — which is precisely the quantity an inverse folding model already reports. ΔΔG then falls out as a scaled difference of log-likelihoods taken over all four corners of the cycle: mutant and wild-type, bound and unbound. The unbound state is approximated by scoring each chain independently against its own backbone, carved out of the complex structure.

The paper, from Zhejiang University with collaborators at the University of Adelaide, Northeastern University, MIT and Ant Group, describes two modes of the same forward pass. BA-Cycle is training-free: a pretrained ProteinMPNN checkpoint is used unchanged, with no ΔΔG labels anywhere in the procedure. BA-DDG fine-tunes that same checkpoint on ΔΔG labels, treating both the network parameters and the thermodynamic factor k_BT as learnable, under a KL penalty that holds the model near its original inverse-folding distribution. It appeared at ICLR 2025 as a Spotlight.

#Key Features

• Explicit unbound state: The scorer evaluates the separated chains as well as the complex, supplying a physical inductive bias that likelihood-difference methods omit. Removing it costs most of the accuracy — plain ProteinMPNN reaches per-structure Spearman 0.2741 and ESM-IF 0.2019, against BA-Cycle's 0.3201.
• Label-free scoring mode: BA-Cycle needs no ΔΔG data and no fitting of any kind, yet reaches per-structure Spearman 0.3201, above the previous unsupervised best of 0.2632 and comparable to empirical energy functions.
• Alignment rather than plain fine-tuning: The supervised loss adds a KL term anchoring the fine-tuned model to the pretrained reference distribution. Substituting supervised fine-tuning or DPO for that objective drops per-structure Spearman to 0.4769 and 0.3913 respectively, against 0.5134.
• Three parameter sets, not one checkpoint: SKEMPI v2 is split into three structure-disjoint folds, and the supervised variant is trained under 3-fold cross-validation, so the released weights are three fold-specific parameter sets rather than a single model.
• Tolerates predicted structures: Swapping crystal structures for AlphaFold 3 predictions at inference barely moves the numbers — per-structure Spearman 0.7459 versus 0.7322 on the common test subset.

#Technical Details

The backbone is ProteinMPNN — a message-passing graph neural network over backbone geometry with an autoregressive sequence decoder — and no new architecture is introduced; the contribution is the estimator wrapped around it and the objective used to align it. Any released ProteinMPNN checkpoint (the vanilla and soluble weight sets at noise levels 0.02 through 0.30) can be plugged in. Evaluation uses SKEMPI v2, 7,085 mutations across 348 complexes, in three structure-disjoint folds so no complex appears in both training and test. BA-DDG reaches overall Pearson 0.7118, Spearman 0.6346, RMSE 1.4516, MAE 1.0151 and AUROC 0.7726, with per-structure Pearson 0.5453 and Spearman 0.5134 — ahead of every supervised baseline reported, on every one of the seven metrics.

#Applications

Because the estimator produces an absolute ΔG as well as a difference, it transfers to three tasks off the SKEMPI distribution. On a 566-complex antibody-antigen subset of SAbDab with binding labels, it reaches Spearman 0.385 against experimental binding energies, ahead of DSMBind at 0.374 and FoldX at 0.299. As a reranker over DiffDock-PP samples in rigid protein-protein docking, it selects poses by estimated ΔG and raises the fraction of sub-5 Å C-RMSD predictions. And used as a sequence designer, the ΔΔG-aligned model assigns the five known affinity-enhancing CDR mutations of a SARS-CoV-2 antibody higher preference probability (47.03% mean, versus 42.47% for the unaligned ProteinMPNN) out of 494 candidate single-point substitutions — evidence that aligning for binding energy also shifts what the model generates.

#Impact

The result argues that the gap between a pretrained inverse folding model and a good ΔΔG predictor is less a matter of more pretraining than of aligning the model to the physics of the quantity being predicted — and that the alignment machinery built for language models transfers once a thermodynamic objective replaces a preference one. The authors state the limits plainly: the method needs a crystal or a reliable predicted structure, assumes the mutant backbone is identical to the wild type, and ignores side-chain conformations, which are known to matter for ΔΔG. Code and the fold-specific weights are public but licensed for non-commercial academic use only.