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Neuro-symbolic inverse folding that turns a backbone into a Potts model and hands it to an automated-reasoning solver for constrained design.
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An autoregressive inverse folding model fixes residue 12 before it has seen residue 80. If it picks alanine there — a safe, high-probability choice — the arginine that would later have anchored a stabilizing hydrogen-bond network is no longer reachable, and nothing in the decoder can go back. Practitioners work around this by sampling at very low temperature, which sharpens the distribution but quietly abandons the chain rule the method was built on.
EffieDes separates fitness estimation from search. Its neural component, EffieNN, reads a backbone and emits Effie — a fully decomposable Potts model that assigns a 20×20 interaction score matrix to every pair of nearby residues, so that the score of any complete sequence is just the sum of its pairwise terms. Sequence design then becomes an explicit discrete optimization problem over that score function, solved by toulbar2, an automated-reasoning prover that returns a provably optimal sequence rather than a sample. Because the objective is written down instead of hidden in a decoder, design requirements enter as formal constraints on the solver: positional symmetry, a bounded amino-acid alphabet, or a positive/negative multi-state objective, none of which require retraining the network.
EffieDes comes from the Toulouse Biotechnology Institute with MIAT and the LISM in Marseille, published in Advanced Science in 2026.
pytoulbar2 returns optimal solutions; the LR-BCD low-rank
convex relaxation trades exactness for polynomial-time scaling and matched exact solutions
in the authors' benchmarks.EffieNN encodes a backbone through SE(3)-invariant pairwise features: the 25 interatomic distances between the N, Cα, C, O and virtual Cβ atoms of each residue pair, expanded over 16 Gaussian radial basis functions, plus a 16-dimensional sinusoidal encoding of sequence separation and a chain-identity flag. Six repeated blocks of a gated MLP and a residual MLP process each residue's 128 nearest neighbours into an environment embedding; a final residual MLP turns each pair of embeddings into the 20×20 score matrix. The default checkpoint holds 3,170,640 parameters. Training uses E-PLL, a variant of Besag's pseudo-loglikelihood built to handle the strongly unfavourable score terms that standard PLL underweights, on two Protein Data Bank corpora: Ingraham et al.'s CATH 4.2 single-chain split (17,000 / 600 / 1,200 structures) and ProteinMPNN's multi-chain assembly set (23,358 training clusters), with Gaussian coordinate noise added during training. On the single-chain benchmark EffieDes reaches 33.0% native sequence recovery against 17.9% for Rosetta, and exceeds the autoregressive Structured Transformer, GVP and ProteinMPNN as well as the Potts-based COORDinator and TERMinator. Its designs score higher AlphaFold 2 pLDDT in single-sequence mode than the native sequences of the same backbones.
Both validated case studies are ones where constraints dominate. Redesigning bacterial microcompartment shell protein RMM into a hetero-hexamer meant favouring the AB assembly while disfavouring AA and BB under symmetry; in a tripartite-GFP screen, 12 of 14 EffieDes pairs assembled well above negative controls against 2 of 10 for ProteinMPNN, and the best design formed stable hexamers by size-exclusion chromatography. In the second study, RFdiffusion partial diffusion generated new CDR backbones for the MR17 sybody against the immune-evasive SARS-CoV-2 XBB.1.16 receptor-binding domain. Of nine candidates tested, only the EffieDes design NbRM-E1 bound, at 64 nM affinity, blocking ACE2 and discriminating XBB.1.16 from the Delta variant.
EffieDes is an argument that inverse folding's bottleneck has moved from representation to search, and that a small network paired with an exact solver can beat a larger one that decodes greedily. Telling is the cross-scoring result: ProteinMPNN rated EffieDes's multi-state designs better than its own, locating the deficit in sampling rather than in learned knowledge. The tradeoffs are real. Constrained optimization over a Potts model is NP-hard and slower than autoregressive sampling; the score function is pairwise and protein-only, with no ligands or many-body terms; the nanobody result rests on nine tested designs and is presented as a proof of concept. The released code and checkpoints carry a CC BY-NC-ND 4.0 licence, barring commercial use and derivative works even though the article itself is CC BY. ESMFold and AlphaFold 2 were used only to score designs, not inside the method.
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