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StabilityArc: Decoding Protein Sequence Embeddings into Generalizable Stability Landscapes

Aaron L. Feller, Andrew D. Ellington, Claus O. Wilke

arXiv:2610.00742v1q-bio.BMcs.LG

TL;DR

Protein stability effects vary by sequence, although recurring biochemical constraints may support transfer to unseen proteins. STABILITYARC applies a shared decoder to protein representations, achieving 0.7134 all-variant macro Spearman, 0.0608 above ProSST-2048 in strict protein holdout.

  • Problem

    Protein-specific stability landscapes make it uncertain whether a decoder trained across proteins can predict mutation effects in an unseen target.

    Source: Introduction · p. 1

  • Method

    STABILITYARC applies a shared decoder to evolutionary representations to predict substitution effects, and its predictions can serve as a prior for target-specific optimization.

    Source: Method · p. 2, Introduction · p. 2, Discussion · p. 4

  • Results

    0.7134 all-variant macro Spearman is 0.0608 above the leading model, ProSST-2048, in cross-protein transfer.

    Source: Results · p. 3

  • Takeaways & Limitations

    The same predicted landscape is used under strict protein holdout before measurements and as a prior for target-specific optimization after measurements arrive.

    Source: Conclusion · pp. 4–5

    The evaluation is retrospective, uses one random seed per outer fold, and covers only single and double substitutions; target sequences may have appeared in ESMC pretraining, and singleton or orphan proteins may be more challenging.

    Source: Discussion · p. 4

Abstract

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Every protein has a unique stability landscape, but the physical consequences of mutation are governed by recurring biochemical constraints. We test whether a shared decoder, trained on measurements from diverse proteins, can interpret these constraints in an unseen target, enabling cross-protein transfer for initial experimental round prescreening. We present StabilityArc , which maps frozen ESMC-600M residue representations through a shared RoPE transformer to an Lx20 matrix of substitution effects; a symmetric, contact-aware residual aids in predicting epistasis in simultaneous substitutions. In 66 strict leave-one-protein-out evaluations covering 134,794 ProteinGym variants, StabilityArc achieves 0.7134 Spearman correlation, exceeding the strongest zero-shot baseline, ProSST-2048 (0.6526), by 0.0608. We further explore the utility of this method by providing the score as a prior for Kermut, achieving Spearman correlation of 0.8280 across three supervised split schemes, improving on Kermut's reported 0.8167.

Introduction

Protein stability landscapes vary by sequence, yet mutation effects reflect recurring biochemical constraints. STABILITYARC tests whether a shared decoder can transfer these patterns to an unseen protein and support engineering before target measurements are available.

Introduction

  • Target stability measurements are often costly, slow, and unavailable, while high-throughput deep mutational scanning has mapped mutation effects in many proteins.These existing measurements provide a potential cross-protein training resource.Source: Introduction · p. 1
  • Because the same substitution can be benign or damaging in different contexts, the paper asks whether a shared decoder transfers to an unseen protein.The proposed premise is that recurring constraints, including packing frustration, unsatisfied charge, and solvent exposure, may be learned across proteins.Source: Introduction · p. 1
  • STABILITYARC decodes frozen ESMC-600M wild-type embeddings into effects for all 20 substitutions per site, adding a contact-aware residual for double-mutant epistasis.Target DMS labels are withheld during evaluation; attention-derived contacts provide a label-free target description.Source: Introduction · p. 2, Figure 1 · p. 2
  • The study evaluates the landscape both for blind variant ranking before target measurements and as a prior for Kermut after measurements arrive.Kermut then revises the landscape using target-assay data, structure, and variant embeddings.Source: Introduction · p. 2

Method

STABILITYARC uses a shared transformer decoder to produce wild-type-relative substitution effects and a contact-aware interaction term for double mutations. The resulting predictions can also supply Kermut’s prior while its Gaussian process adapts to target-assay data.

Shared wild-type decoder

  • Frozen ESMC-600M residue embeddings pass through a four-layer transformer with rotary position embeddings to produce residue states.A linear head predicts effects for each amino-acid substitution, with parameters shared across proteins.Source: Method · p. 2

Multiple mutations with contact-aware composition

  • For double mutations, the model sums the two single-substitution scores and adds a learned interaction term based on sequence distance and predicted physical contact.Contact probabilities come from frozen ESMC attention maps rather than experimental coordinates.Source: Method · p. 2

Learning objective

  • Training combines Huber loss with pairwise ranking loss, using batches of 1,024 variant pairs to match measured orderings.Double-mutant labels are centered and scaled within each assay using single-mutant-label medians and median absolute deviations.Source: Method · p. 3

Supervised prior

  • Kermut uses STABILITYARC’s protein-held-out prediction as its prior mean while retaining target-assay training data for posterior adaptation.Its covariance combines structural mutation similarity with an RBF kernel over ESM-2 variant embeddings.Source: Method · p. 3

Experimental Setup

The evaluation holds out each protein’s labels to test cross-protein transfer across 66 stability assays. Supervised adaptation follows ProteinGym’s official random, modulo, and contiguous splits.

Data and hold-one-protein-out protocol

  • The benchmark covers 66 ProteinGym stability assays and 134,794 variants, with 68,855 singles and 65,939 doubles.Each of 66 outer models excludes all labels for one protein; its wild-type sequence and frozen contacts remain available at inference.Source: Experimental Setup · p. 3
  • Each assay’s pooled Spearman correlation concatenates singles and doubles, and the reported score is the unweighted mean across assays.Models train for 40 epochs with AdamW, learning rate 10^-4, weight decay 10^-3, and up to 40,000 measured variants per training assay.Source: Experimental Setup · p. 3

Comparisons

  • Cross-protein comparisons use methods with complete coverage of the same variants across all 66 assays, reporting pooled, single-only, and double-only macro Spearman.Supervised adaptation uses ProteinGym’s official five-fold random, modulo, and contiguous splits, producing 990 GP fits.Source: Experimental Setup · p. 3

Results

STABILITYARC leads the reported cross-protein ProteinGym comparisons, while its results against StabilityOracle on T2837 vary by metric. Using its prediction as Kermut’s prior improves results across all three supervised split schemes.

Cross-protein transfer

  • 0.7134 all-variant macro Spearman is 0.0608 above the leading model, ProSST-2048, and STABILITYARC also leads single- and double-mutant rankings.The evaluation scores each assay with a model trained without that protein’s labels.Source: Results · p. 3
  • On T2837, STABILITYARC improves recall and accuracy but decreases Spearman, AUROC, and precision versus StabilityOracle.The comparison is a second cross-protein evaluation.Source: Results · p. 3

Supervised adaptation

  • 0.8280 overall mean exceeds Kermut’s reported 0.8167 when STABILITYARC replaces only its prior input, with improvement on every official split.The gain is smallest for random splitting and largest for contiguous splitting; Kermut still uses target-assay labels and other features.Source: Results · p. 4, Table 2 · p. 4

Discussion

StabilityArc predicts stability from sequence without requiring input coordinates, using a shared decoder to capture recurring constraints across distinct protein folds. Its evaluation is retrospective and limited to single and double substitutions, with possible challenges for singleton or orphan proteins.

Discussion

  • StabilityArc operates purely on sequence and achieves highly competitive stability prediction without requiring input coordinates.The authors note that protein language models perform best on families well represented in their pretraining data.Source: Discussion · p. 4
  • A shared transformer trained across proteins predicts distinct stability landscapes by applying a decoding rule to rich evolutionary representations.The authors report improvement over purely evolutionary baselines in zero-shot settings and describe the model as an effective prior for supervised adaptation.Source: Discussion · p. 4
  • Evolutionary likelihood can conflate stability with other selective pressures, while StabilityArc aims to isolate folding constraints using wild-type ESMC representations.The target sequence is excluded from training, so the decoder cannot memorize its specific mutational pathways.Source: Discussion · p. 4
  • Evaluation is retrospective, uses one random seed per outer fold, and covers only single and double substitutions; ESMC pretraining may include target sequences, and singleton or orphan proteins may be challenging.The authors attribute the mutation-order scope to data availability and note that language models perform best on families represented in pretraining.Source: Discussion · p. 4

Conclusion

StabilityArc provides a shared wild-type-relative landscape under strict protein holdout before target measurements, then uses that same landscape to support target-specific optimization as measurements arrive.

Conclusion

  • Before experimental measurements, the shared decoder produces a complete wild-type-relative landscape under strict protein holdout.The conclusion describes this as establishing a new state of the art for matched zero-shot stability prediction.Source: Conclusion · p. 4
  • As measurements arrive, the same landscape supports target-specific optimization and surpasses reported Kermut benchmarks without changing base kernels or data splits.The authors frame these two information regimes as actionable priors for protein engineering campaigns.Source: Conclusion · p. 5

A.1 Comparison to StabilityOracle on T2837

On a matched T2837 subset, StabilityArc has higher recall and accuracy than StabilityOracle, while StabilityOracle has stronger pooled correlation and AUROC.

A.1 Comparison to StabilityOracle on T2837

  • The matched cohort is nearly balanced, with 962 destabilizing and 922 non-destabilizing mutations.Source: §A.1 · p. 8
  • 0.527 vs. 0.376 recall and 0.705 vs. 0.669 accuracy favor StabilityArc, while pooled Spearman 0.718 vs. 0.606 and AUROC 0.852 vs. 0.804 favor StabilityOracle.The paired comparison covers 1,884 shared mutations across 19 targets, using ∆∆G ≥1 kcal/mol as the positive class.Source: Table 3 · p. 8, §A.1 · p. 8
  • The comparison uses shared mutations from 19 targets with more than 30 shared mutations and defines the positive class as ∆∆G ≥1 kcal/mol.Source: Table 3 · p. 8

A.2 Mutation-Order Decomposition

Strict held-out predictions have higher macro Spearman on single substitutions than on double substitutions; the double-mutant value averages assays with defined correlations.

A.2 Mutation-Order Decomposition

  • 0.6946 macro Spearman on singles and 0.4119 on doubles, with the latter averaged across assays with defined double-mutant correlation.Table 4 presents zero-shot StabilityArc performance by mutation order.Source: Table 4 · p. 8, §A.2 · p. 8

A.3 Multiple mutations with contact-aware composition.

For double mutants, StabilityArc adds a symmetric, contact-aware epistasis correction to the sum of the two single-substitution scores. The correction uses mutation-aware residue-pair features, sequence separation, and a contact feature.

A.3 Multiple mutations with contact-aware composition.

  • The two mutation-aware site vectors add each decoder contextual site state to a learned embedding of the substituted amino acid.The decoder states and amino-acid embeddings are each 256-dimensional.Source: §A.3 · p. 8
  • A 770-value residual input combines three residue-pair feature vectors with sequence separation and an ESMC attention-derived contact feature.The pair features are ui + uj, |ui − uj|, and ui ⊙ uj.Source: §A.3 · p. 8
  • A two-layer network maps the 770-dimensional input to a scalar epistasis correction that modifies the additive double-mutant score.With a zero residual, the double mutant is treated as additive; a nonzero residual captures whether the combined effect is more or less harmful than the two single substitutions summed.Source: §A.3 · p. 9
  • Swapping the two substitutions leaves every residual input feature unchanged, making the composition symmetric by construction.Source: §A.3 · p. 9
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