StaB-ddG: Thermodynamic Binding Predictor

• The paper introduces StaB-ddG, a transfer-learning model that parameterizes binding free energy changes as differences between complex and monomer folding energies.
• It leverages a pretrained inverse-folding network, ProteinMPNN, using structure-conditioned log-likelihoods as a proxy for folding energy to predict mutational impacts on protein interfaces.
• The model enforces thermodynamic invariants like antisymmetry and mutational path independence, achieving state-of-the-art accuracy with dramatically lower computational runtime.

Searching arXiv for the StaB-ddG paper and closely related stability-prediction context. StaB-ddG is a transfer-learning-based deep learning predictor of mutational effects on protein-protein binding free energy. Introduced in the 2025 preprint "Predicting mutational effects on protein binding from folding energy" (Deng et al., 7 Jul 2025), it parameterizes binding through folding energies rather than treating binding affinity prediction as an entirely separate task. The central construction, termed “Stability-to-Binding” (StaB), uses a thermodynamic identity in which the binding energy of a complex is represented as the folding energy of the complex minus the folding energies of the isolated binding partners. StaB-ddG then instantiates this parameterization with a pretrained inverse-folding model, ProteinMPNN, whose structure-conditioned sequence log-likelihood is used as a proxy for folding energy (Deng et al., 7 Jul 2025).

1. Thermodynamic parameterization

The defining equation of the StaB formulation is

$$\Delta G_\text{bind}(A{:}B) \;=\; \Delta G_\text{fold}(A{:}B)\;-\;\Delta G_\text{fold}(A)\;-\;\Delta G_\text{fold}(B),$$

where $\Delta G_\text{fold}$ is the free-energy difference between folded and unfolded states. For a mutation from wild type $A{:}B$ to mutant $A'{:}B$, the corresponding binding free-energy change is

$$\Delta\Delta G_\text{bind}(A{:}B \rightarrow A'{:}B) = \Delta\Delta G_\text{fold}(A{:}B \rightarrow A'{:}B) - \Delta\Delta G_\text{fold}(A \rightarrow A').$$

This reduction of binding prediction to folding-energy prediction is the conceptual core of StaB-ddG (Deng et al., 7 Jul 2025).

The paper emphasizes three formal properties of this parameterization. First, it is antisymmetric: $\Delta b_\theta(s,s') = -\Delta b_\theta(s',s).$ Second, it satisfies mutational path independence: $$\Delta b_\theta(s,s') = \Delta b_\theta(s,s'') + \Delta b_\theta(s'',s').$$ Third, it is presented as expressive: in principle, because $p_\theta$ is modeled by a sufficiently expressive neural network, the predictor can fit arbitrary binding-energy measurements exactly on finite datasets (Deng et al., 7 Jul 2025).

These properties are significant because many deep-learning predictors for mutational energetics do not satisfy antisymmetry or path independence by construction. StaB-ddG therefore belongs to a class of thermodynamically structured predictors in which the representation itself constrains the algebra of mutation effects. A plausible implication is that part of its empirical behavior derives from these structural invariants rather than from scale alone.

2. Score construction and model architecture

StaB-ddG begins with a pretrained inverse-folding model as a proxy for folding energy: $f_\theta(s) = \log p_\theta(s),$ where $p_\theta(s)$ is a sequence probability model. The specific model used is ProteinMPNN, an autoregressive, structure-conditioned inverse-folding network based on a deep message-passing neural network (Deng et al., 7 Jul 2025).

The binding score is then defined as

$\Delta G_\text{fold}$0

and the predicted mutational effect on binding is

$\Delta G_\text{fold}$1

This difference-of-differences construction is what the paper identifies as the StaB-ddG predictor (Deng et al., 7 Jul 2025).

The architecture takes backbone structure as input together with sequence, and it can handle multichain complexes and multiple mutations more naturally than many stability predictors. For each prediction, the method evaluates up to six systems: complex and both partners for wild type, and complex and both partners for mutant. In practice, the same backbone structure is used for all terms, under the assumption that the backbone does not change much upon mutation or binding (Deng et al., 7 Jul 2025).

This choice has methodological consequences. It makes the predictor computationally simple relative to methods that explicitly remodel conformations, but it also limits the model when mutation-induced backbone rearrangements are substantial. The paper lists the absence of explicit backbone-change modeling among the method’s limitations (Deng et al., 7 Jul 2025).

3. Sequential transfer learning

The training protocol is a sequential fine-tuning strategy with three stages (Deng et al., 7 Jul 2025).

The first stage is zero-shot initialization: pretrained ProteinMPNN weights are used directly, with the log-likelihood proxy interpreted through the StaB parameterization. The second stage fine-tunes on the Megascale stability dataset, comprising 412 proteins and 776,298 folding stability measurements. The folding-loss objective is expressed through

$\Delta G_\text{fold}$2

with a mean-squared error loss over mutant-reference pairs. This stage is intended to adapt ProteinMPNN’s likelihoods to better reflect folding energetics (Deng et al., 7 Jul 2025).

The third stage fine-tunes on SKEMPIv2.0, described as the largest public binding benchmark. The paper reports that SKEMPIv2.0 originally contains 7,085 mutant entries, and after filtering yields 201 complexes and 4,541 mutants. A train/test split is then performed after structural homology clustering, giving 121 complexes in training and 80 complexes in test. The binding-loss objective uses the StaB-derived score differences $\Delta G_\text{fold}$3 against experimental binding-energy differences (Deng et al., 7 Jul 2025).

This transfer-learning design is central to the model’s rationale. Binding datasets are comparatively limited, whereas folding data are much more abundant. StaB-ddG therefore attempts to leverage advances in protein sequence modeling and folding stability prediction for binding prediction. The paper characterizes this as a way to compensate for the scarcity of binding data by exploiting a pretrained inverse-folding prior and a large folding-stability corpus (Deng et al., 7 Jul 2025).

4. Variance reduction and inference protocol

ProteinMPNN introduces stochasticity through randomized decoding order and Gaussian backbone noise. To reduce this variance, StaB-ddG incorporates two explicit techniques (Deng et al., 7 Jul 2025).

The first is antithetic variates: the same stochastic seed, decoding order, and backbone noise are used for wild type and mutant, thereby reducing variance by inducing positive covariance. The second is Monte Carlo averaging: predictions are averaged over multiple samples, with the paper stating that the method typically ensembles over 20 predictions (Deng et al., 7 Jul 2025).

These procedures improve both zero-shot and fine-tuned performance and also stabilize training. In the ablation study, no antithetic variates leads to substantially worse performance, and no pretraining is much worse. The study also reports that omitting the folding stage weakens overall performance, whereas a linear amino-acid offset correction gives little to no gain; predicted apo structures via AlphaFold 3 show no significant improvement in per-interface Spearman; and using $\Delta G_\text{fold}$4 weighting instead of $\Delta G_\text{fold}$5 produces no meaningful difference (Deng et al., 7 Jul 2025).

A particularly important finding is that pretrained inverse-folding initialization matters greatly: training from scratch on folding data performs much worse than starting from ProteinMPNN (Deng et al., 7 Jul 2025). This indicates that StaB-ddG is not merely a generic supervised regressor on energetic labels. Its performance depends materially on the inductive bias encoded in the inverse-folding model.

5. Datasets, metrics, and benchmark performance

The principal data sources are PDB for structures, the Megascale stability dataset, and SKEMPIv2.0 for binding-energy measurements. Two additional out-of-distribution case studies are also included: a Yeast surface display binder dataset from Cao et al. (2022), and a TCR mimic antibody dataset curated by the authors from SPR measurements (Deng et al., 7 Jul 2025).

The main evaluation metric is per-interface Spearman correlation. The paper also reports Pearson correlation, RMSE, and AUROC for whether mutation increases binding affinity. Per-interface metrics are averaged across complexes, and only complexes with at least 10 mutants are included in the main per-interface Spearman to reduce noise. For overall metrics, the paper uses cluster bootstrap standard errors (Deng et al., 7 Jul 2025).

On the held-out SKEMPIv2.0 test split, StaB-ddG achieves the following benchmark results (Deng et al., 7 Jul 2025):

Metric	Result
Per-interface Spearman	0.45
Per-interface Pearson	0.49
Per-interface RMSE	1.41 kcal/mol
Overall Spearman	0.53
Overall Pearson	0.53
Overall RMSE	1.72 kcal/mol
Overall AUROC	0.73

The paper compares against FoldX, Flex ddG, Surface-VQMAE, RDE-Net, Prompt-DDG, DiffAffinity, PPIformer, ProMIM, and unsupervised inverse-folding baselines ProteinMPNN and ESM-IF1. Its stated comparative findings are that StaB-ddG is the best or tied-best deep learning method on the benchmark, that it matches FoldX/Flex ddG-level accuracy on the authors’ controlled split, and that many prior deep-learning methods underperform force-field methods when evaluated without leakage. It also reports that ProteinMPNN zero-shot is already surprisingly competitive, outperforming prior deep-learning baselines (Deng et al., 7 Jul 2025).

A simple ensemble of StaB-ddG + FoldX is reported as the strongest combined result, with per-interface Spearman 0.53, overall Spearman 0.61, overall RMSE 1.62 kcal/mol, and overall AUROC 0.78 (Deng et al., 7 Jul 2025). This suggests that the StaB parameterization and FoldX capture partly complementary signals.

6. Runtime, case studies, strengths, and limitations

A major practical claim is computational efficiency. The paper reports that on the benchmark of 4,451 mutants, StaB-ddG requires about 13 NVIDIA-5090 GPU-minutes, corresponding to about 0.2 seconds per mutation, whereas FoldX requires about 260 CPU hours or about 210 seconds per mutation, and Flex ddG requires roughly 15 CPU hours per mutation. On this basis, StaB-ddG is described as around 1000× faster than FoldX while maintaining comparable accuracy (Deng et al., 7 Jul 2025).

The zero-shot and supervised results are treated separately. Zero-shot inference with pretrained ProteinMPNN, the StaB parameterization, and variance reduction already gives strong performance and is close to FoldX/Flex ddG on the test results. Fine-tuning on Megascale stability data improves binding prediction on the training split, but on the held-out SKEMPI test split the stability-fine-tuned model can be slightly worse than zero-shot for some metrics; the paper attributes this to the small number of test clusters and out-of-distribution effects. After binding-data fine-tuning, full StaB-ddG reaches its best SKEMPI performance (Deng et al., 7 Jul 2025).

The two auxiliary case studies illustrate both promise and limitation. On the yeast-display dataset of designed small binders, the paper reports that fine-tuning on folding stability and binding both help, but that the complex-only folding score sometimes outperforms the full binding parameterization. The interpretation offered is that the assay readout is confounded by protein expression, which is related to folding stability. The authors therefore introduce a variant

$\Delta G_\text{fold}$6

and find best performance around $\Delta G_\text{fold}$7 rather than exactly 1 (Deng et al., 7 Jul 2025). On the TCR mimic case study, curated from 30 mutational measurements across 6 TCR mimic antibody complexes, the overall Spearman is 0.13 ± 0.39, which the paper presents as too noisy for strong conclusions (Deng et al., 7 Jul 2025).

The strengths explicitly claimed for StaB-ddG are that it uses a thermodynamically grounded decomposition, leverages abundant folding data, preserves antisymmetry and path independence, delivers strong zero-shot performance, reaches state-of-the-art deep learning accuracy, is much faster than classical force-field methods, and naturally supports multi-mutation and multichain inputs. Its listed limitations are that it does not explicitly model backbone changes upon mutation, may struggle on flexible interfaces, remains dependent on the quality and size of available folding and binding datasets, faces out-of-distribution generalization challenges, and can be affected by assays whose readouts are confounded by properties such as expression (Deng et al., 7 Jul 2025).

7. Interpretation, misconceptions, and relation to broader ddG prediction

StaB-ddG concerns protein-protein binding free-energy changes upon mutation, not folding-stability prediction alone. Its distinctive claim is not that binding can be read off from complex structure directly, but that mutational binding effects can be parameterized as differences of folding-like scores across complex and monomeric states (Deng et al., 7 Jul 2025). A common misunderstanding would be to treat it as a purely sequence-based mutational predictor; in fact, the model is explicitly structure-conditioned through ProteinMPNN and evaluates backbone-conditioned likelihoods for complexes and partners separately.

Another potential misunderstanding is to interpret its reported correlations against an implicit ceiling of 1.0. Work on protein stability-change prediction has shown that for $\Delta G_\text{fold}$8 datasets, the best achievable Pearson correlation can be limited by measurement uncertainty and dataset spread, with a theoretical upper bound

$\Delta G_\text{fold}$9

and with current datasets often implying a ceiling around 0.7–0.8 (Montanucci et al., 2018). That analysis was derived for protein stability-change datasets rather than the StaB-ddG binding benchmark, so it should not be transferred mechanically. Nevertheless, it supports a broader caution already relevant to StaB-ddG: absolute correlation values are inseparable from label noise, dataset composition, and evaluation protocol (Montanucci et al., 2018).

Within that broader landscape, StaB-ddG’s principal contribution is a new framework that parameterizes binding through folding energies, uses ProteinMPNN as a pretrained folding proxy, fine-tunes sequentially on folding and binding data, and achieves FoldX-level accuracy with ~1000× lower runtime on the reported benchmark (Deng et al., 7 Jul 2025). Its significance lies in showing that a thermodynamically constrained transfer-learning formulation can make inverse-folding models competitive for protein-protein interface mutational scanning, while also preserving algebraic properties that are often absent in unconstrained predictors.