Boltzmann-Aligned Inverse Folding Model as a Predictor of Mutational Effects on Protein-Protein Interactions
Authors: Xiaoran Jiao
Weian Mao
Wengong Jin
Peiyuan Yang
Hao Chen
Chunhua Shen
Venue: ICLR 2025 Spotlight (2025)
Keywords: Mutational Effects; Protein-Protein Interactions
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Predicting the change in binding free energy ($\Delta \Delta G$) is crucial for understanding and modulating protein-protein interactions, which are critical in drug design.
Due to the scarcity of experimental $\Delta\Delta G$ data, 
existing methods focus on pre-training, 
while neglecting the importance of alignment.
In this work, we propose Boltzmann Alignment technique to transfer knowledge from pre-trained inverse folding models to prediction of $\Delta\Delta G$.
We begin by analyzing the thermodynamic definition of $\Delta\Delta G$ and introducing the Boltzmann distribution to connect energy to the protein conformational distribution. 
However, the protein conformational distribution is intractable. Therefore, we employ Bayes’ theorem to circumvent direct estimation and instead utilize the log-likelihood provided by protein inverse folding models for the estimation of $\Delta\Delta G$. 

Compared to previous methods based on inverse folding, our method explicitly accounts for the unbound state of the protein complex in the $\Delta \Delta G$ thermodynamic cycle, introducing a physical inductive bias and achieving supervised and unsupervised state-of-the-art (SoTA) performance.
Experimental results on SKEMPI v2 indicate that our method achieves Spearman coefficients of 0.3201 (unsupervised) and 0.5134 (supervised) on SKEMPI v2, significantly surpassing the previously reported 
%SoTA values
SoTA results 
of 0.2632 and 0.4324, respectively.
Furthermore, we demonstrate the capability of our method in binding
energy prediction, protein-protein docking, and antibody optimization tasks.

Code is available at [https://github.com/aim-uofa/BA-DDG](https://github.com/aim-uofa/BA-DDG)

Published as a conference paper at ICLR 2025
BOLTZMANN-ALIGNER INVERSE FOLDING MODEL AS A PREDICTOR OF MUTATIONAL EFFECTS ON PROTEIN- PROTEIN INTERACTIONS
Xiaoran Jiao"; Weian Mao
Wengong Jin',
Peiyuan Yang',
Hao Chen'i Chunhua Shen! 1.41
Zhejiang University, China
MIT, USA
Northeastern University, USA Ant Group
ABSTRACT
Predicting the change in binding free energy (AAG) is crucial for understanding and modulating protein- protein interactions, which are critical in drug design. Due to the scarcity of experimental AAG data, existing methods focus on pre-training, while neglecting the importance of alignment. In this work, propose Boltzmann Alignment technique to transfer knowledge from pre-trained inverse folding models prediction of AAG. We begin by analyzing the thermodynamic definition of AAG and introducing the Boltzmann distribution to connect energy to the protein conformational distribution. However, the protein conformational distribution is intractable. Therefore, we employ Bayes' theorem to circumvent direct estimation and instead utilize the log-likelihood provided by protein inverse folding models for the estimation of AAG.
protein-protein
Compared to previous methods based inverse folding, our method explicitly accounts for the unbound state of the protein complex in the A AAG thermodynamic cycle, introducing physical inductive bias and achieving supervised and unsuper- vised state-of toitte-of-hheeeeee indicate that method achieves Spearman coefficients of 0.3201 (unsupervised) and 0.51 1.5134 (supervised) on SKEMPI v2, significantly surpassing the previously reported SoTA results of 0.2632 and 0.4324. respectively. Furthermore, we demon- strate the capability of our method in binding energy prediction, docking, and antibody optimization tasks.
the-art art (SoTA) performance. Experimental results on SKEMPI v2
protein
Code is available at http:://github..ommmaa cociii---oa/Peeee BA-DDG
Camplex
G coll--ae G
Grar Greee
AG
rrboudd stoee
bousd aate
Imger: Sappenso
Input: 3D Civelinccs
AG
-GG Ai
AG sw
AG rea
AG
Inveme Felding Midel
Sequence Decoder
Ourpet: lng-lbbebood
AG
lage
G
Figure 1: Overview of the Boltzmann Alignment technique. Left: inference with protein inverse folding model. Right: illustration of thermodynamic cycle in the modulation of protein-proted interactions.
XJ and WM contributed equally. Work was done when WM was visiting Zhejiang University. HC and CS the corresponding authors.

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INTRODUCTION
Protein- proteiinpnnnnnnn interactions (PPIs) are fundamental to the execution diverse and essential biological functions across all organisms. High-fidelity computational modeling of protein-protein protein interac- tions is indispensable. The interaction properties of protein-protein binding can be quantitatively characterized by binding free energy (AG), the difference in Gibbs free energy between the bound state and the unbound state. Predicting the change in binding free energy (AAG), also known as the mutational effect, is crucial to modulating protein-protede interactions. Accurate prediction of AAG facilitates the identification mutations that enhance or decrease the binding strength informs the efficient design of proteins, thus accelerating the development of therapeutic interventions and deepening our understanding of biological mechanisms.
Deep learning has demonstrated significant potential in protein modeling (Lin et al., 2022; Abramson et al., 2024), inspiring paradigm shift in computational methods for predicting A AGG Traditional biophysics-bard based and statistics- based approaches (Park al., 2016; Alford et al., 2017; Delgado et al., 2019) are increasingly being replaced by deep learning techniques (Shan et al., 2022a; Liu al., 2023). Despite advancements, AAG prediction is still hindered by the scarcity of annotated experimental data. Consequently, pre-training on extensive unlabeled data has emerged as prevalent strategy for AAG prediction (Luo et al., 2023: Wu al., 2024). Recent studies observe that structure prediction models and inverse folding models implicitly capture the energy landscape (Bennett et al., 2023; Widatalla al., 2024; Lu al., 2024). Although effective, these pre-training-basee approaches simply employ supervised fine-tuning (SFT) and neglect the importance of alignment. Since SFT may result in catastrophic forgetting of the general knowledge gained during unsupervised pre-traine pre-training. there remains an opportunity for better knowledge transfer.
In other biological tasks, recent studies have adapted alignment techniques from large language models, such as direct preference optimization (DPO) (Rafailov et al., 2023), to integrate experimental fitness information into biological generative models (Zhou et al., 2024; Widatalla et al., 2024; Chennakesavalu et al., 2024; Liu et al., 2024). However, directly adopting these alignment techniques for A AAG prediction is inadequate, as they lack the physical inductive bias required for energy-related biological tasks.
In this work, we propose a technique named Boltzmann Aligmment to transfer knowledge from pre- trained inverse folding models to AAG prediction. We first analyze the thermodynamic definition of AAG and introduce the Boltzmann distribution to connect energy with protein conformational distribution, thereby highlighting the potential of pre-trained probabilistic models. However, the protein conformational distribution is intractable. To address this, we employ Bayes' theorem to circumvent direct estimation and instead leverage the log-likelihood provided by protein inverse folding models for AAG estimation. Our derivation provides rational perspective on the previously observed high correlation between binding energy and log- likelihooooo from inverse folding models (Bennett et al., 2023; Widatalla et al., 2024; Shanker et al., 2024). Compared to previous inverse folding-based methods, our method explicitly considers the unbound state of the protein complex, enabling fine-tuning of inverse folding models in manner consistent with statistical thermodynamics. Our contributions can be summarized as follows:
We propose Boltzmann Alignment, which introduces physical inductive bias through Boltz- mann distribution and thermodynamic cycle to transfer knowledge from pre-trained inverse folding models to AAG prediction. We not only provide an alignment technique, but also offer insight into the high correlation previously observed between binding energy and log-likelihood in inverse folding models.
Experimental results on SKEMPI v2 indicate that our method achieves Spearman coefficients of 0.3201 (unsupervised) and 0.5134 (supervised) on SKEMPI v2, significantly exceeding the previously reported SoTA values of 0.2632 and 0.4324, respectively. Further ablations demonstrate that our approach outperforms previous inverse bolding-based methods and other alignment techniques. Additionally, we showcase the broader applicability of our method in binding energy prediction, protein-protein docking, and antibody optimization.
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RELATED WORK
2.1 ALIGNMENT OF GENERATIVE MODELS
The prevailing pre-training approach for generative models, which focuses maximizing the likelihood of training data, often falls short in aligning with specific user preferences. Consequently, there is growing interest in integrating task-specific information while maintaining the generative capabilities, especially in large language models (LLM). A commonly used alignment method is supervised fine-tuning (SFT), where models undergo additional training on curated datasets with specific annotations, utilizing a straightforward loss function. However, SFT poses the risk of overfitting to the fine-tuning dataset, which may result in catastrophic forgetting of the general knowledge gained during unsupervised pre-training. Much of the current alignment paradigm relies on reinforcement learning from human feedback (RLHF) (Ouyang et al., 2022). Within this framework, human preferences provided as pairwise rankings are used to train reward model, which can then optimize a policy using proximal policy optimization (PPO) (Schulman et al., 2017). An alternative approach, known as direct preference optimization (DPO) (Rafailov al., 2023), serves as a plug-and-play method that maximizes the likelihood of preferences. Numerous recent studies have expanded on the concepts of RLHF and DPO (An al., 2023; Azar et al., 2023; Meng et al., 2024: Zhang et al., 2024).
Despite these advancements LLM, developing effective methods integrate experimental fitness information into biological generative models remains a crucial open question. Park et al. (2023) and Chennakesavalu et al. (2024) explore alignment in the context of inverse molecular design, enhancing the desired properties of generated compounds against a drug target. Liu et al. (2024) fine-tunes retrosynthetic planning models with a preference-basee loss to improve the quality of generated synthetic routes. AbDPO (Zhou et al., 2024) introduces direct energy- preference optimization to structure-sequence antibody co-design diffusion model, producing antibodies with low energy and high binding affinity. Mistani & Mysore (2024) incorporates DPO into protein language models to generate peptides with desirable physicochemical properties that bind to a given target protein. ProteinDPO (Widatalla et al., 2024) imbues inforre protein language model with biophysical information through DPO, enabling it to score stability and generate stable protein sequences. These efforts collectively underscore the potential of alignment techniques in advancing the performance of biological generative models.
2.2 PROTEIN-PROTEL INTERACTION MODELING
Protein-protein interaction modeling has been extensively studied for decades, primarily concentrating on two key questions: where proteins interact, known as binding site prediction (Tubiana et al., 2022; Fang et al., 2023), and how they interact, addressed by protein-protein docking (Yan et al., 2020; Ketata et al., 2023). Recently, AlphaFold3 (Abramson et al., 2024) reaches almost 80% success rate of predicting general protein complex structures, effectively tackling both the "where" and "how" of protein-proted interactions. However, structure is not everything (Lowe, 2023); biomolecular interactions cannot be fully captured by static structures alone. A comprehensive understanding requires appreciating the dynamic processes of association and dissociation between protein partners (Lu et al., 2024), which are quantified by measures such as the binding affinity (Kd) or binding free energy (AG). Predicting the change in binding free energy (AAG) is thus crucial for modulating protein-protein interactions; it enables the identification of mutations that enhance or diminish binding strength, which is essential for efficient protein design. For example, in antibody discovery, accurately predicting AAG is fundamental to antibody maturation.
variety of methods have been developed to predict AAG. Traditional approaches can be categorized into two main types: biophysical and statistical methods. Biophysical methods (Park et al., 2016; Alford et al., 2017: Delgado et al., 2019) use energy calculations to model how proteins interact at the atomic level, but they often struggle with balancing speed and accuracy. Statistical methods (Geng et al., 2019; Zhang et al., 2020) depend on feature engineering, utilizing descriptors that capture geometric, physical, and evolutionary characteristics of proteins. Traditional approaches depend heavily on human expertise and struggle to accurately capture complex interactions between proteins. Recently, deep learning- based approaches have emerged. Despite advancements in end-to- end learning approaches (Shan et al., 2022a), AAG prediction is still limited by the lack of annotated experimental data. As result, pre-training on extensive unlabeled data has become common
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strategy for improving predictions, involving various pre-training proxy tasks such protein inverse folding (Yang et al., 2020), side-chain modeling (Luo et al., 2023; Liu et al., 2023; Mo et al., 2024), and masked modeling (Wu et al., 2024). These in-depth explorations of pre-training proxy tasks not only establish a solid foundation but also highlight the urgent need for transferring acquired knowledge accurately predict AAG.
METHOD
Based on the Boltzmann distribution and thermodynamic cycles, as illustrated on the right side of Figure I, we first establish the connection between AAG and protein sequence likelihoods, which we call Boltzmann Aligmment (Sec. 3.1). Next. we present method (Sec. 3.2) that integrates the inverse folding model into Boltzmann alignment. This method is named BA-Cycle and uses the inverse folding model to evaluate A AGG by predicting the likelihoods of protein sequences, as shown on the left side of Figure Upon BA-Cycle, we introduce a method named BA-DDG (Sec. 3.3) to fine-tune the inverse folding model using AAG-labeled data, introducing an inductive bias from statistical thermodynamics.
3.1 BOLTZMANN ALIGNMENT
To simplify the explanation, we introduce the case where the complex consists of two chains, chain A and chain B; however, the following content can be extended to cases with more chains. The binding free energy (AG) of the complex is the difference between the Gibbs free energy of the bound state, denoted as Goad, and the Gibbs free energy of the unbound state, denoted as Gunbna Furthermore, using the Boltzmann distribution (Atkins et al., 2023), we can express the binding free energy (AG) terms of the probabilities of the two chains being the bound state, Pund: and the unbound state, Punbod, with the partition function eliminated by the two-state comparison:
AG Gond
Gunbad
- (log Pbod
log Punbad)
(1)
where ky is the Boltzmann constant and T is the thermodynamie temperature. Specifically, the probabilities Phod and Puntud represent the probabilities of the protein complex structure being in the bound conformation Xond and the unbound conformation Xunbnd respectively, when the protein complex sequence SAB is given. Therefore, Pbod and Punbad can be expressed as the conditional probabilities p(Xond SAB) and p(Xunbnd SAB). where we simplify and approximate Xbnd and Xunbod as the backbone structure of the protein complex. Substituting these conditional probabilities into Eq. gives:
AG = T ((ogp(XGba 8AB) log (XC (AA))
Estimating p([| 8) poses several challenges. First, most current protein structure prediction models typically predict a single conformation and are not inherently probabilistic. Although these models provide uncertainty metrics such as pLDDT, pAE, and pTM (Abramson et al., 2024), and while these metrics have been observed to correlate with binding free energy (Lu et al., 2024), they do not offer a true probabilistic interpretation. Second, although recent efforts (Jing et al., 2023; 2024; Abramson et al., 2024) aim to introduce probabilistic models, specifically diffusion models, these neural networks learn to estimate the score Vx log p(X( 8) rather than p(X 8). Moreover, due to the relatively low sample efficiency of diffusion models, directly estimating p(X 8) remains intractable. Therefore, we use Bayes' theorem to circumvent direct estimation:
p(8 13) p(X) p(8)
xx 8)
Substituting this Bayes' theorem equation into Eq. and eliminating the protein complex sequence probability p(SAB) gives:
AG -knT. (log p(8Au (onu) p p(Kons)
p(SAB
Kuntand) (Funtoas)
llog
(4)
p(8AB) p(SAR Xrmat) ((Goon))
p(8AB)
T log
(5)
p(8AB Kumbond) p(ppp (Xuntma))
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At this point, we have established the connection between the conditional probability of the protein sequence p(8 X) and AG. Next, based on this, we further analyze the connection between the conditional probability of the protein sequence p(S X) and AAG. Specifically, AAG represents the difference between the AG of the wild type and the AG of the mutant type. The wild type and mutant type refer to the unmutated and mutated protein complexes, respectively. To distinguish between these two types, we denote them by adding "mut" and "wt" in the upper right corner of the notation; for example, A represents the AG' of the mutant type. With this notation, we can express A AG based on Eq. 5 as follows:
AAG AGmit AGW
(6)
log
p( p(8A
log
P p
AB
Innd
p(SAB
gmut
mmt
p( (00nnbad
Sww AB
Xww
unbmaa)
pp (emmmaaa
pp
The backbone structure of the mutant type, X is actually unknown. To address this issue, introduce the assumption used in previous methods that the protein backbone structure remains unchanged before and after mutation. Therefore, can approximate X be equal to Xnphod and Xou to be equal to X Based on this assumption, we can eliminate the probability terms in Eq.
AAG -kpT (log
P(SAB
bed
log
p (SwL
AB
wt
X
(8)
p
unbed
Xww unbnd
3.2 PROBABILITY ESTIMATION
Eq. 8 transforms AAG into the likelihoods of protein sequences P(SAB X). Here, we demonstrate the method of estimating the sequence probabilities of the bound state, p(8AB Xxma), and the unbound state, P(8AB Xumnhna), using the inverse folding model. Since we assume that the backhone structure remains unchanged before and after mutation, i.c., X0 X the evaluation method for both the wild type and mutant type is identical, and no additional discussion is required.
The bound state. In our task, the backbone structure Xood of the bound state usually known. Therefore, the inverse folding model can directly evaluate the probability p(SAB Xond). We denote the probability predicted by the inverse folding model as (S Xona), where 6 is the model parameter.
The unbound state. The unbound state is typically not explicitly provided in known backbone structure; therefore, propose alternative probability estimation method. The unbound state approximately represents the scenario where chains A and of the complex are relatively far apart, with minimal interactions between them. Thus, a reasonable estimation approach is independently evaluate these two chains using the inverse folding model. We denote the structure and sequence of chain A XA and SA, and those of chain B Xg and Sg. The estimation method for P(SAB (uubbnd) can be expressed as:
P(SAB (ambmaa (8 Xx) (8 XB)
where (8 [x)) and (Sp XB) the probabilities predicted by the inverse folding model.
Unsupervised estimation of AAG. Based on the estimation method described above, we can utilize pretrained inverse folding model, ProteinMPNN (Dauparas al., 2022), achieve unsupervised
evaluation of AAG. We name this approach BA-Cycle, which can be expressed as:
AAG -k (log
( X
(Smul yymut)
bnd
log
pa ( (
(10)
pa
(quut
pa (Sg
pa (SWE
XX)
pa (SWE
2OWL
Comparison with previous work. Previous work (Bennett et al., 2023: Cagiada et al., 2024: Widatalla et al., 2024; Shanker et al., 2024) attempts to use protein inverse folding models to predict AAG. However, these studies do not explicitly account for the unbound state Punbad in the thermodynamic cycle. We denote these methods as AAGPrev summarized as:
AAGrey -khpT -log Po (a X log po (8 (
(gmur
(11)

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3.3 SUPERVISION
We propose BA-DDG, a method that leverages AAG-labeled data to fine-tune BA-Cycle through Boltzmann Alignment. BA-DDG employs forward process identical to that of BA-Cycle. During training, the parameters 0 of the inverse folding model and kg in Eq. 10 are treated as learnable parameters that undergo optimization. The objective of BA-DDG is minimize the discrepancy
between the ground truth AAG and the predicted AAG, while maintaining the distribution of the original pre-trained model, denoted as the reference model distribution Prer(8 XC). The corresponding loss & Boltzmann can be expressed as;
L Boltzmann
BAG AAG| - -BDKL 23 lptt (8 (3)
(12)
minimize predicted error
distributional penalty
where 33 is hyperparameter that controls the strength of the distributional penalty.
4 EXPERIMENTS
In this section, we investigate three key questions through a series of experiments: (1) whether the physics-infoo -nsfrm-informme alignment technique we propose can achieve state-of-the-art (SoTA) accuracy
the SKEMPI v2 dataset under both unsupervised and supervised settings (Sec. 4.2); (2) whether the introduced thermodynamic cycle is indeed effective and has advantages over traditional SFT and DPO methods; (3) whether predicted structures can effectively replace crystal structures as inputs in our method (Sec. 4.3). Before addressing these questions, we first introduce the benchmarks and baselines (Sec. 4. Additionally, we explore potential applications of our method, taking binding energy prediction, protein-protein docking and antibody optimization as examples (Sec. 4.4).
4.1 BENCHMARK
Dataset. The SKEMPI v2 dataset (Jankauskaité al., 2019), the extensive annotated mutation dataset for 348 protein complexes, includes 7,085 amino acid mutations along with changes in thermodynamic parameters and kinetic rate constants. Despite lacking structures of the mutated complexes, it serves as the most well-establishe benchmark for AAG prediction. To prevent data leakage. we follow Luo et al. (2023) and Wu et (2024), first dividing the dataset into 3 folds by structure, ensuring each fold contains unique protein complexes. This division forms the basis of our 3-fold cross-validation process, where two folds are used for training and validation, and the third fold is reserved for testing. This approach yields 3 different sets of parameters and ensures that every data point in SKEMPI v2 is tested once.
Evaluation metries. To thoroughly assess the performance of AAG prediction, utilize a total of 7 metrics. This includes 5 overall metrics: (1) Pearson correlation coefficient, (2) Spearman's rank correlation coefficient, (3) minimized RMSE (root mean squared error), (4) minimized MAE (mean absolute error), and (5) AUROC (area under the receiver operating characteristic). To calculate AUROC, binary classification labels assigned mutations based the sign of the AAG predictions. In practical settings, the correlation for individual protein complexes tends to be of greater importance. Consequently, we group mutations by their structural characteristics, calculate the Pearson and Spearman correlation coefficients for each group, and then report the average of these per-structure correlations 2 additional metrics.
Baselines, We compare our AAG predictors, BA-Cycle and BA-DDG, with state-of-the-art unsu- pervised and supervised methods, respectively. Unsupervised methods are categorized into three groups: (I) traditional empirical energy functions such as Rosetta Cartesian AAG (Alford et al., 2017) and FoldX (Delgado et al., 2019); (2) sequencelevollttinn-
approaches, exemplified by ESM-1v (Meier et al., 2021), Position-SSeeiff Scoring Matrix (PSSM), MSA Transformer (Rao et al., 2021), and Tranception (Notin et al., 2022); (3) structure-informed pre-training-bee not trained on A AAG labels, such ESM-IF (Hsu et al., 2022), MIF-Alogits (Yang et al., 2020), RDE-Linear (Luo et al., 2023), and a model pre-trained to predict residue B-factors that are then used to predict AAG. Supervised methods can be divided into categories: (1) end-to-end learning mod- els. including DDGPred (Shan et al., 2022a) and a model that utilizes a self- attention based network (Jumper et al., 2021) as the encoder but employs MI.P directly predict AAG (End-to-Ende (2)
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Table 1: Mean results of 3-fold cross- cross- validation the SKEMPI v2 dataset. Bold and underline indicate the best metrics for methods trained and not trained on the AAG labels, respectively.
Per-Structure
Overall
Supervision
Method
Pearson
Spear.
Pearson
Spear.
RMSE
MAE.
AUROCT
Rosetta
0.3284
0.2988
0.3113
0,3468
16173
1.311
0.6562
FoldX
0.3789
0.3693
0.3120
0,4071
1.9080
1.3089
0.6582
ESM-1v
0.0073
00.1188
0.1921
0.1572
1. 1.9609
1.3683
0.5414
PSSM
0.0826
0.0822
0.0159
0.0666
1.9978
1.3895
0,5260
x
MSA Transformer
0.1031
0.0868
0.1173
0.1313
1,9835
1.3816
0.5768
Tranception
0.1348
0.1236
0.1141
0.1402
2.0382
1.3883
0,5885
B-factor
0.2042
0.1686
0.2390
0.2625
2.0411
1.4402
0.6044
ESM-IF
0.2241
0.2019
0.3194
0.2806
1.8860
1.2857
0.5899
AlF--logit
0,1585
0.1166
0.2192
1.9092
1.3301
RDE-Linear
0,2903
0.2632
0.4185
0.3514
1.7832
1.2159
0.6059
BA-Cycle
0.3722
0.3201
0.4552
0.4097
1.8402
1.3026
0.6657
DDGPred
0.3750
0.3407
0.6580
0,4687
1,4998
1.0821
O. 0.6992
End-to-End
0.3873
0.3587
0,6373
0.4882
1,6198
1.1761
0.7172
MIF-Network
0.3965
0.3509
0.6523
0.5134
1.5932
1.1469
0.7329
RDE-Network
0.4448
0.4010
0.6447
0,5584
1.5799
1.1123
0.7454
DiffAffinity
0.4220
0,3970
0.6609
0.5560
1.5350
1.0930
0.7440
Prompt-DDG
0.4712
0.4257
0.6772
0.5910
1,5207
1.0770
0.7568
ProMIM
0.4640
0.4310
0.6720
0.5730
1,5160
1.0890
0.7600
Surface- Surface-VQMAF
0.4694
0.4324
0.6482
0.5611
1.5876
1.1271
0.7469
BA-DDG
0.5453
0.5134
0.7118
0.6346
1.4516
1.0151
0.7726
ceuuttre-informer pre-training --a-rriinin--beedd methods fine-tuned on AAG labels, including MIF-Network (Yang et al., 2020), RDE-Network (Iuuo al., 2023), DiffAffinity (Liu al., 2023). Prompt-DDG (Wu et al., 2024), ProMIM (Mo et al., 2024), and Surface- VOMeEE (Wu & Li, 2024).
4.2
MAIN RESULTS
Comparison with baselines. According to Table 1, our BA-DDG outperforms all the baselines across all evaluation metrics. Notably, it demonstrates significant improvement per-structure correlations, highlighting its greater reliability for practical applications. BA-Cycle achieves compa- rable performance empirical energy functions and surpasses all unsupervised learning baselines. Detailed results for single-point, multi-point, and all-point mutations are available in Table 6.
Visualization for correlation analysis. We present scatter plots experimental and predicted AAG for three representative methods in Fig. 2, along with their overall Pearson and Spearman correlation scores. Additionally, Fig. shows the distribution of per-structure Pearson and Spearman correlation scores, well as the average results across all structures. It is evident that BA-DDG outperforms other methods both qualitative visualization and quantitative metrics.
RDE-Network
Prompt-DDG
BA-DDG
Pearson-e
Pearson
0.7118
0.6346
Predicted
-10
Expartmental ANG
Expertmental 4AG
Experimental &GG
Figure 2: Comparison of correlations between experimental AAG and AAG predicted by three representative methods.
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1.0
1.0-
Pe-Structure Nearion
Per-Stuccure Spearman
0.0-
-0.3
-0.5
0.2741
0.3201
RDE-Unear
ProteinMPNN
By-Cycle
RDE Network
Promptt-O0 DDG
BA-DOG
ADE-Liear
PyoteloMPNN
BA-Gyde
nDE-Network
Prompt DDG
BAODG
Figure 3: Distributions of per-structure Pearson correlation scores and Spearman correlation scores for six representative methods.
4.3 ABLATION STUDY
Ablation study on thermodynamic cycle. As shown in Table 2, we evaluate the impact of thermody- namic cycle using 3-fold cross- voss--vlliation on the SKEMPI v2 dataset. We compare our training freee version BA-Cyele the basic usage of protein inverse folding models, as demonstrated previous studies (Bennett et al., 2023; Cagiada et al., 2024; Widatalla et al., 2024). As described in Eq. 11, these studies do not account for thermodynamic cycle, as they consider only Pbod and neglect Punbod Disregarding thermodynamics significantly harms performance, BA-Cycle outperforms ESM-IF and the original ProteinMPPNN.
Table 2: Ablation study on thermodynamic cycle. We report the mean results of 3-fold cross-validation on the SKEMPI v2 dataset. Bold indicate the best metrics.
Per-Structure
Overall
Method
Pearson f Spear.
Pearson f Spear.
RMSE
MAE +
AUROC
ESM-IF
0.2241
0.2019
0.3194
0.2806
1.860
1.2857
0.5899
ProteinMPNN
0.2825
0.2741
0.2753
0.3112
1.9869
1.4048
0.6191
BA-Cycle
0.3722
0.3201
0.4552
0.4097
1.8402
1.3026
0.6657
Ablation study on supervision methods. As presented in Table 3, we evaluate the impact of various supervision methods. The training and inference settings are the same as in the main results. The implementation details of other alignment techniques can be found in Appendix A.1. Boltzmann supervision yields the best performance across all evaluation metrics, compared other alignment techniques like SFT and DPO. These results clearly demonstrate the effectiveness of our proposed methods.
Table 3: Ablation study on supervision methods. We report the mean results of 3-fold cross-validation on the SKEMPI dataset. Bold indicate the best metrics.
Per-Structure
Overall
Supervison
Pearson f Spear.
Pearson
Spear.
RMSE +
MAE
AUROC
SFT
0.5167
0.4769
0.7048
0.6240
1.4661
1.0346
0.7725
DPO
0.4212
0.3913
0.5397
0.4870
1.7399
1.2422
0.7036
Boltzmann
0.5453
0.5134
0.7118
0.6346
1.4516
1.0151
0.7726
Inference with predicted structures. The SKEMPI v2 benchmark includes wild-type crystal structures, which are also used by previous state-of-the-art methods such as Prompt-DDG (Wu et al., 2024) and RDE (Luo et al., 2023). However, crystal structures of mutants often unknown, and using wild-type structures for mutants can introduce errors, especially with multiple mutation sites. In practical applications, such antibody design, only sequence information may be available without a template crystal structure. To assess the usability AAG prediction models in various practical scenarios, we investigate whether fine-tuned ProteinMPNN relies crystal structures inputs
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to predict AAG, presented in Table 4. While the performance with AlphaFold3 predicted structures is slightly lower, the differences are minimal, indicating that our method does not strictly require crystal structures when reasonably accurate predicted structure is available.
Table 4: Comparison of inference with AlphaFold3 (Abramson et al., 2024) predicted structures and crystal structures. We report the mean results 3-fold cross-validation on the common subset of Test Set I from SKEMPI as defined in SSIPe (Huang et al., 2019) and the SKEMPI dataset employed in DSMBind (Jin et al., 2023). During the 3-fold cross-validation, models are trained on the SKEMPI v2 dataset using crystal structures as inputs and validated the subset using AlphaFold3 predicted structures, Both the AlphaFold3 predicted structures and the dataset are provided by Lu et al. (2024).
Per-Structure
Overall
Structure
Pearson t
Spear.
Pearson
Spear.
RMSE
MAE
AUROC
Crystal AlphaFold3
0.8057
0.7322
0.8584
0.7946
1.3948
0.9713
0,8437
0.8017
0.7459
0.8545
0.7821
1.4122
0.9817
0.8314
4.4
APPLICATION
4.4.1
BINDING ENERGY PREDICTION
Antibody design is vital for treating diseases such as cancer and infections. Although we lack a com- prehensive explanation for canceling out p(X(ra) and p(Xunnus) in Eq. 5, BA-DDG approximate AG using only inverse folding:
AG ~ kgT (log P XAB) (log,a(SA, XA) + log Pe(B (GB)))
(13)
We benchmark untibody-antigen binding energy predictors, with the experimental setup proposed in DSMBind (Jin al., 2023). DSMBind is an unsupervised method trained on 3,416 antibody- antigen complexes from SAbDab (Schneider et al., 2021). SAbDab has over 3,500 non-redundant antibody-antiggen complex structures, but only 566 of them have binding energy labels. Other methods involve pre-training on the entire binding energy dataset from SKEMPI, followed by fine-tuning on antibody-antigen data from SKEMPI. We evaluate these methods on a SAbDab subset of 566 complexes with binding energy labels. As depicted in Fig. 4 (left), BA-DDG achieves Spearman correlation 0.385, outperforming other methods.
4.4.2 RIGID PROTEIN- COOTEIN-PRROEI DOCKING
DiffDock-PP (Ketata al., 2023) diffusion generative model specifically designed for rigid protein-protedd docking. It learss to translate and rotate unbound protein structures into their bound
0.385
0.8
Spearman Correlation
0.350
0.3
0.2
0.180
Fraction with
0.119
Perfect Selection
Diffiock-PP
DAG
0.0
0.3
Rosetta
FoloX
ESM-IF AF2
DSMBind BA-DOG
30
&G Prediction Mathods
Number of generative sampless
Figure 4: Left: The Spearman correlation between predicted and true binding free energy (AG) on the SAbDab test set. Right: Performance of selection methods for rigid protein-protein docking as the number of generative samples increases. "Perfect Selection" shows the best possible performance with ideal selection method. "Diffdock-PP" refers to the confidence model proposed by Diffdock- PP (Ketata et al., 2023). "BA-DDG" involves using our method to estimate AG for selection. Performance is assessed by calculating the fraction of 13 antibody complex generation tasks the DIPS test set (Townshend et al., 2019) that achieve C-RMSD of less than 5Å.

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conformations. The docking process comprises two primary steps. First, the diffusion model generates samples. Then, a pre-trained confidence model evaluates these samples to identify the one with the highest confidence score, which is used as the final docking result. BA-DDG can serve as an approximate binding free energy (AG) estimator and can be employed as selection method in diffusion-basee docking process. A lower AG' indicates more spontaneous and favorable transition from the unbound to the bound state, corresponding to higher confidence score for the generative docking sample. By integrating BA-DDG into the diffusion-based docking process, we provide robust method for selecting the most plausible docking conformation, as presented in Fig. 4 (right).
4.4.3 ANTIBODY OPTIMIZATION
Antibody optimization against SARS-CoV-2. Beyond serving as an energy scoring function, BA-DDG also acts structure-based protein designer, similar to ProteinMPNN. Consequently, we are curious whether the ProteinMPNN fine-tuned for AAG prediction tends to generate sequences with higher affinity. Shan et al. (2022b) identify five singl-poinn mutations in a human antibody targeting SARS-CoVe that significantly enhance its neutralization effectiveness. These mutations selected from pool of 494 possible single-point mutations within the heavy chain CDR region of the antibody. We calculate the perplexity differences and preference probabilities of these 494 possible single-point mutations relative to the wild-type sequence. Specifically, normalized per-amino acid perplexity is obtained by subtracting the average per-amino acid perplexity of all possible sequences from that of the mutant sequence. Preference probabilities are derived using the Bradley-Terry model (Bradley & Terry, 1952) applied to the predicted probabilities of wild-type and mutant sequences. The results, as presented in the Table 5, show that the fine-tuned BA-DDG generally achieves lower normalized perplexity and higher preference probabilities compared to the original ProteinMPNN, indicating a tendency to generate sequences with potentially higher binding affinity and improved neutralization effectiveness. Results on multi-point mutations, provided in the Table 7, further support this conclusion. This suggests that fine-tuning for AAG prediction can enhance the design of more effective antibody sequences.
Table 5: Normalized per-amino acid perplexity and preference probabilities of the five favorable mutations sequence the antibody against SARS- AARS-CoV-2 (Shan et al., 2022b) by original and fine-tuned ProteinMPNN.
Metric
Method
TH31W
AH53F
NH57L
RH103M
LH104F
Average
ProteinMPNN
6.018
0.179
0.401
2.895
2.521
2.403
Perplexity 4
BA-DDG
1.979
0.429
0.809
2.416
0.992
1.325
ProteinMPNN
12.61 %
62.55%
75.62%
13.93%
36.20%
42.47%
Preference f
BA-DDG
37.24%
68.65%
56.51%
25.10%
47.63%
47.03%
DISCUSSION AND CONCLUSION
We propose Boltzmann Alignment, method that leverages physical inductive bias through the Boltz- mann distribution and thermodynamic cycle to enhance AAG prediction by transferring knowledge from pre-trained inverse folding models. Experiments on SKEMPI v2 yield Spearman coefficients of 0.3201 (unsupervised) and 0.5134 (supervised), significantly surpassing previous wate-of-the-ar values of 0.2632 and 0.4324. Additionally, we demonstrate the broader applicability of our approach in binding energy prediction, protein-protein docking, and antibody optimization.
Our method has certain limitations that we aim to address in future work. Firstly, our approach requires crystal structures or reliable predicted structures as input; in cases where mutant protein structures are unavailable, we assume that the mutant backbone structure is identical to that of the wild-type protein; take parts of the complex backbone structure the backbone structure of single proteins. This reliance on structural data may limit the applicability and effectiveness our method. Moreover, current model does not consider side-chain conformations, which may be essential for AAG prediction. Incorporating side-chain flexibility could enhance predictive accuracy and provide deeper insights into protein-proted protein interactions.
The positive societal impact is that this work can assist in drug design and virtual screening potentially. No negative societal impact is perceived.
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ACKNOWLEDGMENTS
This work was supported by the National Key R&D Program of China (NO.2022ZD0160101) and the National Natural Science Foundation of China (No. 62206244).
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Fang Yang. Kunjie Fan, Dandan Song, and Huakang Lin. Graph-based prediction of protein- protein interactions with attributed signed graph embedding. BMC Bioinformatics, 21, 2020. doi: 10. 00001////112299900000336666 URL https://// /tt/kii..../ spr springer. www/articce//////eeccoo 8/ fwwltext..ttttoo html.
Ning Zhang, Yuting Chen, Haoyu Lu, Feiyang Zhao, Roberto Vera Alvarez, Alexander Goncearenco, Anna Panchenko, and Minghui Li. Mutabind2: predicting the impacts of single and multiple mutations on ppootenn interactions. iScience, 23(3), 2020.
Ruiqi Zhang, Licong Lin, Yu Bai, and Song Mei. Negative preference optimization: From catastrophic collapse to effective unlearning. arXiv preprint arXiv: 2404.05868, 2024. URL https:/ // arxiv. orgg abs 2404. 05868v1.
Xiangxin Zhou, Dongyu Xue, Ruizhe Chen, Zaixiang Zheng, Liang Wang, and Quanquan Gu. Antigen-specific antibody design via direct energy-based preference optimization. arXiv preprint arXiv: 2403.16576 2024. URL https: / wwwpiiiwogg/b//////eee 16576v1
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Published as a conference paper at ICLR 2025
A
IMPLEMENTATION DETAILS
A.1
OTHER ALIGNMENT TECHNIQUES
A.1.1
SFT
The training objective of trivial SFT is as follows:
SSFT
AAG Are
Drr.
1lerr (S X))
(14)
minimize predicted error
distributional penalty
A.1.2 DPO
We utilize weighted DPO algorithm proposed in Widatalla et al. (2024). The weighted DPO objective simply minimization of the KL-divergence between the distribution parameterized by the generative model and numerical scores (AAG' labels).
A.2 MODEL
In ProteinMPNN, part of the input protein sequence be designed, and the rest is fixed; decoding skips fixed regions but includes them in the context for designing the remaining positions during autoregressive decoding. When estimating AAG with ProteinMPNN, we designate the mutation sites Sp to be designed while fixing the rest of the sequence S Sp. Let (51, $2..... 8a) represent a randomly sampled decoding order, a permutation the mutation sites Sp. The joint probability
(S(S X) can be expanded step by step into the product of model-pree predicted probabilities for each amino acid site using the conditional probability formula:
(S X) (S X, Sp)
(15)
= SS {rs} X, So U (s1)) po(1s1} X, Sp)
(16)
A.3 TRAINING
A.3.1
HYPER-PARAMETER
We train the model over 20,000 iterations using the Adam optimizer, with learning and a batch size of 2. The small batch size is because we need to include both the wild-type and mutant complexes along with their respective monomer structures in single batch for each iteration. The model is insensitive to the loss weight parameter /, so it is typically set to low value, such as 0.001, during training.
at 0.0001
For the inverse folding model, we utilized the pre- mr--triine ProteinMPNN, which includes 3 MPNN layers. It considers the 30 nearest neighbors to construct edges and an embedding dimension of 256.
A.3.2 HARDWARE
All our experiments are conducted on a computing cluster with CPUs of AMD EPYC 7763 64-Core 3.52GHz and single NVIDIA GeForee RTX 4090 24GB GPU.
A.4
ASSUMPTION
Independence approximation in the unbound state.
The unbound state generally refers to a condition where no significant inter-chain interactions exist. While weak inter-chain interactions (e.g., transient or solvent-mediated interactions) may occasionally occur in this state, such interactions typically exert minimal influence on free energy calculations. This supports the common and effective assumption of treating the unbound state independent prob- abilities for individual chains, a simplification that substantially reduces computational complexity while introducing negligible error.
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Published as a conference paper at ICLR 2025
Conversely, inter-chain interactions dominate in the bound state. To explicitly model these critical interactions, we calculate the bound state's s probability by inputting the entire complex into Protein- MPNN. This approach retains all inter-chain interactions through their explicit representation as edges in the model's graph structure.
B ADDITIONAL RESULTS
B.1 BINDING ENERGY PREDICTION
We compare BA-DDG with several representative methods under single-point, multi-point, and all- point mutations on SKEMPI v2. The results reported in Table 6 demonstrate that BA-DDG achieves the best overall performance for single-point mutations and the best per-structure performance for multi-point mutations. Notably, BA-DDG performs better on single-point mutations compared to multi-point mutations, which may be related the autoregressive decoding of ProteinMPNN. In our BA-DDG, when dealing with multi multi-point mutations, the probability estimation for a new site depends on the estimation the previous site. This coupling might affect performance, presenting an opportunity for future improvements.
Table 6: Performance comparison under single-, multi- and all-point mutation on SKEMPI v2, where bold denotes the best metric under each setting.
Per-Structure
Overall
Method
Mutations
Pearson
Spear:
Pearson f
Spear.
RMSE
MAE
AUROC
all
0.3284
0.2988
0.3113
0.3468
1.6173
1.1311
0.6562
Rosetta
single
0,3510
0.4180
0.3250
0.3670
1.1830
0.9870
0.6740
multiple
0.1910
0.0830
0.1990
0.2300
2.6580
2.0240
0.6210
all 0.3789
0.3693
0.3120
0.4071
1.9080
1.3089
0.6582
FoldX
single 0,3820
0,3600
0.3150
0,3610
1.6510
1.1460
0.6570
multiple
0.3330
0,3400
0.2560
0,4180
2.6080
1.9260
0,7040
all 0.3750
0.3407
0.6580
0.4687
1.4998
1.0821
0.6992
DDGPred
single
0.371 I
0.3427
0.6515
0.4390
1.3285
0.9618
0.6858
multiple
0,3912
0.3896
0.5938
0.5150
2.1813
1.6699
0.7590
all 0.3873
0.3587
0.6373
0.4882
1.6198
1.1761
0.7172
End-to-End
single
0.3818
0.3426
0,6605
0.4594
1.3148
0.9569
0.7019
multiple
0.4178
0.4034
0.5858
0.4942
2.1971
1.7087
0.7532
0.4448
0.4010
0.6447
0.5584
1.5799
1.1123
0.7454
RDE-Network
single
0.4687
0.4333
0.6421
0.5271
1.3333
0.9392
0.7367
multiple
0.4233
0.3926
0.6288
0.5900
2.0980
1.5747
0.7749
all 0.4220
0.3970
0.6609
0.5560
1.5350
1.0930
0,7440
DiffAAfinity
single
0.4290
0.4090
0.6720
0.5230
1.2880
0.9230
0,7330
multiple
0.4140
0.3870
0.6500
0.6020
2.0510
1,5400
0.7840
all 0.4712
0.4257
0.6772
0.5910
1.5207
1.0770
0.7568
Prompt-DDG
single
0.4736
0.4392
0.6596
0,5450
1.3072
0.9191
0.7355
multiple
0.4448
0.3961
0.6780
0.6433
1.9831
1.4837
0,8187
all 0.4640
0.4310
0.6720
0.5730
1.5160
1.0890
0.7600
ProMIM
single
0.4660
0.4390
0.6680
0.5340
1.2790
0.9240
0.7380
multiple
0.4580
0.,2500
0.6660
0.6140
1,9630
1.4910
0.8250
0.5453
0.5134
0.7118
0.6346
1.4516
1.0151
0.7726
BA-DDG
single
0.5606
0.5192
0.7321
0.6157
1.1848
0.8409
0.7662
multiple
0.4924
0.4959
0.6650
0.6293
2.0151
1.4944
0.7875
B.2 ANTIBODY OPTIMIZATION
We provide results on multi-point mutations, which further support the conclusion that fine-tuning ProteinMPNN for AAG prediction enhances the design more effective antibody sequences. These findings confirm that the fine-tuned BA-DDG generally generates sequences with lower perplexity and higher preference probabilities, indicating higher binding affinity and improved neutralization effectiveness.
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Published as a conference paper at ICLR 2025
Table 7: Normalized per-amino acid perplexity and preference probabilities for the multi-point mutation sequences derived from multiple optimization rounds the antibody against SARS-CoV-2 (Shan et al., 2022b), as predicted by the original and fine-tuned ProteinMPNN.
Perplexity
Preference
Mutations
BA-DDG
ProtcinMPNN
BA-DDG
ProtcinMPNN
RHI03M,LHIOG
1,556
2.524
32.12%
17.60%
TH30P,RHI03M
1.023
1.310
53.22%
45.09%
TH31W,RH103M
1.669
3.894
36.87%
13.63%
AH39F.RH103M
1.658
6.312
31.13%
2.478%
100M
1.465
2.600
36.04%
15.20%
NH57L.RHI03M
1.366
0,936
44.32%
57.68%
TH3OP.RHIOSM,
1.151
2.181
45.21
22.29%
1.442
2.941
39.40%
22.71%
TH30P, TH31 W.RHI03M
1.203
2.606
45.74%
22.44%
1H39F.RH103M_LHIOO
1,300
4.621
37.94%
4.705%
AH39F.NH55LLRHIOO
1,500
4,929
34.63%
3.416%
HISSL.NH55L.RH10SS
1.210
1.403
42.93%
36.75%
AH39F.NH57L.RHIII
1.409
2.329
38.18%
15.82%
TH33P,AH.39,RRM ROMM
1.136
2.841
43.07%
10.82%
1.606
6.742
34.08%
2,438%
FH3IW.NH55L,RRHH
1.419
3,302
39.33%
18.19%
THL3PP.NH5LL.RHOOOO
1.012
0,948
52.97%
51.40%
THB/W.NHS7L.RHI0M
1,465
2.556
40.62%
27.91%
AIB9FTHHBOPRRHIIMMMEHHHG
1.081
3,036
44.56%
7.513%
Average
1.351
3.053
40.65 %
20.95%
18


Reviews:
[{"review_id": "FCU5M5FcEA", "reviewer": "Reviewer_V65x", "summary": "This paper employs pre-trained inverse folding models based on the Boltzmann distribution and thermodynamic cycles to associate energy with log-likelihood from inverse folding models for predicting ΔΔG. It introduces both unsupervised and supervised inverse folding models, each achieving state-of-the-art (SoTA) accuracy on the SKEMPI v2 dataset. Additionally, the study demonstrates that the proposed thermodynamic cycle is effective and offers advantages over traditional SFT and DPO methods. Notably, the method does not strictly require crystal structures when a reasonably accurate predicted structure is available. Furthermore, the paper explores applications of this approach in binding affinity energy prediction, protein-protein docking, and antibody optimization.", "questions": "1. In Section 4.1, Dividing the dataset into 3 folds by structure cannot strictly prevent data leakage, different protein complexes might have similar protein binding structures, can you elaborate more about the method you used to split data and prevent data leakage? \nCould you explain more about data partition process, why it can help to reduce data leakage process?\n\n2. Could you explain more about data partition process, and why it can help to reduce data leakage process?\n\n3. The SKEMPI dataset includes both single-point mutations and multiple-point mutations. Given the varying complexity, predicting binding affinity for single-point mutations may be less challenging and could potentially yield more accurate prediction results compared to multiple-point mutations. This raises the question: why not consider training separate models tailored for single and multiple mutation binding affinity prediction tasks, rather than using a single model for both?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. It creatively used Boltzmann Alignment, which introduces physical inductive bias through Boltzmann distribution and thermodynamic cycle to link binding energy and log-likelihood in inverse folding models.\n\n2. This work achieved SOTA and outperforms other SFT and DPO methods. The method can not only be used in binding energy prediction, but also be used in  protein-protein docking, and antibody optimization.", "weaknesses": "1. The code is not available,  it should be open-sourced upon publication.\n\n2. Dividing the dataset into 3 folds by structure cannot strictly prevent data leakage, different protein complexes might have similar protein binding structures.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TMs79qlVEZ", "reviewer": "Reviewer_XU4j", "summary": "In this paper authors propose a novel, thermodynamics inspired, approach for predicting binding free energy change upon mutation (ddG) building, in particular, on the capabilities of protein inverse folding models. Validation of the method employs standard literature benchmark (SKEMPI v2 curating and integrating a vast number of experimental measurements of ddG across various types of proteins). Beyond that, authors demonstrate applicability of their method across several tasks (binding energy prediction, antibody optimisation and docking). The reported results, in general, significantly outperform a spectrum of modern methods presented in the relevant literature both in supervised and unsupervised context.", "questions": "- In section 4.4.3 authors utilise dataset from Shen et al (2022) however focus only on point mutations. This dataset is, I think, much richer and contains double and triple mutants from multiple optimisation rounds. I believe it would be important to expand this section to show proposed model performance more extensively. This, I believe, has a potential to boost the impact and trust in the model in a typical antibody design scenario. \n- Following on sec 4.4.3 - preference probabilities are a good metric but they in my view they are a bit abstract. I think a simpler metric of e.g. how the method ranks particular mutation would be more interpretable (as they relate to simple consideration of how many designs one can screen in the wet lab before finding a particular hit). \n- In the typical design scenario, as the problem is hard and the reported performance of the method is not perfect, one can also consider the uncertainty of the prediction which is an important and frequently used feature in e.g. protein folding models. It could potentially strengthen the paper if authors could discuss and provide more information on how uncertainty estimation could be introduced to the model.\n- In appendix B - authors write \"We compare BA-DDG with several representative methods under single-point, multi-point, and\nall-point mutations on SKEMPI v2\". It's not clear to me what is the difference between multi-point and all-point mutations. Is the all-point a union of point- and multi-point mutations (I'd assume so by looking at the following Table) ? For clarity authors can consider to explain this more in the paper. \n- The discussion about computational (non-ML) methods for ddG estimation is scarce. Even though it's purely ML venue, I miss a bit more thorough discussion of how the proposed method relates to force-field methods utilising more nuanced thermodynamical cycles / approaches like MM-GBSA/PBSA, FEP, TI, etc.", "limitations": "", "rating": 10, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The paper is very well written and, I believe, easy to follow both for machine-learning and also, to large extent, for biology-oriented audiences thus extending its potential impact. The limitations and weaknesses are appropriately discussed. It focuses on relevant and important problem in protein science - predicting the energetic effect of mutation on the free energy of protein-protein complex formation. The contribution is clearly original, correctly references and builds upon several already existing contributions in the field (in particular - inverse folding models, direct preference optimisation). Most importantly, benchmark reports significant improvement across several investigated metrics on commonly-accepted dataset (SKEMPI) and described ablations and controls (folded structures) strengthen the confidence in the reported result.", "weaknesses": "- Method is structure based, it requires at least experimentally resolved or confidently predicted complex structure,\n- The representation of protein is rather coarse, only backbone. Side-chain atoms and solvent molecules are omitted yet they are obviously important drivers of protein-protein interactions.\n- No representation of dynamics (structures are represented as static snapshots), which can affect the method performance for mutations inducing significant conformational changes.\n- The described method seems to excel at point mutations and there's a trend towards decreased performance in more complex multiple mutations.\nMajority of those weaknesses are highlighted and discussed by the authors in the appropriate sections across the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "K7dA4IFwAh", "reviewer": "Reviewer_Mp9v", "summary": "The paper presents Boltzmann Alignment, a novel approach for predicting changes in protein-protein binding free energy due to mutations. It utilizes pre-trained inverse folding models and introduces physical inductive bias through the Boltzmann distribution.", "questions": "Are there any specific types of mutations or protein interactions where the authors have observed the method to be particularly effective or challenging? Sharing such insights could help guide future research directions.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The integration of Boltzmann distribution within the framework to enhance ∆∆G prediction is innovative and addresses a significant challenge in computational biology.\n- The authors effectively showcase the versatility of their method in binding energy prediction, protein-protein docking, and antibody optimization, indicating its broad applicability.\n- The paper is well-organized, and the results are presented clearly, making it easy for readers to follow the methodology and findings.", "weaknesses": "I haven't identified any significant weaknesses.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "lLAwre2bZF", "reviewer": "Reviewer_5mfi", "summary": "The paper proposes a novel and interesting method that leverages Boltzmann Alignment to establish a more sophisticated connection between inverse folding tasks and binding free energy (ΔΔG) prediction. Despite relying on somewhat idealized approximations, the method leverages a thermodynamic cycle and the principles of the Boltzmann distribution to incorporate both bound and unbound states of the protein complex, offering a physically motivated alignment technique that addresses limitations of traditional pre-trained inverse folding models.  Through evaluations on the selected SKEMPI v2 dataset, the paper demonstrates that the method achieves significant improvements over existing approaches in both supervised and unsupervised settings.  Overall, the paper provides a new perspective for integrating domain knowledge into alignment techniques.", "questions": "1) Could the authors explain the reasons for the relatively low MAE reported in Table 2?\n\n2) Could the authors clarify how they determined the unbound state approximation for independent chain probabilities (Equation 9)?  The paper provides some explanation on this point, but it lacks sufficient detail.\n\n3) The transformation between energy and probability, along with the approximation of unbound state probabilities, partially explains the high correlation between the inverse folding task and ΔΔG prediction. However, within the neural network, the sophisticated design of model doesn’t appear to provide additional information gain. \n\nGiven the strengths of this paper, I would consider raising my score if the authors can address my concerns.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "1) The paper is well-written.\n\n2) The approach achieves state-of-the-art results compared to baselines.\n\n3) The paper effectively incorporates domain-specific priors, specifically leverages Boltzmann principles to connect energy with probability, along with the assumption that unbound states can be approximated as independent probabilities for each chain. Though this assumption is idealized, it still is an interesting approach that introduces a motivated alignment.\n\n4) The paper demonstrates practical applicability on binding energy prediction, protein-protein docking and antibody optimization tasks.", "weaknesses": "1) The method makes strong assumptions, particularly in treating the unbound state as independent probabilities for each chain, which oversimplifies the inter-chain interactions. Additionally, the predictions of inverse folding model’s do not fully align with the predicted probabilities (not the ground truth), introducing biases when single-chain probabilities are combined to approximate complex states. This approximation may result in significant deviations in some situations.\n\n2) The method has only been validated on a limited dataset, which lacks sufficient evidence to demonstrate the generalizability of the approach and its underlying assumptions.\n\n3) It seems that the paper lacks sufficient discussion on how improvements in the inverse folding model would translate to gains in this approach.  It’s also unclear which specific module in this sophisticated approach contributes most significantly to the information gain.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Spotlight)