Accurately Predicting Protein Mutational Effects via a Hierarchical Many-Body Attention Network
Authors: Dahao Xu
Jiahua Rao
Mingming Zhu
Jixian Zhang
Wei Lu
Shuangjia Zheng
Yuedong Yang
Venue: NeurIPS 2025 poster ()
Keywords: Protein Mutational Effects
Protein-Protein Interactions
Binding Free Energy
Hierarchical Many-Body Attention
Primary area: machine_learning_for_sciences
TL;DR: We present H3-DDG, a model that predicts binding free energy changes by modeling higher-order many-body interactions, achieving state-of-the-art performance in protein mutational effect prediction.

Abstract: Predicting changes in binding free energy ($\Delta\Delta G$) is essential for understanding protein-protein interactions, which are critical in drug design and protein engineering. However, existing methods often rely on pre-trained knowledge and heuristic features, limiting their ability to accurately model complex mutation effects, particularly higher-order and many-body interactions.
To address these challenges, we propose H3-DDG, a Hypergraph-driven Hierarchical network to capture Higher-order many-body interactions across multiple scales. By introducing a hierarchical communication mechanism, H3-DDG effectively models both local and global mutational effects.
Experimental results demonstrate state-of-the-art performance on multiple benchmarks. On the SKEMPI v2 dataset, H3-DDG achieves a Pearson correlation of 0.75, improving multi-point mutations prediction by 12.10%. On the challenging BindingGYM dataset, it outperforms Prompt-DDG and BA-DDG by 62.61% and 34.26%, respectively.
Ablation and efficiency analyses demonstrate its robustness and scalability, while a case study on SARS-CoV-2 antibodies highlights its practical value in improving binding affinity for therapeutic design.

Accurately Predicting Protein Mutational Effects via a Hierarchical Many-Body Attention Network
Dahao Xuli*, Jiahua Raol.", Mingming Zhu', Jixian Zhang", Wei Lu',
Shuangjia Zheng".1 Yuedong Yang!./
"Equal Contribution |Corresponding Authors
1 Sun Yat-sen University 2 Aureka Biotechnologies SShangaii Jiao Tong University shuangjia zheniias.zaeajittaa edu. yangyd25email. sysu. edu. cn
Abstract
Predicting changes in binding free energy (AAG) is essential for understanding protein-protein interactions, which are critical in drug design and protein engineer- ing. However, existing methods often rely on pre-trained knowledge and heuristic features, limiting their ability to accurately model complex mutation effects, partic- ularly higher-order and many-body interactions. To address these challenges, we propose H3-DDG, a Hypergraph-drivs order many-body interactions across multiple scales. By introducing hierarchical communication mechanism, H3-DDG effectively models both local and global mutational effects. Experimental results demonstrate state-of-the-art performance on multiple benchmarks. On the SKEMPI v2 dataset, H3-DDG achieves a Pearson correlation of 0.75, improving multi-poin mutations prediction by 12.10%. On the challenging BindingG GYM dataset, it outperforms Prompt-DDG and BA-DDG by 62.61% % and 34.26%. respectively. Ablation and efficiency analyses demonstrate its robustness and scalability, while a case study on SARS-CoV. antibodics highlights its practical value in improving binding affinity for therapeutic design.
Hierarchical network capture Higher-
Introduction
are fundamental to numerous biological processes, driving key cellular functions such signal transduction (21). immune response [35] 22], and
Protein-protein interactions (PPIs) 19 9 12
metabolic regulation 40 A precise understanding of how mutations alter binding free energy (AAG) in PPIs is critical for wide range of applications, including drug design 7 20
protein engineering [5], and elucidating the molecular basis of disease [33.
Binding free energy quantifies the thermodynamie stability of protein complexes and is inherently governed by the physical interactions between amino acids. These interactions span multiple spatial and structural scales, from pairwise atomic forces-such hydrogen bonding and van der Waals interactions- higher-order many-body effects, including hydrogen bond networks and π r stacking interactions. Accurately modeling these intricate interactions is essential for predicting the functional and structural consequences of mutations [3) This becomes particularly challenging in multi-point mutation scenarios, where complex interdependencies between mutation sites often emerge, further complicating the prediction task.
Accurately predicting AAG remains critical yet challenging task, existing computational methods face inherent limitations. These methods can be categorized into structure- -ased approaches and inverse bolding-based models. Structure-based approaches leverage well-designed training tasks, such as protein inverse folding [39], side-chain modeling [26 23 28), masked modeling [7), and data augmentation 38 to extract protein representations from structural data. However, they often
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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fall short in effectively transferring the learned structural knowledge to AAG prediction. This shortcoming arises from their limited capacity to explicitly model higher-order and many-body interactions, which are crucial for capturing the physicochemical impacts of mutations.
On the other hand, inverse folding- -aased models, such as ProteinMPNN-DDGG [T0 and BA-DDG 18) predict AAG by estimating likelihood differences between native and mutant sequences relative to stability. While these models perform well for single-point mutations, they rely on indirect proxies, such as Boltzmann-Alignmenn, to approximate binding free energy. This reliance limits their effectiveness in multi poiti-poiit mutation scenarios, which involve intricate interdependencies among mutation sites and require a deeper understanding of protein energetics and many-body interaction dynamics. These limitations underscore the need for an approach capable of capturing higher-order interactions and adapting to the complexity of multi-point mutation scenarios.
In this work, introduce H3-DDG, a Hy Hypergraph-driven Hierarchical network capture Higher- order many-body interactions across multiple scales for AAG predictions. By leveraging a many- body attention communication mechanism, H3-DDG effectively models higher-order and many-body interactions across multiple scales, enabling precise predictions of binding free energy changes, particularly in challenging multi-point mutation contexts.
Experimental results demonstrate of-te-of-the-art performance across multiple benchmarks. On the SKEMPI v2 dataset [7]. H3-DDG achieves Pearson correlation of 0.75, improving multi-point mutations prediction by 12. 10%. On the challenging BindingGYM dataset [24]. it outperforms Prompt-DDG and BA-DDG by 62.61% % and 34.26%, respectively. Notably, in ablation studies, the many-body attention mechanism proves to be critical, contributing a 5.4% improvement in prediction accuracy when incorporated. Additionally, the hypergraph-driven hierarchical design enables the model to effectively capture long-range dependencies, which are essential for accurately modeling complex mutation scenarios. A case study on SARS-CoV-2 antibodies further highlights H3-DDG's ability to predict binding affinity changes with high precision, demonstrating its practical utility in real-world applications. These results underscore the capability of H3-DDG to handle intricate mutational landscapes and its potential for broad applicability in protein engineering and drug design. The key contributions of this work are as follows:
We introduce a hierarchical communication mechanism to model local and global interactions, capturing higher-order effects like hydrogen bond networks and π π stacking.
We propose a many-body attention network to explicitly model higher-order and many- interactions, enabling robust predictions in complex mutational scenarios.
H3-DDG achieves state-of- performance on multiple benchmark datasets, outperforming BA-DDG by 12.10% in multi-point mutation prediction on the SKEMPI v2 dataset and by 34.26% on the BindingGYM dataset.
2 Related Work
Efforts to predict the change in binding free energy (AAG) have resulted in variety of computational approaches, broadly categorized into two main types: (1) methods leveraging structure-basee training tasks and (2) methods utilizing inverse folding models for AAG prediction. While these approaches have shown promise, they also highlight significant limitations, particularly in capturing higher-order interactions and complex multi-poin mutation effects 30 32]
The first category focuses on designing training tasks that utilize structural information to enhance the modeling of protein energetics. These include techniques such as protein inverse folding (39], side-chain modeling [26] 23, (8), and masked modeling [37]. These approaches attempt to extract meaningful representations of protein structures by optimizing for tasks aligned with physical princi- ples of molecular interactions. However, their reliance on pre-trained knowledge limits their ability to explicitly model higher-order and many-bodk interactions, which are critical for understanding the thermodynamic effects of mutations. This gap restricts their utility in directly predicting AAG, particularly in complex mutation scenarios.
The second category focuses on adapting inverse folding models to predict AAG 25
Models such as P [10] and BA-DDG [8] leverage the ability of inverse folding models to assess the likelihood of native and mutant amino acids within a structural context. These methods predict
A AGG by estimating the differences in likelihood scores between native and mutant sequences with

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(a] Model Overview
(c) a e-body Attention
Manykoody
Mesage Passing
3-bodd Antention
Attemtoon a Mur. Stee
X
LaverNor
2-body
Pooleg
o Rase chau
Mrr. Residve
(b) Many Attention
2-bodyy Interaction
Graph Construction
ALL Nodes
Passing
3-body Attention
Feedback
Pooling
Hyper Edges
Attin
HyperGraph
4-body Attention
Sampling
Mutation
Quad
Mutation Sulgraph
Figure (a) Overall framework H3-DDG, (b) Many-body attention mechanisms across hierarchical levels and their attention patterns. The first layer constructs full-residue graph and applies 2- 2-body message passing: the second layer performs spatial pooling form a mutation-centered hypergraph and applies 3- 3-body attention between hyperedges; the third layer extracts fine- fineggrinnd subgraphs around mutation sites and applies localized 4-body attention within each mutation subgraph. (c)
Detailed computational flow of the 4-body attention module within the mutation subgraph.
their relative stability. However, likelihood- based scoring serves as indirect proxy for binding free energy changes and often fails to capture explicit physical interactions critical to AAG prediction. Moreover, their performance degrades significantly in multi-poin mutation scenarios, where the interdependencies between mutations require a nuanced understanding of higher-order effects.
To address these challenges, we introduces a hierarchical communication mechanism and a many- body attention network to explicitly model local and global interactions across multiple seales. These innovations capture higher-order and many-body effects, such as hydrogen bond networks and stacking, while explicitly modeling mutation interdependencies in multi-point mutation scenarios.
3 Methodology
this section, we introduce H3-DDG, Hypergraph-driven, Hierarchical, and Higher-order interac- tion network designed to predict binding free energy changes (AAG) in protein-protein interactions (PPIs). The overall workflow is illustrated Figure
3.1 Preliminaries and Notations
We represent protein graph G EV, where each node i V represents a residue with feature vector h, and each edge (i, E E encodes interactions via feature vector eij.
Building on ProteinMPNN-DDE folding. we also fine-tune a pretrained inverse folding model (ProteinMPNN (6) to tackle this task. H3-DDG extends the capabilities of the inverse folding model by introducing hierarchical graph construction and many-body body higher-order attention, enabling it to effectively capture complex dependencies across multiple mutation sites and improve protein representation learning
10 and BA-DDG [18, which link AAG prediction with inverse
To predict binding free energy AG, we compute amino acid probabilities and use negative log- likelihoods surrogate. For a wild-type (wt) complex and its mutant (mut) counterpart, the binding

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free energy change is defined as:
AAG = Am AG
3.2 Hierarchical Graph Construction for Multi-Scale Modeling
Residue-Level Graph. As described in Section 3.1 each residue i represented by a feature vector h,, and each edge (i, encodes spatial or chemical interactions via feature vector eij.
Following the approch ProteinMPNN [6, residues are represented using key atoms: N, Ca, C, O, and C3, To construct the amino acid-level graph. Edges are formed by identifying the top-k nearest neighbors based on Ca-Co distances. Each edge (i, incorporates geometric features using radial basis functions (RBFs) [4] over 25 atom pair distances (e.g., N-N, C-C). For a given distance dij.
the RBF is defined as:
RBF (R) exp (- ddi p4
(-("s-
==
K,
2
where μt are K predefined centers and is the bandwidth.
These R features are concatenated with relative positional encodings PE.j. which include sequence offsets and chain identities. The final edge features esy are computed as:
Cij- LayerNorm (We [PE;] [BBF)))
where We is the learnable parameters and [- -I] denotes concatenation. This graph effectively captures residue-level spatial and chemical interactions while preserving sequence context.
Mutation-Centerre Hypergraph. Directly applying higher-order attention on amino acid-level graphs is computationally expensive, with complexity scaling as O(N3) or O(N*), as demonstrated in 16 30). To address this challenge, we construct a mutation-centert hypergraph that reduces computational complexity while preserving critical local and global interactions.
We construct the hypergraph by clustering residues into hyperedges that capture higher-order spatial dependencies. Clustering is initialized at mutation sites to prioritize biologically salient regions, then expanded by iteratively adding residues with maximal Euclidean distance from existing centroids. Each residue assigned its nearest centroid based Ca coordinates. Hyperedge features (e) computed via mean prooiin over constituent residue embeddings h, yielding a compact representation that preserves structural topology and improves computational efficiency.
This cutation-centerre hypergraph construction ensures that the influence of mutation sites retained during graph compression and facilitates the efficient modeling of higher-order interactions. For further implementation details, refer to Appendix A.I
Sine-Grained Mutation Subgraph. To capture the local effects of mutations, we extract fine- grained subgraphs centered on each mutation site. These subgraphs include all residues with Ca atoms within an 8Á radius of the mutation centroid in 3D space, preserving key structural and biochemical contexts. Node and edge features in these subgraphs. denoted as ((m) and (m)), respectively, enable localized analysis of conformational changes and energetic impacts, providing focused view of mutation- mutation-induced induced effects on binding affinity.
3.3 Many-Body Attention Network
In this section, we describe the many-body attention mechanisms applied at different hierarchical levels of the graph. These include pairwise (2-body) message passing the residue-level graph, triplet (3-body) attention between hyperedges the mutation-centered hypergraph, and quadruplet (4-body) attention within fine-grained mutation subgraphs, as illustrated in Figure
2-body Message Passing in Residue-level Graph. We utilize message passing mechanism to jointly update node features h, and edge features e, in the residue-level graph (Section 3.2. Node-wise messages Ah; are computed by projecting concatenated node and edge features through

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multi-layer perceptron (MLP):
Ah;
Σ JEN(
Wm3 & @W @ (Wm. [,, e.yl))
where [-I1-] denotes vector concatenation, ø is the GELU activation, and Wm1. Wm2, Wma learnable projection matrices. The node features h, are updated via a residual edge with layer normalization and position-wise feed-forward network (FFN):
h; < LayerNorm (h; + Dropout(Ahi)
(5)
h; LayerNorm (h; (fo))))(FFN(h)))))
(6)
Edge features eij are updated using the updated node features through similar MLP-based mecha- nism:
ei + LayerNorm (ei, + Dropout (W 6 (W",2 (W [h; e,j))))
This mechanism enables the model to integrate residue-level spatial and chemical interactions efficiently across the residue-level graph.
3-body Attention Mechanism for Hyperedge Interactions. Building on the global structural context learned from 2-body message passing in the full-residue graph, we implement 3-body attention mechanism capture higher-order interactions between hyperedges in the nutation-centered hypergraph (Section 3.2 Here, each hyperedge is represented by its feature vector he)), capturing the residue cluster-level information.
To model pairwise relationships between hyperedges, first construct pairwise interaction tensor ((0) E NRNNND where the number of hyperedges and D is the feature dimension. Here, and f.g) is computed as:
j index hyperedges in the hypergraph. Each element
fl = ((h(") (e) & o(h("))
(8)
where ø is non-linear activation function (e.g., GELUU) and & denotes the outer product.
An asymmetric attention mechanism is employed by linearly projecting f through learnable weight matrices and biases to obtain the query vector qıj = W, p(e) f + by key vector kj² = W& + bx- and value vector Víą- = Wor + by- In addition, the mechanism introduces a bias term b, and gating vector gi via separate linear projections for adaptive modulation. The triplet attention scores aijk then computed using gated softmax function:
-kj
kjk
Cijk Softmax
bik
a (gax),
where Softmax ensures that the attention weights are normalized over hyperedge neighbors, and (ga) applies a sigmoid activation to adaptively modulate the attention.
Each hyperedge aggregates attention attention-weighted messages from its spatial neighbors, and the aggre- gated features are fused with the corresponding full-residue node feature hy(s) via residual addition, followed by layer normalization:
v5k) 1)
hr LayerNorm
hr(s) + Dropout
Σ
Σ aijk Vik
(10)
jEN())
Here, r(i) denotes the mapping from hyperedge index to the corresponding residue index in the residue-level graph.
4-body Attention Mechanism around Mutation Sites. To capture higher-order interactions in the mutation environment, we extend the 3-body attention mechanism to 4-body attention on the Fine-Grained Mutation Subgraph (Section 3.2 where (m) and (m) denote the node and edge features of the mutation subgraph. This subgraph focuses on residues within an 8A radius of mutation site, enabling the model to learn localized interactions among residue quadruples. The
5

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extension increases computational complexity by only constant factor, preserving scalability while capturing more complex interactions. The full computational process is illustrated in Figure )T.)
Specifically, we construct two interaction tensors to encode localized multi-residue interactions as inputs the 4-body attention mechanism:
M = ((,,"")) o ((()))) S - ((b (m)) d(eja) (mm)
(11)
Here, & is non-linear activation function (e.g., GELU), and & denotes the outer product. The tensors ffm)) E N and f/ NxEXD respectively encode node-node and node-edge interactions, where N and E are the number of residues and edges on the mutation subgraph, and D is the feature dimension. Indices i, k, refer to nodes within the mutation subgraph.
Inspired by cross-attention, the tensors jiz
p(m) and f/
are projected into query, key, and value vectors:
Oi
Wg s KJR1 WE f(m)
VJkI
W.
fikt
(m)
(12)
bas Wo I Bin W Sát
(13)
where Wg. WA W., W,, and W are learnable projection matrices.
The quadruplet attention scores Aijkl are computed via gated softmax function:
aijht = Softmax
qí
Kjm
bist
(giit).
(14)
vd
Each node in the mutation subgraph aggregates attention-weighted messages from its spatial neigh- bors, and the aggregated features are fused with the original node features via residual connection, followed by dropout and layer normalization:
(m)
LayerNorm
h (T) + -ropoutt
aight VzKt) Σ JEN()) k.
Σ
(15)
This 4-body attention mechanism enables the model to encode complex, localized interaction motif's around mutation sites, thereby improving its ability predict binding free energy changes with structural and biophysical fidelity.
3.4 Prediction Module and Learning Objective
Following the multi-scale representation learning with many-body attention in Section 3.3 we obtain a residue-level representation h Nd Let (s....., &N be the amino acid sequence. Inspired by autoregressive models like ProteinMPNN, we model P(s; sei h) to compute the negative log-likelihoods Ewt and Emu for wild-type and mutant sequences. As RDE-Netoork [26) and BA-DDG [18), single-chain contributions are subtracted to isolate binding effects, yielding energy-like scores:
AAGpeo = AG
AG
Eut
ecomplex
emmmomee
-
ecomplex
E
enmommmer
(16)
mma
We minimize the mean squared error between ApGr and AAGree over n training samples:
1 Σ
LMSE
(AAG pred AdGune
(17)
1=1
4 Experiments
4.1 Experimental Settings
Datasets. We used SKEMPI v2 [17, a benchmark with 7.085 mutations across 348 protein complexes, to evaluate AAG prediction. Following prior work (26, 37]. we split the data into three non-overlapping folds by complex to avoid data leakage. Additionally, we evaluated on BindingGYM 24 the largest dataset for protein-protein interactions, with 508,962 curated entries and high proportion of multi-point mutations. We used the hardest inter-assay split, focusing on the fold with the most multi-point mutations for testing (details in Appendix A.2

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Table 1: Mean results of 3-fold cross-validation SKEMPI v2 under single- multi-, and all-point mutations. Bold and underline indicate the best and second-bes best results.
Overall
Per-Structure
Method
Mutations
Pearsont
Spear:
RMSE
MAEI
AUROCT
Pearson"
Spear:
all
0.3113
0.3468
1.6173
1.1311
0.6562
0.3284
0.2988
Rosetta
single
0.3250
0,3670
1.1830
0,9870
0.6740
0.3510
0.4180
multiple
0.1990
0,2300
2.6580
2.0240
0.6210
0.1910
0.0830
0.3120
0,4071
1.9080
1.3089
0.6582
0.3789
0.3693
FoldX
single
0.3150
0,3610
1,6510
1.1460
0.6570
0,3820
0.3600
multiple
0.2560
0,4180
2.6080
1.9260
0.7040
0.3330
0.3400
all
0.6447
0.5584
1.5799
1.1123
0.7454
0,4448
0.4010
RDF-Network
single
0.6421
0.5271
1.3333
0.9392
0.7367
0,4687
0.4333
multiple
0.6288
0.5900
2.0980
1.5747
0.7749
0.4233
0.3926
all 0.6609
0,5560
1.5350
1.0930
0.7440
0,4220
0.3970
DiffAffiiity
single
0.6720
0.5230
1,2880
0,9230
0.7330
0.4290
0.4090
multiple
0.6500
0.6020
2.0510
1.5400
0.7840
0.4140
0.3870
0.6772
0.5910
1,5207
1.0770
0.7568
0.4712
0.4257
Prompt-DDG
single
0.6596
0.5450
1,3072
0.9191
0.7355
0,4736
0.4392
multiple
0.6780
0.6433
1.9831
1.4837
0.8187
0,4448
0.3961
all
0.6720
0.5730
1,5160
1.0890
0.7600
0,4640
0.4310
ProMIM
single
0.6680
0,5340
1.2790
0.9240
0.7380
0,4660
0.4390
multiple
0.6660
0.6140
1.9630
1.4910
0.8250
0,4580
0.4250
all 0.71188
0.6346
1,4516
1.0151
0.7726
0,5453
0,5134
BA-DDG
single
0.7321
0.6157
1.1848
0.8409
0.7662
0,5606
0,5192
multiple
0.6650
0.6293
2.0151
1.4944
0.7875
0.4924
0.4959
0.7501
0.6604
1.3665
0.9612
0.7920
0.5686
0.5281
H3-DDG
single
0.7471
0.6374
1.1560
0,8080
0.7803
0,5750
0.5295
multiple 0.7341
0.6913
1.8320
1.3880
0.8309
0.5520
0.5323
ARA-DIG
multiple +10.39%
+9.85%
+9.08%
+7.12%
+5.51%
+12.10%
+7.34%
Baselines. We compared H3-DDG against unsupervised and supervised methods. Unsupervised approaches include energy-based models (e.g.. Rosetta [1. FoldX [8],, evolutionary sequence models
(e.g., ES [27). Tranception (29)), and senncturr-guidde pretrained models (e.g.. ESM-IF [15].
MIF-Alogits (3))) Supervised methods include end-to-end architectures (c.g.. DDGPred (3] and
uuerainingg-inettuing frameworks (c.g., MIF-Network (39), RDE-Network (26). DiffAffinity (23
Prompt-DDG (37), ProMIM (28). Surface- VQMAA [36), MSM-Mut 14,, BA-DDG (88).
Metrics. We use five metries: Pearson, Spearman, RMSE, MAE, and AUROC. For SKEMPI, in addition to the global metrics, we also report per-structure metrics. For BindingGYMM, metrics reported per-DMS (deep mutational scanning). Detailed metrie definitions and calculations provided in Appendix A.3
Implementation details. The hyperparameters and hardware details are provided in Appendix A.4 The code is available at https: pettps://githae thub. com/biomed- AI/H3-DDC
4.2 Results on SKEMPI v2 Dataset
As shown in Table H3-DDG outperforms existing baseline approaches across all evaluation metrics in the all-, single- and multi point mutation scenarios. Notably, in practical applications where affinity modulation through multi-point amino acid mutations is particularly critical, H3-DDG demonstrates significant advantages in the multi-mutation prediction task: achieving a Spearman correlation coefficient of 0.7341, which is 10.39% higher than the second-best method; at the per-structure level, this metric reaches 0.5520, surpassing the second-best approach by 10..0%. Additional comparisons with more baseline methods provided in Appendix B.2 Table 6
7

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1,0
1.0
Por spcarnan
Se-Struttre
0.0-
0.0-
0.5-
0.5-
0.4924
6.3961
0,4059
01763
0.4140
0.3070
RDE ROE-Linee
SimAthrity
Prompt mimp
BA-22X
H3-000
RED- REEE-Liaar
DiMAdioiiy
Promptt DDG
BA-DDG
HS-DDG
Figure Distribution per-structure Pearson and Spearman correlation coefficients for multi-point mutations, evaluated across five representative methods.
Table 2:
Performance comparison under <3, 23 and all-point mutations on BindingGYM, where bold and underline denotes the best and second-best results under each setting.
Per-DMS
Method
Mutations
Pearson?
Spearmant
AUROCI
RMSE,
ALL
0.0998
0,2050
0.5341
3.4974
ProteinMPNN
<3
0.1137
0,2439
0.5404
3,2328
23
0.0734
0.1614
0.5930
5.5921
ALL
0,1320
0.1217
0.5658
1,2419
BA-Cycle
<3
0.1385
0.1386
0,5620
1.0925
23
0.0830
0.1955
0.6190
2.5822
ALL
0.1880
0.1818
0.5198
1.5216
Prompt-DDG
<3
0.2160
0.2179
0.5273
1.3499
23
0.1841
0,2008
0.6070
3,5747
ALL
0.2277
0,2142
0.5310
1.1182
BA-DDG
<3
0.2553
0,2471
0.5395
0.9716
23
0,2037
0.2259
0,6307
2.5191
ALL
0.3057
0,2725
0.5703
1.1294
H3-DDG
<3
0.3322
0.3031
0.5745
1.0758
23
0.2472
0.2755
0.6734
2.4976
ADA-DDG
2 3
+21.35%
+21.96%
+6.77%
+0.85%
These results enabled by introduction of hierarchical communication mechanism combined with many-body attention network. This proposed framework effectively models both local and global interactions, capturing higher-order effects such complex synergistic and many-body interactions in mutational scenarios. As further illustrated in Figure 2 the per-structure distributions of Pearson and Spearman correlation coefficients across five representative methods show that H3-DDG achieves significantly higher correlation values, with distributions concentrated in bigh-correlation regions, highlighting its robustness compared other approaches.
stacking and explicitly addressing
4.3 Results on BindingGYM YM Dataset
To validate the robustness of H3-DDG, we evaluate it on the larger and more challenging BindingGYM dataset, demonstrating its scalability and generalizability. As shown in Table H3-DDG outperforms all baseline methods across all metrics, achieving the highest Pearson correlation (0.3057), which surpasses the second-best method (BA-DDG) by 34.26%. Particularly in the 23 mutation scenario, it also achieves the best Spearman correlation (0.2755), exceeding the second- best method by 21. 1996.. Additionally, H3-DDG achieves the best AUROC across all mutations and demonstrates competitive RMSE. These results highlight H3-DDG's is robustness, scalability, and effectiveness for accurately predicting protein-protein binding complex mutational landscapes, especially in multi-point mutation scenarios.

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While H3-DDG's RMSE under single-poing mutations is slightly higher than the baseline methods (e.g., BA-DDG), this can be attributed to the BindingGYM dataset spanning different DMS experi- ments, where the absolute AAG values vary significantly across experiments. However, we focus more on the ranking and correlation within each DMS experiment, making the Pearson and Spearman metrics more critical for evaluation.
4.4 Ablation Study
Ablation Study on Pooling Types. As shown in Table H3-DDG out- performs other graph pooling meth- ods like DifiPool [41] and MinCut-
Table 3: Ablation study of pooling and many-body attention mechanisms under multi-point mutations on SKEMPI v2.
Pooling Type
Attn. Around
Overall
Pool (3]. which rely on predicted as- signment matrices and fail to prede-
Mut. Sites
Pearsonf
Spear:
RMSE
MAE
BA-DDG
0.6650
0.6293
2.0151
1.4944
fine mutation sites as central nodes. By explicitly designating mutation sites as cluster centers, H3-DDG effec- tively captures long-rau rangerage dependen- cies, enabling superior performance modeling many-body interactions.
DiffPool
0.6959
0.6558
1.9375
1.4843
MinCutPool
0.7004
0.6589
1.9256
1.4693
0.7040
0.6676
1.9161
1.4528
H3-DDG
3-body Attn.
0.7144
0.6732
1.8880
1.4127
b-body Attn.
0.7341
0.6913
1.8320
1.3880
Ablation Study Attention Mech- anisms. Table ! also demonstrates
the importance of many-body attention in AAG prediction. While 3-body attention improves perfor- mance by modeling local interactions around mutation sites, extending to 4-body attention further enhances accuracy by capturing more complex dependencies. These findings highlight many-body attention as key factor in H3-DDG's strong performance and efficient modeling. Our model strikes balance between efficiency and performance, influenced by two main factors: the number of hyperedges in the hypergraph and the number of edges in the 4-body attention. Notably, our method achieves Pearson correlation of 0.7341, surpassing BA-DDG's 0.6650, with a relatively small efficiency trade-off. Additional details are provided in Appendix B. B.4and and B.5
4.5 SARS-CoV-2 Antibody Optimization
Predicting AAG is essential for identifying affinity-enhancing mutations. We target five SARS-CoV. 2 neutralizing mutations (3]] within the heavy-chain CDRs (26 residues, 494 single-point variants). Models are fine-tuned on SKEMPI v2.0 to rank mutations by predicted A AG, with lower values
indicating stronger binding. Table 4 benchmarks performance against top baselines, highlighting mutations ranked in the top 10%. Only our model achieves an average rank below 10%, demonstrating strong generalization and practical utility in antibody design.
Table Rankings the five favorable mutations on the human antibody against SARS-CoV-2 by
various AAG prediction methods.
Method
TH31W
AH53F
NH57L
RH103M
LH104F
Average
MIF-Network
24.49%
4.05 %
6.48%
80.36%
36.23%
30.32%
RDE-Networt
1.62 %
2.02%
20.65%
61.54%
5.47%
18.26%
DifTAffinity
7.28%
3.64%
18.82%
81.78%
10.93%
24.49%
Prompt-DDG
2.02%
6.88%
3.24%
34.81%
6.48%
10.69%
MSM-Mut
6.48%
10.12%
16.19%
19.23%
20.04%
14.41%
BA-DDG
5.26%
15.58%
2.22%
40.28%
7.69%
14.21%
H3-DDD
3.44%
7.48%
2.02%
32.79%
2.63%
9.67%
5
Conclusion
In this work, we introduce H3-DDG, novel framework that leverages hierarchical communication mechanisms and many-body attention to tackle the challenges of protein-protein binding prediction. By explicitly modeling higher-order interactions and designating mutation sites as cluster centers,

---

H3-DDG captures complex dependencies and synergistic effects, particularly excelling in multi mutation scenarios. Evaluations on SKEMPI v2 and BindingGYM show that H3-DDG outperforms thte-offthe-art methods across most metrics, demonstrating robust performance and scalability. While H3-DDG shows promise for protein design and affinity prediction, its performance on large datasets and diverse mutations needs further study. Integrating it with experimental workflows will be key to validating real-world applicability. Future work will tackle these challenges to expand its impact.
Acknowledgments and Disclosure of Funding
This study has been supported by the Guangdong S&T Program [202440101040005), the Guangdong S&T Program [2023B (02331111030002) the National Natural Science Foundation of China [6204120] (200,, the Natural Science Foundation of Shanghai [24ZR 1440600], the China Postdoctoral Science Founda- tion [2025M771540, GZB20250391), the Guangdong Basic and Applied Basic Research Foundation [2025A151506001]] I]. and the Lingang Laboratory [LGL-8888).
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12

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absolute error A Additional Details
A.1 Graph Pooling Method of H3-DDG
To enable scalable learning on biomolecular graphs, H3-DDG employs a deterministic graph pooling strategy that compresses node representations while preserving spatial and functional context. Given residuc-wise features h and their Ca coordinates x E RN we form a reduced set of hyper-nodes via Farthest Point Sampling (FPS) with mutation-aware initialization. Specifically, mutation sites are first selected as initial cluster centroids and additional centroids are iteratively sampled to maximize coverage under Euclidean distance.
Each residue then assigned to the nearest cluster centroid based on the Euclidean distance between its Ca coordinates and the centroids. Feature aggregation is performed within each cluster by computing the mean of the features of all residues assigned to that cluster:
1
h
Σ h :ES
(18)
Sk
where Sy is the set of residues assigned to cluster k. This produces set of K cluster-level represen- tations {he] with K dynamically determined as K = [L/R], where L is the number of valid residues and R a predefined reduction ratio.
Anchored to mutation sites and guided by spatial diversity, our pooling method preserves locality and biological relevance. It is non- non-parametric and efficient, suitable for large variable-length proteins.
A.2 Details of the Inter-Assay Split in BindingGYM
To evaluate generalization to unseen protein-protein interactions, we adopt the inter-assay split strategy from the BindingGYM dataset, following the approach of (24). In this setting, assays are first clustered into five groups based on the sequences of their mutated proteins. Data from one cluster is held out for testing, while the remaining four are used for training. This split evaluates the models' ability to generalize to new assays, which holds significant practical significance.
We evaluate performance under three levels of mutational depth: ALL (all mutants), <3 (mutants with fewer than 3 mutations). and 23 (mutants with 3 or more mutations).
A.3 Details of metric definitions and calculations
For the SKEMPI v2 dataset, we use seven quantitative metrics, including five standard global criteria: Pearson and Spearman correlation coefficients, root mean square error (RMSE), (MAE), and area under the ROC curve (AUROC). To calculate AUROC, mutations are classified based on the sign of AUROC, mutations are classified based on the sign of AAG. In practice, correlations within individual protein complexes are often more relevant. To this end, following RDE-Network (26), group mutations by protein structure, exclude groups with fewer than 10 mutations, and compute correlations separately for each structure. For the BindingGYM, dataset, Per-DMS (deep mutational scanning) metrics, including Pearson, Spearman, AUROC, and RMSE.
A.4 Training Details
A.4.1
Hyper-parameters
We used the Adam optimizer with learning rate of 4e-4 and a batch size of 1, 2, depending GPU memory and graph size. The model was trained for 20,000 iterations with 4 attention heads and hidden dimension of 128. The number of hyperedges the number of edges in the 4-body attention module from 1N, 2N, 3.N, where L and N denote the numbers of residues and nodes, respectively. The pre-trained ProteinMPNN module used its default 3-layer configuration.
selected from L/10, L/6, L/4, and
A.4.2 Hardware
Experiments on dual Xeon Gold 6248R CPUs and an RTX 4090 GPU under Ubuntu 22.04.
13

---

B
Additional Results
B.1 H3-DDG Performance Predicted Complex Structures
To evaluate robustness, we used AlphaFold 3 (AF3) to predict the complex structures for SKEMPI v2 and applied H3-DDG for prediction. While AF3 achieves high-quality structure prediction, its accuracy may still be lower than experimental structures. Importantly, H3-DDG showed only slight decrease in performance on AF3- AF3-predicted structures, with drop of 5.4% in Pearson correlation, demonstrating strong robustness and practical applicability.
B.2 Extended Baseline Comparisons on SKEMPI v2
Table/oreports extended baseline results SKEMPI v2, including additional methods to complement the main text comparisons. These include energy function-basee sequence- and unsupervised approaches, providing broader context for evaluating performance across diverse methodological categories.
B.3 Ablation Results under Different Mutation Depths
Table presents the full ablation results of different pooling strategies and many-body attention mechanisms across mutation types, including single-point, multi-point, and all all-pointt mutations on SKEMPI v2. The results demonstrate that our proposed H3-DDG consistently outperforms bascline pooling methods (e.g.. DifiPPool [4]] and MinCutPool (3] under all mutation settings. Furthermore, incorporating 4-body attention around mutation sites yields the best performance across all metrics, validating the effectiveness of higher-order attention in capturing complex interaction patterns.
B.4 Ablation study on Edge Count in 4-body Attention
We investigate the impact of varying the number of edges in the 4-body attention mechanism around mutation sites on AAG prediction. The number of edges in the 4-body attention is directly proportional to the computational complexity. As shown Table 8 where denotes the number of nodes involved in the 4-body attention computation, selecting 2 N edges yields a computational complexity of 2 S. The results indicate that increasing the number of edges leads to only constant-factor increase in computational cost, yet yields sustained improvements in predictive performance. For example, the Pearson correlation, which was already high at 0.7352, further increases to 0.7501. These findings highlight that adding more edges in the many-bod attention mechanism near mutation sites significantly enhances the model's 'ss capacity to capture complex many- body interactions, while maintaining manageable computational overhead, thereby driving further gains in prediction accuracy.
B.5 Efficiency Analysis
Our model balances efficiency and performance. As shown in Table increasing hyperedges from L/10 L/4 steadily improves Pearson correlation, reaching a peak 0.7501 with L/4 hyperedges and 3.V 4-body edges. This setting maintains acceptable efficiency (4.34 it/s), only slightly slower than BA-DDG (6.25 it/s Pearson: 0.7118). Similarly, increasing 4-body edges from 1.5N 3.V yields incremental gains, indicating denser subgraph modeling enhances accuracy at manageable cost. Additionally, as shown Table 10 larger cutoff radii improve performance by capturing richer structural context, but gains diminish beyond 8 Á while cost rises. Thus, 8 Á is chosen as the optimal cutoff, offering the best accuracy-efio -fffracyeffficinnyy trade-off.
Table 5: H3-DDG Performance on Experimental and AF3-Predicted Structures.
Structure
Pearsont
RMSEJ
AUROCT
AlphaFold3
0.7117
1.4518 1.3665
0.7755
Experimental
0.7501
0.7920
14

---

Table 6: Mean results of 3-fold cross-validation SKEMPI v2 under single-, multi-, and all-point mutations. Bold and underline indicate the best and second-bes best results.
Overall
Per-Structure
Method
Mutations
Pearsont
Spear:
RMSE
MAE]
AUROCT
Pearson"
Spear:
all
0.3113
0.3468
1.6173
1.1311
0.6562
0.3284
0.2988
Rosetta
single
0.3250
0,3670
1.1830
0,9870
0.6740
0.3510
0.4180
multiple
0.1990
0,2300
2.6580
2.0240
0.6210
0.1910
0.0830
0.3120
0,4071
1.9080
1.3089
0.6582
0.3789
0.3693
FoldX
single
0.3150
0,3610
1,6510
1.1460
0.6570
0,3820
0.3600
multiple
0.2560
0,4180
2.6080
1.9260
0.7040
0.3330
0.3400
all
0.6580
0.4687
1.4998
1.0821
0.6992
0.3750
0.3407
DDGPred
single 0.6515
0,4390
1.3285
0.9618
0.6858
0.371 1
0.3427
multiple
0.5938
0.5150
2.1813
1.6699
0.7590
0.3912
0.3896
all 0.6373
0,4882
1.6198
1.1761
0.7172
0.3873
0.3587
End-to-End
single
0.6605
0.4594
1.3148
0.9569
0.7019
0.3818
0.3426
multiple
0.5858
0,4942
2,1971
1.7087
0.7532
0,4178
0.4034
0.6447
0.5584
1.5799
1.1123
0.7454
0.4448
0.4010
RDE-Network
single
0.6421
0.5271
1,3333
0.9392
0.7367
0,4687
0.4333
multiple
0.6288
0,5900
2.0980
1.5747
0.7749
0,4233
0.3926
all 0.6609
0.5560
1,5350
1.0930
0.7440
0,4220
0.3970
DiffAffinity
single 0.6720
0.5230
1.2880
0.9230
0.7330
0,4290
0.4090
multiple
0.6500
0.6020
2.0510
1.5400
0.7840
0.4140
0.3870
all 0.6772
0,5910
1,5207
1.0770
0.7568
0,4712
0.4257
Prompt-DDe
single
0.6596
0,5450
1,3072
0,9191
0.7355
0.4736
0.4392
multiple
0.6780
0.6433
1,9831
1.4837
0.8187
0.4448
0.3961
0.6720
0.5730
1,5160
1.0890
0.7600
0.4640
0.4310
ProMIM single
0.6680
0,5340
1,2790
0.9240
0.7380
0,4660
0.4390
multiple
0.6660
0.6140
1.9630
1.4910
0.8250
0,4580
0.4250
all 0.7118
0.6346
1.4516
1.0151
0.7726
0.5453
0.5134
BA-DDG
single 0.7321
0.6157
1.1848
0.8409
0.7662
0.5606
0.5192
multiple
0.6650
0.6293
2.0151
1.4944
0.7875
0.4924
0.4959
all 0.7501
0.6604
1.3665
0.9612
0.7920
0.5686
0.5281
H3-DDG
single
0.7471
0.6374
1.1560
0.8080
0.7803
0.5750
0.5295
multiple
0.7341
0.6913
1.8320
1,3880
0.8309
0.5520
0.5323
+5.38%
+4.07%
+5.86%
+5.31%
+2.51%
+4.27%
+2.86%
ABA-DIG
single +2.05%
+3.52%
+2.43%
+3,91%
+1,84%
+2.57%
+1.98%
multiple
+10.39%
+9.85%
+9.09%
+7.12%
+5.51%
+12.10%
+7.34%
B.6 Scatter Plot of Prediction Results
Figure we present scatter plots comparing experimental and predicted AAG values for the three methods under multi-poing mutation scenarios.
Prompe-DD
Pearson 0583
0,5780
Pearson 0.7341 Spearman 0.5015
Spearman 0,4247
Spearmar - 0.6433
Peddcted 0BG
Expermental DGG
Expertmental DOG
Exporimenta DDG
Figure 3: Comparison of predicted and experimental AAG across methods.
15

---

Table 7: Ablation study of pooling types and many-body attention mechanisms across mutation types on SKEMPI v2.
Pooling Type
Attn. Between
Attn. Around
Overall
Mutations
Hyperedges
Mutation Sites
Pearsont
Spear:
RMSE,
MAEJ
all 0.7261
0.6407
1,4209
1.0079
DiffPool
3-body Atin.
single
0.7344
0.6256
1.1804
0.8336
multiple
0.6959
0.6558
1.9375
1.4843
all
0.7275
0.6456
1.4178
1.0027
MinCutPool
3-body Attn.
single
0.7324
0.6333
1.1841
0.8342
multiple
0,7004
0.6589
1.9256
1.4693
0.7317
0.6485
1.4085
0.9923
H3-DDG
3-body Attn.
single
0.7383
0.6273
1.1728
0,8242
multiple
0.7040
0.6676
1.9161
1.4528
all
0.7352
0.6509
1.4007
0,9805
H3-DDG
3-body Attn.
3-body Attn.
single
0.7355
0.6326
1.1782
0.8243
multiple
0.7144
0.6732
1.8880
1.4127
all 0.7501
0.6604
1.3665
0.9612
H3-DDG
3-body Attn.
4-body Atm.
single 0.7471
0.6374
1.1560
0.8080
multiple
0.7341
0.6913
1.8320
1.3880
Table Ablation on the number edges near mutations within 4-body attention on SKEMPI v2.
Overall
Per-Structure
Complexity Mutations
Pearson
Spear.
RMSE
MAET
AUROCT
Pearsont
Spear:
all
0.7352
0.6509
1.4007
0.9805
0.7895
0.5663
0.5227
0(W1))
single
0.7355
0.6326
1.1782
0.8243
0.7851
0.5758
0.5246
multiple
0.7144
0.6732
1.8880
1.4127
0.8098
0.5372
0.5156
0.7461
0.6570
1.3760
0.9719
0.7941
0.5660
0.5231
((2 (W1*) single
0.7455
0.6365
1.1591
0.8128
0.7850
0.5790
0.5341
multiple
0.7279
0.6815
1.8500
1.4079
0.8262
0.5449
0,5310
all single 0.7471
0.7501
0.6604
1.3665
0.9612
0.7920
0,5686
0,5281
0(3 IM12) multiple 0.7341
0.6374
1.1560
0.8080
0.7803
0.5750
0.5295
0.6913
1.8320
1.3880
0.8309
0.5520
0.5323
Table 9: Impact of hypergraph and subgraph configurations efficiency and performance. T. is the residue count, and T./ denotes the number of hyperedges (floor division). 3N means the 4-body attention has three times as many edges nodes.
Number of Number of Edges in 4-body Attn.
Training Speed (iterations/sec)
Training Time (mins/epoch)
Method
Pearsonf
Hyperedges
BA-DDG
0.7118
6.25
5.94
L/10
0.7418
5.11
7.27
L/6
3N
0.7482
4.68
7.93
L/4
0.7501
4.34
8.55
H3-DDG
1.5N
0.7420
4.40
8.44
L/4
2.N
0.7461
4.38
8.48
3N
0.7501
4.34
8.55
Table 10: Impact of Cutoff Radius on Model Performance and Efficiency.
Cutoff of Mut. Subgraph(A)
Training Speed (iterations/sec)
Pearsont
MAET
0.7378
0,9834
4.52
0.7501
0,9612
4.32
0.7511
0.9602
4.03
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Reviews:
[{"review_id": "tlcOB9jKQU", "reviewer": "Reviewer_GsHY", "summary": "This paper introduces H3-DDG, a hypergraph-driven hierarchical network to predict higher-order many-body interactions across multiple scales. The authors compared the performance of their method with that of others and demonstrated improved performance, especially in cases with three or more mutations.", "questions": "Can the authors discuss how the improvement translates into better performance in downstream tasks? It seems that the overall improvement over BA-DDG is relatively minor.", "limitations": "The authors discussed the limitations.", "rating": 4, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: The topic is undoubtedly critical to assessing the implications of protein mutations. The methods are clearly described with detailed comparison results. \n\nWeaknesses: The proposed methods are ad-hoc, although the proposals are all sensible. It is unclear what the practical implications of the improvement in prediction are, e.g., how these will translate into better drug targets, etc. Additionally, a discrepancy exists between the performance improvement reported in the abstract and that reported in the tables, which lowers the confidence in the results presented in the paper. Therefore, we have several questions followed by the previous mentioned weakness:\n\n1. The results are not reliable and the authors should include more discussions for ablation studies and hyper-parameter tuning. Do the authors also adjust the hyper-parameters of other baseline to make a fair comparison?\n\n2. The authors should mention the criteria for selecting the k-body attention design, as it seems that there is no unified rule for selecting a suitable k across all different tasks, and thus the authors should spend more context to discuss the effect of k.\n\n3. For the anti-body optimization task, it seems that H3-DDG did not perform well for RH103M, while other baseline methods such as MSM-Mut shows stronger performances. Could the authors explain more about the performance difference and what is the preference of proposed method?", "was_revised": true, "final_justification": "I think this paper is good for publication.", "rebuttal": "We sincerely thank the reviewer for recognizing the significance of our work and the clarity of our methodology and results. Briefly, the reviewer has two main concerns: (1) the **reliability** and **fairness** of the experimental comparisons, including ablation studies and hyper-parameter tuning, and (2) the rationale for design choices (such as the $k$-body attention) and the interpretation of performance differences across tasks. Below, we summarize the reviewer's questions and provide point-by-point responses and clarifications.\n\n> W0 (1): The practical implications of the improvement in prediction.\n\nR: Our proposed method **advances protein representation learning by explicitly modeling many-body interactions at multiple scales**. This approach not only improves the prediction of protein mutation effects, but also has the potential to strengthen downstream applications that depend on high-quality protein representations, such as protein function prediction, drug target interaction analysis, and protein engineering.\n\nTo illustrate the practical utility for drug discovery, we have evaluated our method on an antibody dataset for $\\Delta\\Delta G$ prediction, a key task in therapeutic antibody optimization, as accurate $\\Delta\\Delta G$ prediction facilitates the identification of affinity-enhancing mutations. Specifically, on the SARS-CoV-2 antibody benchmark, our method achieves an average rank of 9.67% for identifying favorable mutations, as measured by the proportion of top-ranked beneficial mutations (see Table 4), outperforming all baseline approaches.\n\nNotably, our method is **the only approach to achieve an average rank below 10% across all tested mutations**, highlighting its strong generalization capability and significant practical relevance for antibody design and drug development.\n\n> W0 (2): The discrepancy exists between the performance improvement reported in the abstract and that reported in the tables.\n\nR: We have rigorously checked all reported values to ensure accuracy and consistency. The improvements stated in the abstract are calculated as follows:\n\n* SKEMPI v2.0 dataset: The 12.10% improvement refers to the relative gain of H3-DDG over BA-DDG in the per-structure Pearson correlation metric (see Table 1).\n* BindingGYM dataset: The 62.61% and 34.26% improvements refer to H3-DDG's gain over Prompt-DDG and BA-DDG, respectively, in the Pearson correlation metric (see Table 2).\n\nAll results in the paper have been cross-validated to avoid inconsistencies.\n\n> W1: The reliability of the experimental results and more discussions for ablation studies and hyper-parameter tuning.\n\nR: All experimental setups strictly follow established protocols from prior works (BA-DDG, Prompt-DDG), ensuring fair and reliable comparisons. We have also tuned the hyper-parameters for all baselines as their published optimal settings.\n\nWe evaluated H3-DDG's hyperedge construction against DiffPool and MinCutPool, achieving the best performance (see table below). This is primarily because DiffPool and MinCutPool, which are based on learned assignment matrices, cannot explicitly set the mutation site as a central node within each cluster. As a result, they may group the mutation site with unrelated residues, potentially weakening the effect of the mutation. In contrast, the H3-DDG approach **ensures that the mutation site is always central in the constructed hyperedges**, enabling more precise modeling of local many-body interactions and thus leading to superior predictive performance.\n|Hyperedge Construction|Pearson|Spearman|RMSE|MAE|\n|-|-|-|-|-|\n|DiffPool|0.7261|0.6407|1.4209|1.0079|\n|MinCutPool|0.7275|0.6456|1.4178|1.0027|\n|H3-DDG (ours)|**0.7317**|**0.6485**|**1.4085**|**0.9923**|\n\nWe further investigated the impact of increasing hyperedge count and edge density in the mutation subgraph, finding that higher connectivity with 4-body attention **notably improves prediction accuracy at a moderate computational cost**, detailed in the following tables. Specifically, denser hyperedge and subgraph constructions enable the model to better capture complex local interactions, resulting in consistently higher Pearson correlations and lower error metrics, while maintaining efficient training speeds. This demonstrates that richer local connectivity is beneficial for modeling protein mutations, as long as computational complexity remains manageable.\n|Num of Hyperedges|Pearson|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|\n|L/10|0.7418|5.11|\n|L/6|0.7482|4.68|\n|L/4|**0.7501**|4.34|\n\n|Num of Edges in Mut. Subgraph|Complexity|Pearson|Spear.|RMSE|MAE|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|-|-|-|-|\n|N|O(\\|$N^3$\\|)|0.7352|0.6509|1.4007|0.9805|4.50|\n|2N|O(\\|$2 \\cdot N^3$\\|)|0.7461|0.6570|1.3760|0.9719|4.38|\n|3N|O(\\|$3 \\cdot N^3$\\|)|**0.7501**|**0.6604**|**1.3665**|**0.9612**|4.34|\n\nFinally, we evaluated the impact of different cutoff radius for extracting the mutation subgraph. As the cutoff radius of the mutation subgraph increases, prediction performance improves due to the inclusion of more relevant structural context. However, beyond 8 Å, the performance gains become marginal while computational cost continues to rise. \n|Cutoff of Mut. Subgraph(Å)|Pearson|Spear.|RMSE|MAE|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|-|-|-|\n|5|0.7378|0.6538|1.3951|0.9834|4.52|\n|8|0.7501|**0.6604**|1.3665|0.9612|4.34|\n|12|**0.7511**|0.6518|**1.3644**|**0.9602**|4.03|\n\n> W2: The criteria for selecting the k-body attention design.\n\nR: We thank the reviewer for raising this point. The choice of $k$ in H3-DDG is made to **balance expressive power and computational cost**. Many-body effects are well-established as essential for modeling protein energetics (as also noted by other reviewers, #z7aD, #zCJg), but computational complexity increases exponentially with $k$. Therefore, we employ higher-order attention (4-body) only within the mutation subgraph, where modeling complex local interactions is most critical, while utilizing 3-body attention in the hypergraph and standard 2-body attention elsewhere.\n\nAblation studies demonstrate that introducing higher-order attention layers leads to substantial improvements in predictive accuracy, particularly for multi-point mutations where many-body interactions are most pronounced. These results confirm that integrating both 3-body and 4-body attention is crucial for accurately modeling protein mutation effects, with the largest gains observed when both are combined.\n\n|2-Body Message Passing|3-Body Attn. Between Hyperedges|4-Body Attn. Around Mut. Sites (Subgraph)|Mutations|Pea.|Spear.|RMSE|MAE|\n|-|-|-|-|-|-|-|-|\n|$\\checkmark$|--|--|all|0.7111|0.6351|1.4530|1.0304|\n||||single|0.7199|0.6107|1.2071|0.8558|\n||||multiple|0.6792|0.6651|1.9804|1.5034|\n|$\\checkmark$|$\\checkmark$|--|all|0.7317|0.6485|1.4085|0.9923|\n||||single|0.7383|0.6273|1.1728|0.8242|\n||||multiple|0.7040|0.6676|1.9161|1.4528|\n|$\\checkmark$|$\\checkmark$|$\\checkmark$|all|**0.7501**|**0.6604**|**1.3665**|**0.9612**|\n||||single|**0.7471**|**0.6374**|**1.1560**|**0.8080**|\n||||multiple|**0.7341**|**0.6913**|**1.8320**|**1.3880**|\n\n> W3: The performance difference of the anti-body optimization task.\n\nR: Thank you for this insightful question. Although H3-DDG achieves the best average performance across all mutation sites, we acknowledge that its performance on RH103M is slightly lower than that of MSM-Mut.\n\nBased on additional structural analysis, we believe this difference may be attributed to the unique and complex local environment at the RH103M site. This discrepancy could arise from limited coverage of similar structural cases in the training set or the presence of an atypical local energy landscape that presents particular challenges for predictive modeling. On the other hand, the modeling assumptions inherent to MSM-Mut may, by chance, align more closely with the specific structural or energetic characteristics of RH103M, resulting in slightly better performance for this particular mutation.\n\nNevertheless, H3-DDG achieves the best average performance (**9.67\\% $\\downarrow$**) across all mutations and demonstrates superior generalization and robustness across diverse mutation sites, whereas MSM-Mut (average 14.41%) shows advantages only in a small number of specific cases, such as RH103M. These findings not only underscore the need for continued advances in modeling complex mutation environments, but also highlight the strength of our approach: the higher-order attention and explicit many-body interaction modeling in H3-DDG provide a principled and scalable framework.\n\n> Q1(2): The improvement over BA-DDG.\n\nR: Compared to BA-DDG, H3-DDG introduces substantial advances both in model design and capability. As reviewer #z7aD noted, our use of hypergraph representations combined with many-body attention mechanisms (up to 4-body) is well-motivated. Conventional approaches like BA-DDG primarily capture pairwise interactions and thus overlook important higher-order effects such as hydrogen bond networks, $\\pi-\\pi$ stacking, or cooperative salt bridges, which are critical for accurate protein representation.\n\nH3-DDG addresses this limitation by explicitly modeling many-body and long-range dependencies through hierarchical communication and higher-order attention on hypergraphs. By leveraging different $k$-order attentions for various structural hierarchies, H3-DDG is able to capture both local and global interaction patterns that are inaccessible to pairwise models. \n\nThis enhanced representational power enables H3-DDG to more accurately model the complex, cooperative effects underlying protein stability, especially for challenging scenarios like multi-point mutations. As a result, downstream predictive performance is significantly improved. Specifically, as reported in the results section, H3-DDG **achieves a 12.10% improvement over BA-DDG in Pearson correlation**, demonstrating both the practical utility and the effectiveness of our modeling innovations."}, {"review_id": "ZSX5hlr5Q7", "reviewer": "Reviewer_z7aD", "summary": "This paper introduces H3-DDG, a novel  hierarchical network designed to predict binding free energy changes (`ΔΔG`) in PPIs mutants. The proposed captures higher-order interactions that are crucial for understanding mutational effects. The authors demonstrate SOTA on SKEMPI v2 and BindingGYM benchmarks. The authors also present a case study on SARS-Cov-2 antibody design.", "questions": "* Could this architecture be adapted for related tasks like protein-ligand binding affinity prediction or enzyme design?\n* Given the success of AF3 and similar methods (Chai-1/ Boltz) , how does H3-DDG perform on predicted structures versus experimental structures?\n*  How sensitive is the method to the clustering approach for hypergraph construction?", "limitations": "* The model is trained on SKEMPI v2, which has known biases towards certain protein families and mutation types. How does this affect performance on underrepresented protein classes in the training dataset (membrane proteins etc) \n\n* The 4-body attention is restricted to local mutation subgraphs, potentially missing long range allosteric effects. \n\n* The model assumes standard conditions but `ΔΔG` is highly dependent on temperature, pH, and ionic strength. \n\n* The paper doesn't discuss GPU memory requirements. The 4-body attention on mutation subgraphs likely requires substantial memory, limiting application to large complexes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "#### Strengths \n\n* The use of hypergraph representations with many body attention mechanisms (up to 4-body) is well-motivated. This directly addresses the limitation of existing methods that primarily model pairwise interactions, missing crucial higher-order effects like hydrogen bond networks and `π-π` stacking.\n\n* The performance improvements are substantial - 12.10% better than BA-DDG on multi-point mutations in SKEMPI v2, and 34.26% improvement on BindingGYM\n\n* The hierarchical graph construction with mutation centered hypergraphs cleverly reduces computational complexity from O(N^3) or O(N^4) to manageable levels while preserving critical interaction information needed for model performance \n\n#### Weaknesses\n* the paper lacks theoretical analysis of why the specific choices (e.g., 8A radius for mutation subgraphs, specific hyperedge construction) are optimal. Some ablation on these hyperparameters would strengthen the work. \n* Table 8 shows that H3-DDG is still ~30% slower than BA-DDG in training. For very large protein complexes or proteome-wide screens, this could be limiting.  \n* The evaluation is limited on SKEMPI v2 and BindingGYM. Testing on additional datasets (Abdesign etc) would better demonstrate generalizability claims. \nThe paper doesn't compare against some recent methods like ThermoMPNN or the latest co-folding based approaches for stability prediction.", "was_revised": true, "final_justification": "The rebuttal is quite clear and answers all of my questions to my satisfaction. However, I'm keeping my scores the same", "rebuttal": "We appreciate the reviewer's careful review of our paper, positive feedback, and recognition of our work, particularly the novelty of our approach and the meaningfulness of our experiments. Below, we address the concerns point by point:\n\n> W1: The Analysis of Hyper-parameters\n\nR: We thank the reviewer for highlighting the importance of hyperparameter analysis. We have conducted comprehensive ablation studies to investigate the impact of different choices in hyperedge construction, attention order, and mutation subgraph cutoff radius.\n\nWe compared our hyperedge construction with DiffPool and MinCutPool. Our hyperedge construction achieves the best performance. This is primarily because DiffPool and MinCutPool, which rely on learned assignment matrices, cannot explicitly ensure that the mutation site serves as the central node in each cluster. H3-DDG always centers the mutation site in constructed hyperedges, enabling more precise modeling of local many-body interactions and leading to superior predictive accuracy.\n|Hyperedge Construction|Pearson|RMSE|\n|-|-|-|\n|DiffPool|0.7261|1.4209|\n|MinCutPool|0.7275|1.4178|\n|H3-DDG|**0.7317**|**1.4085**|\n\nWe further performed ablation on the order of attention (2-body, 3-body, and 4-body). These results highlight the value of explicit higher-order modeling, especially for complex scenarios involving multiple mutations.\n|2-Body Message Passing|3-Body Attn. Between Hyperedges|4-Body Attn. Around Mut. Sites (Subgraph)|Mutations|Pea.|Spear.|RMSE|MAE|\n|-|-|-|-|-|-|-|-|\n|$\\checkmark$|--|--|all|0.7111|0.6351|1.4530|1.0304|\n|$\\checkmark$|$\\checkmark$|--|all|0.7317|0.6485|1.4085|0.9923|\n|$\\checkmark$|$\\checkmark$|$\\checkmark$|all|**0.7501**|**0.6604**|**1.3665**|**0.9612**|\n\nWe also conducted a hyperparameter analysis of edge density in the 4-body attention mechanism, showing that increased the edge density in the mutation subgraph (with 4-body attention) improves prediction accuracy with only moderate additional computational cost. \n|Num of Edges in Mut. Subgraph|Complexity|Pearson|RMSE|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|-|-|\n|N|$O(\\|\\mathcal{N}\\|^3)$|0.7352|1.4007|4.50|\n|2N|$O(2 \\cdot\\|\\mathcal{N}\\|^3)$|0.7461|1.3760|4.38|\n|3N|$O(3 \\cdot\\|\\mathcal{N}\\|^3)$|**0.7501**|**1.3665**|4.34|\n\nFinally, we evaluated different cutoff radius for mutation subgraph extraction. As the cutoff radius increases, performance improves due to the inclusion of more relevant structural context. However, after 8 Å, the performance gain becomes marginal while computational cost continues to rise.\n|Cutoff of Mut. Subgraph(Å)|Pearson|MAE|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|-|\n|5|0.7378|0.9834|4.52|\n|8|0.7501|0.9612|4.34|\n|12|**0.7511**|**0.9602**|4.03|\n\n> W2: Large-scale Applications on larger complex or proteome-wide screens\n\nR: Thank you for raising the important issue of scalability to large protein complexes and proteome-wide screens. The key innovations of H3-DDG lie in its scalable, hypergraph-based many-body attention, providing several advantages: (1) **Hierarchical Attention:** Different orders of attention (2-body, 3-body, 4-body) are applied at appropriate structural levels, focusing computation where it matters most. (2) **Controllable Hypergraph Construction:** Hypergraphs efficiently capture both long-range and many-body interactions, with user-controllable hyperedge number and scope to balance accuracy and cost. (3) **Tunable Efficiency:** Key parameters (e.g., number of 4-body edges, mutation subgraph radius) are adjustable, allowing efficient scaling to large systems.\n\nIn practice, we have found that even for very large proteins (e.g., the largest proteins in the SKEMPI v2 dataset with over 3,000 residues), H3-DDG can be efficiently trained and evaluated on a single 4090 GPU (24GB memory). This demonstrates the method's suitability for large-scale and high-throughput applications.\n\n> W3: Limited Evaluation Scope\n\nR: Thank you for raising this important point regarding the evaluation scope.\n\nIn this work, we focused on SKEMPI v2, BindingGYM, and SARS-CoV-2 antibody datasets because they are widely recognized benchmarks for protein–protein binding affinity and mutation effect prediction. We acknowledge that a more comprehensive evaluation, including Abdesign and recent baselines, would further strengthen our claims. As shown below, we evaluated H3-DDG on the **S669** benchmark dataset used in ThermoMPNN and under the same experimental setup, demonstrating that H3-DDG achieves state-of-the-art performance. We will include these results in revised manuscript.\n|Method|Pearson|RMSE|\n|-|-|-|\n|ProteinMPNN|0.26|3.32|\n|ThermoMPNN|0.43|1.52|\n|H3-DDG|**0.56**|**1.48**|\n\n> Q1: Applicability to Related Tasks\n\nR: Thank you for the question. H3-DDG is readily extensible to related tasks such as protein–ligand binding affinity prediction and enzyme design. Its hypergraph-based k-body attention can be adapted to different molecular contexts by redefining the region of interest. For example, in protein–ligand binding affinity prediction, the model can focus higher-order attention on the interface between the protein and ligand, capturing cooperative interactions between multiple residues and ligand atoms. In enzyme design, the attention mechanism can be centered on the enzyme active site and its interactions with substrates or cofactors, enabling a precise modeling of the functional environment. The core model architecture remains unchanged, demonstrating H3-DDG's flexibility and broad applicability in molecular modeling.\n\n> Q2: Performance on Predicted vs. Experimental Structures\n\nR: Thank you for this insightful question. To evaluate robustness, we used AlphaFold 3 (AF3) to predict the complex structures for SKEMPI v2 and applied H3-DDG for $\\Delta\\Delta G$ prediction. While AF3 achieves high-quality structure prediction, its accuracy may still be lower than experimental structures. Importantly, H3-DDG showed only a slight decrease in performance on AF3-predicted structures, with a drop of **5.4%** in Pearson correlation, compared to experimental structures—significantly less than the performance drop observed for BA-DDG (**10.7%**). H3-DDG thus maintains state-of-the-art accuracy even on predicted structures, demonstrating strong robustness and practical applicability.\n|Method|Structure|Pearson|RMSE|AUROC|\n|-|-|-|-|-|\n|BA-DDG|Experimental|0.7118|1.4516|0.7726|\n||AF3 |0.6356|1.5655|0.7226|\n|H3-DDG|Experimental|0.7501|1.3665|0.7920|\n||AF3 |0.7117|1.4518|0.7755|\n\n> Q3: Sensitivity to Clustering in Hypergraph Construction\n\nThe hyperedge construction method has been mentioned in the response to **W1**. Here we further investigated the impact of the number of hyperedges, where $L$ is the number of nodes and $L / 10$ is the number of hyperedges, meaning there are on average 10 nodes per hyperedge. Increasing the number of hyperedges leads to notable improvements in prediction accuracy, with only moderate additional computational cost.\n|Num of Hyperedges|Pearson|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|\n|L/10|0.7418|5.11|\n|L/6|0.7482|4.68|\n|L/4|**0.7501**|4.34|\n\n> L1: Dataset Bias and Generalization\n\nR: Thank you for highlighting this important point.\n\nWe acknowledge that SKEMPI v2 is biased toward certain protein families and mutation types, which may limit generalization to underrepresented classes such as membrane proteins. To address this, we have supplemented our evaluation with the BindingGYM benchmark, which offers greater structural and functional diversity—including more challenging and less-represented protein classes. H3-DDG achieves strong performance on BindingGYM, indicating good generalizability beyond SKEMPI v2 biases. Additionally, we performed transfer learning and independent validation on the SARS-CoV-2 benchmark, as well as additional experiments on protein thermostability, further demonstrating the robustness and adaptability of H3-DDG to novel protein families and mutation scenarios.\n\n> L2: Long-Range Interaction Modeling\n\nR: Thank you for raising this concern. A key innovation of H3-DDG is its hierarchical architecture, which enables efficient modeling of both local and long-range interactions. While 4-body attention focuses on local mutation subgraphs, H3-DDG integrates 2-body message passing across the entire graph and 3-body attention across the hypergraph. This allows information to flow between distant sites, effectively capturing long-range allosteric effects. Compared to traditional GNNs that rely on deep stacking for long-range propagation, our hierarchical approach is more direct and effective.\n\n> L3: Lack of conditions of DDG\n\nR: We acknowledge this limitation. The current model assumes standard experimental conditions and does not explicitly account for factors such as temperature, pH, or ionic strength, all of which can significantly influence DDG values. We will include this limitation in the discussion section and consider condition-specific modeling as an important direction for future work.\n\n> L4: GPU Memory and Scalability\n\nR: H3-DDG leverages a hypergraph representation to efficiently model higher-order interactions while keeping GPU memory usage within a practical range. Although 4-body attention is applied only to local mutation subgraphs, the overall design ensures that increases in modeling capability do not come with prohibitive memory costs.\n\nThe table below compares GPU memory usage for different attention strategies at the same batch size. As shown, H3-DDG delivers clear performance gains with only a modest increase in memory consumption. This demonstrates that the hypergraph-based approach achieves an effective balance between modeling power and computational efficiency, making it feasible for large protein complexes.\n|Method|Attn. Between Hyperedges|Attn. Around Mut. Sites (Subgraph)|Pearson|Memory Used|\n|-|-|-|-|-|\n|BA-DDG|--|--|0.7118|13872MB|\n|H3-DDG|3-body|--|0.7317|14864MB|\n||3-body|3-body|0.7352|15390MB|\n||3-body|4-body|**0.7501**|15692MB|"}, {"review_id": "BqUbvUg4M1", "reviewer": "Reviewer_tCDj", "summary": "The paper proposes a neural network architecture to estimate free energy differences based on the output probabilities of an inverse folding model. The main contribution is a many-body attention mechanism operating on various graph and hypergraph representations.", "questions": "See above, further:\n- What is the raionale to choose 3-body interaction on the pooled graph and 4-body interaction on the mutation subgraph? Why not both the same or the other way around?\n- Can you quantify the added value of using a clustered graph instead of the full graph? How much is runtime reduced by this? Would it be feasible to run a comparison of the model on an unclustered graph?\n- L186: How does 4-body attention only increase complexity by constant factor?\n- Is using a pretrained ProteinMPNN necessary? Do they add performance? Can the model be trained from scratch? How do you justify using the pretrained weights for a model that has significantly different architecture?", "limitations": "The discussion of limitations is very brief with one sentence in the conclusion. I would recommend to expand on this, and also discuss runtime complexity and scaling with various hyperparameters.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 1, "significance": 3, "originality": 2, "strengths_and_weaknesses": "While the introduction starts rather clearly, the methods lack rigor and clarity. Many elements are not defined or detailed (eg which 25 atom pair distances exactly in L118? How is K defined in Eq 2? How are positional encodings exactly computed, how is chain identity factored in? What is the precise definition of the hypergraph and its hyperedges? How are hyperedges constructed, by merging any two adjacent edges? Are they directed? What are the dimensions of the weight matrices W in the attention? How are hyperedge features $f_{ij}$ projected, are they flattened? What are the hyperparameters of the clustering? How were they chosen? What is the metric used in Table 4? etc.) Unfortunately this lack in clarity makes it hard to follow their (rather complex) model setup, and prevents reproducibility.\n\nThe motivation is sensible and the adressed problem is very relevant. However the claim that the proposed network learns hydrogen bond networks or $\\pi - \\pi$ stacking remains unsubstantiated. \n\nWhile I appreciate the presence of ablation studies, I have difficulties understanding what was done in the pooling ablation. Which part of the model was replaced, what were the baselines? A bit more context would be good here. I also wonder whether the observed performance gains might stem from the added graph representations and not the attention mechanisms. An ablation of the attention while keeping the full graph, the clustered graph, and the mutation subgraph (modeling them with ProteinMPNN) seems to be a relevant experiment here.\n\nI further wonder about the effect of hyperparameters. How does performance depend on eg the hypergraph construction?\n\nThat said, the experimental results are good and add value to the field. But given the issues of clarity and reproducibility I unfortunately cannot recommend to accept at this stage. Since there is no revision, I leave it to the discretion of the AC whether to trust that these issues will be addressed.", "was_revised": true, "final_justification": "I appreciate the authors' efforts in answering my questions and improving clarity, and acknowledge it by increasing my score to a borderline reject. Since I cannot verify that my main concerns about clarity and reproducibility have been sufficiently addressed in the revision, I leave it to the AC to trust whether these issues will be resolved.", "rebuttal": "We sincerely thank the reviewer for their detailed and constructive feedback, and we apologize for the insufficient details regarding ProteinMPNN in the Methods section of our manuscript. We have carefully addressed each comment, and will ensure that all relevant clarifications and improvements, particularly the additional details on methods, are thoroughly incorporated into the revised manuscript. The reviewer's suggestions have been invaluable in improving the quality and clarity of our work.\n\n> W1: The clarity of Methods\n\nWe thank the reviewer for highlighting these important points regarding the clarity and rigor of our Methods section. We apologize for the lack of detail, particularly regarding ProteinMPNN, and will ensure that all relevant information is clearly described in the revised manuscript. We wish to emphasize that **these details refer to module settings that are exactly the same as those used in the previous work ProteinMPNN**. \n\n1. Which 25 atom pair distances in L118? How is $K$ defined in Eq 2?\n\nThe 25 atom pair distances follow the setting in ProteinMPNN: all possible pairs between the backbone atoms (N, Ca, C, O) and the Cb atom of each residue (e.g., the Ca-Cb pair represents the distance between the Ca and Cb atoms).\nThe value of $K$ is set to 16, which represents the number of RBFs used to encode atomic pair distances into continuous feature vectors, consistent with ProteinMPNN.\n\n2. How are positional encodings exactly computed? How is chain identity factored in?\n\nThe positional encoding is computed by calculating the relative position offset between residues and applying one-hot encoding, followed by a linear projection. Chain identity is encoded as a binary indicator (1 if the two residues are on the same chain, 0 otherwise), which is concatenated to the positional offset and input into the positional encoding module.\n\n3. What is the precise definition of the hypergraph and its hyperedges? How are hyperedges constructed?\n\nWe use the standard definition of a hypergraph: a hypergraph is an ordered pair $H = (V, E)$, where $V$ is the set of nodes and $E$ is a set of subsets of $V$, each subset being a hyperedge. In H3-DDG, nodes correspond to amino acids, and each hyperedge consists of one or more amino acids that are grouped together based on spatial proximity using distance-based clustering. Hyperedges are not constructed by merging adjacent edges, nor are they directed.\n\n4. What are the dimensions of the weight matrices $W$ in the attention? How are hyperedge features $f_{ij}$ projected?\n\nThe projection weight matrices $W$ in the attention module have dimensions `[hidden_dim, hidden_dim]`, (typically hidden_dim=128). Hyperedge features $f_{ij}$ are not flattened; they are directly projected using a learnable weight matrix while preserving their original tensor structure.\n\nWe appreciate the reviewer's attention to these details and will revise the Methods section to ensure full transparency and reproducibility.\n\n> W1: The metric used in Table 4?\n\nR: We thank the reviewer for the question. The experimental setup and evaluation metric in Table 4 strictly follow the protocols established by MSM-Mut, Prompt-DDG, and other baselines. Specifically, **the metric shown is the percentile rank of each beneficial mutation among all possible mutations for the protein (494 sites in total)**. For each method, we predict the ΔΔG for all possible mutations and rank them from lowest to highest. The percentage shown in the table indicates the rank position of each beneficial mutation. For H3-DDG, the TH31W mutation is ranked within the top 3.44% of all possible mutations.\n\n> W1 & W3 & W4: The ablation study and hyperparameters of clustering.\n\nR: We thank the reviewer for the insightful comments regarding the ablation studies and clustering hyperparameters. We address both points below and will ensure to clarify these details in the revised manuscript.\n\n**Hypergraph Ablation Details**: We compared our hyperedge construction with DiffPool and MinCutPool. Our hyperedge construction achieves the best performance. **H3-DDG always centers the mutation site in constructed hyperedges**, enabling more precise modeling of local many-body interactions and leading to superior predictive accuracy.\n|Hyperedge Construction|Pearson|RMSE|\n|-|-|-|\n|DiffPool|0.7261|1.4209|\n|MinCutPool|0.7275|1.4178|\n|H3-DDG (ours)|**0.7317**|**1.4085**|\n\n**Ablation of Attention Mechanisms**: In response to the reviewer's suggestion, we further implemented versions where we retained the enhanced graph representations,namely, the full graph, the clustered graph, and the mutation subgraph (using ProteinMPNN), but used only 2-body attention mechanisms. The ablation results show that **simply enhancing the graph structure without higher-order attention does not achieve the same level of performance improvement**.\n|Full Graph|Between Hyperedges|Around Mut. Sites (Subgraph)|Pearson|RMSE|\n|-|-|-|-|-|\n|2-body|$\\times$|$\\times$|0.7111|1.4530|\n|2-body|2-body|$\\times$|0.7205|1.4332|\n|2-body|2-body|2-body|0.7248|1.4239|\n|2-body|3-body|$\\times$|0.7317|1.4085|\n|2-body|3-body|4-body|**0.7501**|**1.3665**|\n\n**Clustering Hyperparameters**: Hyperedges are constructed by clustering amino acids based on spatial proximity. We investigated the impact of the number of hyperedges, where $L$ is the number of nodes and $L / 10$ is the number of hyperedges, meaning there are on average 10 nodes per hyperedge. Increasing the number of hyperedges leads to notable improvements in prediction accuracy, with only moderate additional computational cost.\n|Num of Hyperedges|Pearson|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|\n|L/10|0.7418|5.11|\n|L/6|0.7482|4.68|\n|L/4|**0.7501**|4.34|\n\nAll ablation results and details of hyperparameter selection will be explicitly described in the revised manuscript to ensure clarity and reproducibility.\n\n> W2: The Motivation of this work\n\nR: We thank the reviewer for recognizing the motivation and significance of our work. As noted by Reviewer #zCJg, our model achieves significant improvements **in challenging multi-point mutation scenarios where the exponential mutation space poses significant challenges**. Our method directly tackles the shortcomings of previous methods that focus mainly on pairwise interactions, often overlooking crucial higher-order effects such as hydrogen bond networks and $\\pi$-$\\pi$ stacking.\n\nTo further support our claims, we will include visualization analyses in the revised manuscript, illustrating cases where our model successfully captures known higher-order interactions.\n\n> Q1: Rationale for Using 3-Body and 4-Body Interactions\n\nR: We thank the reviewer for raising this important question. The choice to use 4-body attention in the mutation subgraph and 3-body attention on the pooled graph is to balance expressive power and computational efficiency. Higher-order (4-body) interactions are most critical near mutation sites, where local many-body effects matter most and the subgraph size is manageable. For the broader graph, 3-body attention captures important non-pairwise effects globally without excessive computational cost.\n\nOur ablation studies further support this design choice: adding higher-order attention layers leads to significant improvements in predictive accuracy. \n|Around Mut. Sites (Subgraph)|Pearson|RMSE|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|-|\n|3-body|0.7352|1.4007|4.50 |\n|4-body|**0.7501**|**1.3665**|4.34|\n\n> Q2: Clustered Graph vs. Full Graph\n\nR: We thank the reviewer for this insightful question. To quantify the added value of using a clustered graph instead of the full graph, we attempted to run our model on unclustered (full) graphs. However, we found that for proteins with more than approximately 700 amino acids, the memory consumption exceeded 40GB GPU memory; **for proteins larger than 1000 residues, memory usage could surpass 80GB**.\n\nAs shown bellow, for proteins in SKEMPI with fewer than 500 amino acids, the clustered graph reduced runtime by **approximately 1.8× compared to a hypothetical full graph**. This makes our approach scalable to realistic protein sizes, while maintaining or even improving predictive performance.\n|Method|Training Speed (its/sec) $\\uparrow$|\n|-|-|\n|w/o Hypergraph|3.19|\n|with Hypergraph|**5.76**|\n\n> Q3: The constant factor on the 4-body attention complexity\n\nR: The 4-body (node-node-edge) attention increases complexity by only a constant factor **compared to 3-body attention**, because both have overall $O(|\\mathcal{N}|^3)$ complexity, but 4-body adds a multiplicative constant $k$ (the edge-to-node ratio): $O(k \\cdot |\\mathcal{N}|^3)$. By controlling $k$ through sparsity in the graph, the increase remains a constant factor.\n\n> Q4: Necessity of Using Pretrained ProteinMPNN Weights\n\nR: We thank the reviewer for this important question. Using pretrained ProteinMPNN weights is indeed beneficial in our setting. We observed that initializing with pretrained weights leads to consistently better performance and faster training compared to training the model from scratch.\n\nTo further validate this point, we conducted additional experiments comparing models trained with and without pretrained initialization. As shown below, without pretraining, the Pearson correlation for our method drops by **13%** , while BA-DDG shows a larger decrease of **17%**.\n|Method|Pearson|RMSE|AUROC|\n|-|-|-|-|\n|BA-DDG|0.7118|1.4516|0.7726|\n|BA-DDG (w/o pretrain)|0.6046|1.6463|0.7387|\n|H3-DDG|0.7501|1.3665|0.7920|\n|H3-DDG (w/o Pretrain)|0.6622|1.5487|0.7435|\n\nWe will clarify these points and include the comparative results in the revised manuscript.\n\n> L1: Discussion\n\nR: Thank you for the suggestion. We agree and will expand the discussion of limitations in the revised manuscript, including more detail on runtime complexity, scaling behavior, and memory requirements. The detailed results and analysis will be moved to the Discussion section."}, {"review_id": "We3xwnAqFW", "reviewer": "Reviewer_zCJg", "summary": "This paper presents H3-DDG, a hypergraph-driven hierarchical network designed to capture higher-order many-body interactions for predicting binding free energy changes ($\\Delta \\Delta G$) in protein-protein interactions. The method constructs three hierarchical graph representations: residue-level graphs, mutation-centered hypergraphs, and fine-grained mutation subgraphs, employing 2-body, 3-body, and 4-body attention mechanisms to model complex interactions across multiple scales. H3-DDG achieves state-of-the-art performance on SKEMPI v2 and BindingGYM datasets, with particularly strong results in challenging multi-point mutation scenarios, demonstrating a 12.10% improvement over BA-DDG in multi-point mutations on SKEMPI v2.", "questions": "**Q1**. How does H3-DDG compare with the recently proposed Light-DDG method in terms of both performance and computational efficiency?\n\n**Q2**. Can the hierarchical embeddings and many-body interaction representations learned by H3-DDG be effectively transferred to other protein engineering tasks?\n\n**Q3**. How sensitive is the method's performance to the choice of clustering parameters? \n\n**Q4**. What is the relative contribution of each hierarchical level (2-body, 3-body, 4-body) to the final performance, and how does this vary across different types of mutations? \n\n**Q5**. Given the computational requirements of the hierarchical many-body attention, what are the practical limitations for real-time protein design applications?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### **Strengths**\n\n---\n\n**S1**. Predicting $\\Delta \\Delta G$ for protein-protein interactions is crucial for drug design and protein engineering. The authors clearly analyze the limitations of existing methods in handling higher-order and many-body interactions, particularly for multi-point mutations where the exponential mutation space poses significant challenges.\n\n**S2**. The paper is generally well-written with clear presentation of the hierarchical architecture. The model design is simple yet effective, with well-motivated many-body attention mechanisms that effectively capture both local and global interactions. The hierarchical design effectively balances computational complexity with biological interpretability.\n\n**S3**. Extensive experiments across multiple benchmarks (SKEMPI v2, BindingGYM) demonstrate strong performance improvements. Thorough ablation studies convincingly show the effectiveness of each component, and practical validation on SARS-CoV-2 antibody optimization demonstrates real-world applicability.\n\n**S4**. The method achieves significant improvements in the challenging multi-point mutation scenarios, addressing a key limitation of existing approaches that struggle with complex interdependencies between mutation sites.\n\n### **Weaknesses**\n\n---\n\n**W1**. While the authors mention \"manageable computational overhead,\" detailed runtime comparisons with baseline methods are missing from the main text. Given the hierarchical nature and higher-order attention mechanisms, comprehensive computational cost analysis is crucial for practical adoption.\n\n**W2**. The repeated residual connections in equations (5) and (6) are unconventional and may preserve more original features, but this design choice detailed justification.\n\n**W3**. The paper lacks comparison with very recent methods like Light-DDG [1], which reportedly achieves 89.7$\\times$ inference acceleration and 15.45\\% performance gains over previous SOTA methods.\n\n---\n\n**Reference**\n[1] Wu et al. A Simple yet Effective DDG Predictor is An Unsupervised Antibody Optimizer and Explainer. ICLR 2025.", "was_revised": true, "final_justification": "The authors have adddressed my main concerns and I will keep my current positive scores.", "rebuttal": "We sincerely thank the reviewer for the positive feedback on our method's novelty, effectiveness, and practical impact, as well as for the detailed review and insightful comments. Below, we provide point-by-point responses.\n\n> W1: Computational Cost Analysis\n\nR: Thank you for highlighting the need for detailed runtime comparisons. We have supplemented the main text with comprehensive computational efficiency results. As shown below, incorporating higher-order attention significantly improves performance (Pearson from 0.7118 to 0.7501), while training speed remains within an acceptable range:\n|Method|Attn. Between Hyperedges|Attn. Around Mut. Sites (Subgraph)|Pearson|Training Speed (its/sec)|\n|-|-|-|-|-|\n|BA-DDG|--|--|0.7118|6.25|\n|H3-DDG|3-body|--|0.7317|5.65|\n||3-body|3-body|0.7352|4.50|\n||3-body|4-body|**0.7501**|4.34|\n\nThese results demonstrate that the performance gains from many-body attention come at a manageable computational overhead.\n\n> W2: Residual Connections in Equations (5) and (6)\n\nR: Thank you for your feedback. The repeated residual connections in equations (5) and (6) are inspired by the original ProteinMPNN design. In our multi-layer interaction modeling, such residual connections help preserve original features in deeper networks, improving stability and information flow. This design choice ensures the model can benefit from complex higher-order representations without losing essential input information.\n\n> W3 & Q1: Comparison with Light-DDG\n\nR: We appreciate the suggestion to include comparisons with recent methods. We have added a comparison with Light-DDG [1] using the per-structure Pearson and Spearman results reported in their paper:\n\n|Method|Pearson|Spearman|\n|-|-|-|\n|Light-DDG|0.5440|0.5004|\n|H3-DDG|**0.5686**|**0.5281**|\n\nRegarding training efficiency, Light-DDG requires data augmentation for each fold, i.e., training on all other folds to generate augmented data, leading to multiple training runs per split and thus lower overall efficiency. In contrast, H3-DDG is trained directly on the original data, making it more efficient in terms of total training time. \n\nWe acknowledge that Light-DDG achieves faster inference speed, but our method offers a better trade-off between accuracy and overall training efficiency.\n\n[1] Wu et al. A Simple yet Effective DDG Predictor is An Unsupervised Antibody Optimizer and Explainer. ICLR 2025.\n\n> Q2: Applicability to Related Tasks\n\nR: Thank you for the question. H3-DDG is designed to be highly extensible to related tasks such as protein-ligand binding affinity prediction and enzyme design. The core mechanism, hypergraph-based k-body attention, is modular and can be easily adapted to different molecular contexts.\n\nFor protein-ligand binding, the higher-order attention (e.g., 4-body) can be applied to the protein-ligand interface instead of the mutation subgraph, capturing cooperative interactions between residues and ligand atoms. Similarly, for enzyme design, the method can focus $k$-order attention on the enzyme active site and its interaction with substrates or cofactors.\n\nIn all cases, the main adaptation is to redefine the region of interest for higher-order attention based on the task (e.g., mutation site, interface, or active site). The underlying model architecture and workflow remain unchanged, demonstrating H3-DDG's flexibility and potential for broad application in molecular modeling tasks.\n\n> Q3 & Q4: The Analysis of clustering parameters and Ablation\n\nR1: We thank the reviewer for highlighting the importance of hyperparameter analysis. We have conducted comprehensive ablation studies to investigate the impact of different choices in hyperedge construction, attention order, and the number of hyperedges. The main findings are summarized below:\n\nWe compared our H3-DDG hyperedge construction with DiffPool and MinCutPool (see table below). Our hyperedge construction achieves the best performance. This is primarily because DiffPool and MinCutPool, which rely on learned assignment matrices, cannot explicitly ensure that the mutation site serves as the central node in each cluster. Consequently, they may group the mutation site with irrelevant residues, weakening the model's ability to capture the local effect of mutations. In contrast, H3-DDG always centers the mutation site in constructed hyperedges, enabling more precise modeling of local many-body interactions and leading to superior predictive accuracy.\n|Hyperedge Construction|Pearson|Spearman|RMSE|MAE|\n|-|-|-|-|-|\n|DiffPool|0.7261|0.6407|1.4209|1.0079|\n|MinCutPool|0.7275|0.6456|1.4178|1.0027|\n|H3-DDG (ours)|**0.7317**|**0.6485**|**1.4085**|**0.9923**|\n\nWe further investigated the impact of the number of hyperedges, where $L$ is the number of nodes and $L / 10$ is the number of hyperedges, meaning there are on average 10 nodes per hyperedge. Increasing the number of hyperedges leads to notable improvements in prediction accuracy, with only moderate additional computational cost.\n|Num of Hyperedges|Pearson|Training Speed (its/sec)$\\uparrow$|\n|-|-|-|\n|L/10|0.7418|5.11|\n|L/6|0.7482|4.68|\n|L/4|**0.7501**|4.34|\n\nWe performed ablation on the order of attention (2-body, 3-body, and 4-body):\n\nAdding 3-body attention markedly improves performance (Pearson from 0.7111 to 0.7317). Incorporating 4-body attention around mutation sites yields a further gain (Pearson to 0.7501). These results highlight the value of explicit higher-order modeling, especially for complex scenarios involving multiple mutations.\n\n|2-Body Message Passing|3-Body Attn. Between Hyperedges|4-Body Attn. Around Mut. Sites (Subgraph)|Mutations|Pea.|Spear.|RMSE|MAE|\n|-|-|-|-|-|-|-|-|\n|$\\checkmark$|--|--|all|0.7111|0.6351|1.4530|1.0304|\n||||single|0.7199|0.6107|1.2071|0.8558|\n||||multiple|0.6792|0.6651|1.9804|1.5034|\n|$\\checkmark$|$\\checkmark$|--|all|0.7317|0.6485|1.4085|0.9923|\n||||single|0.7383|0.6273|1.1728|0.8242|\n||||multiple|0.7040|0.6676|1.9161|1.4528|\n|$\\checkmark$|$\\checkmark$|$\\checkmark$|all|**0.7501**|**0.6604**|**1.3665**|**0.9612**|\n||||single|**0.7471**|**0.6374**|**1.1560**|**0.8080**|\n||||multiple|**0.7341**|**0.6913**|**1.8320**|**1.3880**|\n\nOur ablation studies demonstrate that the hypergraph-based construction and many-body attention mechanisms of H3-DDG are crucial to its superior performance. The chosen hyperparameters are well-justified by empirical results and offer strong predictive power while maintaining reasonable computational efficiency.\n\n> Q5: Large-scale and Real-time Applications\n\nThank you for raising the important issue of scalability to real-time protein design applications.\n\nThe key innovations of our proposed method H3-DDG (which is specifically designed with scalability and efficiency), the use of hypergraph-based many-body attention, enable several advantages over traditional approaches like BA-DDG.\n\n1. **Hierarchical Attention with Adaptive Complexity**\n\nWe apply different orders of attention (e.g., 2-body, 3-body, 4-body) to different structural hierarchies, allowing computational resources to be focused where most needed without excessive overhead.\n\n2. **Controllable Hypergraph Construction**\n\nBy leveraging hypergraphs, we can efficiently capture long-range and many-body interactions. Importantly, the number of hyperedges and the scope of each hyperedge are controllable, allowing us to balance modeling power and computational cost.\n\n3. **Tunable Hyperparameters for Efficiency**\n\nThe hyperparameters such as the number of edges in 4-body attention and the cutoff radius for mutation subgraphs are all user-controllable. This flexibility allows users to tailor the method for large-scale applications while keeping computational complexity manageable.\n\nIn practice, we have found that even for very large proteins (e.g., the largest proteins in the SKEMPI v2 dataset with over 3,000 residues), H3-DDG can be efficiently trained and evaluated on a single 4090 GPU (24GB memory). This demonstrates the method's suitability for large-scale and high-throughput applications."}]

Author rebuttal:

Meta-review: The paper introduces a hypergraph-driven hierarchical architecture to predict free body energy in PPI mutants.The core contribution is a many-body attention mechanism which operates on multiple scales, leveraging graph and hypergraph representations. 

The paper has been praised by the reviewers for addressing a known limitation of existing methods, technical novelty and empirical performance especially. The rebuttal resolved almost all concerns, with only a single reviewer leaning towards rejection, although it appears that all their concerns were addressed.

I recommend acceptance, subject to implementing all the changes and revisions suggested by the reviewers.
Decision: Accept (poster)