DualMPNN: Harnessing Structural Alignments for High-Recovery Inverse Protein Folding
Authors: Xuhui Liao
Qiyu Wang
Zhiqiang Liang
Liwei Xiao
Junjie Chen
Venue: NeurIPS 2025 poster ()
Keywords: Protein Inverse Folding
Structure Alignments
MPNN
High Recovery
Primary area: machine_learning_for_sciences
TL;DR: DualMPNN is a template-guided dual-stream message passing network that leverages structural alignments to enhance inverse protein folding accuracy through alignment-aware attention.

Abstract: Inverse protein folding addresses the challenge of designing amino acid sequences that fold into a predetermined tertiary structure, bridging geometric and evolutionary constraints to advance protein engineering.  Inspired by the pivotal role of multiple sequence alignments (MSAs) in structure prediction models like AlphaFold, we hypothesize that structural alignments can provide an informative prior for inverse folding. In this study, we introduce DualMPNN, a dual-stream message passing neural network that leverages structurally homologous templates to guide amino acid sequence design of predefined query structures. DualMPNN processes the query and template proteins via two interactive branches, coupled through alignment-aware cross-stream attention mechanisms that enable exchange of geometric and co-evolutionary signals. Comprehensive evaluations across on CATH 4.2, TS50 and T500 benchmarks demonstrate DualMPNN achieves state-of-the-art recovery rates of 65.51\%, 70.99\%, and 70.37\%, significantly outperforming base model ProteinMPNN by 15.64\%, 16.56\%, 12.29\%, respectively. Further template quality analysis and structural foldability assessment underscore the value of structural alignment priors for protein design.

DualMPNN: Harnessing Structural Alignments for High-Recovery Inverse Protein Folding
Xuhui Liao, Qiyu Wang, Zhiqiang Liang, Liwei Xiao, Junjie Chen'
School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, China
(xuhuiliao, qiyuwang, 11 aaggzhiiiaagg,.... wtt.://iiiiiiii.iiiiiiiaaaaeaa lileeiiiao] hit. edu.edduco [xohuiliao.gyyuuang junjiechen@hit. edu.
Abstract
Inverse protein folding addresses the challenge of designing amino acid sequences that fold into a predetermined tertiary structure, bridging geometric and evolu- tionary constraints to advance protein engineering. Inspired by the pivotal role of multiple sequence alignments (MSAs) in structure prediction models like Al- phaFold, hypothesize that structural alignments can provide informative prior for inverse folding. In this study, we introduce DualMPNN, a dual-stream message passing neural network that leverages structurally homologous templates to guide amino acid sequence design of predefined query structures, DualMPNN processes the query and template proteins via two interactive branches, coupled through alignment-awars cross-stream attention mechanisms that enable exchange of geometric and co-evolutionary signals. Comprehensive evaluations across on CATH 4.2, TS50 and T500 benchmarks demonstrate DuaLMPNN achieves of- the-art recovery rates of 65.51%, %; 70.99%, and 70.37%, significantly outperforming base model ProteinMPNN by 15.64%, 16.56% 12.29%, respectively. Further template quality analysis and structural foldability assessment underscore the value of structural alignment priors for protein design.
Introduction
Protein inverse folding addresses the computational challenge of identifying amino acid sequences that fold into a predefined tertiary structure [[] As the inverse the traditional protein folding problem that predicts structures from sequences, this task is critical for advancing protein engineering 3 4), enabling broad applications in drug discovery, peptide design, synthetic biology, and enzyme design 7. Despite its broad utility, protein inverse folding remains hindered by three key challenges: (1) the non-injective mapping between sequences and structures, where diverse sequences can adopt geometrically similar folds (structural degeneracy);
(2) the computational intractability of exhaustively exploring the vast sequences space; (3) the difficulty of ensuring thermodynamic stability and experimental feasibility designed sequences.
Recent advances in computational methods have made incremental progress. Energy- baaed methods (Rosetta K Yue et al. [9] leverage physical potentials but struggle with conformational sampling. Combinatorial optimizing methods (Craig et al. [T]] Kleinberg et al. (II) address sequence space complexity but lack scalability. Deep learning models (ProteinMPNN 12), GraDe-IF([3), ESM- IF FF have improved design efficiency through learned sequence-structure relationships. However, these methods often fail resolve structural degeneracy, producing sequences that prioritize structural compatibility over functional stability. Consequently, achieving high-recovery sequence design that both fold into target structures and exhibit native-like stability remains an open challenge.
*Correponniing author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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A promising strategy to address degeneracy involves integrating evolutionary or structural priors into the design framework. Multiple sequence alignments (MSAs) have proven instrumental in struc- ture prediction tools (like AlphaFold [5) and Ros encoding evolutionary constraints that guide folding simulations. We posit that homologous structural motifs captured by structural alignments offer complementary prior knowledge for inverse folding. Unlike sruuence-based MSAs, structural alignments directly encode conserved spatial and physicochemical constraints across ho- mologs, providing blueprint for stable sequence-structure compatibility. Preliminary experiments, in which randomly initialized ProteinMPNN's s node embeddings with a certain proportions of correct and perturbed sequence templates, support this hypothesis by improved sequences recovery rates (Supplementary Table SI. suggesting that structural homology informs viable sequence design. In this work, we present DuaIMPNN, dual-stream message passing neural network that leverages structural alignments to guide high-recovery inverse protein folding. DuaIMPNN jointly reasons over query structure geometry and homologous structural templates via interactive branches. The nodes in the query branch are iteratively updated from homologous structural templates-derived amino acids through alignment-aware cross-stream attention mechanisms. Consequently, DualMPNN learns to disentangle degenerate sequence solutions while preserving stability constraints, leading to significant improvements recovery rate of inverse protein folding. The contributions of our work are summarized as: (1) Dual-stream architecture for structural priors. We proposed the first framework to explicitly integrate structural alignments-deri derived templates into inverse protein folding via dual-stream framework, enabling simultaneous learning of target. (2) Impact of template quality. We systematically quantify how template selection (e.g. structural similarity) impacts sequence recovery, establishing guidelines for optimal structural alignment utilization in protein design. Structural priors derived from homologous templates can inspire new strategies for protein design. (3) State-of-the-art performance. Evaluations across three benchmarks (CATH, TS50 and T500) demonstrate that DualMPNN achieved sfate-of-the-an in sequence recovery rates, out- performing the base model ProteinMPNN by at least 12%. These results underscore its robustness and capability to leverage structural homology for high-fidelity design. The code is available at
2
Related work
Graph Neural Networks (GNNs) for Protein Design. GNNs have emerged a dominant paradigm for modeling protein structures, offering an inductive bias that aligns naturally with the spatial and rela- tional dependencies of residues. By representing proteins as graphs, where nodes encode residue-level features (amino acid embeddings) and edges capture pairwise geometric relationships (e.g. distances or angular orientations), GNNs enable direct learning of sequence-structure compatibility [17]. Early approaches, such as protein design was formulated as conditional node classification task, predicting amino acid identities given a fixed backbone coordinates [8] 19 Subsequent advancements intro- duced SE(3)- -qquivariant architectures 20 21 critical for generalizing across structural conformations. These methods excel at capturing local geometric constraints but often struggle to resolve global topological degeneracy, where distinct sequence neighborhoods map to similar structural motifs.
which preserve rotational and translational invariance
Diffusion Models for Sequence-Structure Co-Design. To address the one-to-mane mapping inherent in inverse folding, recent work has integrated diffusion models with GNN backbones. These frameworks treat sequence design as a stochastic denoising process, iteratively refining sequences to match target structures while sampling from a learned distribution of plausible solutions. For instance, GraDe-II[[L3 employs a graph diffusion framework to model seidue--wise dependencies, achieving improved recovery rates in structurally ambiguous regions. Similarly, MaskDPD combines masked language modeling with diffusion to probabilistically explore sequence space, demonstrating robustness to backbone perturbations. While difffusion models mitigate degeneracy by sampling diverse solutions, their reliance purely geometric features limits their ability to incorporate evolutionary or structural priors that could further constrain the design space.
Dual-Stream Architectures for Multimodal Learning. Dual-stream neural network architectures, although primarily explored outside the protein domain, offer compelling insights into multi-modal and hierarchical representation learning. These architectures employ two parallel processing pathways to extract and fuse complementary information from distinct input modalities or feature scales. In computer vision, dual-stream models have achieved notable success. For example, DS-Net 2

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Structure Alignments with Foldseek
B. Dual-Stream Message Passing Neural Network
Protein Backbone
Query MPNN
Structural Alignments
Encoder
Decoder
Uodaste
Probussttie
Query Proteins
Autorggemsiee
Input
Herative
Distences
Edges
Rodiee
Edges
Nodie
-Seqpencel
Zeros
Foldseek
Attention
Aligned Indices
TMscore
Allgned Domalnns
Template MPNN
Encoder
Decoder
Updena
Undste
Allined
Maddate
Proteins
Input
Edges
Edges
ISqueece
Distncea
Figure Illustration of DualMPNN model. DualMPNN leverages structural templates as prior knowledge to guide the inverse protein folding through dual-branch processing. Structural templates are identified using Foldseek against the PDB. Query branch processes geometric features from backbone atom coordinates to perform sequence recovery through inverse folding. Template branch leverages aligned template structures and sequences to guide the query branch's s sequence recovery. These two branches share the identical MPNN components.
simultaneously captures fine-grained local patterns and global context, outperforming single-stream baselines in image classification tasks. Dual-stream Reasoning Network (DRNet) 24 designed for abstract visual reasoning demonstrates strong generalization across multiple benchmarks by jointly modeling spatial and semantic
Beyond vision, dual-stream architectures have been applied to sign language recognition [25] and behavioral analysis [26]. showcasing their ficxibility in processing heterogeneous input sources such that dual-stream architectures may hold promise for leveraging the rich prior information encoded in homologous structural templates.
video and spatiotemporal patterns. These successes suggest
Methods
We introduce DualMPNN that integrates structural alignments as prior information to guide the inverse protein folding through dual-branch processing (Fig. I. Given a query structure G, - (V,, q. E,)) and a homologous structural template G, (V.. E,), where V, and V, represent residues, and E, and E, represents pairwise residue relationships, DualMPNN learns recover the sequence 8y by jointly reasoning over Gg and G.
3.1 Structural Templates Acquisition
Homologous templates are identified using Foldseek 27 against the Protein Data Bank (PDB). Foldseek takes one protein structure as input and returns a list of candidate proteins, sorting by their similarity. To prevent data leak from identical proteins or other chains of the same protein from being used as pairings, we exclude near-identical matches (TM-score > 0.99) as well as same PDB IDs. The remaining highest similar template is structurally aligned to query structure via TM-align 28 yielding residue correspondences = {(ig, and global similarity scores STM [0, 1]. There some certain cases of the structure alignments according to TM-scores (see Supplementary B).

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3.2 Protein Representation
In this study, we employed ProteinMPNN as the base model. Therefore, the query representation and template representation follow the formula of ProteinMPNN. Their key difference lies in the availability of sequence information. For templates, their sequences are known, allowing the node features be initialized using the corresponding amino acid sequences. In contrast, the query protein does not have sequence information available.
Query Representation (Gg): Query representation is the as the base model ProNeinMPNN. Since the sequence to be designed, node features are initialized to zeros. The edge features are pairwise distances between five backbone-derived positions:
Eg
(cl a, b C,,, Sijjs Tog
where virtual C3 atom is estimated geometrically from N-C.-C coordinates. Tig denotes the length of the template sequence.
Template Representation (G:): The template representation uses the same formula for edge features E, { } to calculate pairwise relationships among residues. The amino acid sequence information incorporated via one-hot encoding, which includes 20 standard amino acid types along with 1 additional "unknown" type. The resulting node features represented as:
=
= (v; E {0, 3 i (1, L.).
(2)
where Le denotes the length of the template sequence. This integration of sequence priors enables the template branch to provide richer contextual information compared to the query branch.
Alignment Representation (A):: The query and template structures are aligned via TM-align to extract detailed domain alignment information. The alignment representation A = (A, Jc). S) includes aligned pairs A (igs and a global measure score The aligned pairs A (ig.1e) is denoted:
At)g = (
matched
(3)
otherwise
where tuple (c) indicates the i-th amino acid of query protein aligned with j-th amino acid
of template protein, in E fl,... Lig, (l.....gh jr E (l.... Lt). The sets of matched nodes query and template structures are Aquery (ig ((g,)i)) = 1) and Atemplate (irlA (fq. = 1}.
respectively.
3.3
DualMPNN Architecture
3.3.1 MPNN Module
The shared MPNN module employs a hierarchical encoder-decoder architecture with interleaved message passing between structural encoding and sequence decoding stages. The node and edge embeddings are computed in encoding stage: hy = VW, E R Nxd hg = EW. E Nx xd where N denotes node number, K denotes the number of neighbors for each aggregated node, d denotes hidden dims, W, and W. denote learnable weights. Notably, the node features V are exclusively incorporated into the template branch, while the hidden states hy within the query branch are initialized as zero vectors.
Structure Encoder. The MPNN encoding stage comprises three successive message-passing layers, each employing shared architectural schema.
Node Update: (1) Construct message function. Collect the node features from neigh-
bors h
neigh
+
h where + denotes stacking along the third dim and h hreigh
TR Nxxd Then expand the dims of hy for concatenation by E R Nxxxd Concate- nates the features høv Cat(hiv hneigh hr) and then constructs the message function MLP(hgv) Nxxxd (2) Passing step of messages. Utilizing the aggregated

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message to update nodes by the following functions:
Ah Σ
m (1..))))
(4)
hy (hy + Dscocr) + (2 + (i(Avv))))
(5)
Edge Update: (1) Construct message function. The message function is nearly the same as that in node update. The hy and hg used for the computation updated in the previous node update step. (2) Passing step of messages. Utilizing the aggregated message to update edges by the following function:
h Ng + D2(m))
(6)
where (-) denotes normalization layer, D(-) denotes dropout layer and F(-) denotes feedforward layer. Score denotes the attention score from the interactive alignment-aware attention, see Eq.
Sequence Decoder. The MPNN decoder comprises three hierarchical decoding layers, each ingesting node-edge feature pairs from the encoder outputs while incorporating the native protein sequence embeddings to perform autoregressive sequence recovery.
Autoregressive decoding. The sequence decoder takes both sequence embeddings and node embeddings as input and generates outputs through chain-rule factorization:
pa(s)u,e) e) = II pa (s118et, USt, e)
where denotes the I-th node that is decoding, each generated element 8 depends on the latent node tンΛ, edge states and previously generated elements 8e1- The sequence will be decoded sequentially. For each node i, we consider the following:
neigh (1) For node features: hy,
h hgv Cat Cat hy heigh, hg]. where node
aggregates the next up latent node features hiv to update.
(2) For sequence embeddings: hg,
neigh
+ k=1
S. hgs Cat Cat(hg; h neigh .hgl, where
node aggregates the previous sequence features h to update.
(3) Message construction and passing: hgsv Cat]hgv:hes]] ms MLP
Ahy K
m (ink)) hy N2 Ds(score) D2(F(N Di )))))
where [ represents row-wise concatenation, A/(-) denotes normalization layer, D(-)
denotes dropout layer and FF-) denotes feedforward layer, score denotes the attention score from the interactive alignment-aware attention, Eq. X
Iterative Sampling. During inference, the decoder employs autoregressive sampling to iteratively generate sequence embeddings. At step t, it synthesizes a subsequence st conditioned historical outputs {$1a-1} and predicted node features h.k from latent projections.
3.3.2 Interactive Attention Layer
The DualMPNN architecture employs a cross-modal attention layer to enable synergistic information exchange between the query and template branches. The interaction leverages structural alignment- guided attention to fuse query and template features. Let hv R4xd and hV R xd denote node embeddings from the query and template MPNN encoders or decoders, respectively. The query-key-value projections are computed as: W1 hy [Aquery]. K W2 h4 (eemptate)]
W3 [Atempaatee)] where Q K, V E A share the same shapes, L the length of aligned residue pairs; Wi, W2, W3 E Idddd learnable projection matrices; Aquery N44 and
5

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Atemplaee N are the aligned residue indices extracted from the TM-align output that controls the attention area between the query and template branch.
The attention score is calculated and utilized by the following functions:
score = a x K
x V x
(8)
Vd
by queryy = (hy gueryy + D(score))
(9)
where S E [0, 1] is the TM-score between query and template proteins. NV-), ((), denote normalization, dropout, and softmax layers, respectively,
Interactive attention will be applied within every encoder and decoder layer. This mechanism enables prior information guidance between the branches each layer, allowing the model to refine its internal projections in a context-aware manner. Structure seapment-guideed sequence recovery provides bridge between protein structure and sequence space. It enhances ability recover protein sequences with aligned structures by incorporating evolutionary and structural constraints.
Experiments
4.1 Experimental Protocol
Dataset. We trained and evaluated DualMPNN on CATH, following the standardized data partition from prior work GraphTrans, (17) and GraDe-IF [T3. The proteins are categorized into division of 18,024 proteins for training, 608 for validation, and 1,120 for testing. The model is tested different categories: short, single-chain, and all proteins. The short chain category is those with sequence lengths shorter than 100. The single-chain category contains only those models in which the single chain accounted for the entire protein record in the PDB. Additionally, we tested our model on the T500 and TS50 datasets introduced by DenseCPD 29 which includes 9,888 structures for training and two distinct test datasets containing 50 (TS50) and 500 (T500) structures, respectively.
Training setup. The MPNN blocks possess a hidden dimension of 128 for the node and edge projections. The number of neighbors for each aggregated node is 48 in the query MPNN and 4 in the template MPNN. The interactive attention layer shares the same hidden dimension as the MPNN block. In addition, we utilize dropout rate of 0.1 to avoid overfitting both in the MPNN block and in the attention layer. The model is trained on 40 epochs, and the learning rate scheduled by the Adam optimizer.
Generation of Structure Alignments. We utilize Foldseek [7 to perform multiple structural alignments for given query protein. The search mode is "eary-search". The alignment-type is "TM aligmment". The prefilter-ne mode is "nofilter". Other arguments are default. After generating protein candidates, We filter them by removing the same protein and those with TM-scores greater than 0.99 to prevent data leak from identical proteins.
Evaluation Metric. The quality of recovered protein sequences is evaluated using two key metrics: perplexity and recovery rate. Perplexity quantifies the alignment between the model's predicted amino acid probability distribution and the actual residues observed at each sequence position, with lower values indicating superior model-data compatibility. The recovery rate measures predictive accuracy by calculating the percentage of amino acids in the reconstructed sequence that correctly match the native protein sequence, with higher values reflecting enhanced sequence reconstruction capability from structural inputs. The quality of protein structure alignment is quantified by TM-score and RMSD. TM-score employs a length- normalized assessment that evaluates both local structural matches and global topological similarity, producing values ranging from 0 to 1, with scores above 0.5 generally indicating biologically meaningful structural relationships. RMSD measures the average spatial deviation between corresponding C., atoms in superimposed structures, with lower values indicating stronger geometric congruence.
4.2 Inverse Folding
Table 1 shows the results of the different structure-aware models in the CATH, T500 and TS50 datasets. DualMPNN achieves state-of-the-ar performance across all metrics, demonstrating superior sequence recovery capabilities and lower perplexity scores. Specifically, our model reaches recovery

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Table 1: Comparison of recovery rate and perplexity performance CATH, TS50, and T500.
Models marked with f use CATH v4.3, the rest use CATH v4.2. PPL denotes perplexity, Rec. denotes recovery rate.
CATH
TS50
T500
Models
PPL 4
Rec. % t
PPL J
Rec.
PPL + Rec.%
Short
Single
All
Short
Single
All
STRECTGIN 17
8.29
8.74
6.40
29.44
28.26
35.91
5.40
43.89
4.98
45.69
GRAPHTRANS
10
8.39
8.83
6.63
28.14 14
28.46
35.82
5.60
42.20
5.16
44.66
GCA 80
7.09
7.49
6.05
32.62
31.10
37.64
5.09
47.02
4.72
47.74
GVP 31
7.23
7.84
5.36
30.60
28.95
39.47
4.71
44.14
4.20
49.14
GVP-LARGE
6,12
32.60
39.40
39.20
ALPHADESIGN
7.32
7.63
6,30
34.16
32.66
41.31
5.25
48.36
4.93
49.23
ESM-IFI [E]
8.18
6.33
6.44
31.30
38.50
38.30
PROTEINMPNN 12
6.21
6.68
4.57
36.35
34.43
49.87
3.93
54.43
3.53
58.08
PIFOLD
6.04
6.31
4.55
39.84
38.53
51.66
3.86
58.72
3.44
60.42
GRADE-IF
5.49
6.21
4.35
45.27
42.77
52.21
3.71
56.32
3.23
61.22
DualMPNN
4.42
5.04
55.97
52.41
65.51
2.76
70.99
2.71
70.37
a
b
1.0
ProteinMPNN
0.3
0.9
Recovery Rate
0.8
Improvement
0.2
0.7
-0.6
DuaIMPNN
0.4
0.1
0.5
0.2
0.0
0.3
... [0. 0.3)
[0.3, 0.51
[0.5,
<0.3
0.3-0.5
0.5-0.7
0.7-0.9
0.9-0.99
0.1
[0.7. 0.91
[0.9. 0.99]
(43)
(197)
(171)
(408)
(301)
0.5
0.7
TMscore Interval (Num of Proteins)
ProteinMPNN
Figure 2: Impact of template quality on sequence recovery rate. (a) Violin plot comparing sequence recovery rates of DualMPNN and ProteinMPNN across distinet TM-score intervals the CATH test set. (b) Scatter plot of per-pres per-protein recovery rates, colored by TM-score intervals. Points above the dashed parity line (y .>) highlight instances where DualMPNN outperforms the baseline, particularly for high-quality templates (TM-score > 0.5).
rate of 65.51% % and perplexity of 3.19. The recovery rate improved 13.3% compared to GraDe-IF. Since most of the data from CATH consists of oligomers or multimers, the chains within these assemblies are significantly influenced by interchain interactions 34. In multichain proteins, such interactions induce context-dependent conformational plasticity, causing identical sequences to adopt distinct structural geometries in oligomeric assemblies compared to their monomeric states. This occurs through cooperative adjustments backbone dihedrals, side-chain rotamers, and quaternary- stabilized folding motifs. Therefore, single chains particularly challenging to predict in the CATH dataset. However, DualMPNN leverages direct guidance from prior structural information, enabling more accurately predict single-chain structures, reaching recovery rate of 52.41% % and perplexity of 5.04. Short chains also face the challenge accurate prediction
lack of similar data within the dataset, which makes difficult. Despite this limitation, DualMPNN demonstrates its robustness by achieving an impressive recovery rate of 55.97 %,, showcasing its ability to handle even the most data-scarce scenarios effectively. Furthermore, the results in T500 and TS50 datasets (Table also show that DualMPNN remains the best performance across all metics, reaching a recovery rate of 70.37% 70.99% and perplexity of 2.71, 2.76 in T500, TS50, respectively.

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4.3 Template Quality Matters
To evaluate the impact of template quality. we divided the CATH test dataset based on their TM-scores against the corresponding template proteins into five categories: [0, 0.3), [0.3, 0.5), [0.5, 0.7), 0.9), (0.9, 0.99]. Among the alignments, 880 proteins had a TM score greater than 0.5, while 240 proteins had TM score less than 0.5. We then compared the performance improvements
DualMPNN against ProteinMPNN within these categories. in Das. a). DualMPNN demonstrates significant advantages over ProteinMPNN when the template quality exceeds TM score of 0.5, with improvements becoming more pronounced as the quality of the structural alignment increases. Specifically, DualMPNN achieves recovery rate of 58.7% 61.5% and 84.0%, outperforming the baseline model ProteinMPNN by 13.4%, 13.5% and 31.3%, within the TM score interval of (0.5,0.7), (0.7,0.9) and [0.9,0.99], respectively.
shown
Furthermore, we compared the recovery rate performance and DualMPNN (Fig. b)). The diagonal line indicates equal performance between the two models. Points above the diagonal represent cases where DualMPNN outperforms ProteinMPNN, while points below the diagonal represent cases where ProteinMPNN performs better. We observed that ProteinMPNN rarely achieves a recovery rate above 70%, while DualMPNN can easily recover certain protein sequences with a recovery rate above 70%, and in some cases, even close to 100%.
certain protein between ProteinMPNN
These results highlight DualMPNN's superior ability leverage high-quality templates for accurate sequence recovery. However, our model does have some limitations. For templates with low quality, it remains challenging to significantly improve sequence recovery performance. Fortunately, with the help of Foldseek, we can identify a large number of high- high-quality templates through structural alignments, which ensures that the approach remains practical and effective in real-world applications.
4.4 Ablation Study
To evaluate the contributions of the components in DualMPNN, conducted ablation study Starting with ProteinMPNN, we incorporated aligned domain node initialization using template proteins. By leveraging the prior knowledge of template proteins, the recovery rate improved significantly, increasing from 49.87% to 61. 61.29%. Next, we utilized dual-stream protein message passing neural network update node projections within the encoding and decoding layers, where nodes were directly updated by added features. Additionally, we used interactive attention layers to refine the node features, enabling the model to sense contextual information and enhance protein sequence recovery. The interactive attention layers contributed significantly, increasing the recovery rate from 62. 13% to 64.78% and reducing perplexity from 3.48 to 3.23. Finally, by applying the TM score as a similarity bias between the template and query proteins, DualMPNN achieved a recovery rate of 65.35% and maintained perplexity of 3.20. This demonstrates the effectiveness of each component in improving sequence recovery and model performance. Furthermore, we discovered that sampling 10 times at the inference stage with different random seeds and using the most frequent amino acid type as the answer further improved the recovery rate to 65.51 51% and reduced the perplexity 3.18.
(Table
Table Ablation study on different components of DualMPNN on CATH. PPL denotes perplexity,
Rec. denotes recovery rate.
PPL
Rec. % t
Configuration
Short
Single-chain
Short
Single-chain
A
Baseline Model
6.21
6.68
4.57
36.35
34,43
49.87
B
A + Node init by template
5.35
5.83
3.55
50.85
47.03
61.29
C
B + Dual-stream update
4,82
5.54
3.48
53.78
50.23
62.13
D
C Interactive attention update
4.57
5.23
3.29
54.95
51.11
64.78
E
D + TM score bias
4.46
5.09
3.20
55.74
52.19
65.35
F
E. + Sample 10 times
4.42
5.04
3.18
55.97
52.41
65.52
4.5
Generalization
To assess generalization on novel samples, we stratified test proteins by structural similarity (TM- score) to the training set. As summarized in Table DualMPNN is substantially better than

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ProteinMPNN, especially at low similarity. For TM-score < 0.3, DualMPNN attains 66.9% recovery vs. 50.9% for ProteinMPNN; for 0.3-0.5, 60.5% vs. 45.3%; and for 0.5-0.7, 58.6% vs. 40.9%. These marginal gains indicate robustness beyond close structural matches and highlight superior performance on structurally novel cases, indicating that DuaIMPNN does not simply rely on near- neighbor memorization but scales across the full novelty spectrum.
Table 3: Comparison of generalization in terms of structural similarity (TM-score) or sequence identity stratification.
Generalization
TM-score (Test vs Train)
Sequence Identity (Test vs Template)
Benchmarks
<0.3
0.3-0.5
0.5-0.7
0.7-0.9
0.9-0.99
<0.3
0.3-0.5
0.5-0.7
0.7-0.9
0.9-0.99
Samples
706
307
73
29
5
803
153
79
32
ProteinMPNN
50.9
45.3
40.9
45.1
48.1
48.5
52.4
48.0
50.7
51.8
DualMPNN 66.9
60.5
58.6
74.5
71.6
60.6
68.4
83.8
87.1
95.5
To validate the model generalization on low-quality templates, we binned test samples by sequence identity to templates and compared recovery across five identity ranges. DualMPNN exhibits strong performance in all bins, achieving 60.6% recovery even sequence identity <0.3. While recovery rate increases with template quality (higher identity), DualMPNN shows a consistently larger improvement margin. This indicates more effectively leverages higher-quality template signals without sacrificing performance when they are weak. These results are corroborated by TM-score analysis, confirming gains are consistent across both evolutionary (sequence) and structural (TM-score) notions of divergence. In addition, lower perplexity (where Section 4.2 reported) aligns with higher recovery on both the test and holdout splits, suggesting better-calibrated sequence distributions that translate into improved top-1 design accuracy without sacrificing stability.
4.6 Foldability
To validate the foldability of the generated protein sequences, we fold them with Alp [S] and Alphafold3 [5 then align the folded structures with the native structures using TM-align to compare their similarity. Following [[3 we evaluate each novel sequence by the TM-score between its predicted structure and the native structure, where a TM-score above 0.5 indicates successful design. We fold 100 generated sequences from the CATH test set (first 100 sequences ordered alphabetically by PDB ID), and summarize the results in Table 4
Under Alphafold2 inference, DualMPNN attains success rate of 94%, mean TM-score of approxi- mately 0.86, an average PLDDT near 0.91, and an RMSD around 1.5 A. These results indicate that the sequences produced by DualMPNN not only fold into well-defined structures but also receive high model confidence. Native sequences processed by AF2 exhibit an average PLDDT of about 0.91, which underscores that the confidence of our generated sequences approaches that of the native counterparts. When evaluated with Alphafold3, DuaIMPNN reaches success rate of 95%, mean TM- close to 0.87, an average DLDDT near 0.92, and RMSD values on the order of 1.4 A. Relative to ProteinMPNN under AF3, DuaIMPNN delivers higher success, stronger structural similarity, and higher confidence while maintaining comparable geometric deviation. Collectively, these results demonstrate that DuaIMPNN produces sequences that fold reliably, attain high structural agreement with native targets, and are assigned consistently high confidence by modern structure predictors.
Table 4: Foldability comparison between generated structures and the native structures. The methods with are generated by Alphafold3 and the rest using Alphafold2.
Method
Successt
TM score
avg PLDDT
avg
RMSD 1
PiFOLD
85
0.80
0.22
0.84 + 0.15
1.67 + 0.99
ProteinMPNN
94
0.86 + 0.16
0.89 +
1.36 = 0.81
GRaDe-IF
94
0.86 + 0.17
0.86
+ 0.08
1.47 + 0.82
DualMPNN
0.86 0.16
0.91 0.10
1.49 1 0.86
ProteinMPNN + DualMPNN
94
0.86 + 0.18
1.41 0.76
95
0.87 0.16
0.92 0.11
1.39

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Recovery
Recovery 0.69
Recovery
TM score:
TM score: 0.97
TM score: 0.95
Avg. PLDDT: 92.6
Avg. pLDDT: 95.8
Avg. pLDDT: 93.3
RMSD: 1.10
RMSD: 0.92
RMSD: 1.52
Figure 3: Folding comparison of generated sequences (blue) and native sequences (orange).
Specific cases of folded sequences, selected from the CATH test set, are presented in Fig. The three folded structures (3GA2, 3GOC, and 3HKV) exhibit sequence recovery rates of 0.53, 0.69, and 0.88, respectively. All achieved TM scores greater than 0.95 and average PLDDT scores exceeding 0.92, which comparable the native sequences. The generated structures are well-aligned with their native counterparts, highlighting the exceptional foldability of DualMPNN.
5 Conclusion
We introduce DualMPNN, a dual-stream message-passinng neural network that synergizes geo- metric and co-evolutionary signals from query structures and their structurally aligned homologs. DualMPNN a novel paradigm that leverages structural alignments as informative priors for in- verse protein folding. The architecture comprises two distinct branches, which interact through alignment-aware cross-attention mechanisms, enabling feature enhancement while maintaining weight independence. Extensive empirical validation demonstrates DualMPNN's vate-of-the-aie art performance, surpassing existing baselines by significant margins. Structural validity assessments confirm the biological plausibility of designed sequences, with AlphafFold--prediite structures exhibiting high confidence and geometric fidelity to native backbones. Crucially, we identify a TM-score threshold of 0.5 critical determinant of template utility, beyond which structural homology significantly enhances sequence recovery.
Our work underscores the transformative potential of structural alignment priors in protein design, bridging geometric constraints with evolutionary insights to advance sequence generation accuracy. By circumventing reliance explicit sequence covariation data, DualMPNN offers scalable framework for de novo protein engineering, with implications for designing functional proteins in low-MSA regimes. Future directions include integrating dynamic template selection strategies and extending the framework to multi-state protein design. This approach not only advances computational protein engineering but also deepens understanding of the structure-sequence interplay in biology.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (62573164) Guangdong Basic and Applied Basic Research Foundation (2025A15150101855) Guangdong Provincial Colleges and Universities Key Areas Program (2025ZDZX0779), Key Project of Heilongjiang Provincial Natural Science Joint Foundation (ZL2025E003), Shenzhen Science and Technology Program KCXF22022377110000000000
JCY1200238807093318883 18038, X000)//9944440000000000002299990
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16. Declaration of LLM usage

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Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
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Supplementary Files
A Preliminary Experiments
Before this work begins, we've performed some preliminary experiments to evaluate the feasibility. Our initial hypothesis is that the node information within the graph network constructed by Protein- MPNN can significantly enhance model performance when enriched with prior knowledge derived from sequences corresponding to homologous structures. In ProteinMPNN, these node features are originally initialized to zero, leaving substantial room for improvement by incorporating more infor- mative priors. Theoretically, augmenting this initialization with sequence context from homologous structures should effectively improve the model's s accuracy by providing a richer representation the underlying protein features.
On the CATH dataset, we initialized a certain proportion of the ProteinMPNN node features with the native protein sequences, while another certain proportion was initialized with incorrect sequences. This setup aimed to simulate the characteristics of amino acids in homologous structural pairings, where some regions share identical sequences while others contain mismatches. The purpose of this approach was to better mimic real-world scenarios where structural alignments provide partial but imperfect sequence information. The preliminary experimental results are shown in Table ST When the wrong initialization rate is fixed, increasing the correct initialization rate improves recovery. For example, with 0% wrong rate, recovery rises from 49.87 49.87% (0% correct) to 54.57% (10%) and 61.39% (30%). At fixed correct rate, higher wrong initialization lowers recovery. With 10% correct, recovery drops from 53,422 53,42% (20% wrong) 51.82% (40%); with 20% correct, it drops from 58.67% (10%) to 52.61%% % (60%). Both correct and wrong initialization rates markedly affect recovery, underscoring the importance of template quality. This is consistent with the analysis in Section 4.3.
Table S1: Sequence perplexity and recovery rate under different initializing ratio in preliminary experiments.
Init ratio
Perplexity|
Recovery rate*
Correct
Wrong
Zeros
0%
0%
100%
5.41
49.87%
10%
0%
90%
4.09
54.57%
10%
20%
70%
4.12
53.42%
10%
40%
50%
4.73
51.82%
20%
10%
70%
4.53
58.67%
20%
60%
20%
4.62
52.61%
30%
0%
70%
3.77
61.39%
30%
20%
50%
3.85
60.01 %
40%
40%
20%
3.57
62.11% %
Cases of Protein Templates in Five TM-score Intervals
Protein templates are divided into five intervals: [0, 0.3). [0.3, 0.5). 0.., 0.7), (0.7, 0.9), [0.9, 0.99]. There are some cases query-template proteins down below (Fig. S1 each presents a combined view of sequence and structural alignment between query protein and a template protein, typically used to assess homology modeling or structural similarity. On the left, the sequence alignments highlight the correspondence between residues in the query and template, with matched or similar residues indicated by colored symbols, where exact matches often shown as aligned letters, and conservative substitutions marked with symbols such as plus signs. Gaps introduced to optimize alignment are represented by dashes. The sequence alignments are annotated with residue indices to indicate positional context. On the right, ribbon diagrams overlay the 3D structures of the two sorcins-commonl, using distinct colors (blue for the query and orange for the template) to visually demonstrate structural conservation. Quantitative metrics such TM-score, RMSD, aligned length, and matched length are usually provided to objectively evaluate the quality of the alignment, with higher TM-scores and lower RMSD values indicating greater structural similarity.
These template cases illustrate the structure and sequence similarities between proteins across different TM-score intervals. When the TM-score is below 0.5, the alignment tends to be short, and the type of aligned amino acid shows low similarity. In contrast, when the TM-score exceeds 0.5, the alignment length increases, and the residue-level correspondence improves significantly. These examples support the findings presented in Section 4.3 of the experiments, further highlighting the critical role of template quality in influencing the accuracy of sequence recovery by the model.

---

Query: 31T8.D
Template: 6DDV.C
TW-score=0.22 27, 65, Aligned length-91, Matched length-21
3VLL8/002//400LPPPGG 59
252 T 234
TY 3
Query: A
Template: 3BCV.A
TM-acore=0. 43, RM3D=2. 13, Aligned length=111, Matched length=32
117 PON.ETTA.DBBLLLTTPEPPPP..
SAA.://AAAASTTP........E.ETEEAAE BEELLLLEEV 193 DK3 + +4
H4 F2
GWAIST
+DI
78
(OP.TIAAKKAAAATTSSTTTTOOOOOIIII 115
Query: 3FK9.A
Template: 3SND A
TM--coreeO.co 63, RMSD-2. 19, Aligned length-108, Natched length=38
WWW.P//ILOOOONNNAAAOOOOOOOOO SESTSSLEEEEEEEETTT SWVSNPPLKGGLSSN-- VIFDEEKI
WEETG
KG+7
75 VBWW://TAAAIRROBAAARRRO WWW.ROOE-VEEELAAAGGAAAE 122 V E--- G++ X
Let E
LF
DE IF
V-BYEWWFEERTTOEEE AYSERSKPPPLAPPPP..
Query: 2ANY
Template: 200K.
TN-score-0.8L. RMSD-2.17, Aligned length-134, Matched length-15
81
LEDR -R-DKOKA
УP-НAE Re+
82
139
Query: A
Template: 4NZ.J.A
TY-score--.. ,5,, RMSD-1.77, .7, Aligned length-359, Matched length-154
WOLOGRTE WES.IEEEEELRSSAAAAANAA WWWTLLLLLL WWW.://WWAAAASSSS/PPPPPPOO E. TP MGNHHNY E+ 7 Go LAY Y+EIDO G++ +* FP GIB +ADY
82
WWAKCAALATYBBAA0/////WPPP +G-KLLIYYDA++ G5
371 LUEEGPPLLGYYBBAA00000000 XAA.://ww............AA/A/AAAAA. AANGHAAAAAAAASA LVS
249
361 SESAGEEWAATVGE-NNEEEERR
CEMG+
+GDI-D
250
309
-Y+SIPS-VV +PLL DVR+
It ++TA-X00 LG Q+++ -Hd Pl++ RKAY
305
350
410
-WA.LLTT---OOEELTLLLLAOOOOO 454
Figure S1: Five cases of protein templates across different TM-score intervals. The query-template pairs with higher structural TM-scores tend to exhibit more similar sequence alignments.


Reviews:
[{"review_id": "eowFNoNAqE", "reviewer": "Reviewer_Cx1H", "summary": "This paper presents DualMPNN, a dual-stream message passing neural network that improves inverse protein folding by leveraging structurally aligned templates through TM-align and attention-based feature fusion. The model shows significant gains in sequence recovery and perplexity over existing methods (e.g. ProteinMPNN), particularly when high-quality templates are available. Extensive ablation and benchmark evaluations demonstrate the model’s robustness and architectural soundness.", "questions": "Suggestions for improvement\n\n- Stricter homology filtering: To ensure generalization and avoid template leakage, consider filtering training/test pairs using sequence identity thresholds (e.g., <30%), in addition to TM-score and PDB-based exclusions.\n\n- Include SCOP-based evaluations: Evaluating the model on SCOP-classified domains would help validate whether DualMPNN generalizes across different evolutionary and topological classifications, complementing the current CATH-based benchmarks.\n\n - Why not use AlphaFold3? Given the availability of AlphaFold3, the authors should either validate foldability using the updated model or strongly justify the continued use of AlphaFold2. Additionally, they could leverage structures excluded from AlphaFold2 training but included in AlphaFold3 as a valuable test set for assessing generalization.\n\n - Incorporate functional or structural plausibility metrics: Beyond recovery and perplexity, authors could evaluate conservation of functional motifs, residue-level confidence, or validate structure-function relationships via experimental assays or in silico function prediction.\n\n- Analyze diversity and entropy under poor templates: To support the claim of robustness under low-quality alignments, the model’s output diversity and per-residue entropy could be measured and compared to baselines, particularly in low TM-score regimes.\n\n- Several complementary metrics could provide deeper insight into the biological plausibility, structural consistency, and functional relevance of the inferred sequences. For instance, structural similarity metrics such as RMSD after in silico folding, confidence scores from AlphaFold (e.g., pLDDT), and physicochemical assessments such as packing quality or solvation energy can help evaluate whether the designed sequences are not only recoverable but also foldable and functionally viable.", "limitations": "Limitations: The authors could strengthen the discussion by acknowledging key limitations, such as:\n\n- There is a lack of functional validation for generated sequences.\n\n- Potential data leakage due to residual homology between training and test sets.\n\n- Reliance on AlphaFold2 for foldability without discussing more recent tools like AlphaFold3.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n\n- Comprehensive ablation studies demonstrate the contribution of each architectural component: template node initialization improves recovery from 49.9% to 61.3%, cross-stream attention further boosts it to 64.8%, and TM-score modulation leads to a final recovery rate of 65.4%, highlighting the additive benefit of each mechanism.\n\n- Meaningful improvement over baselines: DualMPNN outperforms ProteinMPNN and GraDe-IF across standard benchmarks, consistently achieving higher recovery rates and lower perplexity across CATH, TS50, and T500 datasets.\n\n - The model avoids overfitting in low-TM-score regions due to the masking of unaligned residues and the use of TM-score–weighted attention, which downregulates unreliable template signals. This is supported by empirical evidence: in Figure 2(a), proteins with TM-score < 0.3 show no significant drop in recovery rate compared to ProteinMPNN; and in Figure 2(b), low TM-score cases (blue and orange points) cluster near the diagonal, indicating that DualMPNN neither helps nor harms when template similarity is poor.\n\n- Attention score modulation by the global TM-score allows the model to selectively leverage high-quality templates, leading to recovery gains over 30% when TM-score > 0.9.\n\nLimitations\n\n- Triviality of the core insight: While the paper quantifies the relationship between TM-score and sequence recovery, the central finding, i.e. that higher structural similarity leads to better recovery, is intuitive. \n\n- Potential data leakage: The authors only exclude near-identical templates (TM-score > 0.99, same PDB ID), and hence, residual homology may still bias results. The absence of explicit sequence identity filtering raises concerns about the true independence of training and test pairs.\n\n- Lack of functional assessment: The study evaluates sequence recovery but does not test whether the generated sequences are functional, foldable, or biologically plausible beyond AlphaFold confidence metrics.\n\n - No direct test for hallucination: The paper claims robustness to low-quality templates, but does not evaluate whether it generates unrealistic or misleading sequences in such cases. There is no analysis of output diversity, entropy, or structural viability in weak-alignment settings.", "was_revised": true, "final_justification": "I am increasing my score to accept following a thorough and thoughtful rebuttal.\n\nResolved Issues:\n\n- Homology concerns were addressed with sequence identity–stratified analysis.\n\n- Foldability validated using AlphaFold3.\n\n- Additional biophysical and diversity metrics support plausibility and robustness under poor templates.\n\nRemaining Issues:\n\n- SCOP-based evaluation is deferred but acknowledged.\n\n- Functional validation is still lacking but clearly stated as a limitation.\n\nGiven the new empirical results, I now recommend acceptance.", "rebuttal": "Thank you for your careful review and constructive suggestions with regard to our manuscript. While the correlation between structural similarity and sequence recovery is intuitive, our work is **the first to effectively incorporate structural alignments into inverse folding** via TM-score–modulated attention and dual-stream message passing. By turning this simple idea into a practical and robust framework with strong empirical gains, our method not only advances performance but also provides a useful paradigm for leveraging structural prior knowledge in protein design.\n\n# Responses to Questions:\n\n1. To illustrate the homology filtering and data leak issues, we evaluated the effect of homology by **partitioning test samples according to their sequence identity with templates**. All test samples were binned accordingly into **five sequence identity** ranges, and then compared the sequence recovery between **ProteinMPNN** and **DualMPNN** across these bins.\n\n   As shown in the table below, DualMPNN demonstrates robust performance across all sequence identity bins, achieving a recovery rate of **60.6%** even **when sequence identity is below 0.3**. These results underscore that our model’s effectiveness does **not stem from sequence leakage**, but rather from **its ability to learn homology features from templates** of varying quality. Furthermore, as template quality improves (higher sequence identity), recovery rates increase significantly, **which aligns with expectations** and further validates our model’s capacity to effectively leverage high-quality templates for improved sequence recovery. We will include these analyses in the revised version.\n\n   |Sequence Identity between Test Samples and Templates|< 0.3|0.3 - 0.5|0.5 - 0.7|0.7 - 0.9|0.9 - 0.99|\n   |----------------------------------------------------|------|---------|---------|---------|----------|\n   |**Number of Test Samples**|**803**|**153**|**79**|**53**|**32**|\n   |ProteinMPNN Recovery|48.5%|52.4%|48.0%|50.7%|51.8%|\n   |DualMPNN Recovery|**60.6%**|**68.4%**|**83.8%**|**87.1%**|**95.5%**|\n\n2. We agree that SCOP provides a rigorous framework for evaluating generalization across evolutionary and topological classes. While time constraints prevent us from completing SCOP-based experiments during the rebuttal period, we will include them in the revised version of the paper.\n\n   To illustrate model generalization in the meantime, for each test sample, we identified its maximum TM-score relative to the training set and grouped the test set into five TM-score ranges. Both **ProteinMPNN** and **DualMPNN** were then evaluated across these structural similarity bins to analyze their generalization performance under varying levels of structural similarity between the training and test sets. As shown below, **DualMPNN maintains strong performance even in low structural similarity regions**, demonstrating its ability to generalize beyond closely related folds. These results already provide solid evidence of our model’s robustness across diverse structural families and great generalization performance.\n\n   |TM-score of Test Samples against Train Set|< 0.3|0.3 - 0.5|0.5 - 0.7|0.7 - 0.9|0.9 - 0.99|\n   |------------------------------------------|------|---------|---------|---------|----------|\n   |**Number of Test Samples**|**706**|**307**|**73**|**29**|**5**|\n   |ProteinMPNN Recovery|50.9%|45.3%|40.9%|45.1%|48.1%|\n   |DualMPNN Recovery|**66.9%**|**60.5%**|**58.6%**|**74.5%**|**71.6%**|\n\n3. To further validate the foldability of sequences generated by **DualMPNN**, we have predicted their structures using **AlphaFold3** and compared the results with AlphaFold2 predictions. These results demonstrate the excellent foldability of sequences generated by DualMPNN, achieving strong folding performance on both AF2 and AF3. This further highlights the reliability and robustness of DualMPNN. The outcomes are summarized below.\n\n   |Models|Success ↑|TM-score ↑|pLDDT ↑|RMSD ↓|\n   |-----|---------|----------|-------|------|\n   |ProteinMPNN (AF2)|94|0.860 ± 0.16|0.89 ± 0.10|1.36 ± 0.81|\n   |ProteinMPNN (AF3)|94|0.858 ± 0.18|0.88 ± 0.12|1.41 ± 0.76|\n   |DualMPNN (AF2)|94|0.862 ± 0.16|0.91 ± 0.10|1.47 ± 0.86|\n   |DualMPNN (AF3)|**95**|**0.871 ± 0.16**|**0.92 ± 0.11**|**1.39 ± 0.80**|\n\n4. To further evaluate the rationality of the generated sequences, we evaluated DualMPNN across the following metrics on CATH test set:\n\n   **(1) Perplexity**:\n      Perplexity is a widely used proxy for plausibility in generative protein models. On the CATH dataset, DualMPNN achieves a **PPL of 3.18 (Table 1 in main paper)**, which indicates that the model generates highly probable sequences under its learned distribution.\n\n   **(2) Physicochemical Properties**:\n       We evaluated two key sequence-level biophysical indicators: **GRAVY score (hydropathy)** and **polar residue composition**. DualMPNN shows distributions that closely match natural sequences, and significantly outperforming ProteinMPNN in mimicking these properties (**Average denotes the average score of all samples**).\n\n      |GRAVY|[-0.8,-0.6)|[-0.6,-0.3)|[-0.3,0)|Average|\n      |-----|-----------|-----------|--------|-------|\n      |Natural sequences|10.45%|34.46%|35.09%|-0.3233|\n      |DualMPNN|7.95%|32.14%|36.52%|-0.2586|\n      |ProteinMPNN|16.79%|39.29%|19.82%|-0.5404|\n\n      |Percentage of polar residue|35%~45%|45%~55%|55%~70%|35%~70%|Average|\n      |---------------------------|-------|-------|-------|-------|-------|\n      |Natural sequences|9.73%|57.14%|31.07%|97.94%|52.21%|\n      |DualMPNN|12.77%|58.09%|26.29%|97.15%|51.30%|\n      |ProteinMPNN|5.98%|50.71%|40.27%|96.96%|54.39%|\n\n   **(3) Amino Acid Distribution**:\n      We compared the residue distribution of sequences generated by **DualMPNN** and **ProteinMPNN** against that of natural sequences. Notably, the **bond values indicate maximum offsets compared to the natural residue distribution**. The results below demonstrate that **DualMPNN effectively mimics natural amino acid residue distributions**. By leveraging template priors, DualMPNN better captures the nuanced residue patterns of natural sequences compared to ProteinMPNN.\n\n      |Amino Acid (%)|A|C|D|E|F|G|H|I|K|L|M|N|P|Q|R|S|T|V|W|Y|\n      |--------------|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|\n      |Natural sequences|7.8|1.3|6.1|7.3|4.5|6.7|2.4|5.9|6.1|9.2|1.5|4.2|4.4|3.9|5.1|5.8|5.5|7.3|1.3|3.6|\n      |DualMPNN|9.0 **(+1.2)**|1.1 (-0.2)|6.1 (+0.0)|9.3 (+2.0)|4.4 (-0.1)|6.8 (+0.1)|1.9 (-0.5)|5.6 (-0.3)|6.2 (+0.1)|9.8 (+0.6)|1.1 (-0.4)|3.8 (-0.4)|4.7 (+0.3)|2.5 (-1.4)|4.7 (-0.4)|5.5 (-0.3)|5.2 (-0.3)|7.8 **(+0.5)**|1.1 (-0.2)|3.4 **(-0.2)**|\n      |ProteinMPNN|6.6 **(-1.2)**|1.0 **(-0.3)**|6.4 **(+0.3)**|14.6 **(+7.3)**|3.7 **(-0.8)**|6.4 **(-0.3)**|1.2 **(-1.2)**|4.9 **(-1.0)**|9.1 **(+3.0)**|10.8 **(+1.6)**|0.63 **(-0.87)**|3.6 **(-0.6)**|5.2 **(+0.8)**|1.0 **(-2.9)**|3.5 **(-1.6)**|4.9 **(-0.9)**|4.5 **(-1.0)**|7.5 (+0.2)|1.0 **(-0.3)**|3.7 (+0.1)|\n\n   These results suggest that DualMPNN generates **low-perplexity sequences while capturing physicochemical patterns and foldability signals**, resembling natural proteins and outperforming ProteinMPNN in producing **biologically plausible sequences**, even without explicit functional training.\n\n5. To assess robustness under low-quality templates, we selected a subset of **TM-score < 0.5** (240/1120) test samples and evaluated **output diversity** and **sequence entropy**. These results suggest that DualMPNN does not introduce excessive randomness under weak structural alignment, performing comparably to natural sequences in terms of diversity and entropy. This demonstrates its **robustness to low-quality templates** and **resistance to hallucination**.\n\n   |Metrics|Diversity|Entropy|\n   |-------|---------|-------|\n   |Natural sequences|0.5108±0.2733|2.801±1.040|\n   |ProteinMPNN|0.4935±0.2664|2.659±1.054|\n   |DualMPNN|0.5204±0.2456|2.835±0.926|\n\n6. We have added experiments on **packing quality** and **solvation energy**. Solvation energy is divided into two components, **Solvation Polar Energy** and **Solvation Hydrophobic Energy**, for a detailed presentation. While packing quality is not a directly quantifiable single metric, we evaluated **van der Waals interaction energy (VDW Energy)** and **van der Waals clash energy (VDW Clash Energy)** as proxies to reflect packing quality. The results in the below table show that DualMPNN demonstrates a balanced performance across solvation and packing-related metrics, highlighting our model's ability to generate sequences with **high structural quality and stability, closely resembling natural proteins**.\n\n   |Metrics (kcal/mol)|Solvation Polar|Solvation Hydrophobic|VDW Energy|VDW Clash Energy|\n   |------------------|---------------|---------------------|----------|----------------|\n   |Natural sequences|239.47±149.92|-232.41±149.97|-176.66±112.95|10.87±10.44|\n   |ProteinMPNN|233.46±147.80|-237.21±155.32|-176.80±114.11|8.87±7.08|\n   |DualMPNN|236.57±150.70|-236.21±153.66|-176.27±112.69|8.60±7.50|"}, {"review_id": "r5kKUUtAYN", "reviewer": "Reviewer_ASyn", "summary": "The paper proposes a dual stream network architecture for the inverse folding problem which incorporates information from structural alignments by cross-attention between two instances of a base inverse folding model such as ProteinMPNN. The authors demonstrate improved performance compared to baselines and highlight the importance of good templates.", "questions": "- Leakage, see above. Are templates at test time limited to training samples or is data leakage otherwise prevented?\n- Is the template strictly required at inference or can the model be run without? Is the performance then comparable to a bad template (with low TM) or worse?\n- How were the hyperparameters for the similarity threshold (99%) and the neighbors in query and template model (which also differ strongly) chosen?\n- How long did it take to run the alignment for all training data? This might also be relevant in the limitations. Is the dataset available?\n\nThe following questions are more for my own interest, I don’t require them to be answered:\n\n- Does the template branch focus more on the node label or the geometric edge label information? Do you have any indications how this is weighted, eg through an ablation of the geometric edge features?\n- It would be interesting to see how DualMPNN performs on structural holdouts (eg from FoldSeek clustering) compared to ProteinMPNN, which would point towards generalization to novel folds, although I understand that this is out of scope for this rebuttal.", "limitations": "- As mentioned above, if the runtime is significantly increased through the alignment, that should be mentioned.\n- Also, while the availability of templates is discussed, the authors discard this with the argument that in a real-world scenario there will likely be some template available. I would argue here that one of the primary applications of inverse folding models is the sequence design for novel protein folds, where such templates might not be available. (I would just recommend here to let the limitation stand as it is without trying to remedy it.)", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The proposed idea is simple and clean, and the text is well written and easy to follow (apart from a few typos, see below).  The inverse folding problem is currently very relevant in the context of protein design, and the experiments are well conducted and focus on a few key aspects such as ablations and the dependence on template quality.\n\nI am only concerned about data leakage from the alignment step, especially when provided during evaluation. One might argue that DualMPNN gains unfair advantage through the additional information which was not available to ProteinMPNN. As the similarity threshold is quite high (99%), a near-identical template could potentially be selected for a test protein, in which case the low-hanging fruit for the model is simply to map the template sequence to the query sequence. It would be good if the authors take great care to discuss this point in the paper, as it is a little sensitive topic.\n\nI, in principle, would recommend to accept the paper as it is well executed, but I reserve to change my assessment based on the author discussion of this critical point.", "was_revised": true, "final_justification": "The authors have addressed my concerns on data leakage, in fact, the performance gains on low sequence similarity are rather impressive. I would recommend to also include these additional results in the final revision.\n\nI am sure the tool will prove useful to the protein design community (if released accessibly with code and data ;) and I hence recommend to accept the submission.", "rebuttal": "# Responses to Questions\n\n1. We appreciate the reviewer for raising concerns about potential data leakage during evaluation. To rigorously address this and demonstrate DualMPNN's generalization capability, we conducted two targeted analyses:\n\n    **(1) Impact of Sequence Identity with Templates.** We stratified test sequences based on their sequence identity to templates into 5 bins, and then compared the sequence recovery between **ProteinMPNN** and **DualMPNN** across these bins. The results in the below table demonstrate that most test-template pairs exhibit low sequence identity (<0.5). Crucially, **even at very low sequence identity (<0.3)**, DualMPNN achieves **60.6% sequence recovery**, significantly outperforming the 48.5% sequence recovery of ProteinMPNN. This strongly indicates that the performance improvement of our model **does not stem from data leakage** but rather a result of **effectively leveraging the evolutionary information from homologous structural templates to enhance recovery**. Additionally, as the sequence identity further improved, our model can fully exploit this information to better assist sequence recovery for query proteins. This is both **reasonable and in alignment with expectations**.\n\n   |Sequence Identity between Test Samples and Templates|< 0.3|0.3 ~ 0.5|0.5 ~ 0.7|0.7 ~ 0.9|0.9 ~ 0.99|\n   |----------------------------------------------------|------|---------|---------|---------|----------|\n   |**Number of Test Samples**|**803**|**153**|**79**|**53**|**32**|\n   |ProteinMPNN Recovery|48.5%|52.4%|48.0%|50.7%|51.8%|\n   |**DualMPNN Recovery**|**60.6%**|**68.4%**|**83.8%**|**87.1%**|**95.5%**|\n\n   **(2) Impact of Structural Similarity to Training Data.** To further validate the generalization, we partitioned the test proteins based on their structural similarity (TM-score) relative to the closest training proteins. The results in the below table show that DualMPNN consistently outperforms ProteinMPNN across all structural similarity bins, including the lowest region (<0.3 TM-score). This confirms DualMPNN's robustness to novel protein folds absent from the training set. \n\n   | TM-score of Test Samples against Train Set | < 0.3     | 0.3 - 0.5 | 0.5 - 0.7 | 0.7 - 0.9 | 0.9 - 0.99 |\n   | ------------------------------------------ | --------- | --------- | --------- | --------- | ---------- |\n   | **Number of Test Samples in bins**         | **706**   | **307**   | **73**    | **29**    | **5**      |\n   | ProteinMPNN Recovery                       | 50.9%     | 45.3%     | 40.9%     | 45.1%     | 48.1%      |\n   | **DualMPNN Recovery**                      | **66.9%** | **60.5%** | **58.6%** | **74.5%** | **71.6%**  |\n\n    Together, these experiments demonstrate that DualMPNN’s performance improvements arise from its capacity to utilize structural templates and generalize to novel folds, not data leakage.\n\n2. If there is no template information at inference, the model will degrade as the base model ProteinMPNN. However, it remains operational in this scenario.\n\n3. The similarity threshold of 99% was selected specifically to exclude cases where the query and template were identical. For the number of neighbors in the template branch, we initially employed 48 neighbors. However, we reduced this to 4 neighbors after observing that recovery performance remained uncompromised while memory usage decreased dramatically. Consequently, the final configuration for the template branch utilizes 4 neighbors.\n \n4. The alignment was performed using Foldseek. For the CATH4.2 dataset, the multi-structure pairwise search was completed in **about 1 hour**, which is approximately **5.6 proteins per second** on 64 CPU cores. The template dataset is Protein Data Bank (PDB), a publicly available resource already integrated into the Foldseek server for direct use. \n\n5. In the template branch, the similar performance observed when reducing the number of neighbors from 48 to 4 indicates that geometric edge features are not particularly critical for the model’s performance. Instead, the model primarily learns sequence-related features from the template protein, which are embedded in the node representations. This highlights that the node features, rather than edge features, play a more significant role in the template branch.\n\n6. According to your suggestion, to evaluate the generalization of our model on novel proteins, we clustered the structural similarities between the test and train sets and extracted test proteins with low similarity to the training set. Subsequently, we filtered out 523 proteins from the original 1120 test proteins, **forming a new “structural holdouts set”**. We evaluated the performance of both ProteinMPNN and DualMPNN on this filtered test set and compared to their performance on the full test set. The results in the below table show that DualMPNN maintains strong recovery accuracy even for **structurally novel proteins**, achieving a recovery rate of **61.96%** compared to **45.50%** for ProteinMPNN.  In addition, **the results of \"Impact of Structural Similarity to Training Data\" in the response of Q1 also emphasize the generalization of DualMPNN**. Our model leverages existing information to assist in sequence recovery, and as long as the templates are of sufficiently high quality, it can further enhance recovery rates.\n\n   |Model|All Rec.%|All Perplexity|Short Chain Rec.%|Short Chain Perplexity|Single Chain Rec.%|Single Chain Perplexity|\n   |-----|---------|--------------|-----------------|----------------------|------------------|-----------------------|\n   |ProteinMPNN (test set)|49.87|4.57|36.35|6.21|34.43|6.68|\n   |DualMPNN (test set)|65.51|3.18|55.97|4.42|52.41|5.04|\n   |ProteinMPNN (structural holdouts set)|45.50|5.67|34.36|8.13|29.14|9.99|\n   |DualMPNN (structural holdouts set)|61.96|3.59|56.34|4.46|47.43|5.73|\n\n\n# Responses to Limitations\n\n1. As previously mentioned, we employed Foldseek to conduct the structural search task for the CATH dataset. The search completed in approximately 1 hour, processing ~5.6 proteins per second, executed on 64 CPU cores. For each query protein, Foldseek identified multiple candidate template structures. Crucially, these search results were computed once and can be stored locally for reuse in subsequent analyses.\n\n2. We acknowledge the limitation that our method relies on the availability of template structures, which may not always exist for orphan protein folds. However, in practical scenarios, many protein design tasks are based on modifying existing protein structures. In such cases, a large number of homologous proteins or structural fragments can serve as templates. Our method is particularly advantageous in this context, as it does not require a perfect structural match for sequence recovery. **Instead, it can match and utilize fragments of templates to guide the design process.** \n\n   Nevertheless, we recognize this as a limitation when applying our approach to proteins with entirely novel folds and will leave this point as a clear area for future improvement.\n\n# Responses to Paper Formatting Concerns\n\nThank you for your valuable feedback. We will address the following points in the revised manuscript:\n\n1. **Typos**: The noted issues (lines 41, 42, 48, 197, 209, 255) will be corrected before publication.\n2. **References**: For lines 234-239, we will include the suggested reference: *Sikosek, T., & Chan, H. S. (2014). Biophysics of protein evolution and evolutionary protein biophysics.*\n3. **L250**: We will clarify that the “TM score” refers to the similarity between test proteins and their closest template proteins.\n4. **L291**: It means TM-score.\n5. **Notations**: We will harmonize the query/target notations for consistency throughout the manuscript."}, {"review_id": "5amtbOrJAr", "reviewer": "Reviewer_zdFE", "summary": "This paper focuses on the task of inverse protein folding, where a protein backbone structure is given and a plausible amino acid sequence needs to be generated that folds into the given structure. A key contribution of the paper is the use of templates selected from a database using structural alignments, inspired by the common use of multiple sequence alignments (MSA) in forward folding. Specifically, the paper leverages Foldseek to find similar structures to the query structure that needs to be inverse-folded, and then uses these similar structures and the associated sequences to inform the sequence prediction of the new, given structure. This is implemented with a model called DualMPNN, a dual-stream message passing network that in parallel processes the query and the template structures. The method is validated on sequence recovery, perplexity and foldability metrics, and favourable results compared to baselines are reported.", "questions": "I have a few further questions and comments:\n- Please introduce $L_q$ in equation (1).\n- Discussion around equation (3): When exactly is an aligned i-j pair between query and template protein matched? The text does not describe the exact criteria for matching residue pairs -- and most likely those come with hyperparameters that could be worth exploring.\n- Line 132: I assume in $A_{template}=...$, it should be $j_t$ and not $i_t$?\n- Line 205 and following: Why is the number of neighbors for each aggregated node so different in the query MPNN and the template MPNN? It's 48 and 4, respectively.\n- Line 213: The authors say they use \"easy-search\" mode. What does this mean? The author should explain the search algorithm and not just list Foldseek commands.", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The use of structural alignments to find templates that can be leveraged in the inverse-folding task is an interesting and original idea and promising research direction.\n- When well-aligned templates are available (TM-Score > approx. 0.5), the proposed method outperforms previous methods in terms of sequence recovery rate and perplexity.\n- The proposed DualMPNN architecture is novel and appropriately designed for the task at hand.\n- Generally, inverse folding is a highly relevant task in protein design, an important scientific field with impactful applications. Hence, the paper addresses a problem of significance.\n\n**Weaknesses:**\n- The method is inspired by MSAs in forward folding. MSA databases used in folding models are usually huge, consisting of many millions of sequences. In contrast, the paper leverages only the protein databank (PDB) to perform the structural alignments. However, the PDB is orders of magnitude smaller. I wonder whether this is reason for concern; this aspect is not discussed. For instance, could this lead to overfitting to the small PDB? What is the effect of different sizes of the database to find structural alignments? Related, the authors could extend this to not only the PDB, but also the AlphaFold Database (AFDB), which would offer a much larger database to find structural alignments (this may actually boost performance). I think the size of the database from which the templates are identified deserves more discussion and quantitative analysis.\n- The paper uses perplexity and sequence recovery as its two main metrics. However, in inserve-folding there can be multiple sequences that fold into the same structure. Hence, if the model outputs a different sequence than the ground truth one, it may be perfectly fine so long as this sequence still folds into the query structure. Therefore, I believe that sequence recovery and perplexity with the ground truth sequence should be interpreted very carefully. Instead, I believe that foldability is a critical metric -- ultimately, we are fine to predict whatever sequence we want, as long as the correct structure is recovered. However, on foldability, the proposed method is actually worse than ProteinMPNN (see avg RMSD in Table 3), the most popular inverse folding model in the literature (which does not rely on structure templates) -- this is concerning and needs more discussion or should be addressed.\n- In general, one would expect the model to be as good as ProteinMPNN when no templates are used or the templates are not well aligned, and better when useful templates can be found (high TM scores). However, as seen in Figure 2, the method performs worse than ProteinMPNN when the templates are not well aligned (TM score < 0.5). This is concerning.\n- Related, the method outperforms ProteinMPNN on sequence recovery when TM score>0.5. In general, this further supports the concern that the model is essentially overfitting to the templates, i.e. it only achieves good performance when the template TM score is high, i.e. when structures in the template database can be found that are highly similar to the query structure. In those cases, possibly the model largely copies the template sequence? The relation and similarity of the template and predicted sequences is not appropriately discussed or analyzed, unfortunately.\n- It would be interesting to analyze the types of sequences that DualMPNN predicts with the types of sequences that ProteinMPNN predicts. Which of them are more diverse? Does some have certain dominant amino acid types? It is known that ProteinMPNN-predicted sequences follow a distribution different from native sequences. However, I would expect DualMPNN's sequences to follow a more native-like sequence distribution, considering that native sequences inform the sequence prediction through the templates. This deserves a more detailed analysis.\n- The clarity, writing and presentation of the paper could be improved: For instance, the paper discusses many very low-level implementation details in the main text, some of which are difficult to follow (some related questions below). But at the end, the method uses relatively standard message passing neural networks, just with two streams connected via attention (which is an appropriate design, as pointed out under strengths). It would be better to present the non-novel details in the appendix, and instead focus in the main paper on the key novelties and save space for more discussions, analyses and experiments.\n\n**Conclusion:** In summary, I think the direction of using structural alignments to inform sequence prediction in inverse folding is an interesting idea and promising research direction. However, there are many questions and concerns and I don't think the paper is ready for publication in its current form. Hence, I am leaning towards rejection.", "was_revised": true, "final_justification": "The authors provided extensive additional experiments and explanations in the rebuttal addressing my questions and concerns in a satisfactory manner. Therefore, I increased my score and am now happy to suggest acceptance.", "rebuttal": "# Responses to Weaknesses\nThank you for your careful review with regard to our manuscript. Your constructive comments are very helpful for further strengthening the presentation of our paper.\n\n1. **There may be some misunderstanding here.** Our method takes a single protein structure as query, and only the structure with the highest similarity is selected as the template protein. The query and template protein are processed via two interactive branches, coupled through alignment-aware cross-stream attention mechanisms that enable exchange of geometric and co-evolutionary signals. In this study, we utilized PDB solely for identifying templates, not for large-scale representation learning as MSA Transformer. Therefore, **concerns regarding overfitting caused by a smaller database are not applicable to our method.** Additionally, PDB is the largest repository of experimentally determined protein structures, ensuring high-quality and reliable templates. While AFDB is indeed much larger, it is computationally predicted and may lack the same level of experimental validation. This is why we prefer PDB as the source for template protein queries.\n\n2. The foldability was evaluated on three key metrics: **TM score**, **pLDDT**, and **RMSD**. Our method, DualMPNN, achieves the best performance on **TM score** and **pLDDT**, demonstrating superior structural similarity and confidence in predictions. While **RMSD** for DualMPNN is slightly higher than ProteinMPNN, the values for both methods are below 2Å, indicating that the predicted structures remain highly similar to the original structures. To further compare the foldability of sequences generated by DualMPNN and ProteinMPNN, we conducted experiments using the latest **AlphaFold3**. The results are summarized as follows. **DualMPNN achieves the best performance across all three metrics.** These results further validate the robustness of DualMPNN in generating foldable sequences.\n\n   |Models|Success$\\uparrow$|TMscore$\\uparrow$|pLDDT$\\uparrow$|RMSD$\\downarrow$|\n   |-------------------|------------------|------------------|----------------|----------------|\n   |ProteinMPNN(AF2)|94|0.860$\\pm$0.16|0.89$\\pm$0.10|1.36$\\pm$0.81|\n   |ProteinMPNN(AF3)|94|0.858$\\pm$0.18|0.88$\\pm$0.12|1.41$\\pm$0.76|\n   |DualMPNN(AF2)|94|0.862$\\pm$0.16|0.91$\\pm$0.10|1.47$\\pm$0.86|\n   |DualMPNN(AF3)|**95**|**0.871$\\pm$0.16**|**0.92$\\pm$0.11**|**1.39$\\pm$0.80**|\n\n3. We acknowledge that DualMPNN does not improve sequence recovery over ProteinMPNN when the TM score of template is below 0.5. This behavior is expected, as low TM scores typically indicate poorly structural alignment, which can't provide useful evolutionary information to the predictions. Nevertheless, as evidenced by the distribution of results (Fig. 2a in main paper), **DualMPNN maintains comparable to ProteinMPNN in this range**. Besides, ProteinMPNN itself achieves only ~0.4 sequences recovery in these cases. Notably, **78.57% of the test-template pairings** have TM scores greater than 0.5, where DualMPNN consistently outperforms ProteinMPNN. \n\n   Furthermore, cases with TM scores below 0.5 often correspond to orphan sequences in protein data, which are widely recognized as more challenging for sequence recovery. While this remains a limitation, **our method demonstrates the practical value in the majority of real-world scenarios where usable templates are available.**\n\n4. We appreciate the concern regarding potential overfitting to templates. However, our model does not simply copy template sequences; instead, **it effectively learns the relationships and evolutionary correlations between the query and template**. To rigorously test for data leakage, we stratified test sequences by their sequence identity to the templates and compared the sequence recovery across these bins. The results in the below table show that **DualMPNN demonstrates robust performance across all sequence identity bins**, achieving a recovery rate of 60.6% even when sequence identity is below 0.3. This result underscores that our model effectiveness **stems from learning homology features from templates, not sequence leakage**. Furthermore, as template quality improves (higher sequence identity), recovery rates increase significantly, **which aligns with expectations** and further validates DualMPNN’s ability to effectively leverage high-quality templates for improved sequence recovery.\n\n   |Seq Identity (Test vs Templates)|<0.3|0.3-0.5|0.5-0.7|0.7-0.9|0.9-0.99|\n   |----------------------------------|----|-------|-------|-------|--------|\n   |**Number of Test Samples**|803|153|79|53|32|\n   |ProteinMPNN Recovery|48.5%|52.4%|48.0%|50.7%|51.8%|\n   |DualMPNN Recovery|**60.6%**|**68.4%**|**83.8%**|**87.1%**|**95.5%**|\n\n   Additionally, to validate the generalization ability of DualMPNN, we partitioned the test proteins based on their structural similarity (TM-score) against training proteins. As shown below, DualMPNN consistently outperforms ProteinMPNN across different similarity ranges, demonstrating its ability to generalize even in scenarios with low similarity between test and training proteins.  \n\n   | TM-score(Test vs Train) |<0.3|0.3-0.5|0.5-0.7|0.7-0.9|0.9-0.99|\n   |-----------------------|-----|-------|-------|-------|--------|\n   |**Number of Test Samples**|**706**|**307**|**73**|**29**|**5**|\n   |ProteinMPNN Recovery|50.9%|45.3%|40.9%|45.1%|48.1%|\n   |DualMPNN Recovery|**66.9%**|**60.5%**|**58.6%**|**74.5%**|**71.6%**|\n\n5. Thank you for the insightful suggestion. We agree that analyzing the types of sequences predicted by DualMPNN and ProteinMPNN, as well as their respective amino acid distributions, is an important aspect for understanding model performance. To investigate this further, we analyzed the amino acid distributions of sequences generated by both DualMPNN and ProteinMPNN on the CATH test set, comparing them to the ground truth (natural) sequences. The results are summarized in the table below. Notably, the **bond values indicates a maximum distribution offset** when compared to the natural residue distribution. **This analysis reinforces the idea that DualMPNN produces more biologically realistic sequences by incorporating the structural and sequence information from templates.**\n\n    Besides, perplexity is also a metric on plausibility in generative protein models. On the CATH dataset, DualMPNN achieves a **Perplexity of 3.18 (Table 1 in main paper)** , which indicates that the model generates highly probable sequences under its learned distribution.\n\n   |Amino Acid (%)|A|C|D|E|F|G|H|I|K|L|M|N|P|Q|R|S|T|V|W|Y|\n   |--------------|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|\n   |Natural|7.8|1.3|6.1|7.3|4.5|6.7|2.4|5.9|6.1|9.2|1.5|4.2|4.4|3.9|5.1|5.8|5.5|7.3|1.3|3.6|\n   |DualMPNN|9.0 **(+1.2)**|1.1 (-0.2)|6.1 (+0.0)|9.3 (+2.0)|4.4 (-0.1)|6.8 (+0.1)|1.9 (-0.5)|5.6 (-0.3)|6.2 (+0.1)|9.8 (+0.6)|1.1 (-0.4)|3.8 (-0.4)|4.7 (+0.3)|2.5 (-1.4)|4.7 (-0.4)|5.5 (-0.3)|5.2 (-0.3)|7.8 **(+0.5)**|1.1 (-0.2)|3.4 **(-0.2)**|\n   |ProteinMPNN|6.6 **(-1.2)**|1.0 **(-0.3)**|6.4 **(+0.3)**|14.6 **(+7.3)**|3.7 **(-0.8)**|6.4 **(-0.3)**|1.2 **(-1.2)**|4.9 **(-1.0)**|9.1 **(+3.0)**|10.8 **(+1.6)**|0.63 **(-0.87)**|3.6 **(-0.6)**|5.2 **(+0.8)**|1.0 **(-2.9)**|3.5 **(-1.6)**|4.9 **(-0.9)**|4.5 **(-1.0)**|7.5 (+0.2)|1.0 **(-0.3)**|3.7 (+0.1)|\n\n   \n6. Thank you for your constructive suggestions regarding the clarity and presentation of the paper. We will move non-novel and technical details to the appendix in revised version, allowing the main paper to focus on our key contributions, novelties, and more in-depth discussions, analyses, and experiments.\n\n\n# Responses to Questions\n\n1. $L_q$ refers to the length of query proteins.\n\n2. Thank you for your question regarding the criteria for matching residue pairs in Eq. (3). The aligned residue pairs between the query and template protein are pre-defined during the query-template alignment process. Specifically, residue pairs are considered aligned if the atomic distance between them is less than **5 Å**, which is the default threshold used by foldseek. This threshold is passed as a parameter to the model and defines the aligned structural domains. We used this setting without any modifications, but we agree that exploring the impact of varying this hyperparameter could be an interesting direction for future work.\n\n3. Your suggestion is absolutely accurate. In Line 132, the symbol $i_t$ should indeed be corrected to $j_t$. Thank you for pointing out this issue. We will address this in the revised version to ensure clarity and avoid any potential confusion for readers.\n\n4. Initially, we used 48 neighbors in the Template Branch, consistent with the Query Branch. However, we later experimented with reducing the number of neighbors in the Template Branch to 4. This change did not degrade sequence recovery performance, while also reducing memory usage. Therefore, we adopted 4 neighbors in the Template Branch for the final model to strike a balance between performance and computational efficiency. \n\n5. The term \"easy-search\" refers to the default search mode in Foldseek. This mode is designed to efficiently identify structurally similar protein candidates without requiring extensive parameter tuning or alignment strategy adjustments. Since our primary goal was to find structurally similar template candidates for each query protein, we opted for this default mode to simplify the search process. In the revised manuscript, we will improve the description by explaining the search algorithm more clearly and avoid including tool-specific command details."}]

Author rebuttal:

Meta-review: (5,5,5) This paper introduces DualMPNN, a message passing network for inverse protein folding / protein design, which builds upon the ProteinMPNN model. The key innovation is using FoldSeek to find similar protein structures, akin to how sequence-to-structure prediction models leverage related sequences in the forward prediction task. Reviewers found the use of structural alignments intuitive and an original and promising research direction. Reviewers raised concerns about data leakage and generalization, but the authors provided extensive analyses and additional experiments during the rebuttal, satisfactorily addressing all points and strengthening the case for acceptance.
Decision: Accept (poster)