Responses to Weaknesses

Thank you for your careful review with regard to our manuscript. Your constructive comments are very helpful for further strengthening the presentation of our paper.

1. 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.

2. 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.

   Models	Success$\uparrow$	TMscore$\uparrow$	pLDDT$\uparrow$	RMSD$\downarrow$
   ProteinMPNN(AF2)	94	0.860$\pm$0.16	0.89$\pm$0.10	1.36$\pm$0.81
   ProteinMPNN(AF3)	94	0.858$\pm$0.18	0.88$\pm$0.12	1.41$\pm$0.76
   DualMPNN(AF2)	94	0.862$\pm$0.16	0.91$\pm$0.10	1.47$\pm$0.86
   DualMPNN(AF3)	95	0.871$\pm$0.16	0.92$\pm$0.11	1.39$\pm$0.80

3. 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.

   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.

4. 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.

   Seq Identity (Test vs Templates)	<0.3	0.3-0.5	0.5-0.7	0.7-0.9	0.9-0.99
   Number of Test Samples	803	153	79	53	32
   ProteinMPNN Recovery	48.5%	52.4%	48.0%	50.7%	51.8%
   DualMPNN Recovery	60.6%	68.4%	83.8%	87.1%	95.5%

   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.

   TM-score(Test vs Train)	<0.3	0.3-0.5	0.5-0.7	0.7-0.9	0.9-0.99
   Number of Test Samples	706	307	73	29	5
   ProteinMPNN Recovery	50.9%	45.3%	40.9%	45.1%	48.1%
   DualMPNN Recovery	66.9%	60.5%	58.6%	74.5%	71.6%

5. 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.

   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.

   Amino Acid (%)	A	C	D	E	F	G	H	I	K	L	M	N	P	Q	R	S	T	V	W	Y
   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
   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)
   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)

6. 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.

Responses to Questions

1. $L_q$ refers to the length of query proteins.

2. 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.

3. 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.

4. 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.

5. 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.

Responses to Questions

1. 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:

   (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.

   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
   Number of Test Samples	803	153	79	53	32
   ProteinMPNN Recovery	48.5%	52.4%	48.0%	50.7%	51.8%
   DualMPNN Recovery	60.6%	68.4%	83.8%	87.1%	95.5%

   (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.

   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
   Number of Test Samples in bins	706	307	73	29	5
   ProteinMPNN Recovery	50.9%	45.3%	40.9%	45.1%	48.1%
   DualMPNN Recovery	66.9%	60.5%	58.6%	74.5%	71.6%

   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.

2. If there is no template information at inference, the model will degrade as the base model ProteinMPNN. However, it remains operational in this scenario.

3. 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.

4. 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.

5. 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.

6. 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.

   Model	All Rec.%	All Perplexity	Short Chain Rec.%	Short Chain Perplexity	Single Chain Rec.%	Single Chain Perplexity
   ProteinMPNN (test set)	49.87	4.57	36.35	6.21	34.43	6.68
   DualMPNN (test set)	65.51	3.18	55.97	4.42	52.41	5.04
   ProteinMPNN (structural holdouts set)	45.50	5.67	34.36	8.13	29.14	9.99
   DualMPNN (structural holdouts set)	61.96	3.59	56.34	4.46	47.43	5.73

Responses to Limitations

1. 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.

2. 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.

   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.

Responses to Paper Formatting Concerns

Thank you for your valuable feedback. We will address the following points in the revised manuscript:

1. Typos: The noted issues (lines 41, 42, 48, 197, 209, 255) will be corrected before publication.
2. 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.
3. L250: We will clarify that the “TM score” refers to the similarity between test proteins and their closest template proteins.
4. L291: It means TM-score.
5. Notations: We will harmonize the query/target notations for consistency throughout the manuscript.

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.

Responses to Questions:

1. 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.

   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.

   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
   Number of Test Samples	803	153	79	53	32
   ProteinMPNN Recovery	48.5%	52.4%	48.0%	50.7%	51.8%
   DualMPNN Recovery	60.6%	68.4%	83.8%	87.1%	95.5%

2. 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.

   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.

   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
   Number of Test Samples	706	307	73	29	5
   ProteinMPNN Recovery	50.9%	45.3%	40.9%	45.1%	48.1%
   DualMPNN Recovery	66.9%	60.5%	58.6%	74.5%	71.6%

3. 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.

   Models	Success ↑	TM-score ↑	pLDDT ↑	RMSD ↓
   ProteinMPNN (AF2)	94	0.860 ± 0.16	0.89 ± 0.10	1.36 ± 0.81
   ProteinMPNN (AF3)	94	0.858 ± 0.18	0.88 ± 0.12	1.41 ± 0.76
   DualMPNN (AF2)	94	0.862 ± 0.16	0.91 ± 0.10	1.47 ± 0.86
   DualMPNN (AF3)	95	0.871 ± 0.16	0.92 ± 0.11	1.39 ± 0.80

4. To further evaluate the rationality of the generated sequences, we evaluated DualMPNN across the following metrics on CATH test set:

   (1) Perplexity: 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.

   (2) Physicochemical Properties: 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).

   GRAVY	[-0.8,-0.6)	[-0.6,-0.3)	[-0.3,0)	Average
   Natural sequences	10.45%	34.46%	35.09%	-0.3233
   DualMPNN	7.95%	32.14%	36.52%	-0.2586
   ProteinMPNN	16.79%	39.29%	19.82%	-0.5404

   Percentage of polar residue	35%~45%	45%~55%	55%~70%	35%~70%	Average
   Natural sequences	9.73%	57.14%	31.07%	97.94%	52.21%
   DualMPNN	12.77%	58.09%	26.29%	97.15%	51.30%
   ProteinMPNN	5.98%	50.71%	40.27%	96.96%	54.39%

   (3) Amino Acid Distribution: 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.

   Amino Acid (%)	A	C	D	E	F	G	H	I	K	L	M	N	P	Q	R	S	T	V	W	Y
   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
   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)
   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)

   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.

5. 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.

   Metrics	Diversity	Entropy
   Natural sequences	0.5108±0.2733	2.801±1.040
   ProteinMPNN	0.4935±0.2664	2.659±1.054
   DualMPNN	0.5204±0.2456	2.835±0.926

6. 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.

   Metrics (kcal/mol)	Solvation Polar	Solvation Hydrophobic	VDW Energy	VDW Clash Energy
   Natural sequences	239.47±149.92	-232.41±149.97	-176.66±112.95	10.87±10.44
   ProteinMPNN	233.46±147.80	-237.21±155.32	-176.80±114.11	8.87±7.08
   DualMPNN	236.57±150.70	-236.21±153.66	-176.27±112.69	8.60±7.50