SurfDesign: Effective Protein Design on Molecular Surfaces

Thank you for your thoughtful review and detailed feedback. We appreciate your valuable insights, which highlight areas for further improvement and help us enhance our model's utility and rigor. We address each of your points below.

(1) Insufficient Metrics for Functional Preservation: Thank you for your insightful suggestion on introducing metrics to evaluate SurfDesign’s effectiveness in designing sequences for specific functional regions. Following your guidance, we have integrated metrics from [A] and [B] to provide a more comprehensive assessment of SurfDesign’s performance.

Structural Compatibility and Stability (Ref-TM and Ref-pLDDT): Following [A] and PDB-Struct [C], we have incorporated two structure-aware metrics to evaluate how well SurfDesign preserves structural integrity and stability. Ref-TM measures how closely the generated sequences align with the ground truth structure through the TM-score, assessing SurfDesign’s ability to respect structural conditions. Ref-pLDDT provides a per-residue folding stability score for generated sequences, with values based on AF2’s pLDDT confidence. On the same CATH test samples used in [C], SurfDesign achieves outstanding results: a Ref-TM of 0.89 and a Ref-pLDDT of 89.42, demonstrating structural robustness on par with ProteinMPNN (which achieves a Ref-TM of 0.87 and Ref-pLDDT of 87.89). These results substantiate SurfDesign's effective, generalized design capabilities beyond mere memorization, supporting robust performance across diverse structures.

Foldable Diversity and Self-consistency (Foldable Diversity and sc-TM): In addition to the amino acid recovery rate, we have incorporated Foldable Diversity and Self-consistency TM score (sc-TM) as recommended in [B] to further verify the diversity and self-consistency of the generated sequences. Foldable Diversity evaluates only those sequence pairs that are structurally consistent with the input protein backbone, providing a more targeted diversity metric that avoids penalizing high-quality, diverse designs. Self-consistency TM score (sc-TM), following [D], gauges the consistency of structural predictions for generated sequences, leveraging a fixed threshold of $TM_{min}=0.7$ as implemented by [B]. We refer to https://github.com/flagshippioneering/pi-rldif for computation, and the results are shown below (numbers of all baselines are copied from [B] and we thank authors for their contributions). The analysis shows that SurfDesign maintains high structural consistency with competitive diversity, outperforming other methods on foldable diversity metrics and providing substantial evidence of the model’s capability to generate high-quality, diverse sequences that remain faithful to the structural constraints of input proteins.

[A] ShapeProt: Top-down Protein Design with 3D Protein Shape Generative Model. arXiv 2023.12.

[B] Reinforcement learning on structure-conditioned categorical diffusion for protein inverse folding. arXiv 2024.10.

[C] PDB-Struct: A Comprehensive Benchmark for Structure-based Protein Design. arXiv 2023

[D] Diffusion probabilistic modeling of protein backbones in 3d for the motif-scaffolding problem. ICLR 2022.

Thank you for prompting these enhancements, which have allowed us to highlight SurfDesign’s advantages in both structural stability and diversity, underscoring its suitability for functional and structurally informed sequence design.

Dear Reviewer Gipq,

We are glad to hear that our additional experiments successfully addressed your concerns! Thank you for your follow-up question and for sharing your perspective. We appreciate the opportunity to address this important point. As your question is the same as the Reviewer WG2F, please forgive us for using the same answer as a response.

---

Please allow us to recall the basics of traditional IF. As the name implies, IF does the exact opposite of protein folding by trying to predict a sequence that could fold into a desired structure. Models are typically trained on masked protein structures, where side chains are removed, leaving only the backbone atoms (e.g., alpha-carbon, beta-carbon, and nitrogen) as input. Noise or random perturbations may also be added to backbone coordinates during training to enhance robustness.

So a natural question is: how can we derive the backbone structures? Given this setup, there are two primary ways to obtain backbone structures. First is the Experimentally Solved Structures. Experimental methods like X-ray crystallography and cryo-EM provide highly accurate all-atom structures, including both backbones and side chains. In this case, surface-based IF can leverage the precise side-chain information to compute reliable molecular surfaces, making it as effective as, if not more so than, backbone-based IF. This equivalence arises because accurate side chains ensure that surface representations faithfully capture geometric and chemical properties. The second is Predicted Structures from Computational Models. When experimental structures are unavailable, tools like AlphaFold or ESM-Fold are used to predict protein structures. The main challenge here is that (i) methods like AF are generally very good at predicting backbone geometries, particularly for well-structured proteins. (ii) in contrast, predicted side chains can be less accurate, especially for flexible or disordered regions, buried residues, or when modeling interactions with ligands or other proteins. These inaccuracies can lead to misrepresented surface geometry (e.g., incorrect solvent-accessible areas or molecular surface shapes) or incorrect surface properties (e.g., hydrophobicity, charge distribution, hydrogen bonding potential). This discrepancy introduces additional difficulties for surface-based IF, as if the surface representation is noisy or inaccurate, it becomes harder to design desired proteins effectively.

Thus, to summarize, when using experimental structures, surface-based IF should perform well, as the surfaces are accurately represented. This makes them a strong candidate for designing sequences that not only fold into the target structure but also exhibit desired surface functionality (e.g., for binding or catalysis). When using predicted structures, surface-based IF are more vulnerable to inaccuracies in side-chain placement, which could hinder their performance. In such cases, conventional backbone-based IF might have an advantage, as it relies less on the precise placement of side chains. However, as shown in our previous additional results, Despite this, even if we transfer our surface-based IF approach from high-resolution experimental data to predicted structures by ESM-Fold, we observed a decreasing but still good acceptable AAR of 52.66%, which is competitive to backbone-based IF algorithms. This demonstrates its practicality across a range of scenarios. More importantly, the potential of surface-based IF for functional protein design is compelling, as surface properties like binding affinity and specificity are directly tied to biological functions—features that backbone geometry alone cannot capture.

Recent advances have demonstrated the value of combining structure prediction tools with IF models for de novo protein design. For example, given an initial protein sequence, [A, B] use Alphafold to predict its structure and then pass it to ProteinMPNN to sample a number of candidate sequences. These designs are further filtered based on the structural similarity (predicted by AF again) to the ground truth structure, confidence, and sequence diversity. Similar workflows could integrate our surface-based IF, allowing its functional advantages to be realized. However, we acknowledge that the dependency of surface-based IF on accurate side-chain modeling is a practical limitation when predicted structures are used. Addressing this dependency by improving side-chain modeling is an important future direction, though beyond the scope of this work. We will highlight this consideration in the limitations section of our paper to provide a comprehensive comparison of backbone- and surface-based IF approaches.

[A] Computational design of soluble and functional membrane protein analogues. Nature 2024.

[B] Unsupervised evolution of protein and antibody complexes with a structure-informed language model. Science 2024.

Thank you for your constructive feedback and insightful questions. We appreciate the opportunity to address your concerns, as they touch on several core aspects of our work.

(1) Clarification on Practical Applicability and Source of Protein Surfaces: You raise an important point regarding SurfDesign’s reliance on all-atom protein structures for generating surfaces and whether the observed performance improvements may stem from incorporating this additional structural information. While it is true that SurfDesign currently relies on all-atom structures to compute surfaces, we envision future applications where surfaces could be inferred from low-resolution experimental data or predicted structures, expanding SurfDesign’s practical utility. Here, we conducted an additional experiment to investigate the robustness of SurfDesign over predicted surfaces. Specifically, we leverage ESM-Fold to forecast the structures of 1,120 test samples in CATH 4.2 and generate corresponding surfaces. Then we require SurfDesign to design sequences based on these pseudo-surfaces. We discovered that the AAR decreases from 74.13% to 52.66%, which demonstrates SurfDesign's generalization to designing proteins without experimental structures. We hope this ablation study can help you understand SurfDesign's practical application!

Additionally, we note that the inclusion of surface features was carefully designed to enhance functional site representation and complement the protein language model rather than simply encode side-chain details. The improved performance thus reflects SurfDesign’s ability to leverage surface-derived functional features that capture biologically relevant information beyond traditional backbone-centric methods.

(2) Efficiency Analysis: We recognize the importance of assessing SurfDesign’s computational efficiency, especially given its use of surface encoding, which involves more points compared to backbone-only models. After preprocessing the surface data, the primary computational component is our equivariant message-passing neural network (SEMP) for the surface point cloud. To maintain efficiency, we typically stack fewer than five layers of SEMP, and we construct a KNN graph with $𝑘 =4$, so each node only gathers information from a limited set of neighbors. By controlling the number of layers and the node’s receptive field, we ensure that SEMP remains lightweight and computationally efficient while still effectively capturing the geometric and chemical characteristics of protein surfaces.

(3) Additional Experiments on Functional Protein Design: We appreciate your suggestion to explore SurfDesign’s utility beyond inverse folding for functional design tasks such as protein optimization. This aligns well with our goal to apply SurfDesign to tasks that emphasize functional and stability constraints in design. As you recommended, we follow the setting of SurfPro [A] and employ SurfDesign to design proteins that bind to a target receptor with high affinity. Specifically, AF2 pAE_interaction is used to evaluate the binding affinities between the designed binders and target proteins, which is found very effective in distinguishing experimentally validated binders from non-binders. Experimentally confirmed positive complexes of <binder, target protein> pairs across six categories from Bennett et al. (2023) are collected for experiments. Among the 10 categories available, 4 exhibit indistinguishable AF2 pAE_interaction between negative and positive binders. As all baselines were finetuned using the binder design dataset after pretrained on the CATH 4.2 dataset, we keep the same setup and report the result below. The results illustrate that our SurfDesign achieves the lowest average AF2 pAE interaction across six target proteins, which strongly supports our motivation to incorporate surface for functional protein design!

[A] SurfPro: Functional Protein Design Based on Continuous Surface. ICML 2024.

Dear Reviewer WG2F,

Thank you for your thoughtful follow-up questions and for engaging deeply with our work. We appreciate the opportunity to further clarify the application of surface-based inverse folding (IF) and its practical considerations:

(1) Application of Surface-based IF for Functional Protein Design: Your question touches on an essential aspect of surface-based IF. Please allow us to recall the basics of traditional IF. As the name implies, IF does the exact opposite of protein folding by trying to predict a sequence that could fold into a desired structure. Models are typically trained on masked protein structures, where side chains are removed, leaving only the backbone atoms (e.g., alpha-carbon, beta-carbon, and nitrogen) as input. Noise or random perturbations may also be added to backbone coordinates during training to enhance robustness.

So a natural question is: how can we derive the backbone structures? Given this setup, there are two primary ways to obtain backbone structures. First is the Experimentally Solved Structures. Experimental methods like X-ray crystallography and cryo-EM provide highly accurate all-atom structures, including both backbones and side chains. In this case, surface-based IF can leverage the precise side-chain information to compute reliable molecular surfaces, making it as effective as, if not more so than, backbone-based IF. This equivalence arises because accurate side chains ensure that surface representations faithfully capture geometric and chemical properties. The second is Predicted Structures from Computational Models. When experimental structures are unavailable, tools like AlphaFold or ESM-Fold are used to predict protein structures. The main challenge here is that (i) methods like AF are generally very good at predicting backbone geometries, particularly for well-structured proteins. (ii) in contrast, predicted side chains can be less accurate, especially for flexible or disordered regions, buried residues, or when modeling interactions with ligands or other proteins. These inaccuracies can lead to misrepresented surface geometry (e.g., incorrect solvent-accessible areas or molecular surface shapes) or incorrect surface properties (e.g., hydrophobicity, charge distribution, hydrogen bonding potential). This discrepancy introduces additional difficulties for surface-based IF, as if the surface representation is noisy or inaccurate, it becomes harder to design desired proteins effectively.

Thus, to summarize, when using experimental structures, surface-based IF should perform well, as the surfaces are accurately represented. This makes them a strong candidate for designing sequences that not only fold into the target structure but also exhibit desired surface functionality (e.g., for binding or catalysis). When using predicted structures, surface-based IF are more vulnerable to inaccuracies in side-chain placement, which could hinder their performance. In such cases, conventional backbone-based IF might have an advantage, as it relies less on the precise placement of side chains. However, as shown in our previous additional results, Despite this, even if we transfer our surface-based IF approach from high-resolution experimental data to predicted structures by ESM-Fold, we observed a decreasing but still good acceptable AAR of 52.66%, which is competitive to backbone-based IF algorithms. This demonstrates its practicality across a range of scenarios. More importantly, the potential of surface-based IF for functional protein design is compelling, as surface properties like binding affinity and specificity are directly tied to biological functions—features that backbone geometry alone cannot capture.

Recent advances have demonstrated the value of combining structure prediction tools with IF models for de novo protein design. For example, given an initial protein sequence, [A, B] use Alphafold to predict its structure and then pass it to ProteinMPNN to sample a number of candidate sequences. These designs are further filtered based on the structural similarity (predicted by AF again) to the ground truth structure, confidence, and sequence diversity. Similar workflows could integrate our surface-based IF, allowing its functional advantages to be realized. However, we acknowledge that the dependency of surface-based IF on accurate side-chain modeling is a practical limitation when predicted structures are used. Addressing this dependency by improving side-chain modeling is an important future direction, though beyond the scope of this work. We will highlight this consideration in the limitations section of our paper to provide a comprehensive comparison of backbone- and surface-based IF approaches.

[A] Computational design of soluble and functional membrane protein analogues. Nature 2024.

[B] Unsupervised evolution of protein and antibody complexes with a structure-informed language model. Science 2024.

Thank you for your updated comments and thoughtful insights. We appreciate your engagement and the opportunity to address your points further.

(1) Availability of all-atom structures:

The availability of all-atom protein structures, whether experimentally solved or predicted, is beyond the scope of the current IF benchmarks

We discuss the availability of all-atom protein structures in order to answer your previous question below. We attach great value to any of your questions and try our best to reply to them.

However, my concern is more about its application on inverse folding: how do you first obtain the surface based on the all-atom structure for inverse folding?

(2) Comparison with backbone-based IF methods:

as models utilizing predicted all-atom structures fail to outperform backbone-based methods. If the model incorporating an additional modality yields comparable or even worse results, it casts doubt on the future potential of such an approach.

We acknowledge your concern regarding failing to consistently outperform backbone-based methods when utilizing predicted all-atom structures. However, the comparison you mention is not entirely equitable due to the differences in structure quality. To address this, we conducted additional experiments with both predicted and experimental structures.

While transferring our surface-based IF approach from high-resolution data to predicted structures, we observed a decrease in AAR from 74.13% to 52.66%. Despite a performance drop, the results on predicted structures remain acceptable and competitive. Importantly, backbone-based IF also suffers from inaccuracies in structure prediction, as shown by PiFold's drop in AAR from 51.66% (experimental structures) to 47.08% (predicted structures). These results demonstrate that surface-based IF methods can still outperform backbone-based methods in predicted structure scenarios. Moreover, introducing an additional modality, even in the context of predicted structures, enriches the model's understanding and improves its capability to handle functional constraints.

(3) Benefits of surface representations:

what is the advantage of using surfaces over all-atom structures? Most geometry information should also be included within all-atom structures, and surface encoding is non-trivial due to the significantly higher number of points.

[3.1] Functional and Interaction-Driven. Protein surfaces emphasize regions directly involved in molecular interactions, such as binding interfaces or active sites. These surfaces naturally encode features like curvature, solvent accessibility, and electrostatic potential, which are often less apparent from atomic coordinates. For instance, de novo design tasks frequently leverage surface geometry to identify functional patches critical for binding or catalysis without requiring prior knowledge of binding partners [A].

[3.2] Data Efficiency via Abstraction. Surface-based encoding abstracts protein information into a representation that emphasizes interaction-relevant regions while discarding atomic-level details that might be less critical for certain tasks. This abstraction can reduce noise and enhance model interpretability in cases where functional insights are desired.

[3.3] Complementary Information. Surfaces can provide a complementary modality that enriches downstream models. For instance, surface curvature, electrostatics, and hydrophobicity patterns are directly derived from surface geometries and may capture higher-order features not easily accessible from all-atom structures alone. While all-atom structures contain the raw information, explicitly encoding these properties on surfaces can enhance model performance for specific applications, as demonstrated by tools like MaSIF [B] and subsequent surface-based design frameworks.

To summarize, the ultimate goal of protein design extends beyond predicting sequences that fold into a given structure. Instead, it aims to design proteins with specific functional properties, like enzymatic activity or target binding. While traditional IF methods impose geometric constraints via backbones, they often neglect the biochemical property constraints necessary for functional optimization. For example, even proteins with complementary shapes may fail to bind effectively if their charge, polarity, or hydrophobicity distribution at the interface is suboptimal. Surface representations address this limitation by integrating functional properties directly into the design framework, enabling more holistic optimization for desired behaviors.[C].

[A] De novo design of protein interactions with learned surface fingerprints. Nature (2023).

[B] Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning. Nature Methods (2020).

[C] SurfPro. ICML 2024

(4) Optimization and generation of all-atom structures.

the machine learning models in the workflow are optimized based on all-atom structures. Introducing the surface with different dynamics could potentially create an optimization gap.

[4.1] Extending Backbone to Full-Atom Generation: We fully understand your concerns regarding the optimization challenges posed by the use of surface representations. However, recent advancements have successfully bridged the gap between backbone-only generation methods and full-atom structure generation, establishing a robust foundation for incorporating surface geometries into protein design workflows. They show that generating full-atom structures, including side-chain geometries, can significantly outperform backbone-only algorithms (e.g., RFDiffusion, FrameDiff [A]) across diverse protein design tasks. For instance:

AbDiffuser [B]: It jointly designs antibody 3D structures and sequences, leveraging full-atom side-chain flexibility to enhance binding stability and affinity, a crucial factor in antibody design.

PocketGen [C]: Designed for ligand-binding pocket regions, this approach generates full-atom structures to capture the intricate geometries that govern molecular interactions.

PepFlow [D] and PPIFlow [E]: These models consider side-chain torsion angles for target-aware peptide discovery, demonstrating improved binding capabilities by incorporating additional atomic-level flexibility into peptide structures.

PepGLAD [F]: This geometric latent diffusion model integrates side-chain details to refine peptide designs for specific target interactions, further supporting the utility of full-atom approaches.

All those approaches indicate that different side-chain dynamics would not lead to an optimization gap.

[A] SE(3) diffusion model with application to protein backbone generation. ICML 2023.

[B] AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies, NeurIPS 2023.

[C] PocketGen: Generating Full-Atom Ligand-Binding Protein Pockets. NeurIPS 2023.

[D] Full-Atom Peptide Design based on Multi-modal Flow Matching. ICML 2024.

[E] PPFLOW: Target-Aware Peptide Design with Torsional Flow Matching. ICML 2024.

[F] Full-Atom Peptide Design with Geometric Latent Diffusion. arXiv 2024.

[4.2] Benefits of Incorporating Side-Chain (Surface) Dynamics: These methods highlight that integrating side-chain geometries, akin to surfaces, enhances model capabilities rather than introducing optimization gaps. Key benefits include:

Improved Binding Stability and Affinity: Side-chain dynamics directly contribute to molecular interactions, enabling more accurate predictions of binding strength and specificity.

Enhanced Design Accuracy: Full-atom geometries reduce errors in structure prediction and provide finer control over functional optimization.

Task-Specific Flexibility: Models like AbDiffuser and PocketGen show that full-atom representations adapt effectively to tasks requiring detailed geometric insights, such as antibody engineering or ligand binding.

[4.3] Synergy with Surface-Based IF (SurfDesign): Once these full-atom structures are generated, SurfDesign offers a natural complement by refining protein surfaces to optimize sequences further. This relationship mirrors the collaborative interplay observed in other workflows, such as:

RFDiffusion and ProteinMPNN: RFDiffusion generates backbones, while ProteinMPNN predicts sequences. Together, they enable highly effective de novo protein design.

SurfDesign as a Complement to All-Atom Models: SurfDesign extends this paradigm by considering the biochemical and geometric properties of binding surfaces, adding a novel layer of functional optimization to IF methods.

Just as full-atom design has elevated traditional backbone-based methods, SurfDesign provides a new perspective within the IF subfield, emphasizing surface-level biophysical properties for functional improvement. SurfDesign builds upon the strengths of backbone-based IF algorithms like ProteinMPNN and PiFold, offering a complementary tool to full-atom generation models such as PepFlow, PPI-Flow, and PocketGen.

---

In summary, SurfDesign represents a forward-looking strategy that complements recent advances in full-atom protein design. It offers a unique mechanism for optimizing biochemical surfaces, addressing the nuances of functional protein engineering while maintaining compatibility with state-of-the-art all-atom generation workflows.

We hope these clarifications demonstrate the rationale behind surface-based approaches and their potential for advancing protein design. Thank you again for your feedback, which will help us refine and strengthen our study.

Thank you very much for your detailed review and thoughtful feedback. We appreciate your comments and suggestions, which will help us enhance our model and presentation. We address each of your points below.

(1) Metrics for Protein Design: We agree that sequence recovery and perplexity alone may not fully capture SurfDesign’s effectiveness for practical protein design tasks, and we appreciate your insight into this potential limitation. While wet-lab experiments are beyond the scope of our current study, we have included additional metrics as suggested by PDB-Struct [A] to provide a more robust assessment of SurfDesign. Specifically, Ref-TM assesses whether the generated sequences can respect the structure condition, which evaluates the agreement of the ground truth structure with the predicted structures using theTM-score. Ref-pLDD evaluates the folding stability of the generated sequences, which is computed as the mean value of the per-residue confidence estimate pLDDT predicted by the structure prediction models.

We examine SurfDesign on the same 82 test samples of the CATH dataset and results are reported below (numbers of all relevant baselines are copied from PDB-Struct [A] and we thank authors for their contributions). We observe that SurfDesign stands out as the leading design method across the refoldability metrics, competitive with ProteinMPNN. It achieves 0.89 Ref-TM and 89.42 Ref-pLDDT with AlphaFold2 prediction. ProteinMPNN is slightly behind with a 0.87 Ref-TM and 87.89 Ref-pLDDT, followed by LM-Design. This additional analysis, including functional enrichment, diversity, and secondary structure compatibility, provides stronger evidence that SurfDesign's 60-70% sequence recovery rate is not indicative of overfitting but instead suggests effective design, supporting its relevance beyond the training distribution.

[A] PDB-Struct: A Comprehensive Benchmark for Structure-based Protein Design. arXiv 2023

(2) Features and Potential for Data Leakage: We appreciate your concern regarding potential data leakage from features like hydrophobicity and charge. However, we want to restate and clarify that the task we want to solve in this paper is surface-based protein design instead of conventional backbone-based inverse folding. This idea of surface-based design was originally proposed by SurfPro [B], where models design proteins conditioned on both geometric shape and biochemical properties of molecular surfaces. In other words, surface-conditioned protein design targets functional proteins that fold into specified surfaces, denoted as $\mathcal{Q}$, with associated biochemical properties—without relying on explicit backbone information.

Importantly, the goal of protein design extends beyond predicting a sequence that simply folds into a given backbone. For functional design, we aim to create proteins with targeted activities, such as substrate binding or inhibition. Traditional inverse folding is limited in specifying function-related constraints, as it uses only the backbone structure. By conditioning on surface properties like charge and hydrophobicity, our approach imposes additional biochemical constraints crucial for functionality. For example, complementary shapes alone may not ensure effective binding if charges, polarity, or hydrophobicity are poorly positioned.

[B] SurfPro: Functional Protein Design Based on Continuous Surface. ICML 2024.

(3) Typos and Clarity Issues: Thank you for pointing out these minor errors, which we will correct in the revised manuscript. Specifically, we’ll revise “Priliminary” to “Preliminary” (L 104) and replace “LM-DESIGN” with “SurfDesign” in L 365 to eliminate confusion.

Another innovative pathway integrates de novo structure generation modules with inverse folding (IF) techniques in iterative workflows. These pipelines aim to optimize sequences that not only exhibit improved properties, such as enhanced binding affinity, specificity, or catalytic activity, but also maintain structural compatibility with the desired three-dimensional fold. This iterative refinement process allows researchers to explore non-natural mutations while ensuring that the redesigned protein adopts a functional conformation close to its native state.

A particularly impactful area of sequence redesign is antibody engineering, where the complementarity-determining regions (CDRs) are often reengineered to improve binding interactions with specific antigens. The framework regions, which provide structural support to the antibody, are typically preserved to maintain structural integrity and ensure manufacturability. Recent advancements [A,B,C] have leveraged structure-informed protein language models for this purpose. For example, a study [D] employed such models to predict high-fitness antibody sequences constrained by known structural information about the antibody or its complex with an antigen. This approach achieved significant improvements in binding affinity and neutralization potency, highlighting the utility of combining structural insights with ML-driven sequence optimization.

Beyond antibodies, similar methodologies have been applied to enzymes, where sequence redesign can improve catalytic efficiency, substrate specificity, or thermostability. These advancements underscore the transformative potential of integrating computational design with experimental validation, enabling researchers to create proteins with tailored properties for diverse applications in biomedicine, industry, and beyond.

[A] Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures. NeurIPS 2022.

[B] Conditional Antibody Design as 3D Equivariant Graph Translation. ICLR 2023

[C] End-to-End Full-Atom Antibody Design. ICML 2023.

[D] Unsupervised evolution of protein and antibody complexes with a structure-informed language model. Science 2024.

[3.2] Fair Comparisons with Backbone-Based Methods: Your suggestion to limit surface features to those derivable from backbone-only methods for inverse folding comparisons is well-taken. We expect future work to investigate incorporating backbone-derived surface features (e.g., backbone hydrophobicity or backbone-accessible surface area) to enable more equitable benchmarking against backbone-based methods. This adaptation could help bridge the gap and ensure fair comparisons, while also preserving the unique benefits of surface-informed design.

Finally, we greatly appreciate the references to Frame2Seq and MaSIF. We will incorporate these works into our discussion and ensure that the framing of SurfDesign’s contributions is better aligned with realistic applications and fair comparisons in the revised manuscript.

---

Thank you again for your feedback and for raising your score in light of our response efforts. Your insights will help us refine our work and clarify its positioning within the field.

Dear Reviewer FM5g,

Thank you for your detailed comments and for revisiting our work. We truly appreciate that you raised the score and value our efforts to address your concerns. Below, we provide our thoughts and clarifications to your latest suggestions:

(1) Metrics for Protein Design: We are glad to hear that the additional metrics for sequence recovery were well-received and that they help demonstrate that the high sequence recovery rate is not merely a result of overfitting.

(2) Features and Potential for Data Leakage: We acknowledge your concerns about the benchmarking setup and the comparison to backbone-only methods such as ProteinMPNN and PiFold. Our objective is to showcase the utility of surface-based representations in tasks where backbone-only representations may fall short. In contrast, SurfPro [A] serves as the most relevant surface-based inverse-folding (IF) baseline to our method. Experiments on the CATH dataset demonstrate that our SurfDesign significantly outperforms SurfPro by 28.29% in amino acid recovery (AAR) and 23.0% in perplexity. Moreover, our additional results in protein-protein interaction (PPI) design indicate an average improvement of 4.2% in generating more effective functional proteins.

While we agree with your observation that existing backbone-based IF approaches may not serve as direct equivalents to surface-based IF approaches, we argue that ProteinMPNN's use of backbone-only representations is not due to RFDiffusion generating backbone-only structures. In fact, ProteinMPNN (2022) was proposed before RFdiffusion (2023). Its focus on backbone-only information stems from its design to predict sequences solely from backbone structures, while RFDiffusion and subsequent methods like FrameDiff and FlowDiff concentrated on generating backbones.

However, recent studies have extended backbone-only generation to full-atom structure generation, which has become a more prevalent protocol. These methods have demonstrated significantly better performance than backbone-only algorithms (e.g., RFDiffusion, FrameDiff) across a wide range of protein design tasks. For example, side-chain flexibility plays a critical role in binding stability and affinity. To address this, AbDiffuser [B] jointly designs antibody 3D structures and sequences, while PocketGen [C] generates full-atom structures within protein pocket regions. Similarly, PepFlow [D], PPIFlow [E], and PepGLAD [F] consider side-chain angles for target-aware peptide discovery in addition to backbone frames.

All the aforementioned approaches can be leveraged to generate full-atom structures for functional protein design. Once these full-atom structures are available, SurfDesign can seamlessly refine the generated surfaces to obtain optimized sequences. This is analogous to the collaborative relationship between ProteinMPNN and RFDiffusion, where RFDiffusion generates backbones, and ProteinMPNN predicts sequences.

[A] SurfPro: Functional Protein Design Based on Continuous Surface. ICML 2024.

[B] AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies, NeurIPS 2023.

[C] PocketGen: Generating Full-Atom Ligand-Binding Protein Pockets. NeurIPS 2023.

[D] Full-Atom Peptide Design based on Multi-modal Flow Matching. ICML 2024.

[E] PPFLOW: Target-Aware Peptide Design with Torsional Flow Matching. ICML 2024.

[F] Full-Atom Peptide Design with Geometric Latent Diffusion. arXiv 2024.

(3) Proposed Pathways to Strengthen the Study:

[3.1] Addressing the Use Case Concerns: As noted above, recent advancements have introduced full-atom structure generation using diffusion or flow-based generative architectures. Once full-atom structures are obtained, SurfDesign can effectively implement surface-based inverse folding for functional protein design.

I do not see the use case here since for these structures you already have sequences (similar for predicted all-atom structures)

Redesigning protein sequences, even when native (wild-type) sequences are available, is a common strategy in computational biology and protein engineering. This practice arises because native proteins often do not fully meet the specific functional, structural, or stability requirements needed for certain applications. Machine learning (ML) and deep learning (DL) approaches have become essential tools for sequence redesign, offering efficient and scalable solutions for exploring the immense sequence space to introduce beneficial mutations.

One well-established approach involves predicting the impact of specific mutations—quantified as changes in free energy, commonly referred to as $\Delta\Delta G$—to evaluate how mutations might improve stability, binding affinity, or other desirable properties. By directly modeling $\Delta\Delta G$, researchers can prioritize mutations that are most likely to yield enhanced protein function, accelerating the search within the vast mutation landscape.

Thank you for the thoughtful and comprehensive review, as well as for acknowledging the contributions of SurfDesign to surface-based protein sequence generation. It is a great honor to receive a 8-score, which confirms our efforts in this work. Let me address and respond to your questions point by point:

(1) Potential Data Leakage via PLM Training Dataset: We appreciate your suggestion to address possible data leakage. Even though no-PLM ablation experiments have already demonstrated better performance than SurfPro, we further examined the sequences generated by SurfDesign with the training corpus of ESM-2 (UniRef90). The results show that the sampled sequences of SurfDesign have no overlap with any sequence from ESM's training set, namely, the sequence identity is less than 100%. Additionally, the distinct recovery rates for surface and core residues (as shown in Figure 4) support that the model does not merely memorize sequences, as surface recovery is generally lower than core recovery, indicating the model's nuanced understanding of structural features rather than memorization.

(2) Surface Description Differentiability: We acknowledge that the current surface extraction and encoding methods are not differentiable with respect to atomic coordinates, which may limit certain downstream applications. However, as you noted, this work focuses on introducing a robust, invariant representation of protein surfaces, and incorporating differentiability is an exciting direction for future exploration.

(3) Choice of Surface Extraction Method (PyMOL vs. Biopython): We opted for PyMOL over Biopython for surface extraction because PyMOL can provide normal vectors, whereas Biopython only computes surface coordinates (see https://biopython.org/docs/1.75/api/Bio.PDB.ResidueDepth.html) without generating normals. Normal vectors are essential for our surface-based equivariant message passing (SEMP), as they enable us to capture finer geometric features like dihedral angles within the surface point cloud. The "minor difference among toolkits" refers to processing efficiency—both PyMOL and other tools are comparably fast. However, PyMOL’s reliability and precise control over surface generation, even in edge cases, make it the preferred choice. We have clarified this in the paper for transparency.

Minor Errors: Thank you for pointing out these text errors. We have updated the manuscript to correct the unclear wording on line 134, replace "studies" with "studied" on line 457, and ensure consistency in the formatting of numerical data across lines 315, 317, and 322.

---

Once again, we appreciate your detailed feedback and suggestions, which have strengthened the presentation and robustness of our work.

Thank you for your thorough and constructive review. We’re glad that you found SurfDesign’s approach and benchmarks promising and that our methodology demonstrated strong performance across tasks. It is a pleasure and honor to gain your 8-score!

(1) Biological Significance in Protein-Protein Interaction Design: We appreciate your emphasis on protein-protein interaction applications and agree this is a crucial direction for SurfDesign. To this end, we followed SurfPro’s setup [A] and applied SurfDesign to design binders with high affinity to specific target receptors. Binding affinity was evaluated using AlphaFold2's pAE_interaction metric, which has proven effective in distinguishing experimentally validated binders from non-binders. We used <binder, target protein> pairs across six categories from Bennett et al. (2023) as benchmarks. Among the 10 available categories, only six showed significant separation between positive and negative binders based on AF2 pAE_interaction. All baseline models were fine-tuned on a binder design dataset following pretraining on CATH 4.2 to ensure a fair comparison. The results, shown below, demonstrate that SurfDesign achieves the lowest average AF2 pAE_interaction across the six target proteins, underscoring the strength of our surface-based approach for functional protein design!

[A] SurfPro: Functional Protein Design Based on Continuous Surface. ICML 2024.

(2) Clarification on “O optionally” in Backbone Representation: “O optionally” indicates that the backbone representation may or may not include the oxygen atom of the peptide bond, based on context-specific requirements. We’ve clarified this in the revised manuscript.

(3) Calculation of Surface Properties: Surface properties like hydrophobicity, hydrogen bonding potential, and charge are computed using established descriptors derived from biophysical studies. We follow MaSIF[B] and calculate three key invariant point inputs, including the Poisson Boltzmann electrostatics using APBS: https://github.com/LPDI-EPFL/masif/blob/master/source/triangulation/computeAPBS.py, the hydrophobicity:https://github.com/LPDI-EPFL/masif/blob/master/source/triangulation/computeHydrophobicity.py, and the free electrons/protons: https://github.com/LPDI-EPFL/masif/blob/master/source/triangulation/compuSurfDesignteCharges.py.

[B] Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning. Nature Methods.

(4) Clarifications on Table 5: You’re correct—there was a mislabeling in Table 5, and it should indeed refer to SurfDesign rather than MoE-DSR. We have corrected this in the text for accuracy.

(5) Figure 4 Labeling: Thank you for pointing this out. We’ve corrected the erroneous reference in Line 423 from Figure 3.3 to Figure 4.

(6) Surface Isomer Experiments: Regarding the surface isomer section, we realize further detail is needed. We conducted these tests with two well-documented lysozyme surface isomers to explore SurfDesign's robustness to minor structural variations. The isomers we used share the same amino acid sequence but differ in the crystal structure (thus resulting in different surface geometry) due to crystallization conditions, with slight variations in backbone RMSD and ligand/ion interactions. By designing sequences robust to these surface isomers, SurfDesign demonstrates the potential for applications where protein surfaces might slightly differ due to environmental or crystallization conditions, which is relevant in drug discovery and functional protein design. We have expanded these findings in the appendix and provided a visualization of this pair of selected surface isomers (1lyz and 193l) to provide the comprehensive data requested. We expect more future efforts to find surface isomers with more significant distinction in surface geometries and investigate SurfDesign's robustness to these variants.

---

Thank you again for your valuable insights, which will help us further strengthen the presentation and impact of our work.

Thank you for your detailed feedback and for raising important points. We have carefully considered your concerns and provide clarifications below:

(1) Inclusion of Oxygen: You are absolutely correct that oxygen atoms are part of every peptide bond. Upon revisiting our explanation, we realized that our initial description was inaccurate. We referenced LM-Design [A] for this section, but with your kind reminder, we found that their problem formulation contains inconsistencies. In reality, all backbone-based methods always include the oxygen (O) atom.

We have updated our manuscript to clarify this point, ensuring there is no ambiguity. Specifically, we now state:

where $s_i$ belongs to one of the 20 residue types and $\mathcal{X}$ denotes the spatial coordinates for 4 backbone atoms (i.e., $C_\alpha$, $C$, $N$ and $O$).

We deeply appreciate your observation, as it allowed us to correct this oversight!

[A] Structure-informed Language Models Are Protein Designers. ICML 2024.

(2) Surface Isomers: The inclusion of surface isomers was meant to demonstrate SurfDesign’s ability to handle variations in surface geometry or physicochemical properties. By "robust to surface isomers," we intended to show that the model can still design sequences that meet functional criteria even when minor variations exist.

That said, we fully agree with your observation that the recovery rate alone is insufficient to validate this claim. Upon further analysis, we measured the backbone RMSD between the two structures (PDB 1931 and PDB 1lyz), and it is indeed very small (RMSD = 0.13). This confirms your suggestion that the case we presented does not truly represent surface isomerism, and as such, may not be appropriate for inclusion.

Based on your feedback, we have decided to remove this part from the manuscript entirely. We appreciate your constructive input and will explore this aspect more rigorously in future studies.

---

We appreciate your valuable input, which has helped us refine the manuscript further. Thanks again for participating in the discussion!