Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension

Thank you for your insightful and constructive comments, as well as your appreciation of our work in ** novel approach, clear presentation and fundamental principles underlying network design and training **. Below, we provide clarifications and responses to your questions. If any concerns remain unaddressed, please feel free to reach out with further inquiries; we would be happy to engage in additional discussions.

Q1: I would suggest to include a brief analysis of the secondary structure composition of the generated peptides and compare it to native structures (or a representative set of native structures), as well as an examination of where the hotspots tend to be located in terms of secondary structure elements.

We analyzed the secondary structure proportions of native peptides, generated peptides, and hotspot residues in the test set. The results are as follows:

Compared to native peptides, PepHAR-generated peptides and hotspots tend to exhibit a higher proportion of coil regions (bonded turns, bends, or loops) while maintaining similar proportions of helix regions. However, the proportion of strand regions is significantly lower compared to native peptides, indicating that strand regions in the native structure are often replaced by coil regions in the generated peptides. This could be due to subtle differences in structural parameters required for forming strands. We believe that further energy relaxation using tools like Rosetta, OpenMM, or FoldX could help refine the peptide structures to form more accurate secondary structures.

Regarding hotspot occurrences, we observe that hotspots are predominantly located in coil and helix regions, with almost no presence in strand regions. This aligns with interaction principles, where strand regions may represent structural transitions, while the irregular coil regions or the relatively stable helix regions are more likely to serve as functional interaction sites.

Q2: When multiple hotspots are specified, fragments are grown from each hotspot. How does the network ensure that these initially disconnected fragments will eventually fit together? Is this addressed during the extension phase or in the polishing stage? It could be useful to elaborate on the fragment assembly method, and add statistics on how often fragments successfully connect and if there are any strategies used to ensure proper assembly or safeguard this process.

The network addresses the assembly of disconnected fragments through mechanisms implemented in both the extension and correction (polishing) stages:

• Extension Stage: During this phase, each fragment's residue generation is conditioned not only on its own sequence and structure but also on the fragments generated earlier. The network uses structural and sequential information from previously generated fragments to guide the placement of new residues, helping align the fragments in 3D space. This is achieved through training on a combined structure and sequence reconstruction loss, which enforces the network to learn how to grow fragments in a way that facilitates eventual connectivity.

• Correction Stage: In this phase, residues at the junctions between fragments, as well as other intermediate residues, are refined to ensure seamless assembly. The correction stage enforces constraints on positional, orientational, and dihedral angle consistency, enabling previously disconnected fragments to align and fit together properly.

The success rate of fragment assembly can be indirectly measured using the valid metric, which evaluates whether the inter-residue distances fall within acceptable ranges. As demonstrated in Table 3, the correction stage significantly improves these metrics by refining the geometry and resolving inconsistencies introduced during the extension phase. This suggests that the network effectively resolves fragment connectivity issues through a combination of structural alignment and dihedral angle optimization.

Thank you for your insightful and constructive comments, as well as your appreciation of our work in innovatively integrating hotspot residues into peptide design and proposing a robust technical framework. Below, we provide clarifications and responses to your questions. If any concerns remain unaddressed, please feel free to reach out with further inquiries; we would be happy to engage in additional discussions.

Q1: The scaffold generation scenario only considers a small number of hotspots (K=1, 2, 3), with baseline comparisons limited to K=3. it would be insightful to see the performance of the baseline models under different conditions, specifically for K=1 and K=2, which are currently not included. it would be valuable to conduct experiments with a broader range of K values, or explain the insights behind the choice of these values.

We chose K=1, 2, 3 based on the peptide length distribution in our training and test datasets, where 3 represents the minimum peptide length.

To address the impact of varying K values on baseline models in the scaffold generation task, we conducted additional experiments, as detailed in Appendix G.3. The updated results are summarized below. As shown, unlike PepHAR, which benefits from increasing K in terms of geometry and energy metrics, the baseline models show only marginal improvements or even performance degradation. We believe this is due to their training schemes, which do not explicitly condition on known hotspots. Optimizing their training and inference processes for the scaffold setting could potentially improve their performance.

Peptide Scaffold Generation

Thank you for your comprehensive reply to my previous review.You have provided a clear explanation regarding the points I raised. I will maintain my score of 6. I look foward to seeing your work with wider training dataset and incorporating wet lab validations beyond traditional metrics.

Thank you for your insightful and constructive comments as well as your appreciation of our work that combines energy-based hotspot-driven model with autoregressive fragment assembly and using detailed breakdown and comprehensive metrics. Below are some clarifications and answers to your questions. If our response does not fully address your concerns, please post additional questions; we will be happy to discuss further.

Q1: The autoregressive fragment extension process might introduces cumulative geometric errors, especially for longer peptides. I expect the author to quantify the impact of the cumulative errors from autoregressive generation.

We have quantified the cumulative geometric errors in Appendix Fig. 6, subsection G.2. As shown in the figure, peptide length exhibits a strong positive correlation with RMSD, indicating that generating longer peptides results in more cumulative errors due to the autoregressive generation process.

Q2: Regarding the equation, the author should add period to the end if it closes a sentence. I notice that the author missed that in most of the equations in this paper.

We have added commas and periods to the equations where appropriate, with commas for equations within sentences and periods for those that conclude sentences.

Q3: Figure 4 shows the designed peptides are all loops. Given that, I wonder if the SSR % is still meaningful if most of the native and designed peptides are just loops. Because in that case, the model can just produce all loopy structures and get a very high SSR.

The peptide examples in Figures 4 and 5 represent loop regions, as cyclic peptides are among the most promising peptide mediators [1,2,3]. However, helical peptides, such as GPCR peptides, are also representative peptide structures [4,5], and evaluating the secondary structures of peptides remains a widely studied topic [6,7], as shown in previous works [8]. To provide additional context, we calculated the secondary structure labels for the native peptides in the test set, as follows:

Although 58% of residues are loops or irregular regions, other secondary structures, particularly beta strands and alpha helices, are also present. Both loop regions and helical/strand regions play crucial roles in protein interactions, making it important to generate residue structures at precise positions with accurate secondary structures. We believe that assessing the secondary structure rate (SSR %) remains a valuable metric for evaluating the quality of peptide design, which is also conducted in the prior work. We also include another example in Appendix Figure 7 to show that our generated peptides can also have helix structures.

Q4: I suggest that the author further design the sequences for those generated peptide structures using for example, ProteinMPNN and report the recovery rate.

We have added the sequences and recovery rates for each example in Figures 4 and 5. In general, the lower recovery rates indicate structural differences compared to the native structures.

References:

[1] Design of linear and cyclic peptide binders of different lengths only from a protein target sequence. bioRxiv, 2024-06

[2] Hosseinzadeh, Parisa, et al. "Comprehensive computational design of ordered peptide macrocycles." Science 358.6369 (2017): 1461-1466.

[3] Bhardwaj, Gaurav, et al. "Accurate de novo design of membrane-traversing macrocycles." Cell 185.19 (2022): 3520-3532.

[4] Pal, Kuntal, Karsten Melcher, and H. Eric Xu. "Structure and mechanism for recognition of peptide hormones by Class B G-protein-coupled receptors." Acta pharmacologica sinica 33.3 (2012): 300-311.

[5] London, Nir, Dana Movshovitz-Attias, and Ora Schueler-Furman. "The structural basis of peptide-protein binding strategies." Structure 18.2 (2010): 188-199.

[6] Eiríksdóttir, Emelía, et al. "Secondary structure of cell-penetrating peptides controls membrane interaction and insertion." Biochimica et Biophysica Acta (BBA)-Biomembranes 1798.6 (2010): 1119-1128.

[7] Seebach, Dieter, David F. Hook, and Alice Glättli. "Helices and other secondary structures of β‐and γ‐peptides." Peptide Science: Original Research on Biomolecules 84.1 (2006): 23-37.

[8] Li, Jiahan, et al. "Full-Atom Peptide Design based on Multi-modal Flow Matching." arXiv preprint arXiv:2406.00735 (2024).

Dear reviewer mmeW,

Thank you for engaging in discussions with the authors. You state your concerns have been addressed. This usually implies that you think the paper could be above the bar for acceptance, but I see that your score is still at 5. Could you help clarify what your current score is and your recommendation for accepting this paper or not, accompanied by a motivation?

Many thanks,

AC

Thank you for your insightful and constructive comments as well as your appreciation of our work in introducing novel problem decomposition and proposing novel energy-based density model and autoregressive fragment extension. Below are some clarifications and answers to your questions. If our response does not fully address your concerns, please post additional questions; we will be happy to discuss further.

Q1: Many recent works of peptide binder design use AlphaFold2 for scoring (e.g., pAE or iptm). I would like to see the evaluation of designed peptides with such metrics.

In recent works, AlphaFold2 is often used to predict peptide-receptor complex structures and score them using metrics like pLDDT, pAE, and ipTM [2,3,5]. Since there is no gold-standard metric, we propose an empirical evaluation using AlphaFold2 Multimer's ipTM score. This score measures the relative positioning accuracy of the complex’s subunits, with ipTM scores below 0.6 suggesting a failed prediction [7].

We concatenated each generated peptide with the full receptor sequence (not just the binding pocket), and used AlphaFold2 Multimer to predict the complex structures. We then computed the proportion of complexes with ipTM scores above 0.6, indicating successful predictions. This metric, referred to as the "success rate," has been added to Tables 1 and 2 of the revised draft. Below, we also present the success rates for reference. As shown in tables, PepHAR outperforms PepGLAD (latent diffusion) and achieves comparable results to other baselines.

Peptide Binder Design

Peptide Scaffold Generation

We would like to emphasize that scoring using structure prediction models has certain limitations. For example, we occasionally observe that AlphaFold2 fails to position peptides accurately within the binding site, resulting in low prediction confidence. Similarly, we find that ESMFold [9] tends to assign high confidence scores to single-chain peptides but consistently assigns low confidence scores to peptides in complex structures. Therefore, we believe that evaluating binder design from multiple perspectives is essential to identify the most promising candidates for wet-lab experiments [6].

Q2: Regarding Novelty score, can author also show separate metrics for it in supplementary as well: TM-score and sequence identity.

We have provided separate TM-score and sequence identity (AAR) metrics in Appendix G.1 Table 4, and we summarize the results here as well. The TM-score indicates that PepHAR tends to generate peptides that are less similar to native peptides, contributing to higher diversity and novelty. For AAR, PepHAR achieves sequence recovery comparable to RFDiffusion and ProteinGenerator and performs better than PepGLAD. However, relying solely on AAR is not sufficient to evaluate generative models, as it provides limited insight into the ability to capture the broad and diverse distribution of binding peptides. This limitation has also been discussed in the appendix of PepGLAD [10].

Peptide Binder Design

Peptide Scaffold Generation

Q3: For all examples provided, I will suggest authors to also provide the peptide sequence for reference for better understanding.

We have updated Figures 3 and 4 with generated peptide sequences and their sequence identities. Additionally, we corrected a misused PDB code in Figure 4.

Thank you for your insightful and constructive comments as well as your appreciation of our work that divide-and-conquer the peptide design task and utilize hot spot residue information. Below are some clarifications and answers to your questions. If our response does not fully address your concerns, please post additional questions; we will be happy to discuss further.

Q1: Not taking other hotspots or fragments into account in the two stages could make the model ignorant of important information for the geometry and validity.

Thank you for raising this concern. We have clarified the distinction between independent and dependent sampling in our method. At the first stage, hotspots are sampled independently, as our distribution is defined based on residue distributions around the target. This approach makes independent sampling more efficient. In the extension stage, however, generation is conditioned on all existing fragments, including both the target and other residues from the current fragments. As noted in line 279, we explicitly clarify that “E represents the surrounding residues, including the target T and other residues in the currently generated fragments.”

Q2: In the correction stage, are the terms in $J_{\text{bb}}$ only non-zero in those residues that stay at the connection of two fragments? Because other residues in the middle of the fragments should be complying with the consistency constraint from construction. The authors should clarify this.

In the first optimization step, if we only consider the $J_{\text{bb}}$​ term, the residues in the middle of the fragments, which are constructed through dihedral transformation, remain unchanged, while the positions and orientations of the connecting residues are modified, as you noted. However, since we jointly optimize both angles and positions for all residues using $J_{\text{bb}}$ and $J_{\text{angle}}$, updates to the connecting residues can influence their neighboring residues. Additionally, $J_{\text{angle}}$​ directly affects the dihedral angles of the middle residues. As a result, middle residues may also be adjusted in subsequent optimization steps. Overall, the correction stage refines the entire peptide structure. This approach aligns with the physical rationale: when fragments are connected to form a longer peptide, every residue may undergo structural and sequence-level adjustments to ensure consistency and validity.

Q3: How does the correction method proposed in this work (using models directly from the first and second stages) compare with the correction by some empirical methods (like some energy function)?

Our correction stage shares similarities with empirical methods, as both use objective functions to iteratively refine protein structures. However, there are key differences in the design and focus of the methods. Traditional approaches, such as Rosetta [1], FoldX [2], OpenMM [3], Madra X [4] energy functions, rely on physically inspired force fields and finely tuned parameters to optimize both backbone and side-chain structures. In contrast, our method specifically focuses on updating peptide backbone structures and sequences by leveraging gradients from backbone and angle-related terms. This targeted design makes our approach particularly effective for tasks involving backbone angle optimization and sequence updates, though less comprehensive in addressing side-chain adjustments.

To provide a quantitative comparison, we evaluated the performance of our method alongside Rosetta's relax function (backbone movement on):

While our correction method does not achieve the highest performance compared to Rosetta relax, it is clearly more effective than omitting correction altogether. We believe that integrating more finely designed energy functions or adopting aspects of traditional empirical methods could further enhance validity rates. We will include additional discussion on the potential for combining our approach with more sophisticated traditional energy-based refinements.

References:

[1] Alford, Rebecca F., et al. "The Rosetta all-atom energy function for macromolecular modeling and design." Journal of chemical theory and computation 13.6 (2017): 3031-3048.

[2] Delgado, Javier, et al. "FoldX 5.0: working with RNA, small molecules and a new graphical interface." Bioinformatics 35.20 (2019): 4168-4169.

[3] Eastman, Peter, et al. "OpenMM 7: Rapid development of high performance algorithms for molecular dynamics." PLoS computational biology 13.7 (2017): e1005659.

[4] Orlando, Gabriele, et al. "Integrating physics in deep learning algorithms: a force field as a PyTorch module." Bioinformatics 40.4 (2024): btae160.