Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints

Q1: Limited MD Validation: Only two test cases are simulated. A larger sample size and error analysis (e.g., standard deviations across replicates) would improve confidence.

Sorry for the limitation, due to the time and resource limitation, we adopted the rhotheta score as an auxiliary metric to validate our generated peptides. Specifically, we first relax the peptide using a dedicated force field to establish a stable cyclic conformation; thereafter, we further optimize the structure with a rhotheta relaxer and compute the corresponding rhotheta score. Our findings indicate that 85.54% of the target peptides achieve a negative rhotheta score, signifying an energetically favorable state. The rhotheta score is a widely used metric for peptide evaluation, providing an efficient method for assessing large sample sizes.

Q2: The paper does not clarify whether test-time cyclization strategies (e.g., disulfide bonds) involve constraints entirely absent from training. If training data includes residues like cysteines (common in disulfide bonds), the "zero-shot" claim might overstate novelty.

Sorry for the confusion. Here "zero-shot" means that the specific combination of constraints required for cyclic peptides is not present during training. While the training data includes individual unit constraints (e.g., cysteine residues), the exact combination needed for cyclization is not observed. Our method learns combinations of constraints in linear peptides during training and generalizes to their combinations during inference to generate cyclic peptides.

Q3: The theoretical claims are mathematically correct under ideal assumptions, but practical implementations introduce approximations (finite RBFs) that weaken injectivity guarantees. The reliance on external proofs for equivariance is acceptable but leaves a minor risk of inherited errors. Overall, the proofs are valid but lack robustness analysis for real-world settings... The experimental design adequately addresses core claims but lacks rigor in validation: ... missing ablation studies.

We evaluate the influence of the RBFs to the quality of the generation of peptide under most difficult setting: Bicycle peptide(26 samples in test set):

Based on the validation and parameter sensitivity study, we can conclude the necessity of RBF design to support the distance control. Further, an saturation beyond 16 channels is observed, indicating that finite RBFs is enough for empirical performance.

Q4: Reproducibility: While code is provided, computational resource requirements are underspecified.

We train CP-Composer on a 24G memory RTX 3090 GPU with AdamW optimizer. More details can be found in Section C.4.

Q5: Add runtime metrics (e.g., seconds per peptide generation) to Appendix C.4 for scalability assessment.

Here we show the runtime comparison between our method and the baseline method when they both use a 24GB RTX3090 GPU.

Q6: Were generated peptides assessed for chemical synthesizability (e.g., using SAscore or RAscore)? If not, how might impractical structures affect real-world utility?

The SA score is primarily designed for assessing the synthesizability of small molecules and is not directly applicable to peptides, which follow a distinct synthesis methodology. For peptides, higher hydrophobicity can lead to aggregation and hinder synthesis. Thus, we analyze the distribution of GRAVY scores [1], which measure peptide hydrophobicity. The results, provided in the linked analysis（https://anonymous.4open.science/r/Rebuttal-68EF/readme.md), demonstrate that the generated peptides exhibit a hydrophobicity distribution similar to that of natural peptides, suggesting that they are likely to be synthesizable.

Reference： [1] Kyte, Jack, and Russell F. Doolittle. "A simple method for displaying the hydropathic character of a protein." Journal of molecular biology 157.1 (1982): 105-132.

Thank you for your suggestions!

Q1:Comparing against any existing methods specifically designed for cyclic peptide generation is important for contextualizing the performance gains.

We include CADS, an advanced diffusion conditional sampler, and DiffPepBuilder, a model specifically designed for disulfide peptides, as below:

For CADS sampler, we set the w=2 and use the initial noise scale as 0.25. CADS is acceptable under simple constraints but struggles with more complex constraints like disulfide and bicyclic peptides. Notably, our zero-shot approach outperforms DiffPepBuilder, which is specifically designed for disulfide peptides.

Q2: The connection between the ideal conditional score (Eq.2) and the implemented guided score (Eq.3) should be strengthened.

In fact, the rationale of Eq.2 and Eq.3 are linked by the following distribution $\tilde{p}\_t(\mathcal{G}\_\mathbf{z}^{(t)}|\mathbb{C}) \propto p\_t(\mathcal{G}\_\mathbf{z}^{(t)}) p\_t(\mathbb{C}|\mathcal{G}\_\mathbf{z}^{(t)})^w,$ with the corresponding conditional score $\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log \tilde{p}\_t(\mathcal{G}\_\mathbf{z}^{(t)}|\mathbb{C}) =\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log p\_t(\mathcal{G}\_\mathbf{z}^{(t)}) +w\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log p\_t(\mathbb{C}|\mathcal{G}\_\mathbf{z}^{(t)})\approx\epsilon\_\theta(\mathcal{G}\_\mathbf{z}^{(t)},t) + w\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log p\_t(\mathbb{C}|\mathcal{G}\_\mathbf{z}^{(t)}) .$

In particular, Eq.2 directly models $\log p\_t(\mathbb{C}|\mathcal{G}\_\mathbf{z}^{(t)})$ by an externally trained energy function. Eq.3 instead follows classifier-free guidance by rewriting $\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log p\_t(\mathbb{C}|\mathcal{G}\_\mathbf{z}^{(t)})=\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log p\_t(\mathcal{G}\_\mathbf{z}^{(t)}|\mathbb{C})-\nabla\_{\mathcal{G}\_\mathbf{z}^{(t)}}\log p\_t(\mathcal{G}\_\mathbf{z}^{(t)})\approx\epsilon\_\theta(\mathcal{G}\_\mathbf{z}^{(t)},\mathbb{C},t)-\epsilon\_\theta(\mathcal{G}\_\mathbf{z}^{(t)},t),$ which gives Eq.3 after simplification.

Q3：A more thorough analysis of failure cases would be insightful to understand the method's limitations.

As for failure cases, they commonly occur when excessively large controling strength w degrade molecular quality. We analyzed peptide structures generated with w=6 (https://anonymous.4open.science/r/Rebuttal-68EF/readme.md) and found that they often exhibited strained backbones and unrealistic conformations. This highlights the trade-off between guidance strength and structural integrity, suggesting that an adequate selection strategy for w could further improve robustness.

Q4: The relative advantage of CP-Composer is difficult to assess and the section would benefit from a more extensive comparisons with advanced baselines, which should also generalise to this more challenging setting.

First, our model allows arbitrary high-order combinations, as shown in the paper. Second, the comparison with DiffPepBuilder below indicate that, despite being a general zero-shot model, our approach outperforms the baseline specifically designed for disulfide peptides.

Q5: The authors use t-SNE plots to visualise the generation of non-linear peptides. This could be strengthened by adding quantitative sequence analysis and a comparison of training and generated peptide sequences.

Sorry for the confusion. Our current cluster analysis in Figure 6 is already based on the embedding generated from ESM2 model, which outputs embeddings based on the sequence information.

Q6: Could you elaborate on the specific challenges posed by Disulfide and Bicycle peptides for the baselines?

Disulfide and Bicycle peptides need requires more strict constraints than Stapled peptide and Head-to-tail peptide. Dislfide peptide need one distance constraint unit and two type constraint unit. Bicycle peptides need three distance constraint units and three type constraint units. While the Head-to-tail peptide only needs one distance constraint unit and the Stapled peptide needs one distance constraint and two type constrinis easier to reach as both K-D and K-E are accepted.

Q7: Have you investigated any techniques to further improve the success rates, particularly for the higher order combinations?

As an initial attempt at zero-shot cyclic peptide generation, our focus is to demonstrate the feasibility and generalizability of our framework, which already shows promising results. However, in more complex constraint combinations, conflicts may arise, potentially driving the generated peptides in divergent directions. Addressing these conflicts to further improve success rates is an important challenge that we leave for future research.

Thanks for the insightful comments which help improve the quality of our paper!

Q1: The type and distance constraints may not be independent but rather intertwined, which the authors have not discussed.

Sorry for the confusion. We ensure that the constraints are jointly feasible by considering their dependencies both in the data and the model. First, the constraint combinations are sampled from the joint distribution derived from real-world data, based on the dataset during training and based on chemical knowledge during inference. Second, our model inherently accounts for these dependencies, as the constraints are input together and fused within the hidden layers to output the conditional denoising score.

Q2: I believe the authors should compare their approach with basic diffusion models and some recent conditional generative models.

Thanks for the suggestion. We further include two more baseline methods, CADS, an advanced diffusion conditional sampler, and DiffPepBuilder, a model specifically designed for disulfide peptides, as below:

For CADS sampler, we set the w=2 and use the sampler with initial noise scale as 0.25. The results indicate that CADS is acceptable under simple constraints but struggles with more complex constraints like disulfide and bicyclic peptides. Notably, despite being a general zero-shot model, our approach outperforms DiffPepBuilder, which is specifically designed for disulfide peptides.

Q3: For the generated molecules, the authors only evaluate whether the cyclic peptide is successfully generated but do not assess the validity of the generated molecules. In addition to the success rate, they should also consider whether there are any unreasonable atomic types or coordinates in the generated structures, which could be measured using an appropriate metric. For the AA-KL and B-KL metrics, it does not clearly explain how the distribution divergence is computed.

Sorry for the confusion. We assess the validity of generated peptides by evaluating their residue composition and structural features to ensure they resemble natural peptides. Specifically, we use KL divergence on residue types and dihedral angles. AA-KL measures the KL divergence between amino acid distributions in generated peptides and reference peptides, excluding the controlled amino acid types. B-KL quantifies the KL divergence between dihedral angle distributions of generated and reference peptides, ensuring realistic backbone conformations. Additionally, we assess the structural stability of generated peptides using Rosetta energy scores. Our results show that 85.54% of cyclic peptides satisfying constraints achieve negative Rosetta scores, indicating their physical plausibility. This suggests that the model generates valid and stable cyclic peptides.

Q4: In Table 2, the success rate of “2*Stapled” does not change with variations in w. While the paper acknowledges this phenomenon, it does not discuss the possible reasons behind it. What could be causing this? Did the authors check whether the unsuccessful cases at w = 2, 2.5, and 3 were the same set of samples?

We appreciate the insightful question! Upon examining the failure cases for w=2,2.5, and 3, we found that they are nearly identical. This suggests that, beyond a certain threshold, these cases have already collapsed into failure modes. As a result, further increasing the constraint strength does not impact the success rate.

Q5: However, in real-world scenarios, is the combination of these conditions truly linear? (Is adding condition A and condition B really equivalent to A + B?) What do you think about this? Are there any methods to explore this further?

Thank you for your thoughtful question. We think there are some combinations not directly addictive. For example, a bicycle peptide may struggle to also satisfy the stapled peptide constraints, which we have observed in zero success rates for such cases. In most application scenarios, meaningful combinations are ensured by expertise in structural chemistry and biology. Additionally, low success rates for certain combinations can help identify infeasible or unrealistic configurations.