Designing Cyclic Peptides via Harmonic SDE with Atom-Bond Modeling

Q1: "The main weakness I see for this paper in an ML venue is that it is highly specialized to tackle the problem of cyclic peptide design; arguably this is an important application, but the authors seem to propose a rather complex model to handle the cyclic peptide generation task."

A1: Thank you for recognizing the significance of cyclic peptide design. Our method is complex due to two main challenges: limited data on cyclic peptides; common protein representation based on residue frames that inadequately handle unique geometrical constraints and occasional non-canonical amino acids.

Our approach addresses these issues by employing all atom and bond modeling and two integrated modules: AtomSDE and ResRouter. Both are essential and non-redundant. To our knowledge, this is the first generative model for designing cyclic peptides. We hope this sparks further research and advancements in this important field.

Q2: Could the authors provide a baseline (be it a non ML approach) to compare the performance? I am aware of two works for cyclic peptide generation that are very recent (as such the authors are not required to include them for comparison)) e.g. [1,2] although the latter cannot model non canonical amino acids.

Thank you for highlighting this. Both [1] and [2] are awesome works, yet they significantly differ from our approach.

• [1] is a ligand-based drug design (LBDD) method that models the sequence of cyclic peptides using discrete diffusion, optimized by multiple reward functions. It doesn't explicitly incorporate the 3D structure of target proteins, whereas our structure-based drug design (SBDD) method directly designs ligands based on 3D target structures.

• [2] uses modified RoseTTAFold and RFdiffusion with cyclic relative positional encoding to generate macrocyclic backbones. We've already cited [2] in our paper. It only supports head-to-tail cyclization due to its residue-level encoding limitations, whereas our work accommodates all four types of cyclic peptides.

Both works are very recent: [1] was released on November 18, 2024, and [2] on December 23, 2024. As neither has released their code, we are unable to directly compare methods at this time. We will cite these papers and discuss them further in future versions of our paper.

References:

[1] PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion, Tang et al.

[2] Accurate de novo design of high-affinity protein binding macrocycles using deep learning, Rettie et al.

Q3: "It would be helpful to compare a benchmark on a setting which can be handled by other models than CPSDE."

A3: Given that all baseline methods, including ours, can design linear peptides, we compare them under these conditions. Please see our responses to Reviewer Rxgy's Q2 & Q3 for more details. Nonetheless, we continue to emphasize that the principal focus of our work is on cyclic peptide design.

Q4: "How does the generation time compare to alternative peptide generative models ? given all-atom and bond modeling, the sampling time might be heavy."

A4: We benchmark the average time of generating one peptide for all co-design baselines and our methods on a single NVIDIA A100-SXM4-80GB GPU. See the results below.

Given that computational drug design does not demand real-time model response, the inference time of our method is deemed acceptable.

Q1: "It would be great if the authors would release their curated training dataset as well as models and code for the broader community."

A1: We would like to open source our work to contribute to the community.

Q2: "I have some minor wording comments."

A2: Thanks for pointing this out. We will change these words and choose more objective words in the future version of our paper.

Q3: "What exactly is the role of $\sigma_P^{-2}$, when calculating $\mathbf{H}$?"

A3: $\mathbf{H}=\mathbf{L}+\sigma_P^{-2}\mathbf{I}$. $\mathbf{L}$ is the Laplacian matrix. An intuitive explanation is that $\mathbf{L}$ encourages the connected atoms in the graph to be initialized closer. $\sigma_P$ is the standard derivation of the atom coordinates of the protein pocket. An intuitive explanation is that $\sigma_P^{-2}\mathbf{I}$ encourages the atoms to be initialized more scattered when the pocket itself is large. This reflects a useful prior knowledge, as a pocket typically accommodates a ligand that complements its shape.

Q1: "Comparing the generated ligands to known cyclic peptides."

A1: We conducted a comparison of our method with known cyclic peptides.

Vasopressin, a natural cyclic peptide featuring intramolecular disulfide (S-S) bond cyclization, is utilized in the treatment of antidiuretic hormone deficiency, vasodilatory shock, gastrointestinal bleeding, ventricular tachycardia, and ventricular fibrillation [1]. We selected two vasopressin-protein complexes, PDB IDs: 1JK4 and 1YF4, to design cyclic peptides targeting bovine neurophysin II and trypsin, respectively.

The LEDGF binding site of HIV integrase (HIV-IN) represents a promising target for novel inhibitor development. Prior research has leveraged solution cyclization to discover various head-to-tail cyclic peptides interacting with this site [2]. The PDB IDs are 3A** in the following table.

The results are shown as follows:

The results demonstrate that our method successfully designs cyclic peptides with affinity and stability comparable to known cyclic peptides, albeit with slightly lower stability than the reference.

[1] Vasopressin: physiology, assessment and osmosensation, Bichet et al. Journal of Internal Medicine, 2017.

[2] Crystal Structures of Novel Allosteric Peptide Inhibitors of HIV Integrase Identify New Interactions at the LEDGF Binding Site, Peat et al. ChemBioChem, 2011.

Q2: "Figure 1 felt unnecessary, to me."

A2: Figure 1 illustrates the therapeutic advantages of cyclic peptides compared to linear peptides. We would like to move this to the appendix.

Q3: Explain Figure 2, especially the denoising/renoising/ResRouter coupling. "Some intuition on why the renoising is necessary would be helpful."

A3: The generative process is a reverse SDE, where each Euler step consists of two parts: drift (denoising) and diffusion (renoising). See Equation (2) in the paper where the Wiener process introduces the stochasticity.

In Figure 2, AtomSDE adjusts the Atom73 coordinates through denoising and renoising, treating the denoised ligand as an intermediate state. ResRouter alters the chemical graph by predicting amino acid types based on the denoised ligand, which provides more useful signals than the noised ligand. Importantly, ResRouter changes only the atom and bond types in the chemical graphs and leaves the atom73 coordinates unchanged. Similar operations are utilized in [3].

[3] An all-atom protein generative model, Chu et al. PNAS, 2024.

Q4: "AtomSDE only includes the protein target. How are different pockets specified?"

A4: AtomSDE includes both pockets and noisy ligands. Our method aims to design cyclic peptides based on a given binding site. We refer to the protein target as the pockets. This setup aligns with the baselines, such as PepFlow. Specifically, the pockets are defined as residues of the protein target within 10 Angstroms surrounding a known ligand. We will include more details and clarifications in future version of our paper.

Q5: Explain page 2, line 091.

A5: Our method models all atoms and bonds, treating linear and cyclic peptides equivalently since both are composed of the fundamental components—atoms and bonds. Assuming AtomSDE is a well-trained docking model, it facilitates the generative process by encouraging two atoms connected by a chemical bond to be positioned closer together appropriately. By predetermining the cyclization type, we specify the related atom and bond types accordingly. Incorporating bond modeling ensures cyclization occurs naturally in 3D space, as bound atoms are drawn closer during the generative process.

Q6: Page 3, line 154: Why are the 3D structures of the cyclization part unavailable?

A6: The 3D structures of the cyclization segment are unavailable because they belong to what we aim to design.

Q7: "In 4.1, it is not clear to me how the training/test splits are generated using the sequence identity."

A7: Samples are grouped by receptor sequence similarity of 0.3 to create separate training and validation sets. In other words, if two samples are more than 30% similar in sequence, they cannot be in the same set. When receptors have multiple chains, the sequences are concatenated together to determine similarity. This method is widely used in previous works.

Q8: "Can CpSDE be adapted for use on linear peptides? This would allow for a head-to-head comparison against other methods.

A8: Please refer to our responses to Reviewer Rxgy's questions 2 and 3.

Q1: "I find the idea of conditioning generative models using chemical graphs interesting, and also the problem of designing cyclic peptides highly relevant for therapeutics purposes. However, the empirical evaluation of both ideas is inadequate."

A1: Our work focuses on designing cyclic peptides instead of linear peptides, although our method is indeed capable of designing the latter as well. Our method is tailored specifically for cyclic peptide design. Designing linear peptides often involves modeling translation, rotation of residue frames, and side-chain torsion angles—techniques that essentially encompass all-atom coordinate modeling, as seen in methods like PepFlow. However, these techniques fall short for cyclic peptide design due to unique geometrical constraints and non-canonical amino acids involved. This challenge motivated us to introduce two modules: AtomSDE and ResRouter. These modules enable explicit modeling of all atoms and bonds, addressing the limitations of previous methods in cyclic peptide design. In the generative process, AtomSDE adjusts atom coordinates based on chemical graphs, while ResRouter refines these graphs by predicting amino acid types. We hope this explanation clarifies the motivation and contributions of our work.

Besides, we have ablated the effect of Harmonic AtomSDE and ResRouter in designing cyclic peptides. Please refer to Appendix H.3.

Q2: Evaluation of extra boost in linear peptide design.

A2: While designing linear peptides is not our primary focus, we appreciate your suggestion to compare our method with existing baselines in this task.

Our method excels in designing linear peptides with superior affinity and comparable stability among all co-design methods, while also maintaining considerable diversity. Although our method slightly lags behind RFDiffusion, it's worth noting that RFDiffusion often generates helices and relies (also observed for ProteinGenerator) on a two-stage design pipeline (first designing the backbone, then the sequence).

Q3: "Data in crystal form would also allow for evaluating structural properties and reporting against these metrics." "The second aspect is merits of cyclic peptides design which is challenging to evaluate due to the lack of crystal structures of complexes."

A3: Evaluating energy is more critical than assessing RMSD against crystal structures of known binders, as there can be numerous design alternatives and a low RMSD does not always indicate a superior design model [1]. Therefore, we focus primarily on evaluating stability and affinity from an energy perspective. To further validate our findings, we conduct Molecular Dynamics simulations.

We have also designed linear peptides as in Q1&A1 and computed the RMSD against known linear peptide binders, shown as follows:

Our method achieves the lowest average RMSD among all methods, along with a comparable median RMSD.

[1] Antigen-specific antibody design via direct energy-based preference optimization, Zhou et al. NeurIPS 2024.

Q4: "What fraction of data is actually cyclic peptides and why this dataset would be relevant for generating from that class." "If the data on cyclic peptides is sparse how the model can mine useful signal for completing cyclicazation."

A4: Our method successfully designs cyclic peptides despite the training set containing less than 6% cyclic peptide data. This achievement stems not from relying on this small percentage, but from our approach of explicitly modeling all atoms and bonds, surpassing previous methods in depth. Through this fine-grained model, linear and cyclic peptides are treated equivalently as both are composed of the same fundamental components: atoms and bonds. The cyclization type is predetermined, allowing us to specify the related atom types and bond types accordingly. By incorporating bond modeling, we ensure cyclization occurs in 3D space since bound atoms are naturally drawn closer during the generative process. The ResRouter model equally sidesteps dependency on scarce cyclic peptide examples due to its ability to deduce amino acid types based on the contextual atom arrangement within the peptide and its receptor. Thus, it is this distinctive and comprehensive modeling technique that enables overcoming data limitations in cyclic peptide design.