Protein-Ligand Interaction Prior for Binding-aware 3D Molecule Diffusion Models

We sincerely thank you for your time and efforts in reviewing our paper, and your valuable feekback. We are happy to see that you recognize the concept of prior-shifting proposed in our paper is innovative, and the paper's presentation is well-structured and coherent. Please see below for our responses to your comments, and the revised texts are marked in red.

Q1: It would be beneficial to test the method across multiple benchmarks.

A1: We added a comparison to BindingMOAD dataset which is used in DiffSBDD [1], and the other SBDD methods only conducted comparisons on the CrossDocked2020. We preprocessed the data following DiffSBDD. The results are shown in the following table. The results demonstrate that our IPDiff can achieve the best performance by comparing with DiffSBDD and TargetDiff [2].

Q2: “In the forward process, the ways of injecting noises are the same for all training samples with different target proteins.” Even if the noise injection methods remain the same, the original samples' distinctiveness ensures varied forward diffusion outcomes.

A2: We want to convey that in previous diffusion models, the noise added to the atom of ligand is sampled from a normal distribution that is independent of the given pocket. In contrast, our method takes into account the interaction information between the protein and ligand during the noise addition process.

Q3: A comparative analysis with works that learned the beta parameters for forward diffusion would add depth to this study.

A3: We conduct a experiment that makes the beta parameter in TargetDiff learnable. The performance comparison between TargetDiff, TargetDiff with learnable beta and our IPDiff are present below. The results demonstrate that simply make beta parameters learnable for the forward diffusion can not improve the performance of diffusion models for SBDD.

Q4: Compared with self-conditioning proposed in Analog, the novelty of the prior conditioning contribution in this paper appears less significant.

A4: The novel technical contributions of our proposed prior-conditioning mechanism are: (1) It incorporates protein-ligand interaction information modeled in the pretrained prior network into the molecular diffusion model while self-condition can only consider self-prediction molecular information and is unable to model the critical protein-molecule geometric interactions. (2) It introduces a new paradigm that combines the protein-ligand pretraining with protein-conditioned molucular diffusion model, fundamentally different from previous diffusion-only methods. And we have conducted a quantitative comparison between our prior-conditioning and self-conditioning. The results in Table 4 of the manuscript demonstrate that self-conditioning is not effective in SBDD tasks since it can not provide the interaction information between ligands and proteins.

Q5: I am also quite curious whether this prior-shifting idea can be used in class-conditional image generation as different classes are very different.

A5: From a broader perspective, IPDiff represents a cross-modal conditional diffusion model, which is designed to emphasize the interaction between different modalities in the diffusion process and utilize it as a condition. We conduct a preliminary experiment on CIFAR-10 where we incorporate class-image semantic interactions (we obtain the shifts from the combination of class embeddings and image embeddings) into the image diffusion process, the results are in the table below. We can find that in class-conditional image generation, our model can still improve the baseline diffusion model, demonstrating the satisfying generalization ability of our alrorithm.

Reference:

[1] Structure-based Drug Design with Equivariant Diffusion Models, arXiv:2210.13695, 2022.

[2] 3d Equivariant Diffusion for Target-aware Molecule Generation and Affinity Prediction, ICLR, 2023a.

Dear Reviewer F898,

We sincerely appreciate the time and effort you have dedicated to reviewing our paper. Your insightful questions and valuable feedback have been extremely beneficial.

In response, we have (1) provided the performance comparison on another benchmark (2) provided the performance comparisons by extending our methods to other application (i.e., class-to-image generation) for illustrating a boarder impact in AI community.

As the discussion period is approaching its conclusion in two days, we kindly request, if possible, that you review our rebuttal at your earliest convenience. Should there be any further points that require clarification or improvement, please know that we are fully committed to address them promptly.

Thank you once again for your invaluable contribution to our research.

Warm Regards,

The Authors

We sincerely thank you for your time and efforts in reviewing our paper, and your valuable feekback. We are happy to see that you recognize the idea proposed in our paper is novel and well-motivated, the performance improvements are promising. Please see below for our responses to your comments, and the revised texts are denoted in red.

Q1: however, this method requires labeled data and one extra trained network, so comparisons aren’t really apples-to-apples.

A1: It is important to note that one of our baselines, DecompDiff, similarly incorporates external knowledge by using the extra software AlphaSpace to extract ligand-agnostic decomposed priors from the given pocket for the subsequent molecular generation process, while our IPNet ustilizes learnable interaction network to automatically model the protein-ligand binding prior, which is more flexible to use.
Besides, compared to the DecompDiff that relies on the labeled geometric data, our IPNet has the potential to scale, as the interaction clues can be also learned from the sequential data (please refer to Table 3 in the manuscript), which is easier to acquire. Moreover, the decomposed priors in DecompDiff are solely related to proteins, ignoring the fact that different molecules may suggest different protein-molecule interactions. In contrast, our method fully considers the interaction between given proteins and molecules as conditions during the generation process, which is more relevant to the task at hand.

Q2: The proposed method improves over the baseline (diffusion model conditioned on pocket) by relying on supervised learning on PDBbind. This makes the model more complicated to train/use and, more importantly, more difficult to scale

A2: Indeed, we utilize the supervision of binding affinity in PDBBind during training. However, we do not think that this will make our model difficult to use or train. It is important to note that the binding affinity is only used as a supervision in the training of IPNet, and the diffusion model in the second stage does not rely on binding affinity. The purpose of IPNet is to mine some general interaction clues, and we can arbitrarily design the diffusion model without changing the IPNet. Additionally, our method introduces a paradigm that combines a pretrained protein-ligand interaction model with diffusion models for SBDD, which has a boarder impact on AI-for-science community. We have conducted experiments to demonstrate that our IPNet can effectively serve the downstream diffusion model even when it is solely pre-trained on sequential data (please refer to Table 3 in the manuscript). This is significant because precise geometric data is often scarce, while sequential data is abundant. This finding suggests that we can further explore the integration of Self-Supervised Learning or Weakly-Supervised Learning techniques in the training of IPNet solely relying on abundant sequential data, for extracting general interaction-related information and effectively serving the downstream diffusion model. These aspects make our model scalable and open up new possibilities for leveraging large-scale sequential data in SBDD. We are grateful for your insightful suggestion, and we thoroughly explained and discussed it in the Appendix-F revised manuscripted as part of our future work.

Q3: What if PDBBind contains samples that are similar (or identical) to those on the test set of CrossDocked?

A3: We have excluded the molecules used in testing and evaluation of IPDiff from the PDBBind v2016 dataset for IPNet according to the calculated Tanimoto similarity between two molecules. After that, the average Tanomoto similarity between these datasets is only 0.12%. Additionally, we have also calculated the Tanimoto similarity between the molecules generated by IPDiff and the molecules in the training of IPNet, and the average Tanimoto similarity is only 0.079%. Based on these, we believe that there is no issue of information leakage in our method.

Q4: It would be nice to compare how good the generated molecules are in terms of protein-ligand interactions with the pockets. Posecheck (mentioned above) proposes a metric to measure to compute this.

A4: We conduct a comparison between our IPDiff and TargetDiff on the PoseCheck as present below. We can observe that our method achieves the superior performance compared with TargetDiff. We have cited PoseCheck [4] in the Appendix-F of the revised manuscript (marked in red), and we will provide more comprehensive evaluation and analysis of our method on PoseCheck for the future work.

Q5: I feel some details about the training of IPNet are missing.

A5: We have reported more details about the training of IPNet in the Appendix-D.1 of the updated manuscript marked in red, please refer to it.

Q6: “IPDiff is theoretically able to achieve better likelihood compared to previous diffusion models”. Can the authors elaborate on this?

A6: We show IPDiff is theoretically able to achieve better likelihood than previous diffusion models. As the exact likelihood is intractable, we aim to compare the optimal variational bounds for negative log likelihoods (NLL). The objective function of IPDiff at time step t is $E_{q_{\theta_2}}D_{KL}(q_{\theta_2}(x_{t-1}|x_t,x_0,F_0, P)||p_{\theta_1}(x_{t-1}|x_t,F_{0|t+1},F_{0|t},P))$, and its optimal solution is

Dear Reviewer AJPX,

We sincerely appreciate the time and effort you have dedicated to reviewing our paper. Your insightful questions and valuable feedback have been extremely beneficial.

In response, we have (1) provided the theoretical proofs that our IPDiff has capability to achieve better likelihood compared to previous diffusion models, (2) provided more experiments and analysis of prior-shifting mechanism, (3) clarified the scalability of IPDiff, (4) evaluated the performance with more evaluation metrics to address your queries and concerns.

As the discussion period is approaching its conclusion in two days, we kindly request, if possible, that you review our rebuttal at your earliest convenience. Should there be any further points that require clarification or improvement, please know that we are fully committed to address them promptly.

Thank you once again for your invaluable contribution to our research.

Warm Regards,

The Authors

We thank the authors for the answers to questions above.

• Apples-to-apples comparisons: we agree that both DecompDiff and IPDiff are extensions (by leveraging more information) of point cloud-based diffusion models (eg TargetDiff and SBDDDiff).
• IPNet: thank you for the clarifications about the architecture and other questions. This network is a key component of the model and it is good to see more details about it on the paper.
• PDBBind/CrossDocked leaked information: Thank you for the clarification. This is a very important issue for model benchmarking and it needs to be explicitly mentioned in the text. I did not see any comment about this on the manuscript. It is also important to know how much the PDBBind dataset is reduced after the preprocessing.
• Metrics:
  • Where are the DecompDiff results? As we agreed above, comparing with TargetDiff is not very meaningful (since IPDiff is an augmentation of TargetDiff in ways)
  • The table shown by the authors is not very informative and does not allows us to have many conclusions. Are those numbers mean? median? They usually have large variance and are better shown with plots (as in the paper). How they compare to the other baselines (particularly the "ground truth")?
  • The main contribution of the paper is leveraging PL-interactions, yet the authors only show 2 out of 4 of the proposed interactions metrics.
  • Moreover, both clash and strain energy are still very bad compared to other methods (besides TargetDiff).
• Comparison with docking baseline: The authors argue that their approach ids better than the baseline based the results on Table 1. However, even with the incomplete results in Posecheck metrics, we can see that the generated molecules have much more clashes and strain energy than the simple baseline. This indicates that the proposed method is not as good as it sounds in practice.

Based on the comments above, I will keep my rating.

We sincerely thank you for your time and efforts in reviewing our paper, and your valuable feekback. We are happy to see that you recognize that the proposed IPDiff novelty and effectiveness, theoretical proofs in our paper are clearly written and easy to follow, experiments are sufficient and reproducible. Please see below for our responses to your comments, and the revised texts are denoted in red.

Q1: What is the difference in the chemical diversity of the datasets used for training IPNET and IPDfiff? Were the poses used in testing and evaluation of IPDiff excluded from the training set for IPNet?

A1: CrossDocked2020 (the dataset used by IPDiff) is an expanded dataset obtained by recombining protein-ligand pairs from PDBBind (the dataset used by IPNet) and then redocking them. Therefore, the chemical diversity of these two datasets is consistent. And we excluded the molecules used in testing and evaluation of IPDiff from the PDBBind v2016 dataset for IPNet according to the calculated Tanimoto similarity between two molecules. After that, the average Tanomoto similarity between these datasets is only 0.12%. Additionally, we have also calculated the Tanimoto similarity between the molecules generated by IPDiff and the molecules in the training of IPNet, and the average Tanimoto similarity is only 0.079%. Based on these, we believe that there is no issue of information leakage in our method.

Q2: How does the model perform when generating the molecules with larger numbers of rotatable bonds? How does the model generalises into unseen targets and novel pockets?

A2: (1) We report the performance in generating molecules with different numbers of rotatable bonds in the revised Appendix-E and marked in red, please refer to it. (2) All data preprocess and experimental settings in our paper follows previous methods. Specifically, the CrossDocked2020 dataset is partitioned into non-overlapping training and testing sets. The performance on the testing set of CrossDocked2020 can reflect the ability of our model in generalizing to unseen targets and novel pockets.

Q3: What is the percentage of novel molecules generated by the IPDiff?

A3: The percentage of novel molecules generated by the IPDiff is 99.999971%.

Q4: How fast is the docking algorithm on the same hardware and similar sized structures?

A4: The average time consumed for docking a molecule to the given pocket using the Vina Dock algorithm on the same hardware is 27.9 seconds.

Dear Reviewer qHa3,

We sincerely appreciate the time and effort you have dedicated to reviewing our paper. Your insightful questions and valuable feedback have been extremely beneficial.

In response, we have (1) investigated the performance of molecules with a high number of rotatable bonds, (2) clarified the experimental settings and the characteristics of the datasets to address your queries and concerns.

As the discussion period is approaching its conclusion in two days, we kindly request, if possible, that you review our rebuttal at your earliest convenience. Should there be any further points that require clarification or improvement, please know that we are fully committed to address them promptly.

Thank you once again for your invaluable contribution to our research.

Warm Regards,

The Authors

We sincerely thank you for your time and efforts in reviewing our paper, and your valuable feekback. We are happy to see that you recognize the novelty and effectiveness of prior-shifting and prior-conditioning mechanism proposed in our paper. Please see below for our responses to your comments, and the revised texts are denoted in red.

Q1: The paper cites Sattoras et al - and says it's an SE(3) Equivariant neural network - whereas it is E(N) GNN

A1: Thank you for your feedback. The architecture design of networks is not our primary focus of our paper. The backbone of networks utilized in our method just following with previous work [1-3]. And we acknowledge that EGNN [1] we used is an E(3)-equivariant neural network and chirality is also an important property of protein molecules. However, the input of the EGNN is a protein-ligand complex. Thus, for example, given a protein pocket (which is not symmetric in general), a pair of stereoisomers will not share the same representation. This also follows TargetDiff [2]. We appreciate your suggestion and will consider it in our future work.

Q2: The authors haven't shown their IPNet is SE(3) equivariant

A2: The graph in our IPNet is fully-connected, as detailed in the Appendix-D.1. However, even using the KNN graph, IPNet still maintains SE(3) equivariance. The proofs are provided as below: Since atom types are always invariant to SE(3)-transformation during the generative process, we only need to consider the atom coordinates. Recall the equation 13 in the manuscript, and we denoted $x_{t,i}^{C,l}- x_{t,j}^{C,l}$ as $d^{C, l}_{t,ij}$ for simplification. The atom hidden embeddings $h$ and coordinates $x$ can be updated as follow:

Q3: It is unclear how S is trained to ensure the molecule is not distorted to impossible molecules

A3: The original diffusion process inherently introduces noise and denoises to the position of each atom, which can be treated as a shifting process to position of each atom in the previous step. Current molecular diffusion models [1-3] designs reconstruction-based training objective to maximally ensure that the molecule is not distorted to impossible molecules. We follow this and further enhance this shifting process by incorporating protein-ligand interaction prior obtained from a pre-trained IPNet model. These interaction prior preserves informative geometric relationships between intra-molecules and inter-molecules, thus facilitating the 3D molecular generation process. Theoretical proofs are provided in the revised Appendix-B.4, which demonstrate the potential of our method to achieve a better likelihood compared with previous diffusion-based methods. Moreover, the $S_t$ in our method represents the cumulative shift as time step $t$, which is 0 at the beginning and end of the diffusion process by setting the coefficient $k_t$ of $S_t$ as $\sqrt{\bar{\alpha}_t} \cdot (1-\sqrt{\bar{\alpha}_t})$. It means that our method specifically focuses on affecting the positions of each atom in the intermediate steps of the diffusion process without changing the initial and target distributions.

Q4: Using the pocket structure for the diffusion process is counter intuitive. Moreover, without the presence of the ligand, we only have access to the apo structure of the receptor.

A4: Indeed, as you rightly point out, it is necessary and practical to consider apo/holo structures. However, to the best of our knowledge, there are no existing methods for SBDD take apo structures into consideration. The main reasons are that these data is difficult to obtain, and its distribution is very unique, making this task extremely challenging. Therefore, we just follow the task definition and experimental setup as existing computational methods for SBDD [2-8], only considering holo structures. We really appreciate your suggestions and will consider them for future work.

Q5: How are the receptor and ligand graphs constructed - is it based on atom connectivity or distances between atoms?

A5: Yes, in our paper, we follow previous methods like TargetDiff and DecompDiff, representing each atom as a node and encoding the inter-atom distances as edge attributes in the construction of Protein-Ligand graphs.

References:

[1] Satorras, et, al., E(n) Equivariant Graph Neural Networks, ICML, 2021.

[2] Guan et al., 3d Equivariant Diffusion for Target-aware Molecule Generation and Affinity Prediction, ICLR, 2023a.

[3] Guan et al.,DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design, ICML, 2023.

[4] Schneuing et al., Structure-based Drug Design with Equivariant Diffusion Models, arXiv:2210.13695, 2022.

[5] Peng et al., Pocket2mol: Efficient Molecular Sampling based on 3d Protein Pockets, ICML, 2022.

[6] Luo et al., A 3d Generative Model for Structure-based Drug Design, NeurIPS, 2021.

[7] Ragoza et al., Generating 3D molecules Conditional on Receptor Binding Sites with Deep Generative Models, Chem Sci, doi: 10.1039/D1SC05976A.

[8] Liu et al., Generating 3d Molecules for Target Protein Binding, ICML, 2022.

Dear Reviewer ssPe,

We sincerely appreciate the time and effort you have dedicated to reviewing our paper. Your insightful questions and valuable feedback have been extremely beneficial.

In response, we have (1) clarified the task definition and experimental settings of the existing AI-driven SBDD, (2) explained the underlying mechanism of prior-shifting and provided the corresponding theoretical proofs to address your queries and concerns.

As the discussion period is approaching its conclusion in two days, we kindly request, if possible, that you review our rebuttal at your earliest convenience.

Your further comments and insights would be invaluable to us as we strive to enhance our work.

Thank you once again for your invaluable contribution to our research.

Warm Regards,

The Authors

Dear Reviewer ssPe,

Thanks for your further comments, we carefully response to your comments as follows.

Q1: I am partially satisfied with answers to question 3 (however, in my opinion, reconstruction as just an objective doesn't entirely guard against impossible molecules nor does increased likelihood) please let me know if I am missing something here.)

A1: The general purpose of existing generative models (including our models and other generative models [1-3]) is to maximally fit the distribution in the hypothetical space of real molecules. All these generative models can not guarantee all the generated molecules are valid unless we manually add rule-based constraints into the generative process. Moreover, the primary goal in SBDD is to generate molecules that bind tightly to the given pocket, and our method is mainly designed to improve existing generative models from this perspective. And, if necessary, post-processing procedures can be conducted to filter out impossible molecules generated by our IPDiff or other generative models. As demonstrated in our proofs (please refer to the A6 in the response to Reviewer AJPX), our IPDiff exhibits a higher likelihood than previous diffusion-based SBDD methods, indicating that the molecules sampled from our model are more likely to be real and to bind tightly to the given pockets.

Q2: With regard to Q4, I am not satisfied to the answer as - apo structure for receptor alone can be obtained from potentially PDB files of receptor alone (when available) or from ESM type model predictions (they have shown to generate apo structures in the absence of ligands). While this is not crucial for other models as they don't take the pocket structure as an explicit input - the proposed IPDiff does and hence can unfairly benefit the method.

A2: Firstly, our IPDiff introduces a new pretraining-diffusion paradigm for SBDD. In the first stage, IPNet is pretrained to model general protein-ligand interaction priors, while the diffusion model in the second stage fully utilizes the priors provided by IPNet through two novel mechanisms prior-shifting and prior-conditioning. If the apo structure is available or the apo structures predicted by ESM type models are reliable, we can easily extend our IPDiff (including IPNet and the new diffusion model) to these apo structures by recursively or adaptively conduct our prior-shifting and prior-conditioning. Thanks for your constructive suggestions, we will further explore more complex scenarios for future work with our new pretraining-diffusion paradigm.

Secondly, it's important to note that previous methods for SBDD, such as Pocket2Mol [1], DiffSBDD [2] TargetDiff [3], and DecompDiff [4], all incorporate the protein pocket structures as an explicit input during the molecule sampling process. Additionally, DecompDiff utilizes extra open-source software AlphaSpace [8] to obtain molecule templates for the protein-specific molecule generation process. We just strictly follow the task definitions and experimental settings of previous methods [1-7] to ensure fair comparisons.

References

[1] Peng et al., Pocket2mol: Efficient Molecular Sampling based on 3d Protein Pockets, ICML, 2022.

[2] Schneuing et al., Structure-based Drug Design with Equivariant Diffusion Models, arXiv:2210.13695, 2022.

[3] Guan et al., 3d Equivariant Diffusion for Target-aware Molecule Generation and Affinity Prediction, ICLR, 2023.

[4] Guan et al.,DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design, ICML, 2023.

[5] Luo et al., A 3d Generative Model for Structure-based Drug Design, NeurIPS, 2021.

[6] Ragoza et al., Generating 3D molecules Conditional on Receptor Binding Sites with Deep Generative Models, Chem Sci, doi: 10.1039/D1SC05976A.

[7] Liu et al., Generating 3d Molecules for Target Protein Binding, ICML, 2022.

[8] Rooklin D et al., Alphaspace: fragment-centric topographical mapping to target protein–protein interaction interfaces, JCIM, 2015.

Should there be any further points that require clarification or improvement, please know that we are fully committed to addressing them promptly.

Thank you once again for your invaluable contribution to our research.

Warm Regards,

The Authors