Thank you for your comments. Indeed, we would like to use RapidDock as a kind of oracle function in our future work (or to produce embeddings for other models). We are glad you appreciated our efforts to present the ideas in a well-structured way.

To clarify the role of the distance matrices, they are embedded into the self-attention matrices of the encoder (there is no cross-attention). We respectfully disagree with the statement that the embedding of the protein is standard. In fact, this is the key part that enables using the encoder as an end-to-end docking tool for the first time. ESM is an additional external embedding but the precise geometric embedding into the attention matrices is novel. A similar idea has been recently proposed after our submission in Dockformer [1] which is a model for pocket-based docking.

Questions:

Wording: L. 30 “ … will revolutionize medicine” is an unsupported statement, please reformulate. It would be better to focus on the obstacles that need to be overcome and how you tackle those (like in your paragraph 2, L. 34 X.).

We changed “will” to “could”. The next sentence strongly supports the claim.

In l.113f. the authors claim equivariance, however they work with interatomic distances only, making your model invariant.

It’s a fair point that the model is (strictly speaking) invariant (though equivariance is often used interchangeably in the field). We changed the wording.

Permutation loss citation is wrong (e.g. l. 228), cite original paper (Zhu et al. 2022 Direct molecular conformation generation).

Thank you for this remark, we fixed the citation to point to the original paper.

In my opinion, l.419f. “the model demonstrates a strong understanding of the physicochemical principles” is a big stretch - how is this supported in your work? Accurate and fast prediction of ligand poses in proteins doesn’t mean that the model understands the physicochemical principles that lead to those poses, and it is debatable whether this is even needed.

We toned down the wording.

Open questions: Since the prediction time is critical to the paper's claims, I would like to see how much time you spend at inference on average in a) pre-processing, b) prediction, c) reconstruction and d) any form of post-processing.

Following the authors of all our comparison benchmark models, we do not include pre-processing in runtimes. It is dominated by generating conformations which is a highly parallelizable process and will be negligible for docking to thousands of proteins. We do not include pre-processing times also because comparisons to other methods would be problematic. For example, the reported runtimes of AlphaFold 3 include only the GPU wallclock time. NeuralPLexer reports GPU runtimes only as well.
Reconstruction is included in runtimes and is on average about two times longer than the transformer forward pass as we mention in A.3.
Optional post-processing is now described in the Appendix A.6. We hope, however, that the model can be directly fine-tuned on downstream tasks or will be used to produce docking embeddings for other models, without forming the poses.

In l.162f., what is the reasoning for choosing 257 buckets? Are there ablations on higher/lower resolution? How does this affect the performance-inference time tradeoffs? Same questions for the charge embeddings.

Thank you for this remark. Indeed, these ablations would be desirable. There is no reason inference times would change but performance might indeed be affected. The number 257 was chosen for several reasons:

• An uneven number was chosen because we added one special embedding for unknown distances.
• The resolution must be sufficiently high to capture nuances in the molecule representation, e.g., to distinguish the length of the double carbon bond from single carbon bond (1.5 vs 1.3).
• The maximum distance must be sufficient to capture the far-away dependencies interactions between amino acids.

We added some clarifications of these in the paper.

References:

[1] Yang, Zhangfan, Junkai Ji, Shan He, Jianqiang Li, Ruibin Bai, Zexuan Zhu, and Yew Soon Ong. "Dockformer: A transformer-based molecular docking paradigm for large-scale virtual screening." arXiv preprint arXiv:2411.06740 (2024).

Thank you for carefully reading our manuscript and providing constructive feedback. We acknowledge the need for generating conformations. However, this is embarrassingly parallel and will be negligible in docking studies with thousands of proteins. None of the baseline models we compare to report pre-processing times.

We are aware that the experiment in Section 4.2 only confirms the quality of the predicted protein-ligand distances. A better experiment would align the entire predicted structure with the bound complex and compute RMSD or LDDT-PLI metrics only then. This is part of our current work.

Questions:

DiffDock-L (also AlphaFold3 and NeuralPLexer) is a generative approach, so it gives multiple binding poses according to their probabilities. Therefore, its prediction accuracy can be improved by including multiple different poses (Top-n poses) in the evaluation. However, RapidDock is deterministic, so it gives only a single output. (...).

We do not believe that the non-deterministic nature is a shortcoming of our method, especially for high-throughput studies, though various approaches to generating a collection of poses could be considered. The results for other methods were obtained with the parameters recommended by their authors. In particular, DiffDock generates ten poses and chooses the most likely pose via a ranking module.

Since RapidDock requires conformation searches for each molecule before docking, the authors need to clarify whether the reported computational times include the time for conformer searches (...).

As mentioned above, the runtimes do not include preprocessing. For studies with thousands of proteins, they should be negligible. Moreover, the comparisons to other methods would be problematic. We followed the authors of our comparison baselines and do not report preprocessing times. For example, the reported runtimes of AlphaFold 3 include only the GPU wallclock time. NeuralPLexer or DiffDock authors also report GPU inference runtimes only. We added a clarification of what runtimes are reported in Appendix A.3.

The proposed method has been compared with AlphaFold3 and NeuralPLexer. However, the former performs a rigid docking, whereas the latter predicts binding poses only from protein sequences and molecular graphs. (...)

You are absolutely right to point out that AlphaFold3 and NeuralPLexer perform docking-while-folding, which is a more general task. We write about it in detail in the Related Work section. However, it is particularly important to compare RapidDock to the tools that achieve state-of-the-art accuracy whatever they may be.

In the reconstruction of ligand location, predicted distances between ligands and also between ligand-protein may not precisely match with the coordinates of a single pose. (...) Does it require a kind of post-processing?

Thank you for pointing this out. This is a very good point. The results are obtained without any post-processing. Such post-processing can be performed, though, which we now describe in Appendix A.6. However, we believe that in practice – being fully based on a transformer – the model is well-suited for fine-tuning without explicitly forming the poses.

The authors greatly emphasize the importance of proteome-wide docking, but this work does not provide any meaningful analysis except the computational time, (...). The authors may add an additional study verifying that the proposed method can indeed provide meaningful results from the proteome-wide docking (...).

Demonstrating the importance of proteome-wide docking is a topic of our current research. It is a fact, however, that the number of screened proteins for assessing toxicity of new drugs nowadays is limited because of computational constraints and most drugs fail even the first phases of clinical trials. We believe that to answer why this is the case, one needs a full picture of the given molecule’s effects. We think RapidDock is one important step toward enabling that. This approach is already partially utilized in genomics, where similarity of drug effect is measured by the similarity of their expression profiles on a pre-defined set of genes. Demonstrating actual use cases for proteome-wide docking is part of our current work.

Appendix A.6 shows the examples of 3D structures predicted by RapidDock and AlphaFold3. The authors deliberately selected specific examples where RapidDock outperformed AlphaFold3, while they admit that the latter is far better than the former on average. AlphaFold3 even predicted those structures from the sequence-level information. (...).

We include such examples in the new version of the paper.

References

[1] Li, Jie, Xingyi Guan, Oufan Zhang, Kunyang Sun, Yingze Wang, Dorian Bagni, and Teresa Head-Gordon. "Leak proof PDBBind: A reorganized dataset of protein-ligand complexes for more generalizable binding affinity prediction." arXiv preprint arXiv:2308.09639 (2023).

Thank you for carefully reading our manuscript and listing multiple strengths of our method. We also believe that our embeddings of the protein and ligand 3D structures are the key to success.
We appreciate your pointing out the need for improving some of the descriptions of technical details in the paper. We tried to improve them.

Regarding the differences in terms of the number of parameters, we do not think it is particularly relevant here because in practice only speed and accuracy matter. Our main claim is that a properly designed transformer can perform competitively while being much faster than models based on generative modeling.

Your comment about the RMSD metric being imperfect is of course correct. The actual molecule poses can be obtained via post-processing, which we now describe in Appendix A.6. However, we hope that RapidDock will be fine-tuned on downstream tasks directly, or used for obtaining docking embeddings, without forming any poses explicitly.

In Appendix A.7, we now also include examples where RapidDock performs worse than AlphaFold 3. We think a comparison to the most accurate method is sufficient.

Thank you for referring to ETDock and FeatureDock. While these methods use transformers in their pipeline (as do the models in our baseline comparisons), we do not think they are end-to-end blind docking tools fully based on a single transformer, although we admit that such a distinction is not clear-cut. ETDock is composed of several custom modules (Feature Processing, TAMformer, Attention Layer, Message Layer, etc). FeatureDock is not a blind docking tool because the grid around the pocket is input to the model. We agree that these methods should be cited though, and we added a mention of these methods in the paper.

Finally, we are confident that the paper does not contain major grammatical errors. We do acknowledge, though, that there may be occasional typos or misplaced punctuation. We placed the Related Work section after Experiments to better describe other methods as they relate to ours.

Questions:

When comparing runtime in inference mode, did you preprocess the protein, or was the comparison done solely for molecule conformation?

The protein requires minimal preprocessing (only computing the distances), though ESM embeddings need to be ready. The number of proteins in the human body is limited to only about 20,000, however, and the preprocessing can be done “once and for all,” so it can be neglected.

Did you use the same time-splitting approach as previous methods, such as DiffDock and NeuralPlexer, for the dataset?

No, because that approach is known to be very leak-prone. See, for example, [1].

In the statement,
"Only the fixed distances across the molecule’s possible conformations are recorded, and others are denoted by a special value of −1,"
could you clarify why you selected -1 as the special value?

We wanted to use a value that does not correspond to any distance. This value indicates that:

1. The part of the first term inside softmax corresponding to those distances should not be modified (see the definition of $S_m$), and
2. The distance is larger than the maximum distance of 16 (see the definition of $b(x)$).

The special value could be any negative number. We added a clarification.

In the RapidDock attention section, you state,
"First, we multiply the attention scores corresponding to input pairs with known distances (i.e., ligand-ligand within a rigid part and protein-protein) by a learnable scalar $s_m$, one for each layer $m$."
Did you also apply this to protein-ligand pairs? If not, could you explain why?

The scalar $s_m$, together with $z_m$, controls how much the final score is affected by the original score and how much by the distance bias. The protein-ligand distances are unknown, so the model should rely solely on the original attention score. That part could be multiplied by another scalar, but the overall effect would be the same because we already have two scalars, $z_m$ and $s_m$. We added a clarification.

For inference, do you generate one conformation per runtime for each protein-ligand pair?

All conformations need to be generated at inference.

References:

[1] Li, Jie, Xingyi Guan, Oufan Zhang, Kunyang Sun, Yingze Wang, Dorian Bagni, and Teresa Head-Gordon. "Leak proof PDBBind: A reorganized dataset of protein-ligand complexes for more generalizable binding affinity prediction." arXiv preprint arXiv:2308.09639 (2023).

We are truly thankful for your insightful comments. We are glad that you appreciated our choice to pre-train the model on protein folding and represent the protein and ligand 3D data as inductive biases in the attention matrices. We also think these are the key features of RapidDock. We are also grateful for mentioning the clarity of the presentation.

Thank you for noting that in modern drug design molecules are screened against a relatively small number of proteins for assessing toxicity. This is precisely our motivation for developing a model that can quickly dock molecules to all proteins. The number of screened proteins nowadays is limited because of computational constraints. We believe this is the reason most drugs fail even the first phases of clinical trials. To confirm it, one needs a full picture of the given molecule’s effects. For example, a ligand may indirectly cause side effects by yet unknown protein cascades. Or, as you have pointed out, the side effects may be caused by the metabolic products of the drug, which again calls for a fast docking method in particular. Apart from toxicity, a quick binding tool can also allow studying potential beneficial effects, such as decreasing inflammation or speeding up proliferations in the metabolome due to binding to specific receptors, etc.

We appreciate your suggesting a comparison to classical methods. We now include a comparison to SMINA in the paper. We note that there are many papers that include comparisons of deep learning methods to classical tools. The reported speeds of the latter methods are, however, consistently slower than those of most deep learning methods.

Regarding the charge embeddings, we believe that including “per token” numerical values via embeddings is a standard approach, though we admit there are other possible choices. The distance matrices are needed to encode the 3D structure of the protein and the ligand within the transformer in a way that is invariant to translations, reflections, or rotations. The distances describe a protein-protein or ligand-ligand pairwise all-to-all property, so the attention matrix is an appropriate place to include them. We added a clarification of that point in the paper.

Questions:

Is there a better way to determine which atoms are rigid and which are flexible? For example, AutoDock Vina determines if bonds are rotatable using a simple chemical definition, which dictates which atoms are flexible and which are not. Just searching through a lot of generated conformations seems like it might miss bonds that only rotate when exposed to external charges.

Thank you for this question. For sure, the representation is not perfect and could be improved in the future to better capture such aspects. On the other hand, sampling the conformations is implicitly performed with energy weighting. As a result, the distribution of conformations, and therefore the distances obtained, resembles the one found in reality.

Is this model potentially applicable to target fishing? Target fishing is the process of taking an existing drug compound and evaluating it against a large number of potential proteins to see if it can target them. This can be applied for drug repurposing, which is the use of currently approved drugs against new indications based on previously unknown binding against a new protein. This is potentially a strong application of the proposed method, but I do not see it explicitly mentioned in the paper anywhere.

Yes, in fact, that is one of the applications the model is well-suited for. We included a mention of target fishing in the paper.