Paper: Protein Multimer Structure Prediction via Prompt Learning (ICLR-2024)

Reviewer comment (Experiments):
The ablation of the pretraining phase is missing. An experiment without pretraining should be conducted to demonstrate the necessity of the proposed pretraining strategy.

Author response:
**[Cons. 2 Ablation of the pre-training]** Thanks for the valuable suggestion. To address the reviewer's concerns, we establish the baseline without pre-training in the following experiments.
1. **Ours:** Our complete version of the PromptMSP model.
2. **Ours w/o pt:** Our method without pre-training the GIN encoder $\theta$ and the task head $\phi$.

Specifically, the prompt model still exists in **Ours w/o pt**. Unlike **Ours**, the GIN encoder $\theta$ and the task head $\phi$ are initialized on the target task before training and their parameters are then updated together with the prompt model $\pi$.

The experimental results **(with AFM-produced dimers)** are as follows:

| Chain number $N$ |  3   |  4   |  5   | 6 | 7 | 8 | 9 | 10 |Overall|
| -------------- |:----:|:----:|:----:|:----:|:-----:|:-----:|:-----:|:-----:|:-----:|
| Ours w/o pt | 0.64 | 0.60 | 0.45 | 0.38  | 0.40  | 0.33  | 0.34  | 0.34 |0.43|
| Ours  | 0.71 | 0.66 | 0.54 | 0.50  | 0.46  | 0.46  | 0.45  | 0.40 |0.51|

It can be seen that pre-training the graph-level regression model has a significant effect on almost all chain numbers and average performance.

Reviewer comment (Evaluation):
Can you show the correlation between the number of chains and the node degrees to directly validate the claim "multimers with more chains are more likely to yield assembly graphs with high degrees" in section 3.3?

Author response:
**[Q1 Correlation between $N$ and node degrees]** Thanks for the valuable question. To address your concern, we provide the statistics of our source and target data.

First of all, we respectfully explain the definition of **degree** in the original manuscript.
* Degree for the source data: the maximum node degree of each assembly graph in the source data
* Degree for the target data: the degree of the chain (node) to be docked 

In the table below, we show the degree proportions of the generated datapoints with multimers of a specific scale. For example, the value in column "degree=2" of row "$N=5$" represents the proportion of datapoints with degree=2 obtained from 5-chain multimers.

On the source data:
| Proportion |  degree=1   |  degree=2   |  degree=3   | degree=4 | degree=5 |
| -------------- |:----:|:----:|:----:|:----:|:-----:|
| $N=2$  | 100% | 0 | 0 | 0 |  0 |
| $N=3$  | 0 | 100% | 0 | 0 |  0 |
| $N=4$  | 0 | 75% | 25% | 0 | 0  |
| $N=5$  | 0 | 48% | 48% | 4% | 0  |
| $N=6$  | 0 | 58.35% | 39.35% | 1.85% | 0.46%  |

On the target data:
| Proportion |  degree=1   |  degree=2   |  degree=3   | degree=4 | degree=5 |
| -------------- |:----:|:----:|:----:|:----:|:-----:|
| $N=3$ | 100% | 0 | 0 | 0 | 0  |
| $N=4$  | 67% | 33% | 0 | 0 |  0 |
| $N=5$  | 52% | 34% | 12% | 2% | 0  |
| $N=6$  | 43% | 27% | 23% | 6% | 1%  |

Reviewer comment (Presentation):
The paper integrates multiple technical ideas with a complex problem domain, but the presentation is very confusing.

Author response:
We sincerely appreciate the reviewer's insightful suggestions on our paper and his/her valuable time. We sincerely appreciate the reviewer's recognition for the contribution and novelty of this paper, and we apologize for any confusion caused by our presentation.

Reviewer comment (Writing):
The paper relies on many ideas that are less familiar to the average reader in protein ML, and there should be an extensive background section explaining meta-learning, prompt learning, L=3 PPI prediction, etc.

Author response:
**[Cons. 1. Background introduction]** Thank you for bringing this important issue to our attention. It is necessary to provide an introduction to the background knowledge involved. Therefore, we will add relevant explanations in the revised manuscript.

For clarity, we briefly introduce the background knowledge here.
* Meta-learning is a technique that aims to enable models to quickly and efficiently learn from and adapt to new data. Meta-learning is a training technology rather than a deep neural network. **It is well-known for its ability to learn common knowledge from sufficient data and quickly adapt to (new) scarce data.** For the multimer structure prediction (MSP) task, there is a severe imbalance in the number of scales (chain numbers) among multimers, which can be intuitively well-addressed by meta-learning techniques.
* In Section 2, we have introduced the background of prompt learning. In short, prompt learning can narrow the gaps between different data or tasks by **introducing learnable flexibility to the model without the need for fine-tuning the pre-trained model.** For the MSP task, we verified that regardless of whether the problem is modeled as TM-Score prediction or link prediction, there is a knowledge gap caused by the difference in chain numbers (scales) among multimers. This challenge leads to poor performance of training a unified model using data from all scales (please kindly refer to the experimental results in **[Cons. 5]**). **Motivated by this, we aim to use prompt learning to establish connections between data of multiple scales, which allows us to train a unified (prompt) model to handle all samples.**
* **$l=3$ PPI path:** We apologize for the missing explanation. We respectfully explain that $l=3$ path is an important identifier for PPI prediction. The existence of such a path implies that the proteins at both ends of the path will undergo PPI. Since $l=3$ path always has only 4 nodes, this allows us to re-model the link prediction task for multimers of different scales as a 4-node graph-level regression task (TM-Score prediction).

We sincerely thank the reviewers once again for bringing to our attention the importance of these key background knowledge.

Reviewer comment (Reproducibility):
For a procedure with this many moving parts, it is absolutely essential to provide an explicit inference algorithm somewhere.

Author response:
**[Cons. 2. Inference process]** Thanks for the valuable comment. We have reorganized Figure 5 (framework diagram) and added the description of the inference process (Section 4.4).

The inference process is multi-step. For an $N$-chain multimer, we randomly choose a starting chain and then perform $N-1$ assembly steps in order. During each step, we predict linking probabilities of all possible chain pairs and then select the most possible pair for assembly.

Reviewer comment (Presentation):
The paper is made more confusing by certain particular choices of emphasis which serve only to distract the reader on a first pass.

Author response:
**[Cons. 3. C-PPI, Section 3.3 and scales]** We thank for the valuable suggestions. We respectfully merge these three questions together because they are closely connected.

One of the purposes of emphasizing C-PPI is indeed to distinguish our method from MCTS and to demonstrate that using only I-PPI modeling for MSP tasks is biased. However, another crucial factor to consider is that predicting C-PPI (i.e. link prediction) with different chain numbers of multimers can lead to the out-of-distribution (OOD) situation for model's generalization. For clarity, we use "10+1" to denote predicting the next right link on an already assembled 10-chain multimer. **Such OOD issue means that we struggle to use a model trained on "10+1" (C-PPI) data to perform the "29+1" prediction.** This is why we emphasize the importance of "scale" in Section 3.3 and throughout the entire paper.

We apologize for any confusion caused by our unclear presentations. We will remove the wording "oligomers" and restate the relationship between C-PPI and scale in the introduction part.

Reviewer comment (Novelty):
It is not clear why it is important to emphasize C-PPI vs I-PPI. Perhaps the authors are trying to draw a distinction with MCTS, but this is not necessary or within scope. Fully appreciating the difference would require a detailed explanation of the MCTS method, which the paper does not have the time (or need) to explain.

Author response:
**[Cons. 3. C-PPI, Section 3.3 and scales]** We thank for the valuable suggestions. We respectfully merge these three questions together because they are closely connected.

One of the purposes of emphasizing C-PPI is indeed to distinguish our method from MCTS and to demonstrate that using only I-PPI modeling for MSP tasks is biased. However, another crucial factor to consider is that predicting C-PPI (i.e. link prediction) with different chain numbers of multimers can lead to the out-of-distribution (OOD) situation for model's generalization. For clarity, we use "10+1" to denote predicting the next right link on an already assembled 10-chain multimer. **Such OOD issue means that we struggle to use a model trained on "10+1" (C-PPI) data to perform the "29+1" prediction.** This is why we emphasize the importance of "scale" in Section 3.3 and throughout the entire paper.

We apologize for any confusion caused by our unclear presentations. We will remove the wording "oligomers" and restate the relationship between C-PPI and scale in the introduction part.

Reviewer comment (Presentation):
The extended discussion in Section 3.3 seems disconnected from the context of the paper and serves only to make it more confusing.

Author response:
**[Cons. 3. C-PPI, Section 3.3 and scales]** We thank for the valuable suggestions. We respectfully merge these three questions together because they are closely connected.

One of the purposes of emphasizing C-PPI is indeed to distinguish our method from MCTS and to demonstrate that using only I-PPI modeling for MSP tasks is biased. However, another crucial factor to consider is that predicting C-PPI (i.e. link prediction) with different chain numbers of multimers can lead to the out-of-distribution (OOD) situation for model's generalization. For clarity, we use "10+1" to denote predicting the next right link on an already assembled 10-chain multimer. **Such OOD issue means that we struggle to use a model trained on "10+1" (C-PPI) data to perform the "29+1" prediction.** This is why we emphasize the importance of "scale" in Section 3.3 and throughout the entire paper.

We apologize for any confusion caused by our unclear presentations. We will remove the wording "oligomers" and restate the relationship between C-PPI and scale in the introduction part.

Reviewer comment (Writing):
The authors repeatedly distinguish between oligomers and multimers based on size, which is very unconventional and should be fixed.

Author response:
We apologize for any confusion caused by our unclear presentations. We will remove the wording "oligomers" and restate the relationship between C-PPI and scale in the introduction part.

Reviewer comment (Novelty):
The pipeline seems unnecessarily complicated and poorly justified. All else held equal, solutions to hard problems should be as simple as possible, and complexity (even if novel) should at least be sensible and easy to justify once understood.

Author response:
**[Cons. 5. Complex task formulation]** We sincerely appreciate the reviewer for the insightful comment. 

We respectfully clarify that the most intuitive solution for the MSP task is, as the reviewer mentioned, to use only a TM-Score predictor to gradually select the optimal assembly state for each step. This was also our initial attempt in this work. However, we still have to respectfully emphasize the out-of-distribution (OOD) problem caused by the difference in scales (chain numbers).

We would like to present the following confirmatory experiment. 

Specifically, "**$N$ for training**" means that the scale(s) of the multimers we use to train the TM-Score predictor (i.e., predicting the TM-Score of a given assembly graph). For all $10$ models, our test task is the same, which is the MSP task of multimers with $N=7$.

|$N$ for training  |  3   |  4   |  5   | 6 | 7 | 8 | 9 | 10 |6+7|3,4,...,30|
| -------------- |:----:|:----:|:----:|:----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|
| Performance | 0.32 | 0.35 | 0.33 | 0.38  | 0.40  | 0.36  | 0.29  | 0.26 |0.43| 0.22 |

We have several findings:
1. The scale of multimers used for training is recommended to closer to 7. The further the scale $N$ is from 7, the worse the testing performance.
2. Training the model with a combination of multimers with $N=6$ and $N=7$ yields better results than using only $N=7$ multimers for training.
3. Training the model with a combination of multimers of all scales (3, 4, ..., 30) yields worse results than using only $N=7$ multimers for training.

These findings confirm the OOD issue caused by the scales mentioned above. There are connections and gaps between multimers of different scales. Thus **training a separate model for each $N$ or training a unified model with all scales together are both not the ideal approaches.**

The prompt learning we proposed aims to maximize the utilization of common knowledge between different scales, enabling to apply a unified model to handle all scales well.

Reviewer comment (Writing):
Although the paper presents a wealth of ideas, the presentation is too unclear and the complexity insufficiently justified to recommend acceptance in its current form.

Author response:
As the discussion period is nearing its end, we would appreciate it if you could confirm whether our responses have addressed your concerns. If you have any additional comments, we are more than willing to engage in further discussion. 

We will continue to make efforts to improve the clarity of the paper by modifying the presentation. Moreover, we will release the code and checkpoints to facilitate the reproducibility and further research in this area.

Thank you very much for your time and consideration.

Reviewer comment (Presentation):
The method description is very confusing. Figure 5 is very crowded and rather uninformative.

Author response:
**[Cons 1. Method description and Figure 5's organization]** We sincerely apologize for the confusion caused. To address this issue, we have **(1) clearly described the proposed method and (2) made revisions to Figure 5 and the description of meta-learning part. We sincerely appreciate your suggestions, as they have indeed improved the readability and quality of our paper.**

1. Descriptions: 

1.1 **The motivation of our paper:** Under the multimer structure prediction (MSP) task, our main goal is to address the impact of knowledge gap of multimer scales (chain numbers) on C-PPI prediction. 

1.2 **C-PPI knowledge gaps:** In Section 3.3, we validated the existence of gaps and connections in C-PPI knowledge implied by multimers of different scales (chain numbers).

1.3 **$\mathscr{l}=3$ rule prompting (main contribution):** We first **pre-train** the GNN model, which takes an assembly graph as input. Its encoder $\theta^*$ outputs the node-level embeddings and the head $\phi^*$ outputs the predicted TM-Score. During tuning, we update only the prompt model $\pi$ based on the target data (conditional link prediction). For clarity, we refer to the combination of these three modules as a `pipeline`, denoted as $f_{\pi|\theta^*,\phi^*}$. In short, the `pipeline` $f_{\pi|\theta^*,\phi^*}$ outputs the linking probability conditioned on an already assembled portion of the multimer and a newly added chain.

1.4 **Meta-learning:** We respectfully clarify that the meta-learning method we apply is **a training strategy**, rather than **a neural network**. It is responsible for reliable prompt tuning, i.e., to update $\pi$ within $f_{\pi|\theta^*,\phi^*}$. 

2. Revisions: 

2.1 **We have re-organized Figure 5,** where we remove the meta-learning part and clearly show the specific process of training (pre-training, prompt-tuning) and testing.

2.2 We explicitly state in Section 4.3 that meta-learning is **a training strategy** and **explain the purpose** of applying this technique.

2.3 We have added a schematic diagram (Figure 7) to show the process for obtaining prompt tuning results.

2.4 We have included a part (Section 4.4) to introduce the inference stages.

**All revisions can be found in our revised manuscript. We sincerely apologize for any confusion we may have caused.**

Reviewer comment (Presentation):
It is very hard to understand what meta-learning part (section 4.3) is actually doing. A visual step-by-step illustration of prompt fine-tuning can be helpful.

Author response:
**[Cons. 2 The meta-learning part's readability]** Thanks for your valuable suggestions. To make the applied meta-learning technique much clearer, we have revised the entire Section 4.3 and **visualized specific cases to illustrate how it is responsible for prompt tuning.**

**In response, we describe the process as follows.**
* Assuming that the pre-trained model has been well-trained, now we have the GIN encoder $\theta^*$ and the task head $\phi^*$. **They will be frozen from now on.**
* Our goal of prompt tuning is to obtain 2 different prompt models $\tilde{\pi}$ and $\pi^*$ for scales $3\leq N\leq 7$ and $N>7$, respectively. For example, to infer a $10$-chain multimer, we perform 9 assembly steps. In each of the first 6 steps, we apply the `pipeline` $f_{\tilde{\pi}|\theta^*,\phi^*}$ to predict the
linking probabilities of all pairs of chains and select the most likely pair for assembly. Upon this assembled $7$-chain multimer, we apply the `pipeline` $f_{\pi^*|\theta^*,\phi^*}$ to sequentially add the remaining 3 chains.
* **The process of getting $\tilde{\pi}$:** We construct a pool of **tasks** from the link prediction datapoints created from multimers of $3\leq N\leq 7$. Each task contains two sets (a support set and a query set) of link prediction datapoints. **In each epoch, we do three things in order**. (1) Randomly sample $B$ tasks from the task pool; (2) for each of the $B$ support sets, update a separate model starting from $\pi$, resulting in $\pi^{(i)},i-1,...,B$; (3) compute the sum of loss ($\mathcal{L}\_{meta}$) of these all $\pi^{(i)},i=1,...,B$ on the query sets and update $\pi$ with the gradient of $\mathcal{L}_{meta}$ with respect to $\pi$. **After multiple epochs of iteration, we obtain prompt model $\tilde{\pi}$.**
* **The process of getting** $\pi^*$: We create link prediction datapoints from multimers of $8\leq N\leq 30$. Over multiple epochs, we update the previously obtained $\tilde{\pi}$ to $\pi^*$.

Reviewer comment (Novelty):
The introduction of prompt fine-tuning seems an overkill. A simpler approach should work equally well. For example, we can adopt a standard autoregressive link prediction algorithm to this problem. In each step, you predict the link between a pair of proteins and train the model to predict the right link given different prefix graphs.

Author response:
**[Cons. 3 The role of prompt fine-tuning]** Thanks for the valuable suggestions. We fully agree with your description of our task as "predicting the right link given different prefix graphs". Actually, our target task is to follow a similar design, which involves using a prefix graph to predict the linking probability between each undocked chain and each node of the prefix graph. Finally, we take the most likely link as the right link. 

However, one of the contributions of our paper is to verify the existence of a knowledge gap (Figure 4) in the target task for multimers of different scales (chain numbers). **In short, it difficult to train a unified model that can well handle the assembly of both a 5-chain multimer and a 30-chain multimer.**

Inspired by the prompt learning methods, which increases the model's flexibility to narrow the gap between different data or tasks, we adopt a prompt model to construct the "bridge", $\mathscr{l}=3$ path, which can be applied to multimers of varied scales.

The empirical results also validate the importance of prompting. Table 3 shows that without the prompt model and only predicting the right link in order, our model's performance would be significantly reduced.

Reviewer comment (Reproducibility):
Analysis in section 3.3 is unclear. How did you compute Centered Kernel Alignment between two models?

Author response:
**[Cons. 4 Centered Kernel Alignment]** Thanks for the valuable question. We sincerely apologize for not providing a detailed explanation of the calculation process with Centered Kernel Alignment (CKA).

We use Figure 4 to show the knowledge gaps between multimers with varied scales (chain numbers). For example, if we want to analyze the relationship between data of 5-chain and 25-chain multimers, we first train separate 2 models for each of them. We then use the testing multimer as input for such two well trained models and obtain its two versions of representations $\text{X}$ and $\text{Y}$.

**CKA **[re1]** is widely used to compute the relationship between the representations of two models.** First, we compute the Gram matrices for two representations, $\text{K}=\text{X}\text{X}^{\text{T}}$ and $\text{L}=\text{Y}\text{Y}^{\text{T}}$. Then CKA computes:
$\text{CKA}(\text{K},\text{L})=\frac{\text{HSIC}(\text{K},\text{L})}{\sqrt{\text{HSIC}(\text{K},\text{K})\text{HSIC}(\text{L},\text{L})}}$，
where $\text{HSIC}$ is the Hilbert-Schmidt independence criterion.

We find that the model the similarity between two models is quite low (about 0.2), indicating that there are significant gaps between these 2 kinds of training data (5-chain and 25-chain multimers).

Reviewer comment (Experiments):
It's unclear how a new protein is docked to the current assembly in each step. Did you use EquiDock? If so, how do you ensure that EquiDock is not trained on any of your test set instances?

Author response:
**[Cons. 5 Data leakage]** During each step of inference, we predict linking probabilities of all possible chain pairs and then select the most possible pair (right link) to dock. In our experiment part, we apply AlphaFold-Multimer (AFM) to provide dimer structures for each assembly (docking) action.

We have ensured that there is no overlap between our test set and AFM's training set. The description of the training set used in the original AFM paper **[re2]** is as follows: "The training dataset consisted of structures from the Protein Data Bank (PDB) with a maximum release date of 2018-04-30." 

**In our paper, we ensured that:** 
1. The release date of the multimers included in our test set is no earlier than 2018-04-30;
2. The sequence similarity between any chain in our test set and any chain in our training set is no more than 40%.

These two assurances indicate that **there is no data leakage between our test set and AFM's training set**, and there is also no data leakage between our training set and test set.

Reviewer comment (Reproducibility):
At test time, what prompt do you provide to the model? It seems that the prompt is basically the assembly graph that model predicted. I don't see why prompt engineering is useful during training.

Author response:
**[Q1 The process of prompting]** Thanks for the question. We respectfully clarify that we do not introduce any additional information for prompting. At test time, the prompt model automatically constructs **a virtual path (graph)**. During pre-training, we have trained an excellent GNN model to evaluate the correctness of any input graph. Therefore, the pre-trained GNN model evaluates the correctness of the virtual graph constructed by the prompt model, i.e., the probability that two chains have an assembly action (link).

The prompt engineering **[re3,re4]** has been widely proven to narrow the gap between different data (or tasks) by increasing the model's flexibility. In our paper, we focus on the biggest challenge of the multimer structure prediction task: the gaps caused by the varied scales of multimers make it difficult to train a unified model that can be applied to all scales of multimers. **Therefore, prompting technique is naturally suitable for solving this challenge. The unified prompt model is designed to capture the common knowledge of multimers, which enables it to bridge all scales of multimers.**

Reviewer comment (Theory):
definition 1 is problematic. Because in real-world setting for docking, monomer's ground-truth structures could not be provided. So that the correctness could never be 1 in real-world setting.

Author response:
**[Cons. 1 Monomer's ground-truth structures]** We acknowledge and apologize for the ambiguity in the task objective stated under Definition 1. We will revise it as: *With the above definitions, our paper aims to predict assembly graphs (>>2 proteins chains) that maximize the TM-Scores, taking as inputs the residue sequences of proteins and pre-calculated dimer structures (=2 protein chains).*
**However, we respectfully clarify that pre-calculated dimer structures can be obtained from AlphaFold-Multimer without the need for providing ground-truth monomers.**

We strongly agree that the ground-truth monomer or ground-truth dimer structures should not be used in real-world setting. We respectfully emphasize that **our approach did not rely on ground-truth monomer to perform inference in real-world setting**.

|Setting|Inference inputs|Inference intermediate variables |Inference outputs|
|-|-|-|-|
|AFM Dimer|Amino acid sequences|Predicted docking path, Dimer structures predicted by AlphaFold-Multimer|Predicted multimer structure|
|GT Dimer|Amino acid sequences, Ground-truth dimer structures|Predicted docking path|Predicted multimer structure|

Indeed, in this work we propose a framework to predict the best possible protein multimers (>>2 protein chains), taking as inputs the pre-calcuated dimer structures (=2 protein chains). For the pre-calcuated dimer structures, we considered two settings in our **original experiments:** 
* The "AFM Dimer" setting does not involve ground-truth monomer nor ground-truth dimer structures. We predict dimers with AlphaFold-Multimer by inputting only amino acid sequences and our model also only takes amino acid sequences as inputs for predicting the docking path. This setting is applicable to real-world scenarios and consistent with the experimental setup of MoLPC **[re1]** (our baseline). 
* The "GT Dimer" setting may be less realistic under the application scenarios, but we respectfully think that it is not completely meaningless. The performance under this "GT Dimer" setting suggests the effectiveness of the docking paths predicted by ours and the MoLPC baseline.

Reviewer comment (Experiments):
the baselines are so weak. when taking ground-truth structure as input, HDock[2] and xTrimoDock[3] are strong baselines.

Author response:
**[Cons. 2 HDock and xTrimoDock]** We sincerely thank the reviewer's comment. **Firstly, we respectfully clarify once again that our "AFM Dimer" setting does not require any ground-truth monomers as input for real-world inference.** 
* **HDock and xTrimoDock may not be suitable for serving as the baselines.** We have checked HDock's local version and online server, and inquired the HDock team about the potential of performing multimer structure prediction (MSP). We find that HDock is currently unable to perform hetero-protein MSP tasks. We also checked all versions related to xTrimoDock **[re2,re3,re4]**, and even went through the supplementary materials in its NeurIPS'23 submission, but we could not find any available code. **Thus, we could not use HDock and xTrimoDock as baselines to directly predicting multimer structures.** 
* However, we greatly appreciate the suggestion for taking HDock into consideration and have added the "HDock Dimer" setting, where **we use HDock to pre-calculate dimer structures**.
* To further demonstrate that our method is not dependent on ground-truth monomers or ground-truth dimers, we also added the "ESMFold Dimer" setting, where **we use sequences to predict dimer structures with ESMFold**. Under all three settings, our method consistently and significantly outperforms the MoLPC and AlphaFold-Multimer baselines. 

**Overall, we sincerely appreciate the suggestion about HDock which helps yield surprisingly satisfactory experimental results. We consider HDock as a setting to provide pre-calculated dimer structures, rather than a baseline that can directly perform MSP.**

| Setting | AFM Dimer | AFM Dimer | HDock Dimer | HDock Dimer |ESMFold Dimer | ESMFold Dimer |
|---|---|---|---|---|---|---|
| Model | Mean TM-Score | Mean RMSD | Mean TM-Score | Mean RMSD | Mean TM-Score | Mean RMSD |
| AFM | 0.46 | 31.17 | 0.46 | 31.17 | 0.46 | 31.17 |
| MoLPC | 0.42 | 34.21 | 0.50 | 30.76 | 0.39 | 40.73|
| **Ours** | **0.51** | **27.77** | **0.54** | **25.39** | **0.49** | **28.34** |

Detailed experimental results will be shown in Table 9 in the Appendix of our revised manuscript.

Reviewer comment (Experiments):
it could be interesting if you can compare different baselines over different the number of chains. The performance could be reduced when increasing the number of chains.

Author response:
**[Cons. 3 Results over different chain numbers $N$]** Thank you for your valuable insights. Yes, this is important for validating the effectiveness of the proposed method and better understanding the challenges of the MSP task. To this end, we present the performance (mean TM-Score) of all baselines over different numbers of chains in the table below. **It is evident that as the chain number increases, the performance of all baselines across all three settings tends to decline.**

Setting: "AFM Dimer". Best performance is **bolded**.
| Chain Number | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10| overall |
|---|---|---|---|---|---|---|---|---|---|
| Multi-LZerD | 0.48 | 0.47 | 0.35 | 0.32 | 0.32 | 0.33 | 0.27 | 0.29 | 0.35 |
| RL-MLZerD | 0.45 | 0.44 | 0.34 | 0.37 | 0.38 | 0.32 | 0.27 | 0.24 | 0.36 |
| AFM | 0.68 | 0.53 | 0.52 | 0.45 | 0.42 | 0.44 | 0.38 | 0.38 | 0.46 |
| MoLPC | 0.62 | 0.53 | **0.56** | 0.43 | 0.36 | 0.37 | 0.30 | 0.28 | 0.42 |
| **Ours** | **0.71** | **0.66** | 0.54 | **0.50** | **0.46** | **0.46** | **0.45** | **0.40** | **0.51** |

Setting: "HDock Dimer"
| Chain Number | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10| overall |
|---|---|---|---|---|---|---|---|---|---|
| AFM | 0.68 | 0.53 | 0.52 | 0.45 | 0.42 | 0.44 | 0.38 | 0.38 | 0.46 |
| MoLPC | 0.66 | 0.59 | **0.60** | **0.51** | 0.47 | 0.42 | 0.35 | 0.36 | 0.50 |
| **Ours** | **0.74** | **0.69** | 0.56 | 0.48 | **0.49** | **0.46** | **0.44** | **0.42** | **0.54** |

Setting: "ESMFold Dimer"
| Chain Number | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10| overall |
|---|---|---|---|---|---|---|---|---|---|
| AFM | **0.68** | 0.53 | 0.52 | **0.45** | **0.42** | 0.44 | 0.38 | 0.38 | 0.46 |
| MoLPC | 0.52 | 0.50 | 0.41 | 0.39 | 0.36 | 0.27 | 0.33 | 0.33 | 0.39 |
| **Ours** | **0.68** | **0.60** | **0.55** | **0.45** | 0.39 | **0.46** | **0.42** | **0.42** | **0.49** |

We will add these meaningful results to our revised manuscript.

Reviewer comment (Novelty):
missing some related references: [1], [3], [4] [5]  
[1] Ghani, Usman, et.al. Improved docking of protein models by a combination of alphafold2 and cluspro.  
[2] Yumeng Yan, et.al. The HDOCK server for integrated protein–protein docking.  
[3] Yujie Luo, et.al. xTrimoDock: Rigid Protein Docking via Cross-Modal Representation Learning and Spectral Algorithm.  
[4] Mohamed Amine Ketata et.al. DIFFDOCK-PP: RIGID PROTEIN-PROTEIN DOCKING WITH DIFFUSION MODELS. use torsional diffusions to solve rigid protein docking, and the source code is released.  
[5] Lee-Shin Chu et.al. Flexible Protein-Protein Docking with a Multi-Track Iterative Transformer.

Author response:
**[Cons. 4 Missing references]** Thank you very much for the valuable references provided by the reviewer. We will add them to the revised manuscript PDF, which is helpful in improving the quality of our manuscript.

Reviewer comment (Experiments):
when comparing with AlphaFold-Multimer, do you input monomer's ground-truth structure as the template?

Author response:
**[Q1 The Alphafold-multimer baseline]** We respectfully clarify that our method is a **framework to predict the best possible protein multimers (>>2 protein chains) that takes as input dimer structure prediction methods (=2 protein chains)**. Among those dimer structure prediction methods, some ("HDock setting") will take ground-truth monomer structures as input and some ("AFM setting" and "ESMFold setting") will not. **However, under all three of these settings, our method can consistently outperform other baselines.**

Reviewer comment (Experiments):
how does your method perform when using predicted monomer structure? is the method robust?

Author response:
**[Q2 Use predicted monomers]** Thank you for the valuable suggestions. **To obtain pre-calculated dimer structures, the "AFM Dimer" and "ESMFold Dimer" settings both take amino acid sequences as input.** The experiments show that our method can work well with these dimer prediction methods and achieve considerable accuracy. 
Although the dimer prediction methods can affect the final accuracy of our method, our method outperforms AlphaFold-Multimer and MoLPC across all settings.