Thanks for the constructive comments!

1. Experimental Details

Regarding the training/test split, since the proposed model is a pretrain-finetuning model, we use different datasets for the two phases. We use the ZINC dataset (438610 small molecule samples as the training set) to pretrain the model (Sec. 3.1.1, lines 283-293 and Appendix E.1.1). We use the PROTAC-DB dataset during the fine-tuning phase. More specifically, 2943 PROTAC samples of the PROTAC-DB dataset are used for fine-tuning (including both the training and validation sets), while the remaining 327 PROTAC samples of the PROTAC-DB dataset are used as the test set (Sec. 3.1.1, lines 295-300 and Appendix E.1.2).

Regarding the structures sampled from ZINC, they can be viewed as quasi-PROTACs. We follow the existing molecular splitting method on the ZINC dataset for the linker design task in DiffLinker[1]. The molecules are fragmented by enumerating all double cuts of acyclic single bonds that are not within functional groups. The resulting splits are filtered by SA, PAINS, and other criteria. Please refer to Appendix E.1.1.

Regarding the data pre-processing, we do not use SMILES since we focus on 3D structure generation. The input should be conformers. We first generate 3D conformers using RDKit and define a reference structure for each molecule by selecting the lowest-energy conformations. This also follows the practice in [1]. Please refer to Appendix E.1.1.

Regarding the PROTAC data for fine-tuning, we split the PROTAC dataset into training (2943 samples) and test (327 samples) sets. The test set contains 365 unique warhead pairs not seen in the training set to evaluate generalization. The mismatch in numbers (327 PROTACs vs. 365 warheads) arises since some warheads are shared across PROTACs. We will revise it for clarity.

Regarding code, please refer to Appendix E.4, end of page 24.

[1] Ilia Igashov et al., Equivariant 3D-conditional diffusion model for molecular linker design.

2. Model Training and Evaluation

Regarding the computational cost for training and inference, please refer to Appendix E.4, lines 1305-1308. Our model can converge within 77 hours during the pre-training phase. For the fine-tuning phase, the guidance network can converge within 31 hours. For the sampling efficiency, DAD-PROTAC can sample one PROTAC linker within 29 minutes. It is efficient compared to other baselines in Figure 4(a).

Regarding the Link-INVENT, we do not include it as a baseline since it does not use the 3D molecular graphs as the input. However, we can transform the 3D graphs in the datasets to their corresponding SMILES strings or 2D graphs, and then use SMILES/2D graphs to pretrain and fine-tune the Link-INVENT. We then compare it with DAD-PROTAC below. The Link-INVENT performs well on the valid metric but performs quite badly on metrics like uniqueness and novelty. This is because it does not use 3D information and can only generate the linker in the restrained 2D space, making it difficult to generate unique or novel structures. We will cite the Link-INVENT paper[2] and compare its performance with ours.

[2] Jeff Guo et al., Link-INVENT: generative linker design with reinforcement learning. Digital Discovery, 2023.

3. Justification for the 3D Representation

If we only use SMILES or 2D graphs, atoms in the 3D space that are close in the molecule structure can be far away in the SMILES string/ 2D graphs. The 3D representation contains information about relative distance and orientation between the sub-structures, which is vital to successful PROTAC linker design[3]. While 2D representations capture connectivity, they ignore torsional flexibility and spatial constraints critical for PROTAC efficacy. Most SOTA methods(Delinker, DiffLinker, LinkerNet) all use 3D representations. We will add more discussions to the paper. Please check the comparison with Link-INVENT above.

[3] Fergus Imrie et al., Deep Generative Models for 3D Linker Design. Journal of Chemical Information and Modeling, 2020.

4. Benchmarking

Regarding conditional PROTAC linker generation, we leave it for future work (Sec. 4, lines 435-438).

Regarding the rediscovery benchmark, we include the recovery rate (Appendix E.3.4) as the evaluation metric in Tables 1 and 2.

Regarding sample efficiency, please refer to the response to Reviewer 3rte: Performance with different sizes of PROTAC datasets.

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Thank you for the constructive comments!

1. Figure 3

We will make Figure 3 clearer in the final version with fewer annotations and highlight more on how the score correction term is obtained. We will also explicitly annotate the input and output of two phases and each model component.

2. Pre-specified number of atoms

We follow most existing SOTA linker design methods like LinkerNet[1] and also pre-specify the number of atoms. This is because the prediction of the number of atoms in the linker should be solved via a deterministic model, while the generation of the linker (atom coordinates and bonds) should be solved via another generative model. The two steps of the linker design task are usually solved separately. We focus on the generation part of this task in this work.

For the prediction of the number of atoms in the linker, we can use a separately trained GNN to produce probabilities for the linker size. The input is still the molecule fragments. Later, when we ​​generate the linker’s structure, we first pre-specify the linker size based on the maximum predicted probabilities by this separately trained GNN and then use our proposed method in this paper. Since the linker size prediction step and the linker structure generation step are trained separately, no components (density ratio estimation and score correction) in the proposed DAD-PROTAC would be affected. We include the experimental results below. As we can see, the additional training of another neural network for linker size prediction may introduce more errors for the linker size, and thus the performance may degrade. We leave the joint training of both linker size prediction and linker structure generation for future work, as it is currently out of the scope of this work.

[1] Jiaqi Guan et al., LinkerNet: Fragment Poses and Linker Co-Design with 3D Equivariant Diffusion. In NeurIPS 2023.

3. Performance with different sizes of PROTAC datasets

For sample efficiency, we analyze the performance of the proposed DAD-PROTAC with different portions of the PROTAC dataset used during the fine-tuning phase in the table below. We reduce the PROTAC dataset size from 100% (full) to 50%, 25%, and 10%. We also add an extra 20% of samples from the PROTAC-DB 2.0 database as the extended dataset. This non-linear degradation suggests our approach is reasonably robust to limited PROTAC data for fine-tuning. Note that, even at 10% of the PROTAC dataset size, DAD-PROTAC can still outperform the baseline 3DLinker-Fine-tuning approach using 100% of the PROTAC data. For larger datasets, our preliminary experiments with additional data show diminishing returns with 1.2x our current dataset size, suggesting we are approaching the performance ceiling of the current architecture. We will add these results and include a learning curve figure in the final version that visualizes these results for sample efficiency analysis.

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Thank you for the constructive comments!

1. Errors for large $t$

In Eq.(16), we train a time-dependent classifier $W(X_t^L,t)$ with samples from potentially all steps $t$ jointly, instead of training different classifiers $W_t(X_t^L)$ for each step $t$ individually. This means that the training set has both easy samples (t is small) and hard samples (t is large). This will mitigate the issue of differentiating the samples from two domains when t is large. Besides, we can easily add more samples (with larger $m$ and $n$) to the training set to further mitigate this issue. We also compare the classification performance to show the performance of this trained classifier on different groups of $t$ (based on its range) on an additional test set below. This table shows that the model’s performance drop for large $t$ is acceptable. The further incorporation of focal loss to Eq.(16) by putting more focus on hard samples ($t$ is large) is not necessary. We will add it to the ablation study in the final version.

2. Model cheats by counting the number of atoms

The number of atoms is only one of the differences between PROTACs and small molecules. Please refer to Figure 8 of the paper to see other differences, like LogP, which are more likely to be dependent on the distributions of atom coordinates. Therefore, we train the classifier on atom coordinates $X$ in Eq.(16) to encode all potential distribution differences in their chemical space. We specifically design our classifier to prevent this shortcut. We use original features like $X$ as the input rather than global molecular properties like the number of atoms. We validate this by testing the classifier on a separate dataset containing molecular structures with the same atom counts but from different domains (PROTACs and small molecules). The results in the table below confirm that classification accuracy on test samples with the same atom counts remains consistent with the overall results. If we only use atom counts as input, the classification performance would drop significantly.

3. Error propagation and Monte Carlo estimation

From the results in the last point above, we can see that the classification error in this step is quite small, and this alleviates the error propagation issue in the first place. We further find that using MC simulation to estimate the score correction term directly may get slightly better performance, but it is computationally prohibitive. The extended ablation study from Table 2 is summarized below. “direct score correction approximation” refers to the model where we only run MC simulations on a few samples $X_t^L$ to obtain the corresponding score correction terms in Eq.(11) and then train another neural network to learn to approximate this score correction term. “Density ratio estimation via clean samples” refers to the model where we only use clean samples to train the classifier in Eq.(16) (namely, set t =0). More discussion is found in Sec 3.3 in the paper. From the results in the table below, MC simulation suffers from high computational cost, our current design keeps a good balance between effectiveness and efficiency.

4. Other methods for fine-tuning diffusion models

LoRA and DPO are promising for parameter-efficient fine-tuning. However, they assume the source and target domains share a similar latent structure, which is invalid here due to the significant chemical differences between small molecules and PROTACs (Figure 8 in the paper). Our method explicitly models the domain shift via density ratios estimation, which is specifically designed for the linker design task. That said, integrating LoRA-style methods into our framework (e.g., for the correction term) could further improve efficiency. We leave it as future work since it is out of the scope of this paper.

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