EnzymeFlow: Generating Reaction-specific Enzyme Catalytic Pockets through Flow Matching and Co-Evolutionary Dynamics
enzyme design; flow model; protein design; protein evolution
## A1:

#### To further demonstrate the functional validity of EnzymeFlow-generated pockets, we have included additional metrics such as optimal pH, turnover number, and substrate specificity. These metrics indicate that EnzymeFlow-generated pockets align closely with baseline-generated pockets, further supporting the model's capacity to generate functionally relevant structures.
```
|                   |                    | pH   | kcat | km   |
| ----------------- | ------------------ | ---- | ---- | ---- |
| Pocket Evaluation |                    | mean | mean | mean |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC1               | ground truth       | 7.86 | 2.86 | 0.33 |
|                   | EnzymeFlow-abation | 8.40 | 1.08 | 0.28 |
|                   | RFDiffusionAA      | 8.85 | 2.17 | 0.24 |
|                   | EnzymeFlow         | 7.54 | 2.45 | 0.37 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC2               | ground truth       | 7.68 | 1.93 | 0.31 |
|                   | EnzymeFlow-abation | 8.48 | 0.72 | 0.20 |
|                   | RFDiffusionAA      | 8.89 | 1.55 | 0.19 |
|                   | EnzymeFlow         | 7.58 | 2.03 | 0.27 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC3               | ground truth       | 7.49 | 2.18 | 0.09 |
|                   | EnzymeFlow-abation | 8.56 | 0.79 | 0.08 |
|                   | RFDiffusionAA      | 8.79 | 1.36 | 0.08 |
|                   | EnzymeFlow         | 7.64 | 2.49 | 0.08 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC4               | ground truth       | 7.82 | 1.57 | 0.09 |
|                   | EnzymeFlow-abation | 8.48 | 0.78 | 0.10 |
|                   | RFDiffusionAA      | 8.98 | 2.19 | 0.10 |
|                   | EnzymeFlow         | 7.40 | 2.03 | 0.09 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC5               | ground truth       | 7.10 | 2.71 | 0.14 |
|                   | EnzymeFlow-abation | 8.32 | 0.95 | 0.12 |
|                   | RFDiffusionAA      | 8.88 | 1.18 | 0.14 |
|                   | EnzymeFlow         | 7.47 | 2.00 | 0.14 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC6               | ground truth       | 7.63 | 2.03 | 0.47 |
|                   | EnzymeFlow-abation | 8.44 | 0.84 | 0.27 |
|                   | RFDiffusionAA      | 8.98 | 1.99 | 0.33 |
|                   | EnzymeFlow         | 7.43 | 2.92 | 0.46 |
```

## A2:

#### The decision not to integrate MSA and EC class features into the backbone embedding before entering IPA is based on prior experience with AlphaFold models, where MSA integration significantly slows inference. In AlphaFold, MSAs need to be pre-computed during sampling, resulting in slower inference times. To mitigate this, we opted to integrate MSA and EC class features *after* the IPA embeddings, using a cross-attention mechanism to align the MSA, EC features, and IPA embeddings. This approach allows MSAs and EC classes to guide gradient updates during training while avoiding the need to pre-compute MSAs at inference, thus improving efficiency. Our goal is to maintain effective guidance from MSA and EC class information without sacrificing inference speed.

## A3:

#### In Section 5.2 and Figure 8, we explicitly mention ''EnzymeFlow with functions annotated post hoc by CLEAN'', to fairly compare with others annotated post hoc by CLEAN.

## A4:

#### Although ec_embed does not directly enter IPA, it interacts with the IPA embeddings through a cross-attention layer applied after IPA. This cross-attention layer enables the model to conditionally update the IPA-derived embeddings based on the EC class information. By doing so, the EC class feature can guide structural adjustments in line with the target EC class.

## A5:

#### For DEPACT and PocketGEN, we directly adopt their models provided in GitHub. For RFDiffusionAA, we also directly adopt their models provided in GitHub, setting the diffusion steps as 100 (as what they used in training), and predict the sequences post hoc using LigandMPNN with 0.30A Gaussian noise (they suggested we should predict the sequences using inverse folding model post hoc). In Section 5, we also explicitly mention ''We train PocketFlow on EnzymeFill without fixing the backbones.'', as the same setting as we did for training EnzymeFlow, to fairly compare the model.
Answers to Questions Part2
#### Thanks for the feedback. We have been conducting more (a lot) experiments in the past month to get ready for this rebuttal, and aim to address the weaknesses and questions, to demonstrate model’s robustness in designing catalytic pockets.

#### We also agree that in silico evaluations in enzyme pocket design are not enough. We have some collaborations that are working on wet-lab experiment for this task. Our focus on catalytic pocket design rather than complete enzyme design stems from both the scientific challenges and strategic advantages of this approach. Designing a full enzyme from scratch is an extremely complex task. Focusing on catalytic pockets first allows us to solve a foundational aspect of enzyme design by establishing effective reaction sites, which are essential for catalysis. And EnzymeFlow is our first model, we have inpainting, screening, and other related models being developed, aiming at working to enzyme design in silico at some point. And with better screening and filtering, we can send the designed pockets and enzymes to wet-lab. We aim to contribute to advancing well-being through algorithms.


## A1:

#### We trained an ablation model that incorporates only reaction conditions, but excludes additional elements such as co-MSAs and EC conditions. This model, which we refer to as EnzymeFlow-ablation, was trained the same as we did for EnzymeFlow. The performance of the EnzymeFlow-ablation model is compared to the full EnzymeFlow model, which incorporates co-MSAs, EC conditions, and reaction conditioning. The results show that the EnzymeFlow model outperforms the EnzymeFlow-ablation model, as evidenced by the following metrics: lower RMSD, higher alignment scores, lower embedding distance (we use ESM3 encoding for pocket sequences and structures)
```
|                   |                    | rmsd | rmsd | rmsd | tm   | tm   | tm   | Dist  | Dist  | Dist  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| Pocket Evaluation |                    | Top1 | Top3 | Mean | Top1 | Top3 | Mean | Top1  | Top3  | Mean  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC1               | EnzymeFlow-abation | 3.76 | 3.90 | 4.19 | 0.29 | 0.28 | 0.26 | 19.82 | 20.29 | 21.48 |
|                   | RFDiffusionAA      | 3.71 | 3.82 | 4.18 | 0.28 | 0.27 | 0.25 | 7.33  | 8.05  | 9.28  |
|                   | EnzymeFlow         | 1.88 | 2.09 | 2.41 | 0.67 | 0.65 | 0.59 | 0.25  | 0.58  | 1.54  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC2               | EnzymeFlow-abation | 4.02 | 4.19 | 4.35 | 0.23 | 0.23 | 0.21 | 50.31 | 52.33 | 54.15 |
|                   | RFDiffusionAA      | 3.47 | 3.78 | 4.17 | 0.27 | 0.27 | 0.25 | 26.91 | 27.84 | 30.44 |
|                   | EnzymeFlow         | 3.65 | 3.80 | 4.09 | 0.33 | 0.31 | 0.28 | 1.03  | 1.85  | 4.40  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC3               | EnzymeFlow-abation | 3.46 | 3.69 | 4.12 | 0.31 | 0.29 | 0.27 | 9.84  | 10.02 | 11.14 |
|                   | RFDiffusionAA      | 3.25 | 3.50 | 3.96 | 0.31 | 0.30 | 0.27 | 10.83 | 10.96 | 12.22 |
|                   | EnzymeFlow         | 3.18 | 3.32 | 3.84 | 0.39 | 0.36 | 0.32 | 0.42  | 1.08  | 2.19  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC4               | EnzymeFlow-abation | 3.31 | 3.48 | 3.91 | 0.32 | 0.30 | 0.27 | 18.02 | 18.56 | 19.96 |
|                   | RFDiffusionAA      | 3.00 | 3.29 | 3.79 | 0.30 | 0.29 | 0.27 | 14.62 | 15.62 | 17.39 |
|                   | EnzymeFlow         | 2.58 | 2.73 | 2.96 | 0.56 | 0.54 | 0.51 | 0.50  | 1.07  | 2.43  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC5               | EnzymeFlow-abation | 3.48 | 3.66 | 4.06 | 0.29 | 0.28 | 0.26 | 13.71 | 14.01 | 14.81 |
|                   | RFDiffusionAA      | 3.39 | 3.61 | 3.98 | 0.31 | 0.29 | 0.26 | 7.83  | 8.23  | 8.93  |
|                   | EnzymeFlow         | 2.87 | 3.18 | 3.62 | 0.44 | 0.43 | 0.39 | 0.74  | 1.07  | 1.78  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC6               | EnzymeFlow-abation | 3.78 | 3.89 | 4.33 | 0.29 | 0.27 | 0.26 | 21.00 | 22.87 | 24.19 |
|                   | RFDiffusionAA      | 3.43 | 3.69 | 4.12 | 0.30 | 0.29 | 0.26 | 19.08 | 19.73 | 21.21 |
|                   | EnzymeFlow         | 3.14 | 3.32 | 3.73 | 0.43 | 0.40 | 0.36 | 1.23  | 1.45  | 2.56  |
```
Answers to Questions Part1
## A1:

#### Second, we trained an ablation model that incorporates only reaction conditions, but excludes additional elements such as co-MSAs and EC conditions. This model, which we refer to as EnzymeFlow-ablation, was trained the same as we did for EnzymeFlow. The performance of the EnzymeFlow-ablation model is compared to the full EnzymeFlow model, which incorporates co-MSAs, EC conditions, and reaction conditioning. The results show that the EnzymeFlow model outperforms the EnzymeFlow-ablation model, as evidenced by the following metrics: lower RMSD, higher alignment scores, lower embedding distance (we use ESM3 encoding for pocket sequences and structures)
```
|                   |                    | rmsd | rmsd | rmsd | tm   | tm   | tm   | Dist  | Dist  | Dist  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| Pocket Evaluation |                    | Top1 | Top3 | Mean | Top1 | Top3 | Mean | Top1  | Top3  | Mean  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC1               | EnzymeFlow-abation | 3.76 | 3.90 | 4.19 | 0.29 | 0.28 | 0.26 | 19.82 | 20.29 | 21.48 |
|                   | RFDiffusionAA      | 3.71 | 3.82 | 4.18 | 0.28 | 0.27 | 0.25 | 7.33  | 8.05  | 9.28  |
|                   | EnzymeFlow         | 1.88 | 2.09 | 2.41 | 0.67 | 0.65 | 0.59 | 0.25  | 0.58  | 1.54  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC2               | EnzymeFlow-abation | 4.02 | 4.19 | 4.35 | 0.23 | 0.23 | 0.21 | 50.31 | 52.33 | 54.15 |
|                   | RFDiffusionAA      | 3.47 | 3.78 | 4.17 | 0.27 | 0.27 | 0.25 | 26.91 | 27.84 | 30.44 |
|                   | EnzymeFlow         | 3.65 | 3.80 | 4.09 | 0.33 | 0.31 | 0.28 | 1.03  | 1.85  | 4.40  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC3               | EnzymeFlow-abation | 3.46 | 3.69 | 4.12 | 0.31 | 0.29 | 0.27 | 9.84  | 10.02 | 11.14 |
|                   | RFDiffusionAA      | 3.25 | 3.50 | 3.96 | 0.31 | 0.30 | 0.27 | 10.83 | 10.96 | 12.22 |
|                   | EnzymeFlow         | 3.18 | 3.32 | 3.84 | 0.39 | 0.36 | 0.32 | 0.42  | 1.08  | 2.19  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC4               | EnzymeFlow-abation | 3.31 | 3.48 | 3.91 | 0.32 | 0.30 | 0.27 | 18.02 | 18.56 | 19.96 |
|                   | RFDiffusionAA      | 3.00 | 3.29 | 3.79 | 0.30 | 0.29 | 0.27 | 14.62 | 15.62 | 17.39 |
|                   | EnzymeFlow         | 2.58 | 2.73 | 2.96 | 0.56 | 0.54 | 0.51 | 0.50  | 1.07  | 2.43  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC5               | EnzymeFlow-abation | 3.48 | 3.66 | 4.06 | 0.29 | 0.28 | 0.26 | 13.71 | 14.01 | 14.81 |
|                   | RFDiffusionAA      | 3.39 | 3.61 | 3.98 | 0.31 | 0.29 | 0.26 | 7.83  | 8.23  | 8.93  |
|                   | EnzymeFlow         | 2.87 | 3.18 | 3.62 | 0.44 | 0.43 | 0.39 | 0.74  | 1.07  | 1.78  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC6               | EnzymeFlow-abation | 3.78 | 3.89 | 4.33 | 0.29 | 0.27 | 0.26 | 21.00 | 22.87 | 24.19 |
|                   | RFDiffusionAA      | 3.43 | 3.69 | 4.12 | 0.30 | 0.29 | 0.26 | 19.08 | 19.73 | 21.21 |
|                   | EnzymeFlow         | 3.14 | 3.32 | 3.73 | 0.43 | 0.40 | 0.36 | 1.23  | 1.45  | 2.56  |

```

#### Third, thank you for the suggestion. Accurately predicting EC classes is indeed challenging for this generative task. While incorporating EC conditions in generation has shown improvements in backbone structure quality, accurately predicting EC function remains a difficult aspect. We are actively exploring Reinforcement Learning with Human Feedback (RLHF) to enhance generation; specifically, we are using CLEAN as an oracle for EC prediction as part of the reward mechanism. This approach aims to further guide the model to incorporate EC information both implicitly and explicitly, helping to improve accuracy in EC function prediction.
Answers to Questions Part2
## A1: 

#### First, [1] suggests relationships between enzyme commissions, enzyme functions, and catalytic mechanisms. Meanwhile, we also agree with what you suggested, only observing enzyme commission numbers can limit to examining the enzyme catalytic ability. To further demonstrate the functional validity of EnzymeFlow-generated pockets, we have included additional metrics such as optimal pH, turnover number, and substrate specificity. These metrics indicate that EnzymeFlow-generated pockets align closely with baseline-generated pockets, further supporting the model's capacity to generate functionally relevant structures. 
```
## Enzyme-ablation denotes an ablation model without coMSAs and EC guidance in training.
|                   |                    | pH   | kcat | km   |
| ----------------- | ------------------ | ---- | ---- | ---- |
| Pocket Evaluation |                    | mean | mean | mean |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC1               | ground truth       | 7.86 | 2.86 | 0.33 |
|                   | EnzymeFlow-abation | 8.40 | 1.08 | 0.28 |
|                   | RFDiffusionAA      | 8.85 | 2.17 | 0.24 |
|                   | EnzymeFlow         | 7.54 | 2.45 | 0.37 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC2               | ground truth       | 7.68 | 1.93 | 0.31 |
|                   | EnzymeFlow-abation | 8.48 | 0.72 | 0.20 |
|                   | RFDiffusionAA      | 8.89 | 1.55 | 0.19 |
|                   | EnzymeFlow         | 7.58 | 2.03 | 0.27 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC3               | ground truth       | 7.49 | 2.18 | 0.09 |
|                   | EnzymeFlow-abation | 8.56 | 0.79 | 0.08 |
|                   | RFDiffusionAA      | 8.79 | 1.36 | 0.08 |
|                   | EnzymeFlow         | 7.64 | 2.49 | 0.08 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC4               | ground truth       | 7.82 | 1.57 | 0.09 |
|                   | EnzymeFlow-abation | 8.48 | 0.78 | 0.10 |
|                   | RFDiffusionAA      | 8.98 | 2.19 | 0.10 |
|                   | EnzymeFlow         | 7.40 | 2.03 | 0.09 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC5               | ground truth       | 7.10 | 2.71 | 0.14 |
|                   | EnzymeFlow-abation | 8.32 | 0.95 | 0.12 |
|                   | RFDiffusionAA      | 8.88 | 1.18 | 0.14 |
|                   | EnzymeFlow         | 7.47 | 2.00 | 0.14 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC6               | ground truth       | 7.63 | 2.03 | 0.47 |
|                   | EnzymeFlow-abation | 8.44 | 0.84 | 0.27 |
|                   | RFDiffusionAA      | 8.98 | 1.99 | 0.33 |
|                   | EnzymeFlow         | 7.43 | 2.92 | 0.46 |
```

##### [1] Cuesta, S.M., Rahman, S.A., Furnham, N. and Thornton, J.M., 2015. The classification and evolution of enzyme function. Biophysical journal, 109(6), pp.1082-1086.
Answers to Questions Part1
## A3:
#### We also agree with what you suggested, only observing enzyme commission numbers can limit to examining the enzyme catalytic ability. To further demonstrate the functional validity of EnzymeFlow-generated pockets, we have included additional metrics such as optimal pH, turnover number, and substrate specificity. These metrics indicate that EnzymeFlow-generated pockets align closely with baseline-generated pockets, further supporting the model's capacity to generate functionally relevant structures. These are newly conducted experiments, where pockets for RFDiffusionAA are extracted from a whole protein to compare to those generated by EnzymeFlow.

```
|                   |                    | pH   | kcat | km   |
| ----------------- | ------------------ | ---- | ---- | ---- |
| Pocket Evaluation |                    | mean | mean | mean |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC1               | ground truth       | 7.86 | 2.86 | 0.33 |
|                   | RFDiffusionAA      | 8.85 | 2.17 | 0.24 |
|                   | EnzymeFlow         | 7.54 | 2.45 | 0.37 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC2               | ground truth       | 7.68 | 1.93 | 0.31 |
|                   | RFDiffusionAA      | 8.89 | 1.55 | 0.19 |
|                   | EnzymeFlow         | 7.58 | 2.03 | 0.27 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC3               | ground truth       | 7.49 | 2.18 | 0.09 |
|                   | RFDiffusionAA      | 8.79 | 1.36 | 0.08 |
|                   | EnzymeFlow         | 7.64 | 2.49 | 0.08 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC4               | ground truth       | 7.82 | 1.57 | 0.09 |
|                   | RFDiffusionAA      | 8.98 | 2.19 | 0.10 |
|                   | EnzymeFlow         | 7.40 | 2.03 | 0.09 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC5               | ground truth       | 7.10 | 2.71 | 0.14 |
|                   | RFDiffusionAA      | 8.88 | 1.18 | 0.14 |
|                   | EnzymeFlow         | 7.47 | 2.00 | 0.14 |
| ----------------- | ------------------ | ---- | ---- | ---- |
| EC6               | ground truth       | 7.63 | 2.03 | 0.47 |
|                   | RFDiffusionAA      | 8.98 | 1.99 | 0.33 |
|                   | EnzymeFlow         | 7.43 | 2.92 | 0.46 |

```

## A4: 
#### Indeed, our methodology does not rely on binding structures but instead utilizes a ligand transplantation approach with PDB-REDO. This computational chemistry tool is specifically used for us to identify catalytic regions, not conventional binding sites, to reflect the distinct requirements of catalysis. Unlike binding structures, which typically focus on tight binding affinity, our approach identifies catalytic regions where enzymes facilitate reaction processes. Notably, tight binding between an enzyme and its substrate can actually reduce catalytic efficiency, as it may hinder substrate turnover. Instead, catalytic regions are often characterized by flexible, transient interactions that allow for substrate transformation without the constraints of a rigid binding affinity. By targeting these regions, we aim to capture the enzyme's catalytic functionality rather than binding properties, which aligns more closely with the dynamic nature of enzymatic catalysis. We acknowledge that incorporating evaluations from experimental, non-synthetic datasets would further strengthen validation and help mitigate any residual biases. This is a valuable direction, and we are exploring additional validations with experimental datasets to ensure robustness across diverse catalytic environments.
Answers to Weaknesses Part3
## A2:

#### We agree that capturing co-evolutionary information between enzymes and reactions is a challenging yet promising area. Currently, SMILES-based alignment offers a feasible approach, though we acknowledge its limitations, as small molecular changes can indeed create large variations in SMILES. However, to our knowledge, there are no better alternatives for aligning both enzyme and reaction (molecule) evolution at this time, especially given the differences in their modalities. The sensitivity of sequence alignments underscores this issue: SMILES strings often vary significantly among proteins within the same MSA. This sensitivity reflects the diversity of enzyme-catalyzed reactions, where two similar enzymes may catalyze distinct reactions. Additionally, the enzyme space is substantially larger than the reaction space, amplifying the divergence in SMILES even among enzymes within the same MSA. 

#### Looking forward, we aim to address this with our proposed coMSAformer, inspired by MSAformer, to facilitate few-shot experiments on this topic. This approach could help improve the alignment of these evolutionary modalities and overcome some limitations of SMILES-based methods, which we agree is a fascinating area for further exploration.

#### In addition we show more experiments stating the importance of having co-MSAs in modeling. Initially, we trained EnzymeFlow on 32-residue pockets, which provided limited structural and functional signal strength compared to using the full enzyme backbone. To address this, we re-trained EnzymeFlow on a dataset of 64-residue pockets, and this change was also applied to baseline models for a fair comparison. With this approach, we observed notable improvements: the generated pockets showed reduced RMSD, improved structural alignment scores, and lower embedding distances (using ESM3 encoding for pocket sequences and structures).  These new results demonstrate that the inclusion of co-MSAs and EC conditions provides significant improvements in the generation of enzyme catalytic pockets, highlighting the importance of these additional elements in improving both the structural and functional accuracy of the model.
```
## Enzyme-ablation denotes an ablation model without coMSAs and EC guidance in training.
|                   |                    | rmsd | rmsd | rmsd | tm   | tm   | tm   | Dist  | Dist  | Dist  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| Pocket Evaluation |                    | Top1 | Top3 | Mean | Top1 | Top3 | Mean | Top1  | Top3  | Mean  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC1               | EnzymeFlow-abation | 3.76 | 3.90 | 4.19 | 0.29 | 0.28 | 0.26 | 19.82 | 20.29 | 21.48 |
|                   | EnzymeFlow         | 1.88 | 2.09 | 2.41 | 0.67 | 0.65 | 0.59 | 0.25  | 0.58  | 1.54  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC2               | EnzymeFlow-abation | 4.02 | 4.19 | 4.35 | 0.23 | 0.23 | 0.21 | 50.31 | 52.33 | 54.15 |
|                   | EnzymeFlow         | 3.65 | 3.80 | 4.09 | 0.33 | 0.31 | 0.28 | 1.03  | 1.85  | 4.40  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC3               | EnzymeFlow-abation | 3.46 | 3.69 | 4.12 | 0.31 | 0.29 | 0.27 | 9.84  | 10.02 | 11.14 |
|                   | EnzymeFlow         | 3.18 | 3.32 | 3.84 | 0.39 | 0.36 | 0.32 | 0.42  | 1.08  | 2.19  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC4               | EnzymeFlow-abation | 3.31 | 3.48 | 3.91 | 0.32 | 0.30 | 0.27 | 18.02 | 18.56 | 19.96 |
|                   | EnzymeFlow         | 2.58 | 2.73 | 2.96 | 0.56 | 0.54 | 0.51 | 0.50  | 1.07  | 2.43  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC5               | EnzymeFlow-abation | 3.48 | 3.66 | 4.06 | 0.29 | 0.28 | 0.26 | 13.71 | 14.01 | 14.81 |
|                   | EnzymeFlow         | 2.87 | 3.18 | 3.62 | 0.44 | 0.43 | 0.39 | 0.74  | 1.07  | 1.78  |
| ----------------- | ------------------ | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC6               | EnzymeFlow-abation | 3.78 | 3.89 | 4.33 | 0.29 | 0.27 | 0.26 | 21.00 | 22.87 | 24.19 |
|                   | EnzymeFlow         | 3.14 | 3.32 | 3.73 | 0.43 | 0.40 | 0.36 | 1.23  | 1.45  | 2.56  |
```
Answers to Weaknesses Part2
#### Thanks for the feedback. We have been conducting more (a lot) experiments in the past month to get ready for this rebuttal, and aim to address the weaknesses and questions, to demonstrate model’s robustness in designing catalytic pockets:


## A1:  
#### Specifically, we model the changes  from substrates to products using co-MSAs and atom-to-atom cross-attention, which we believe can capture dynamic changes in the reaction process. Previous work, such as ReactZyme [2], has demonstrated that the atom-to-atom cross-attention mechanism can effectively model the changes between substrates and products. While this is not an explicit dynamic model like CLIPzyme [1], which uses transition graphs to model reaction dynamics, ReactZyme’s use of the cross-attention mechanism has shown superior performance in implicitly capturing these dynamics compared to explicit transition graph models. In addition, we evaluate the model's ability to implicitly learn dynamics by measuring substrate specificity (Km) and turnover number (Kcat), and our results indicate that the model produces substrate specificity values close to the ground truth. 
```
## Enzyme-ablation denotes an ablation model without coMSAs and EC guidance in training.
|                   |                    | kcat | km   |
| ----------------- | ------------------ | ---- | ---- |
| Pocket Evaluation |                    | mean | mean |
| ----------------- | ------------------ | ---- | ---- |
| EC1               | ground truth       | 2.86 | 0.33 |
|                   | EnzymeFlow-abation | 1.08 | 0.28 |
|                   | RFDiffusionAA      | 2.17 | 0.24 |
|                   | EnzymeFlow         | 2.45 | 0.37 |
| ----------------- | ------------------ | ---- | ---- |
| EC2               | ground truth       | 1.93 | 0.31 |
|                   | EnzymeFlow-abation | 0.72 | 0.20 |
|                   | RFDiffusionAA      | 1.55 | 0.19 |
|                   | EnzymeFlow         | 2.03 | 0.27 |
| ----------------- | ------------------ | ---- | ---- |
| EC3               | ground truth       | 2.18 | 0.09 |
|                   | EnzymeFlow-abation | 0.79 | 0.08 |
|                   | RFDiffusionAA      | 1.36 | 0.08 |
|                   | EnzymeFlow         | 2.49 | 0.08 |
| ----------------- | ------------------ | ---- | ---- |
| EC4               | ground truth       | 1.57 | 0.09 |
|                   | EnzymeFlow-abation | 0.78 | 0.10 |
|                   | RFDiffusionAA      | 2.19 | 0.10 |
|                   | EnzymeFlow         | 2.03 | 0.09 |
| ----------------- | ------------------ | ---- | ---- |
| EC5               | ground truth       | 2.71 | 0.14 |
|                   | EnzymeFlow-abation | 0.95 | 0.12 |
|                   | RFDiffusionAA      | 1.18 | 0.14 |
|                   | EnzymeFlow         | 2.00 | 0.14 |
| ----------------- | ------------------ | ---- | ---- |
| EC6               | ground truth       | 2.03 | 0.47 |
|                   | EnzymeFlow-abation | 0.84 | 0.27 |
|                   | RFDiffusionAA      | 1.99 | 0.33 |
|                   | EnzymeFlow         | 2.92 | 0.46 |
```
#### This suggests that the model is effectively capturing not only static interactions but also the dynamic aspects of enzyme catalysis, even though these dynamics are not explicitly modeled. We acknowledge that the field of using AI to model reaction transitions and chemical dynamics is still emerging, and as part of our ongoing work, we are exploring additional methods to explicitly model these transitions. For example, we are investigating the identification of reaction centers and assigning atomic weights to regions of the substrate involved in the reaction, with atoms in the reaction center receiving higher attention during the transition. We believe that combining these approaches with attention mechanisms could allow our model to implicitly and more explicitly learn dynamic processes in enzymatic reactions. In summary, while we currently rely on implicit methods (such as atom-to-atom cross-attention) to model dynamic transitions, we are actively exploring ways to explicitly incorporate dynamic changes in the future. The current evidence from our results, particularly in terms of substrate specificity, suggests that the model can effectively capture important aspects of enzyme dynamics.


##### [1] Mikhael, P.G., Chinn, I. and Barzilay, R., 2024. CLIPZyme: Reaction-Conditioned Virtual Screening of Enzymes. arXiv preprint arXiv:2402.06748.
##### [2] Hua, C., Zhong, B., Luan, S., Hong, L., Wolf, G., Precup, D. and Zheng, S., 2024. Reactzyme: A benchmark for enzyme-reaction prediction. arXiv preprint arXiv:2408.13659.
Answers to Weaknesses Part1
## A2 & A3
```
|                   |               | rmsd | rmsd | rmsd | tm   | tm   | tm   | Dist  | Dist  | Dist  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| Enzyme Evaluation |               | Top1 | Top3 | Mean | Top1 | Top3 | Mean | Top1  | Top3  | Mean  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC1               | RFDiffusionAA | 4.46 | 4.76 | 5.36 | 0.48 | 0.44 | 0.38 | 22.38 | 23.79 | 26.89 |
|                   | EnzymeFlow    | 4.13 | 4.36 | 4.83 | 0.62 | 0.58 | 0.53 | 2.41  | 2.92  | 5.49  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC2               | RFDiffusionAA | 4.88 | 5.08 | 5.58 | 0.43 | 0.42 | 0.38 | 5.42  | 6.31  | 8.91  |
|                   | EnzymeFlow    | 5.27 | 5.45 | 5.99 | 0.37 | 0.36 | 0.32 | 5.15  | 6.25  | 8.43  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC3               | RFDiffusionAA | 5.13 | 5.28 | 5.71 | 0.38 | 0.36 | 0.33 | 4.95  | 6.74  | 10.59 |
|                   | EnzymeFlow    | 5.08 | 5.26 | 5.76 | 0.38 | 0.38 | 0.33 | 10.46 | 11.74 | 15.06 |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC4               | RFDiffusionAA | 4.49 | 4.68 | 5.25 | 0.45 | 0.42 | 0.37 | 65.60 | 69.49 | 78.31 |
|                   | EnzymeFlow    | 4.02 | 4.15 | 4.59 | 0.57 | 0.55 | 0.52 | 9.61  | 9.85  | 10.49 |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC5               | RFDiffusionAA | 4.48 | 4.71 | 5.22 | 0.50 | 0.46 | 0.40 | 2.87  | 3.66  | 5.31  |
|                   | EnzymeFlow    | 5.02 | 5.32 | 5.80 | 0.43 | 0.41 | 0.39 | 4.58  | 5.20  | 7.14  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC6               | RFDiffusionAA | 4.53 | 4.89 | 5.50 | 0.45 | 0.43 | 0.38 | 19.38 | 20.76 | 25.87 |
|                   | EnzymeFlow    | 5.76 | 6.00 | 6.42 | 0.34 | 0.32 | 0.28 | 12.24 | 14.73 | 16.87 |
```

## A4:
#### Thank you for the question. Indeed, the analysis on EC (Enzyme Commission) classes does relate to substrate specificity, as EC classification is based on the types of reactions an enzyme catalyzes, which is directly influenced by substrate class. By examining performance across different EC classes, we effectively cover a range of substrate types and provide insight into how EnzymeFlow performs with diverse substrate classes.
Answers to Questions Part3
## A2 & A3:
#### In the past months, we have developed an inpainting model on top of the pocket design model for full enzyme design. The inpainting model is trained on EnzymeFill to satisfy this task. Initially, we trained EnzymeFlow on 32-residue pockets, which provided limited structural and functional signal strength compared to using the full enzyme backbone. To address this, we re-trained EnzymeFlow on a dataset of 64-residue pockets. The inpainting is designed to  inpaint the catalytic pockets to full enzyme structures as you are expecting to see. And the entire framework works by generating pockets from chemical reactions first, then generating enzymes from pockets.  And for comparison to RFDiffusionAA, we extract the pocket from a whole protein generated by RFDiffusionAA and compare it with EnzymeFlow. We should pocket- and enzyme-level evaluations.

With this approach, we observed notable improvements: the generated pockets and full enzymes showed reduced RMSD, improved structural alignment scores, and lower embedding distances (using ESM3 encoding for pocket and enzyme sequences and structures). These enhancements suggest that our model-generated ones more closely resemble real catalytic sites in structure and sequence features, both critical indicators of potential catalytic activity.
```
|                   |               | rmsd | rmsd | rmsd | tm   | tm   | tm   | Dist  | Dist  | Dist  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| Pocket Evaluation |               | Top1 | Top3 | Mean | Top1 | Top3 | Mean | Top1  | Top3  | Mean  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC1               | RFDiffusionAA | 3.71 | 3.82 | 4.18 | 0.28 | 0.27 | 0.25 | 7.33  | 8.05  | 9.28  |
|                   | EnzymeFlow    | 1.88 | 2.09 | 2.41 | 0.67 | 0.65 | 0.59 | 0.25  | 0.58  | 1.54  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC2               | RFDiffusionAA | 3.47 | 3.78 | 4.17 | 0.27 | 0.27 | 0.25 | 26.91 | 27.84 | 30.44 |
|                   | EnzymeFlow    | 3.65 | 3.80 | 4.09 | 0.33 | 0.31 | 0.28 | 1.03  | 1.85  | 4.40  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC3               | RFDiffusionAA | 3.25 | 3.50 | 3.96 | 0.31 | 0.30 | 0.27 | 10.83 | 10.96 | 12.22 |
|                   | EnzymeFlow    | 3.18 | 3.32 | 3.84 | 0.39 | 0.36 | 0.32 | 0.42  | 1.08  | 2.19  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC4               | RFDiffusionAA | 3.00 | 3.29 | 3.79 | 0.30 | 0.29 | 0.27 | 14.62 | 15.62 | 17.39 |
|                   | EnzymeFlow    | 2.58 | 2.73 | 2.96 | 0.56 | 0.54 | 0.51 | 0.50  | 1.07  | 2.43  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC5               | RFDiffusionAA | 3.39 | 3.61 | 3.98 | 0.31 | 0.29 | 0.26 | 7.83  | 8.23  | 8.93  |
|                   | EnzymeFlow    | 2.87 | 3.18 | 3.62 | 0.44 | 0.43 | 0.39 | 0.74  | 1.07  | 1.78  |
| ----------------- | ------------- | ---- | ---- | ---- | ---- | ---- | ---- | ----- | ----- | ----- |
| EC6               | RFDiffusionAA | 3.43 | 3.69 | 4.12 | 0.30 | 0.29 | 0.26 | 19.08 | 19.73 | 21.21 |
|                   | EnzymeFlow    | 3.14 | 3.32 | 3.73 | 0.43 | 0.40 | 0.36 | 1.23  | 1.45  | 2.56  |
```
Answers to Questions Part2
## A1: 
#### We appreciate the opportunity to clarify our rationale. As discussed in the appendices, our focus on catalytic pocket design rather than complete enzyme design stems from both the scientific challenges and strategic advantages of this approach. Designing a full enzyme from scratch is an extremely complex task, with two primary hurdles: (1) accurately generating a complete, functional structure, and (2) identifying the optimal catalytic regions where catalysis actually occurs. Catalytic pockets are the most critical regions of enzymes, as they directly interact with substrates, driving chemical transformations. Focusing on catalytic pockets first allows us to solve a foundational aspect of enzyme design by establishing effective reaction sites, which are essential for catalysis.

#### By taking a bottom-up approach that prioritizes catalytic pocket design, we address the most functionally important region first, aiming to achieve catalytic efficacy at the reaction site. Once reliable methods for pocket design are in place, we can extend this work toward scaffold motifs and eventually full enzyme design, building from a verified functional core. This approach also offers a more achievable pathway for the community: by solving pocket design first, researchers can progressively build up to complete enzymes, reducing the challenge of full enzyme generation. Additionally, while the complete enzyme structure is crucial for overall stability and foldability, its function is driven primarily by the catalytic pocket. We believe this focused pathway will accelerate progress toward enzyme discovery, providing actionable insights into catalytic design that can ultimately be scaled up to full enzyme architectures.
Answers to Questions Part1