AffinityFlow: Guided Flows for Antibody Affinity Maturation

General Reply

Thank you for your insightful comments—they’ve greatly improved our manuscript. We’ve addressed each point and will update the manuscript accordingly.

Claims and Evidence

poor mapping

Thank you for your feedback. We agree that the gap between in silico proxies and experimental KD is a key challenge. Accordingly, we will revise the abstract to state: "Our method, AffinityFlow, achieves state-of-the-art performance in proof-of-concept affinity maturation experiments."

Experimental Designs Or Analyses

difficult to assess significance

We acknowledge that AlphaFlow's inference involves computationally expensive protein conformation modeling, which limited our ability to perform repeated runs. Nonetheless, the reported performance differences, though modest, consistently favor AffinityFlow in functionality and specificity.

dWJS should be trained on ddG<0.

As noted in Section 4.2, we use a sequence-based predictor to select top candidates for dWJS, effectively conditioning dWJS. Moreover, dWJS is trained solely on antibody sequences without antigen context, per the original paper, so filtering by ddG < 0 is not applicable. We also compare the guided version (gg-dWJS) in QKfP's rebuttal, which still underperforms our method.

trouble understanding

We have described the change in binding free energy as the difference between the free energies of the bound and unbound states in Section 2.4 (Lines 127–130). A negative value indicates that the overall free energy of the system decreases upon binding, meaning that the antibody–antigen interaction is energetically favored. We will add these in Section 2.4 (Line 127).

An antibody consists of two heavy chains and two light chains with a similar overall structure. Its specificity is determined by six variable regions known as Complementarity Determining Regions (CDRs), denoted as H1, H2, H3, L1, L2, and L3. Typically, heavy chain CDRs range from $8$ to $16$ amino acids, while light chain CDRs range from $3$ to $10$ amino acids. We will include these in Section 2.1 (Line 80).

difficult to read

(1) Random forest: We used scikit-learn’s RandomForestRegressor with 100 decision trees, training on mutation types (input) and Rosetta-predicted ΔΔG (output). Model was validated using R² on a 20% held-out test set. Feature importances revealed Ala105Leu as the most influential mutation.

(2) Connections to prior studies: Our case study uses the MR17 nanobody (PDB: 7D30) from Yao et al. (2021), which has a reported KD of 83.7 nM. Li et al. (2021) later introduced a mutant, MR17m, with a Lys99Tyr substitution that improved IC50, indicating higher potency (i.e., requiring less antibody to achieve the same effect). They also suggested Lys99Trp could be even more effective—an uncommon mutation that AffinityFlow independently identified.

We will incorporate these discussions into Section 4.6.

predictor predict

The structure-based predictor outputs the negative value of the binding affinity (Kd). We will add this clarification in Section 2.4 (Line 131).

form of predictors

We describe the architectures of both the sequence-based and structure-based predictors in Section 2.4, with detailed hyperparameters provided in Section 4.3. To further clarify, we will include more details regarding the MLP and GVP head in Section 4.3.

Essential References Not Discussed

see the references in Meng et al. 2024.

Thank you for highlighting this survey. We have reviewed Section 2.2.3 ("Hybrid generative models") of Meng et al. (2024) and confirm that key methods such as DiffAb and Chroma have been discussed in our paper. We note, however, that most methods listed in Meng et al. (2024) do not specifically address affinity maturation. To clarify, we will add to Appendix A: "ABGNN pre-trains a novel antibody language model and introduces a one-shot approach for generating both sequence and structure of CDRs. AbDiffuser leverages domain knowledge and physics-based constraints to enhance diffusion modeling. AlphaPanda integrates transformer, 3DCNN, and diffusion models for joint sequence-structure co-design. A more detailed overview can be found in Meng et al. (2024). Notably, these methods primarily focus on general antibody design rather than specifically targeting affinity maturation."

Other Strengths And Weaknesses

very difficult to read

In addition to the points in “Experimental Designs or Analyses”, we will add following clarifications: (1) dSASA (change in solvent-accessible surface area) reflects how well hydrophobic residues are buried and how closely the antibody and antigen interact; (2) Shape complementarity measures how well the two proteins fit together. Both metrics indicate interface quality.

Adolf-Bryfogle et al. (2018) assessed these values for all naturally occurring antibody-antigen interfaces in PDB. The metrics we calculate using Rosetta for our designs, fit well within the distribution observed in that paper.

General Reply

Thank you for your constructive feedback, which has improved the clarity and rigor of our paper. We have addressed all points and will revise the manuscript accordingly.

Methods And Evaluation Criteria:

The clarity of the methods (predictor training).

To further clarify our method, we highlight the following points:

(1) Predictor Architecture: We described the predictor architecture in Section 4.3, where $\alpha$ and $\beta$ represent the parameters of the sequence-based and structure-based predictors, respectively. We will explicitly reiterate these parameter definitions in Section 4.3 to improve readability.

(2) Predictor Training: The training of our predictors involves two phases: (a) Supervised Training: Initially, we train both predictors using labeled antibody-antigen sequence/structure data and their affinity labels. Specifically, we optimize the parameters by minimizing the mean squared error (MSE) loss: $(f_{\alpha}(a) - \Delta G)^2$ for the sequence-based predictor and $(f_{\beta}(x) - \Delta G)^2$ for the structure-based predictor. Here $a$ and $x$ denote the protein sequence and structure respectively and $\Delta G$ corresponds to the negative of affinity. We will explicitly present these in Section 2.4. (b) Co-teaching Fine-tuning: we further refine both predictors using Rosetta-generated labeled data, optimizing the loss in Eq. (9), to further enhances performance.

comparisons of inference time and comparing against methods that also utilize iterative optimization or refinement (if this is not already the case).

We have compared the inference time of our method with language model-based approaches in Appendix D. For methods that do not rely on language models, their iterative optimization process takes less than $10$ seconds per sample. Although these alternative methods are more efficient, in the context of antibody design, achieving high-affinity designs is prioritized over computational speed.

Experimental Designs Or Analyses

I think it would be interesting to compare against ESM combined with your sequence predictor.

Thank you for the insightful suggestion. Our current ESM baseline already incorporates the sequence predictor to select the top three sequences per antigen (Section 4.2).

To further explore your idea, we implemented an MCMC variant: At each step, we use ESM to identify the top 20 most probable mutations, randomly choose one mutation as a proposal, and use the affinity predictor to compute its acceptance probability. We repeat this procedure for a total of 9 steps for consistency.

Evaluating the resulting sequences, we obtain scores for IMP, Sim, and Nat of 65.6, 0.562, and 0.360, respectively. While the IMP score slightly improves (from the original 64.0 to 65.6), it remains inferior to our proposed method. The drop in Sim likely stems from strong antigen-specific guidance every step, while Nat improves due to MCMC’s conservative acceptance. We will incorporate these discussions into Section 4.2.

Essential References Not Discussed

BindCraft relevant

Thank you for highlighting this work. We will add the following to Appendix A:

"BindCraft adopts AF2-multimer to generate a binder backbone and sequence given a known target protein structure, subsequently optimizing the non-interface regions using ProteinMPNN. However, BindCraft is not directly comparable to our method, as it specifically targets binder design with known target structures, whereas our setting focuses on affinity maturation through mutation of existing antibody sequences without direct access to target structures. Moreover, the primary goal of BindCraft is generating new binders, rather than improving binding affinity of existing antibodies."

Other Strengths And Weaknesses

report inference time

Our method does require more inference time due to AlphaFlow’s realistic structure modeling, as discussed in Appendix D. While less efficient than alternatives, it consistently yields better designs. In practice, where wet-lab evaluation dominates cost and time, optimization quality is prioritized over computational speed.

Questions For Authors:

how train $f_{\beta}$ in Eq. 7

We first train $f_{\beta}$ using the MSE loss and then fine-tune it with the loss in Eq. (9). It is not a pre-trained energy function; rather, it is a property predictor built upon the ESM2-GVP backbone. We have described this training procedure and loss in the rebuttal of "Methods and Evaluation Criteria".

confused with notation

Yes, $f_{\alpha}(a)$ refers to the sequence-based predictor, and $f_{\beta}(x)$ refers to the structure-based predictor.

not familiar with comparison methods

All non-language-model-based methods used for comparison—including dWJS, DiffAb, AbDPO, and GearBind—employ iterative optimization loops for refinement. Our results demonstrate that AffinityFlow consistently outperforms these approaches.

General Reply

Your insightful comments have greatly contributed to improving our manuscript, and we sincerely appreciate your time and effort. Each point you mentioned has been addressed, and the manuscript will be updated to reflect these improvements.

Methods And Evaluation Criteria:

Given the nature of the work which is optimization, I expect more baselines that uses optimization techniques. Methods such as ESM and AbLang are not particularly suitable for optimizing for Antigen affinity. The author's also use dWJS as a baseline. Given their method uses classifier guidance, why not use the classified guidance version of the dWJS, i.e., gg-dWJS? Given the limited nature of experiments, I think such expectation is justified.

As discussed in Section 4.2, we employ the same trained sequence-based affinity predictor for final sequence selection across all baselines, including ESM, AbLang, and dWJS. This strategy inherently enables affinity optimization, making these methods valid baselines for comparison.

Thank you for pointing out gg-dWJS. To clarify, we have further conducted experiments with gg-dWJS, employing the trained affinity predictor to guide sampling, following the original gg-dWJS paper. Specifically, for the CDR-H3 region, gg-dWJS achieves IMP, Sim, and Nat scores of 67.2, 0.520, and 0.291, respectively, which are still worse than our method. We observe that the IMP score does not significantly improve compared to the original dWJS (which is 66.1). This suggests that the affinity predictor used in the post-selection step of the original dWJS already contributes effectively to guided generation. We will incorporate this additional discussion into Section 4.4 to clarify this point further.

Questions For Authors:

Given the pitfalls of inverse folding (noisiness for conversion of sequence to structure) and structure optimization (unrealizability of structures), how do you guarantee their method's generated sequences are synthesizable? Did you try synthesizing any samples suggested by your method?

We address the concern regarding synthesizability from three key perspectives:

(a) Realistic Structure: (1) We use AlphaFlow as our protein structure generation framework, which has demonstrated its effectiveness in producing realistic protein conformations. (2) In addition, our Predictor-Corrector method incorporates Amber relaxation at every iteration to refine the protein coordinates, ensuring the generated structures are physically realistic.

(b) Limited Mutation Per Iteration: (1) Although the inverse folding process (mapping structure to sequence) can be noisy, we mitigate this issue by restricting mutations to only 1-3 positions per stage rather than generating the entire sequence at once. This targeted approach reduces noise; (2) Furthermore, we employ a post-selection process using a trained sequence-based predictor to filter out sequences with low predicted affinity.

(c) Biologically Meaningful Case Study: We present a detailed case study in Section 4.6 to demonstrate the biological relevance of our generated designs. Notably, our AffinityFlow model independently identified the Lys99Trp mutation—a mutation previously proposed in Li et al. (2020) as a promising improvement in antibody potency.

These strategies collectively enhance the likelihood that our generated sequences are synthesizable and biologically meaningful. Furthermore, we report Nat (the inverse of perplexity) as a supporting metric. As shown in Table 1, AffinityFlow achieves the highest Nat score among all non-language model-based methods, indicating stronger sequence plausibility.

Did the authors attempt any in vitro experiments?

We have not conducted in vitro experiments at this stage.

Why is flow matching a better option for this work?

We adopt flow matching primarily due to the availability of a pre-trained AlphaFlow framework, which has demonstrated exceptional performance in generating realistic protein conformations. Additionally, recent studies [1, 2, 3] show that flow matching can offer superior effectiveness and efficiency compared to diffusion models.

It is also important to note that our proposed alternative framework and co-teaching module are not inherently tied to the AlphaFlow framework; they can, in principle, be implemented within any sequence-conditioned generative model of structure.

 - [1] Lipman Y, Chen R T Q, Ben-Hamu H, et al. Flow matching for generative modeling[J]. arXiv preprint arXiv:2210.02747, 2022.  ICLR 2023
 - [2] Le M, Vyas A, Shi B, et al. Voicebox: Text-guided multilingual universal speech generation at scale[J]. NeurIPS 2023.
 - [3] Adam Polyak, et al. Movie gen: A cast of media foundation models. 2024.

General Reply

Thank you for your valuable feedback, which has greatly improved our manuscript. We have addressed each comment and will incorporate the revisions accordingly.

Claims And Evidence

I think the architecture of the model is not clearly described. There is relatively little discussion about the Predictor-Corrector and Sequence Mutation.

We provide additional details on both Predictor-Corrector and Sequence Mutation.

(1) Predictor-Corrector is composed of two components. Predictor corresponds to the protein coordinate generation process governed by the learned vector field, and Corrector refers to the Amber energy minimization used to refine the coordinates. We will add the sentence in Line 180.

(2) Sequence Mutation: At each iteration, we apply single-, double-, and triple-point mutations using ProteinMPNN. For each position, we calculate the probability difference between the current and alternative amino acids, selecting the mutation with the highest difference. Double- and triple-point mutations build sequentially on prior mutations. A sequence-based predictor selects the top K (K=3) sequences at each stage for further refinement. We will add this description at Line 191 for clarity.

Theoretical Claims:

I read about Guided Structure Generation, Sequence Mutation, but I'm still confused about the overall framework of the model and how the data is connected.

To clarify the overall framework and data flow, consider this example:

Given antibody and antigen sequences, our goal is to mutate the antibody to improve binding affinity. We begin by linking the antibody and antigen sequences and inputting this linked sequence into the AlphaFlow. Without predictor guidance, AlphaFlow generates conformations consistent with the linked sequence.

However, our objective is to obtain a protein conformation with higher binding affinity. To achieve this, we introduce predictor guidance during the AlphaFlow structure generation phase, a process we call Guided Structure Generation. This guidance steers the generated conformations toward those with high binding affinity. Once a high-affinity structure is obtained, we apply inverse folding to introduce targeted mutations—Sequence Mutation—and feed the updated sequence back into AlphaFlow. This iterative loop continues to optimize binding affinity. This process is described between Lines 42–73.

Other Strengths And Weaknesses:

The description of model architecture is not very clear.

Yes, the model is end-to-end. Our architecture is organized as follows:

(1) ESM-2 serves as the sequence-based predictor and is applied during post-selection (as shown in Figure 1) to choose high-affinity mutants for the next iteration. (2) ESM2-GVP acts as the structure-based predictor and is used for predictor guidance, steering the noisy protein coordinates toward high-affinity conformations. (3) AlphaFlow is the core algorithm, initially trained to transform noisy protein coordinates into clean conformations based on the input sequence. In our framework, AlphaFlow is further guided by ESM2-GVP to bias the generated structures toward higher binding affinity.

We will update Figure 1 to clearly label ESM2, ESM2-GVP, and AlphaFlow, and include an overall algorithm that demonstrates the complete framework in the revised paper.

The SAbDab dataset is small.

We address this issue with the following strategies:

(1) AlphaFlow: AlphaFlow is pretrained on large-scale protein structures. In our method, this pretrained model remains frozen, thereby preventing it from overfitting the small dataset.

(2) Sequence-based (ESM-2) and Structure-based Predictors (ESM2-GVP): Both predictors leverage pretrained ESM-2 models, which have been pretrained on large-scale unlabeled data. During our training, we keep these pretrained backbones frozen and fine-tune only the prediction heads. This reduces the risk of overfitting due to the small number of learnable parameters.

(3) Augmented Dataset via Rosetta Labeling and Co-teaching: To further improve generalization, we introduce a co-teaching module. Initially, the predictors are trained on the limited SAbDab dataset. Next, we augment the training data by generating an additional $4,158$ labeled samples using Rosetta. The co-teaching module then mitigates noise from the augmented data, providing a richer dataset and reducing the risk of overfitting.

These measures collectively ensure that our models remain robust and generalize effectively, despite the limited size of SAbDab.

lacks comparative runtime.

We address runtime in Appendix D: one iteration of our method takes around $10$ minutes for a protein of length $500$, compared to $11$–$18$ seconds for language model-based methods per sample. While these alternatives are faster, our approach yields better designs. In practical settings like antibody design, wet-lab evaluation is the major bottleneck, making optimization quality more critical than generation speed.