ProSpero: Active Learning for Robust Protein Design Beyond Wild-Type Neighborhoods

Thank you for your meaningful and relevant feedback of our work.

W1: Problem formulation

We agree that the ultimate objective of our framework is optimization of protein sequences, not active learning in the traditional sense of model improvement for its own sake. Rather, the latter serves as a proxy objective to achieve the former. We appreciate the opportunity to clarify this point and will revise the manuscript to reflect this more precise framing.

W2: Clarity

While full SMC details are provided in Appendix C, we agree that being more precise would improve clarity. In the revised version, we will incorporate the following changes:

• In Equation 1 of Section 4.2, we will revise the notation of the target distribution from $\gamma(x)$ to $\gamma(x_{1:L})$ , and update all other occurrences of $x$ accordingly within the introductory part of Section 4.2. This change makes explicit that the target is defined over a sequence of residues, improving clarity and alignment with the sequential structure of SMC
• We will begin the L144-167 part with the following paragraph: Rather than trying to directly sample from complex, high-dimensional target distribution $\gamma(x_{1:L})$, in ProSpero we perform approximate inference using SMC, which decomposes the sampling process into a sequence of simpler, unnormalized, intermediate target distributions $\{\tilde{\gamma}(x_{1:l})\}_{l=1}^{L}$ (for background see Appendix C). This allows us to progressively build up sequences residue by residue, while maintaining a tractable approximation of the full design objective"
• We will conclude the line 162 as follows: “Finally, the unnormalized importance weights […] , with the perplexity correction term penalizing sequences that are improbable under the true prior, correcting bias introduced by the constrained sampling”

We hope this revision will make the section clearer and more accessible to the readers.

Importance weights are proportional to the likelihood, as at each step they represent the ratio between the target distribution (i.e. posterior) and the proposal (prior). Resampling particles proportionally to their weights allows us to progressively concentrate samples in high-probability regions under the posterior.

As for the connections between pseudo-marginal MCMC and SMC: in pseudo-marginal MCMC, within a single Markov chain, a single collection of samples is generated whose marginal stationary distribution is exactly the target distribution. The approximation improves with the number of iterations $T$ and is exact in the limit of infinite $T$. In contrast, SMC maintains a population of $N$ samples that evolve over a sequence of intermediate distributions. The empirical distribution formed by these samples converges to the target distribution in the limit of infinite $N$.

W3: Novelty

The motivation behind targeted masking is a biologically motivated strategy that mirrors how experimentalists scan for functionally relevant residues. We demonstrated its effectiveness over random masking in Figure 4D in Section 5.4. For convenience, we summarized the key results in the table below:

Results clearly demonstrate the advantage of targeted over random masking across all noise levels. To improve the clarity of the strategy behind targeted masking, we will improve its description in Section 4.1 in the final paper.

W4: Similarities to CloneBO by Amin et al. [1]

We agree that ProSpero and CloneBO [1] share similarities in guiding a generative model at inference time using SMC. However, the approaches differ meaningfully in both scope and mechanism. First, in CloneBO, the generative model (CloneLM) has been trained specifically for the optimization task by fiting to a distribution of clonal families. In contrast, our method uses a general-purpose, task-agnostic pre-trained generative model, enabling effortless optimization regardless of the protein family. As for the differences in the use of SMC, in CloneBO the authors compute intermediate importance weights directly, as a likelihood ratio between the base CloneLM and a twisted variant incorporating high value sequences (i.e. sequences with experimental measurements) in the conditioned clonal family. In ProSpero, we approximate the intermediate importance weights using the surrogate model, which serves as a tractable proxy for the true likelihood. Moreover, our biologically constrained SMC restricts proposals to charge-compatible amino acids, making certain residues impossible to sample. In contrast, CloneBO does not enforce such constraints; although twisting reduces the probability of sampling undesirable residues, it does not eliminate them entirely.

"It would be of benefit if the authors situate their guidance method relative to other generative guidance methods [...]"

Thank you for this helpful suggestion. We agree that situating our method in relation to existing guidance techniques would help readers better understand our contribution. In the revised version of the manuscript, we will include the following paragraph and expand it further with additional references and examples to strengthen its context and relevance.

Classifier guidance is a technique used to steer generative models during inference, by incorporating gradients from an auxiliary classifier. The sampling is biased toward desired properties by adjusting the generative score with the gradient of the proxy classifier $\nabla_x \log p(y \mid x)$ [2]. However, this approach is not directly applicable in the discrete data domain, where gradients with respect to input tokens are not well-defined. Recently, Nisonoff et al. [3] proposed a technique allowing for classifier guidance in discrete diffusion and flow matching models. Discrete-domain guidance can also be addressed using SMC-based approaches, which guide sequence generation by maintaining a population of partial samples and resampling them based on their likelihood under a target distribution.

RAAs: In practice, what is the impact of using the RAA based on charge particles? [..]

In our ablation study in Section 5.4, we already compare sampling from EvoDiff with and without RAAs constraints. For convenience, as well as given that both of those ablations are constant across noise levels, we summarized the results in the table below:

Motivated by your remark, we will extend our ablation by directly comparing the performance of ProSpero with and without RAAs constraints. The results are shown below:

Both of these tables demonstrate the relevance of RAA constraints, particularly with respect to fitness and novelty. Thank you for prompting this valuable addition.

What value of n_sub was used in practice? [...]

The number of masked sites in each benchmark was determined based on the sequence length, with the number sampled uniformly from the range of 5–15 residues for longer, and 3–10 for shorter sequences. The 5–15 residue masking range reflects common practice in rational design (e.g., for the GFP [4]) and was shown to perform well in silico by Kim et al. [5], who also explored masking 5% of residues. Based on this proportion, we reduced the range to 3–10 residues for shorter sequences like AAV, E4B, and Pab1. The reviewer’s intuition is correct, this parameter directly modulates novelty by controlling how far generated sequences deviate from the wild-type.

Line 147 defines $\pi^{(i)}$ as the order agnostic indices, why is it concatenated in that specific order? [...]

The permutation order was chosen to prioritize charge classes with fewer valid options. The intuition behind this choice is that resolving the most constrained decisions early can help avoid suboptimal completions later in the sequence. We compared different orderings and summarized the results in the table below:

While the results suggest that the intuition is correct, the differences are modest, especially for longer sequences. Thank you for bringing attention to this aspect.

Thank you for the thoughtful and constructive feedback, which helped us improve the manuscript. We hope our revisions address your concerns and would greatly appreciate it if you would consider updating your evaluation of our submission.

References

[1] A. N. Amin et al. Bayesian optimization of antibodies informed by a generative model of evolving sequences. ICLR 2025

[2] P. Dhariwal and A. Nichol. Diffusion Models Beat GANs on Image Synthesis. NeurIPS 2021

[3] H. Nisonoff. Unlocking Guidance for Discrete State-Space Diffusion and Flow Models. ICLR 2025

[4] T. Hayes et al. Simulating 500 million years of evolution with a language model. Science 2025

[5] H. Kim et al. Improved off-policy reinforcement learning in biological sequence design. 2024

We sincerely thank the reviewer for their thoughtful and detailed feedback.

Regarding the primary concern about the lack of wet-lab validation

We share the reviewer’s view on the importance of real-world validation, yet want to emphasize that experimental testing is beyond the scope of our current work. Here, we focus on establishing the methodological foundation of active learning-based, robust protein design, evaluating it on a wide variety of benchmarks. At the same time, we respectfully suggest that the absence of wet-lab results should not diminish the core methodological contribution of our work. As the reviewer acknowledged, the paper’s central thesis and application domain are relevant, and our in silico benchmarking is strong and comprehensive.

We thank the reviewer for highlighting the important and relevant work by Damani et al. [1]. We fully agree that great care must be taken when interpreting surrogate model predictions in regions far from the training distribution. That said, we believe the findings in Damani et al. [1] are not directly transferable to our setting. Their study and its empirical results focus on offline MBO. In contrast, our approach operates in an online active learning setting, where the surrogate is updated with oracle feedback. Crucially, it has been shown that active learning can significantly improve extrapolation and generalization in OOD regimes by enabling the model to iteratively incorporate data from previously unsupported areas of the search space [2]. We understand, however, that as long as the oracle is not a direct measure of biological function, concerns about over-optimism in unexplored regions remain justified.

Regarding the landscapes, in particular AAV

While indeed the AAV landscape is convex in the noise-free setting, it constitutes only one of the eight tasks we evaluate on. The remaining 7 landscapes are non-convex, rugged and more representative of the complexity of real biological functions. Moreover, in the noisy setting, the AAV landscape loses its convexity and resembles the Rough Mt. Fuji model, which has been shown to capture locally valid biological behavior around wild-type sequences in empirical studies [3]. We acknowledge the reviewer’s concern that success on this task alone may not be sufficient to support claims about generalization beyond wild-type neighborhoods. However, particularly in the noisy setting, it remains a valuable component of the evaluation suite.

Regarding the insufficient distribution shifts on evaluated tasks

We appreciate and acknowledge the reviewer's concern regarding the degree of distributional shift present in our evaluation tasks. To address this more directly, following helpful suggestions of the reviewer as well as Damani et al [1], we introduced another 3 tasks evaluating effectiveness of our method under various degrees of distribution shift. In these experiments we used ESMFold as the oracle, which offers high-fidelity feedback better suited for performance assessment in more challenging and realistic settings.

Specifically, from all UBE2I candidate sequences generated by different methods and scored with ESMFold, we selected those within a Hamming distance $\leq 5$ from the UBE2I wild-type to construct the initial dataset $D_0$, consisting of 2624 sequence---pTM score pairs. The average pTM score of $D_0=0.860 ± 0.029$. We then trained a surrogate model $f_\theta$ on $D_0$, and initiated the optimization not from the wild-type sequence, but from a sequence differing from the wild-type by a large number of 35 residues and of an initial pTM score of 0.70. Following the insightful suggestion of the reviewer, we run such optimization for only 4 iterations. The results are shown below:

where by novelty here we mean the distance of top 100 sequences to the starting point, not the original wild-type.

Moreover, we additionally repeated the same experiment, but under an even more severe distribution shift, starting optimization from a sequence differing from the wild-type by a larger number of 75 residues and of an initial pTM score of 0.50. The results are shown below:

Additionally, following the suggestion of Reviewer XJMJ, we repeated the experiment under the first distribution shift setting. To better reflect real-world constraints, we further limited the initial dataset by randomly selecting only 200 data points from $D_0$, resulting in a reduced initial training set with an average pTM score of $0.860±0.023$.

These results demonstrate that our approach can robustly guide exploration toward high-fitness sequences, even under substantial distributional shifts, consistently outperforming competing methods. Moreover, in the setting of the more severe covariate shift with 75 mutations from the wild-type (which is roughly equivalent to half of the entire sequence), the performance gap between our approach and the majority of the baselines widens substantially.

We trust that this additional evaluation directly addresses the reviewer’s concern about insufficient distributional shift in our original experiments. All three tables with the results for these novel landscapes with distribution shifts will be incorporated in the paper. We hope the reviewer will see this extended evidence and evaluation procedure as a meaningful contribution and reconsider their assessment of the paper.

Regarding the performance within early active learning rounds

We thank the reviewer for raising this important and practically relevant point about the typical number of active learning rounds used in real-world protein design workflows. Due to space constraints, we present only the most relevant metric below, namely the maximum fitness achieved within 4 iterations. The revised version of the manuscript will include the full set of results limited to 2 to 4 iterations across all benchmarks.

Notably, even when restricted to a smaller number of iterations, our approach consistently ranks first or second across all tasks, highlighting its effectiveness in low-iteration regimes commonly encountered in practice, as rightly pointed out by the reviewer.

We once again sincerely thank the reviewer for their thoughtful and constructive feedback, which helped us identify and address a key shortcoming in the original submission. In particular, the suggestion to better evaluate performance under distributional shift motivated the introduction of three new tasks designed to test robustness in more realistic and challenging OOD settings. We believe these additions significantly strengthen the paper and directly respond to the concerns raised. We hope the reviewer finds that these revisions adequately address their main points, and we would be grateful if they would consider updating their evaluation of the work in light of these improvements.

References

[1] F. Damani et al. Beyond the training set: an intuitive method for detecting distribution shift in model-based optimization. 2023.

[2] E. R. Antoniuk et al. Active Learning Enables Extrapolation in Molecular Generative Models. 2025.

[3] S. Sinai et al. AdaLead: A simple and robust adaptive greedy search algorithm for sequence design. 2020.

We thank the reviewer for their positive and thoughtful feedback.

Some technical components [...] are formally described but may lack intuitive explanations for readers less familiar with these methods.

While the full details of the SMC procedure are included in the Appendix C, we agree that a more intuitive explanation in the main text could benefit readers less familiar with the method. We will include the following changes in the revised version of our work:

• In Equation 1 of Section 4.2, we will revise the notation of the target distribution from $\gamma(x)$ to $\gamma(x_{1:L})$ , and update all other occurrences of $x$ accordingly within the introductory part of Section 4.2. This change makes explicit that the target is defined over a sequence of residues, improving clarity and alignment with the sequential structure of SMC
• We will begin the L144-167 part with the following paragraph: Rather than trying to directly sample from complex, high-dimensional target distribution $\gamma(x_{1:L})$, in ProSpero we perform approximate inference using SMC, which decomposes the sampling process into a sequence of simpler, unnormalized, intermediate target distributions $\{\tilde{\gamma}(x_{1:l})\}_{l=1}^{L}$ (for background see Appendix C). This allows us to progressively build up sequences residue by residue, while maintaining a tractable approximation of the full design objective"
• We will conclude the line 162 as follows: “Finally, the unnormalized importance weights … , with the perplexity correction term penalizing sequences that are improbable under the true prior, correcting bias introduced by the constrained sampling”

We hope this revision will make the section clearer and more accessible to the readers.

The comparison with all baselines is somewhat uneven, limiting contextual understanding.

We would like to emphasize that our evaluation covers eight diverse protein engineering tasks and in a fair manner compares against ten baselines spanning a wide range of algorithmic approaches, including evolutionary strategies, Bayesian optimization, reinforcement learning, GFlowNets, probabilistic models, and machine-learning-guided directed evolution. In addition to fitness optimization, we show tradeoffs to exploration capabilities, biological plausibility and robustness to surrogate noise, resulting in a comprehensive and multi-faceted comparison. We believe this breadth offers a strong contextual understanding of the advantages of ProSpero relative to existing methods.

While innovative in integrating various ideas, components like SMC and charge-based grouping are adapted from prior work [...]

We agree that SMC has been applied to protein design in prior works [1, 2]. We would like to clarify, however, that introduced by us biologically-constrained SMC represents a novel and principled extension: it allows biological priors to be incorporated directly into the proposal distributions. To specifically emphasize the impact of this contribution, we will complement our existing ablation study with a direct comparison between our biologically-constrained SMC and an unconstrained formulation:

Additionally, we note that reduced amino acid alphabets (RAAs) are by no means standard or widely adopted in this context. Specifically, we refer to the work of Liang et al. [3], concluded with "[...] RAA alphabets have not been fully and maturely used in current research." Given this, we believe that our biologically informed use of RAAs represents an impactful contribution in its own right, representing a notable use case.

PROSPERO’s performance on more complex or out-of-distribution tasks remains untested.

Thank you for raising this relevant point. To address your and other reviewers concerns, we introduced another 3 tasks evaluating effectiveness of our method under various degrees of distribution shift. In these experiments we used ESMFold as the oracle, which offers high-fidelity feedback better suited for performance assessment in more challenging and realistic settings.

Specifically, from all UBE2I candidate sequences generated by different methods and scored with ESMFold, we selected those within a Hamming distance $\leq 5$ from the UBE2I wild-type to construct the initial dataset $D_0$, consisting of 2624 sequence---pTM score pairs. The average pTM score of $D_0=0.860 ± 0.029$. We then trained a surrogate model $f_\theta$ on $D_0$, and initiated the optimization not from the wild-type sequence, but from a sequence differing from the wild-type by a large number of 35 residues and of an initial pTM score of 0.70. We then run such set optimization for 4 iterations. The results are shown below:

where by novelty here we mean the distance of top 100 sequences to the starting point, not the original wild-type.

Moreover, we additionally repeated the same experiment, but under an even more severe distribution shift, starting optimization from a sequence differing from the wild-type by a larger number of 75 residues and of an initial pTM score of 0.50. The results are shown below:

Additionally, following the suggestion of Reviewer XJMJ, we repeated the experiment under the first distribution shift setting. To better reflect real-world constraints, we further limited the initial dataset by randomly selecting only 200 data points from $D_0$, resulting in a reduced initial training set with an average pTM score of $0.860±0.023$.

These results demonstrate that our approach can robustly guide exploration toward high-fitness sequences, even under substantial distributional shifts, consistently outperforming competing methods. Moreover, in the setting of the more severe covariate shift with 75 mutations from the wild-type (which is roughly equivalent to half of the entire sequence), the performance gap between our approach and the majority of the baselines widens substantially.

We trust that this additional evaluation directly addresses the reviewer’s concern about insufficient distributional shift in our original experiments. All three tables with the results for these novel landscapes with distribution shifts will be incorporated in the paper.

Thank you for your constructive and meaningful feedback, which has helped strengthen the manuscript. We hope our responses have addressed your concerns, and would greatly appreciate it if you would consider raising your rating of our submission accordingly.

References

[1] A. N. Amin et al. Bayesian optimization of antibodies informed by a generative model of evolving sequences. ICLR 2025.

[2] L. Wu et al. Practical and Asymptotically Exact Conditional Sampling in Diffusion Models. NeurIPS 2023.

[3] Y. Liang et al. Research Progress of Reduced Amino Acid Alphabets in Protein Analysis and Prediction. Computational and Structural Biotechnology Journal, 2022.

Thank you for taking the time to provide such a detailed and insightful review of our manuscript.

Q1: Number of mutational sites

The number of masked sites in each benchmark was determined based on the sequence length, with the number sampled uniformly from the range of 5–15 residues for longer, and 3–10 for shorter sequences. The range of 5–15 residues aligns with ranges commonly used by experimentalists in rational design for example on the GFP task [1], making this another aspect of our framework that reflects mutagenesis-inspired behavior. Kim et al. [2] have demonstrated that this masking range performs well in silico. Additionally, they experiment with masking 5% of the total residues in a sequence. Based on this, for shorter sequences, such as AAV, E4B, and Pab1, we reduced the masking range to 3–10 amino acids.

Q2: Ablation study on the number of top starting sequences for the candidate generation

Thank you for the helpful suggestion. We added an ablation on LGK, the task requiring generation of the longest sequences, to test the effect of varying the number of top starting sequences (1–128). Results are shown below:

Fewer starting points drive deeper, more directed exploration, resulting in higher novelty and fitness but lower diversity. In contrast, more starting points promote broader, more diffuse exploration, increasing diversity but limiting how far any single trajectory moves from the wild-type across subsequent optimization rounds.

As suspected by the reviewer, this new table brings important insights into the tradeoffs associated with the number of initial sequences and the exploration capabilities and we will incorporate it into the final version of the paper.

Q3: Clarity of lines 144-167

Thank you for the comment. We understand that this section may be difficult to follow without additional context. To support readers unfamiliar with Sequential Monte Carlo, we already refer to Appendix C in line 146, which provides a more detailed mathematical background and explains the overall procedure. To further improve the clarity of this section, the revised version of our work will feature the following changes:

• In Equation 1 of Section 4.2, we will revise the notation of the target distribution from $\gamma(x)$ to $\gamma(x_{1:L})$ , and update all other occurrences of $x$ accordingly within the introductory part of Section 4.2. This change makes explicit that the target is defined over a sequence of residues, improving clarity and alignment with the sequential structure of SMC
• We will begin the L144-167 part with the following paragraph: Rather than trying to directly sample from complex, high-dimensional target distribution $\gamma(x_{1:L})$, in ProSpero we perform approximate inference using SMC, which decomposes the sampling process into a sequence of simpler, unnormalized, intermediate target distributions $\{\tilde{\gamma}(x_{1:l})\}_{l=1}^{L}$ (for background see Appendix C). This allows us to progressively build up sequences residue by residue, while maintaining a tractable approximation of the full design objective"
• We will conclude the line 162 as follows: “Finally, the unnormalized importance weights […] , with the perplexity correction term penalizing sequences that are improbable under the true prior, correcting bias introduced by the constrained sampling”

We hope this revision will make the section clearer and more accessible to the readers.

Q4: Other measures of exploration

Thank you for this insightful suggestion. We agree that the inclusion of the proposed Hamming distances will help to quantify the extent of exploration of our approach. We have computed the average Hamming distance between each starting sequence and its corresponding initial dataset.

As shown, distances for the majority of the tasks are small. This is expected given that most datasets were created by wet-lab scientists applying a limited number of mutations to the wild-type sequence and measuring the activity of such mutated variants. A notable exception is the GFP task, where the initial dataset was created in silico by Kim et al. [2] through random mutagenesis and scoring via the oracle.

We have also computed the average distances between top 100 sequences and the initial datasets:

Such evaluated performance closely resembles the one in Table 3, with ProSpero achieving larger distances than compared models for the majority of the tasks. These results underscore the capabilities of our approach to explore regions of the search space beyond the initial training data, even in cases such as the GFP task, where the initial sequences are not as densely clustered around the wild-type. This new table will be featured in the revised paper.

Q5: Initial dataset size influence on the performance

Thank you for raising this important point. We agree that small initial datasets are common in practice. Following your suggestion, as well as suggestions of other reviewers, we've added an additional task that better reflects real-world settings.

Specifically, from all UBE2I candidate sequences generated by different methods and scored with ESMFold throughout our experiments, we randomly selected 200 of those within a Hamming distance $\leq 5$ from the UBE2I wild-type to construct the initial dataset $D_0$, where the average pTM score of $D_0 = 0.860 ± 0.023$. We then trained a surrogate model $f_\theta$ on $D_0$, and initiated the optimization not from the wild-type sequence, but from a sequence differing from the wild-type by a large number of 35 residues and of an initial pTM score of 0.70. We run such optimization for only 4 iterations, employing ESMFold as an oracle. The results are shown below:

We believe the strong performance of our approach in comparison to the baselines is due to the incorporation of biological priors, which enable efficient exploration even when the surrogate model is weak, whether because of limited training data or distribution shifts. We will include this result in a revised version of the paper.

Q6: Amino acid choice for replacement-based residue scoring

In our work, we confirmed the advantage of residue scoring using Alanine scan over random amino acid substitutions, as shown in our ablation studies in Section 5.4. For convenience, we summarized the key results in the table below:

We did not perform systematic one-to-one comparisons with other specific amino acids. This is because alanine scanning is a well-established strategy in experimental mutagenesis, whereas there is little principled justification for selecting any other single amino acid as a universal substitute with neutral properties. As such, alternative choices lack clear biological or methodological motivation, making direct comparisons difficult to interpret meaningfully.

Q7: Missing citation

Thank you for the suggestion. We agree the cited work is relevant and will include it in the revised manuscript.

Thank you for the thoughtful and constructive comments, which greatly helped us improve the manuscript. We hope we have addressed your concerns, and if so, we would be grateful if you would consider raising your rating of our submission.

References

[1] T. Hayes et al. Simulating 500 million years of evolution with a language model. Science 2025.

[2] H. Kim et al. Improved off-policy reinforcement learning in biological sequence design. 2024.