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REVIEW 4 major objections 5 minor 40 references

Directed Evolution of Proteins via Bayesian Optimization in Embedding Space

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper claims Bayesian optimization over protein language model embeddings finds fitter variants than regression-based directed-evolution methods at the same screening budget.

desk verdict BOES is a plausible and well-executed method — GP-BO directly in ESM-1b embeddings with a single length scale — but the SOTA-superiority claim rests on an uncontrolled external comparison; the paper's own controlled BO comparisons show parity. read the letter →

arxiv 2509.04998 v1 pith:HYD667ZG submitted 2025-09-05 cs.LG q-bio.BM

Matouš Soldát , Jiří Kléma This is my paper
classification cs.LGq-bio.BM
keywords directedevolutionproteinengineeringBayesianoptimizationlanguagemodelssequenceembeddingsGaussianprocessesexpectedimprovementfitnesslandscape
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Directed evolution improves proteins by repeated mutation and screening, but each screen is expensive. This paper puts forward a way to spend that budget more efficiently: instead of training a fitness predictor and then exploiting its predictions, it runs Bayesian optimization directly in the embedding space of a pre-trained protein language model. The method, BOES, fits a Gaussian process with a single fitted length-scale kernel on those embeddings and uses expected improvement to choose each next variant for screening. On the GB1 and PhoQ fitness landscapes, BOES reports higher maximum fitness than the best regression-based methods it compares against when all methods get 80 screens. It also outperforms Bayesian optimization run directly on one-hot encoded sequences, and it constructs its input space without any additional screening.

What carries the argument

The central object is BOES, a Bayesian optimization loop whose input space is the sequence embedding from a pre-trained protein language model (ESM-1b), a 1,280-dimensional numerical vector said to encode function-relevant information. The load-bearing design choice is a Matérn 3/2 kernel over Euclidean distance in this embedding space with exactly one fitted length-scale parameter, so the surrogate model does not need one length scale per dimension. The acquisition function is expected improvement, and each iteration screens the variant with the largest expected improvement over the best fitness seen so far. Because the embedding is computed once from sequences, no screened variants are nee

What would settle it

Measure the rank correlation between ESM-1b embedding distance and fitness difference for all single-mutation pairs in a rugged fitness landscape; if it is near zero or negative, a single-length-scale GP will mis-rank candidates and the reported advantage over regression baselines should disappear.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the high-dimensional embedding space of a protein language model can serve directly as the search space for Bayesian optimization, provided the Gaussian-process kernel is forced to a single effective length scale. This lets expected-improvement optimization see the fitness landscape through a metric that already encodes biological information, rather than through a sequence-space metric built by the modeler. The reported result is concrete: with 80 screened variants starting from the wild-type protein, BOES reaches fitness 7.28 on GB1 and 37.94 on PhoQ, compared with best prior results of 6.20 and 28.19 among the regression-based MLDE methods c

Load-bearing premise

The method assumes that Euclidean distance in the 1,280-dimensional embedding space, compressed into a single fitted length scale, reliably tracks how similar two protein variants' fitness values are.

Editorial extensions

If this is right

  • If the 80-variant results hold up, laboratories can replace a training/exploitation split with an optimization loop and plausibly end with fitter variants from the same number of screens.
  • Because the embedding space needs no screened variants, BOES saves the initial screening rounds required by encodings like positional amino-acid fitness encodings; those screens can instead be used for further optimization.
  • The paper's multi-start robustness runs show BOES reaching the global GB1 optimum within 200 screens even from non-functional starting variants, so performance is not tied to starting near the wild type.
  • The method is representation-agnostic: the same loop should work with other pre-trained protein language models, so improvements in embedding quality should transfer directly to BOES.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural untested consequence is that BOES-style optimization could extend to larger combinatorial libraries than four mutation positions, since the embedding metric replaces the combinatorially sparse one-hot representation; whether the single length-scale kernel remains adequate there is an open question.
  • The single length-scale assumption implicitly treats all directions in embedding space as equally relevant to fitness; landscapes with both smooth and rugged regions would likely benefit from trust-region or multi-scale kernels, which the paper suggests but does not demonstrate.
  • The in silico experiments assume noiseless screening; in a wet lab, screening noise would break the zero-variance GP assumption and may erode the reported advantage.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes BOES, an MLDE method that runs Bayesian optimization (GP with expected improvement) directly in a 1280-dimensional ESM-1b protein sequence embedding space, using a Matérn 3/2 kernel with a single fitted length scale. The authors evaluate BOES in silico on GB1 and PhoQ four-position fitness landscapes. They claim that (i) the PPLM embedding space significantly improves BO over one-hot encoding, and (ii) BOES outperforms state-of-the-art regression-based MLDE methods under the same screening budget. The results include a comparison to published SOTA numbers (Table I), an ablation vs. one-hot GP+EI (Table II), a comparison to other informative-encoding BO methods (Table III), robustness tests over many starting proteins, and t-SNE/NDCG analyses of the learned landscape.

Significance. If the central claims hold, the paper makes a useful contribution: it shows that a pre-trained protein language model can supply a fixed, screening-free representation for Bayesian optimization, avoiding the cost of constructing problem-specific encodings. The strengths are the open-source implementation (DESilico.jl), the large number of repeated-start runs in the robustness study, the explicit disclosure of cases where the comparison is skewed in favor of baselines, and the ablation against one-hot GP+EI. However, the headline SOTA-superiority claim is not yet supported by controlled evidence, as discussed in the major comments. The manuscript is honest about several limitations, including the fact that full ODBO outperforms BOES and that no significance test is attached to the Table III comparison.

major comments (4)
  1. [§VI.B, Table I] The central claim that BOES 'outperforms state-of-the-art MLDE methods' rests entirely on point estimates imported from [9] (AFP-DE 6.20 on GB1, 28.19 on PhoQ) with no error bars, while BOES itself is also reported as a single number per dataset. The only controlled internal comparison against other BO methods (Table III) shows BOES (6.47±1.15) statistically indistinguishable from NaiveBO (6.40±0.79) and TuRBO (6.57±1.02), and the full ODBO variant with prescreening outperforms BOES. Thus the distinctive SOTA-superiority claim depends on an uncontrolled external comparison. Please re-run the regression baselines in DESilico.jl with repeated seeds and identical budget handling, or substantially weaken the claim in the abstract and conclusion.
  2. [§VI.B, Table I] The comparison is confounded by budget structure: regression baselines split the 80-variant screening budget into training and exploitation portions (24+56 or 48+32), while BOES spends all 80 variants adaptively. This is an intended design difference, but the imported baseline numbers may use different fitting details, random seeds, and hyperparameters. The abstract's 'same number of conducted screening in total' therefore conflates total count with resource allocation. A budget-equivalent analysis (e.g., reporting baselines with the same total including their training counts, or running BOES with a fixed initial training set) is needed to support the superiority claim.
  3. [§VI.D, Table II] The claim that the embedding space 'significantly improves' BO over one-hot GP+EI is supported by a single GP+EI value (7.28, no standard deviation) versus BOES 8.14±0.62. The authors disclose that the 20 initial variants for GP+EI are not counted toward the screening budget, which skews the comparison in GP+EI's favor, but without repeated runs and a significance test the phrase 'decidedly confirms' is overstated. Report GP+EI under the same multi-start protocol with error bars, or temper the wording.
  4. [§V, Eqs. (2)–(3); §VI.E–F] The method's core assumption is that Euclidean distance in the 1280-dimensional ESM-1b embedding, compressed to a single length scale θ, is a reliable proxy for fitness continuity. The t-SNE and NDCG analyses are indirect evidence about the GP's predictive ranking, not about the acquisition function's ranking at the few-variant scale where BO operates. As a concrete correctness-risk test, please compare BOES against a variant using cosine distance or an ARD/per-dimension length-scale kernel, and report NDCG of the EI acquisition values (not just GP predictions) with respect to true fitness. If the isotropic-kernel assumption is fragile, the good Table I results may be dataset-specific.
minor comments (5)
  1. [Fig. 1 caption] Typo: 'Best-so-far fitness rogressions' should be 'progressions'.
  2. [Eq. (3)] The notation I·θ² is ambiguous; use θ²I or define θ explicitly as the length-scale parameter. The reader has to infer whether θ enters as 1/ℓ or ℓ.
  3. [Table II] The screening budget entry '20 + 191' for GP+EI is confusing because the text says the 20 initial variants are not counted toward the screening budget. Clarify in the table caption that 191 is the counted budget and 20 are additional free initial samples.
  4. [§VI.F] The NDCG values (0.88, 0.79) are reported without a description of how they are computed (over all variants? top-k? which k?). Add a precise definition.
  5. [§VI.B, Table I] The table header 'Screening budget (24 + 56)|(48 + 32)' is ambiguous; clarify that the two numbers correspond to the two splits used by the regression baselines, and that BOES/NSDE/SMW use the full 80 adaptively.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: BOES is an empirical benchmark comparison with standard online GP fitting; self-citations are implementation references, not load-bearing.

full rationale

The paper's central claim is empirical: Bayesian optimization with a Matérn 3/2 kernel and a single fitted length scale in PPLM embedding space outperforms regression-based MLDE baselines. The GP kernel's length scale θ is fitted by maximum likelihood from already screened variants (Sec. V), which is standard online model fitting, not a fitted input renamed as a prediction. The embedding space from ESM-1b is constructed without screening, so it does not encode the target fitness values. The comparison to one-hot GP+EI (Table II) and to other informative encodings (Table III) is a genuine controlled evaluation, and the claimed advantage over the original sequence space is not definitional. Self-citations (BOSS.jl [32], DESilico.jl [34], the author's Master's thesis [38]) are implementation/reference citations and do not supply any load-bearing uniqueness theorem or ansatz. The Table I comparison imports baseline numbers from [9]; while this raises reproducibility and error-bar concerns, it is not circularity because those baselines are external results, not derived from the present method's fitted parameters or definitions. Overall, the derivation chain is self-contained: BOES's predictions are model outputs from a fitted GP, not identities implied by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on an empirical modeling assumption about ESM embedding geometry and on standard GP machinery. Kernel hyperparameters are fitted from screened data, while the prior width and noise level are hand-set. No new physical or conceptual entities are introduced; the embedding space is a representation from an existing pretrained model.

free parameters (3)
  • GP kernel length scale theta = not reported; estimated by maximum likelihood during each BO iteration
    Controls the width of the isotropic Matern 3/2 kernel in the 1280-dimensional embedding space. It is the main fitted component of the surrogate model and directly affects EI acquisition (Sec. V, Eq. 2-3).
  • Prior standard deviation for theta = sqrt(1280)/3
    Chosen by hand so that the diagonal of the embedding space corresponds approximately to 3 standard deviations under the prior. It influences early GP uncertainty before data accumulate (Sec. V).
  • Observation noise variance = 0 (small epsilon for numerical stability)
    Assumes a noiseless fitness dataset and removes noise from the GP model. This is a modeling choice, not learned from the data, and affects posterior uncertainty and EI values (Sec. V).
assumptions (4)
  • domain assumption ESM-1b embeddings provide a metric in which Euclidean distance correlates with functional similarity and fitness smoothness.
    The kernel and EI acquisition would mislead if nearby embeddings did not imply similar fitness. The paper provides indirect evidence via t-SNE visualizations and NDCG, but no direct proof (Sec. V, VI.E-F).
  • domain assumption Fitness evaluations in the used datasets are effectively noiseless.
    The GP is set with zero variance because the experiments are 'conducted on a noiseless dataset'. Real wet-lab screening is noisy, so this simplifies the benchmark (Sec. V).
  • domain assumption Unmeasured variants can be assigned fitness zero.
    Data preprocessing assigns zero fitness to unmeasured variants following [6] and [9]. This affects the search space and baselines but not the core BOES algorithm (Sec. VI.A).
  • standard math Gaussian process and expected improvement theory, including positive-definiteness of the Matern kernel, applies as standard.
    The surrogate model and acquisition function rely on standard Bayesian optimization machinery (Sec. IV-V).

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Cite this review

Pith. "Pith review of Directed Evolution of Proteins via Bayesian Optimization in Embedding Space." pith.science (2026). https://pith.science/paper/HYD667ZG

@misc{pith2026250904998,
  author       = {Pith},
  title        = {Pith review of: Directed Evolution of Proteins via Bayesian Optimization in Embedding Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HYD667ZG}},
  note         = {Machine review of arXiv:2509.04998}
}
read the original abstract

Directed evolution is an iterative laboratory process of designing proteins with improved function by iteratively synthesizing new protein variants and evaluating their desired property with expensive and time-consuming biochemical screening. Machine learning methods can help select informative or promising variants for screening to increase their quality and reduce the amount of necessary screening. In this paper, we present a novel method for machine-learning-assisted directed evolution of proteins which combines Bayesian optimization with informative representation of protein variants extracted from a pre-trained protein language model. We demonstrate that the new representation based on the sequence embeddings significantly improves the performance of Bayesian optimization yielding better results with the same number of conducted screening in total. At the same time, our method outperforms the state-of-the-art machine-learning-assisted directed evolution methods with regression objective.

Figures

Figures reproduced from arXiv: 2509.04998 by the authors.

Figure 1
Figure 1. Resulting fitness over multiple runs from sampled starting variants. (a, b) Best-so-far fitness progressions. Bold line [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Visualisation of (a, c) GB1 and (b, d) PhoQ embedding space extracted with ESM-1b PPLM with (a, b) true fitness [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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