Abstract
Model-guided directed evolution seeks to identify high-fitness protein variants under limited oracle budgets. Protein language models (PLMs) provide rich representations for this task, but task-agnostic zero-shot scores can be misaligned with a target assay, while supervised search in high-dimensional embedding spaces can make surrogate modeling and uncertainty estimation sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: within mutation-induced residue-level representation changes, a compact, assay-specific set of directions makes fitness variation linearly accessible from few labeled variants. This is a local, supervision-recoverable statement rather than a claim that protein fitness landscapes or global PLM geometry are universally linear. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which estimates an LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition in the learned subspace. Across 10 core ProteinGym assays, 87 extended static-validation assays, and an 18-assay budgeted-search evaluation, SGES improves fitness prediction and search efficiency over zero-shot PLMs and recent ML-guided protein optimization baselines. Controlled comparisons with PCA, random projections, label-shuffled PLS, classical mutation features, and acquisition ablations further isolate the benefit of a fitness-aligned site-delta coordinate.
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Cite this article
APA 7
Ma, S., Xiao, C., Xiao, Z., Gao, A., He, L., Wang, X. Y., Cao, S., & Jia, X. (2026). Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution. https://omanscience.com/en/articles/linear-fitness-subspace-in-protein-language-models-enables-sample-efficient-directed-evolution
MLA 9
Ma, Siyuan, et al. "Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution." https://omanscience.com/en/articles/linear-fitness-subspace-in-protein-language-models-enables-sample-efficient-directed-evolution.
Chicago (author–date)
Ma, Siyuan, Canran Xiao, Zikai Xiao, Albert Gao, Liang He, Xuan-Yu Wang, Shuying Cao, and Xiaojun Jia. 2026. "Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution." https://omanscience.com/en/articles/linear-fitness-subspace-in-protein-language-models-enables-sample-efficient-directed-evolution.
Harvard
Ma, S., Xiao, C., Xiao, Z., Gao, A., He, L., Wang, X. Y., Cao, S. and Jia, X. (2026) 'Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution', Available at: https://omanscience.com/en/articles/linear-fitness-subspace-in-protein-language-models-enables-sample-efficient-directed-evolution.
Vancouver
Ma S, Xiao C, Xiao Z, Gao A, He L, Wang XY, et al. Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution. https://omanscience.com/en/articles/linear-fitness-subspace-in-protein-language-models-enables-sample-efficient-directed-evolution
IEEE
S. Ma, C. Xiao, Z. Xiao, A. Gao, L. He, X. Y. Wang, S. Cao, and X. Jia, "Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution," https://omanscience.com/en/articles/linear-fitness-subspace-in-protein-language-models-enables-sample-efficient-directed-evolution.