Binary Latent Protein Fitness Landscapes for Quantum Annealing Optimization

Protein fitness optimization is a discrete search problem, and the representation used for prediction also determines the neighborhood graph traversed by an optimizer. We introduce Q-BioLat, a framework that maps pretrained protein-language-model embeddings to compact binary codes and fits a quadratic unconstrained binary optimization (QUBO) surrogate with unary and pairwise latent interactions. Our central contribution is an optimization-aware view of representation: binary encodings that are similar in pointwise predictive accuracy can induce different Hamming neighborhoods, local optima, and search trajectories. We formalize when a recoding is only a Hamming-isometric reparameterization and give a constructive example showing that exact pointwise agreement does not imply optimization equivalence. We study experimentally measured GFP and AAV fitness landscapes from ProteinGym. The internal QUBO surrogate is evaluated against labels withheld from QUBO fitting. A conservative retrieval analysis maps optimized codes to measured variants and reports their experimental fitness, while neural decoding of potentially unmeasured sequences is evaluated separately with an experiment-trained sequence surrogate and is interpreted only as model-based candidate prioritization. Across the reported comparisons, PCA followed by per-coordinate median thresholding yields a more balanced and decodable binary space than the post-hoc-zero-threshold AE/VAE baselines, despite the latter's low continuous reconstruction error. In the measured-library retrieval analysis, simulated annealing, genetic algorithms, and greedy hill climbing frequently return high-percentile variants; decoded candidates are reported separately using surrogate-predicted scores.

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.

Protein modification requires navigating an immense sequence space, yet wet-lab validation remains low-throughput and costly. Although computational paradigms including protein language models (PLMs), large language models (LLMs), and LLM-based agents have shown promise in protein modification, their relative efficacy across realistic experimental decision-making settings remains unclear. To bridge this gap, we introduce PFArena, a benchmark comprising four controlled task interfaces that cover single-mutant generation and multi-mutant ranking. By providing varying levels of mutation fitness data, PFArena reflects four representative research scenarios characterized by differing degrees of prior experimental context. We assess six PLMs, six LLMs, and five LLM-based agents using complementary metrics to measure both peak and overall protein modification performance. Our evaluation reveals that model performance shifts systematically with the availability of target-specific experimental evidence: PLMs demonstrate proficiency in open-ended single-mutant generation by leveraging protein-specific priors, whereas LLMs and agents perform strongly in multi-mutant ranking, particularly when target-specific fitness data are available. Nevertheless, all model families face fundamental challenges with increasing search-space size and mutation depth. We release our code and benchmark suite to facilitate reproducible research in model-assisted protein modification.