RosettaSearch: Multi-Objective Inference-Time Search for Protein Sequence Design

We introduce RosettaSearch, an inference-time multi-objective optimization framework for backbone-conditioned protein sequence design that instantiates a closed-loop design-evaluate-refine workflow using large language models (LLMs) as generative optimizers. At each iteration, structured rewards and residue-level feedback from RosettaFold3 drive targeted sequence refinement across multiple candidate trajectories in parallel, within a strictly bounded budget of 75 structure prediction calls per design task. In a large-scale evaluation on $\approx$400 protein redesign tasks, RosettaSearch achieves 18--68\% improvements in structural fidelity metrics over sequences generated by LigandMPNN, translating to a $2.5\times$ improvement in design success rate. Gains are robust under an independent structure predictor (Chai-1) and generalize across two LLM families (o4-mini and Gemini-3), with performance scaling consistently with reasoning capability. We further extend the framework to vision-language models, where rendered images of predicted structures provide spatial feedback that produces richer structural reasoning in the model's chain-of-thought. To our knowledge, this is the first large-scale demonstration that LLMs can serve as effective generative optimizers for backbone-conditioned protein sequence design, yielding systematic gains without any model retraining or fine-tuning.