ProteinMem: Search-Constrained Agents for Fixed-Budget Protein Sequence Optimization

Protein sequence optimization must search combinatorial spaces while spending only a small number of costly evaluations. LLMs provide adaptable biochemical priors, but unconstrained generation can collapse onto one local hypothesis and poorly allocate a limited budget. We introduce ProteinMem, a closed-loop optimizer that explicitly allocates each batch among reward-directed exploitation, diversity-directed exploration, and history-based recombination, while a fixed LLM proposes mutations within code-verifiable constraints. We compare ProteinMem with thirteen matched baselines on avGFP, Ube4b, GB1, and Bgl3 using 100 reward-model queries and five runs per method. ProteinMem achieves the highest endpoint mean on three of four benchmarks, improving over the strongest baseline by $0.032$ on avGFP, $1.624$ on Ube4b, and $0.351$ on Bgl3. Exact tests distinguish the gains on avGFP and Bgl3. These results support explicit search control as an interface between LLM priors and budgeted protein design.