Relaxed Sequence Sampling for Diverse Protein Design

Protein design using structure prediction models such as AlphaFold2 has shown remarkable success, but existing approaches like relaxed sequence optimization (RSO) rely on single-path gradient descent and ignore sequence-space constraints, limiting diversity and designability. We introduce Relaxed Sequence Sampling (RSS), a Markov chain Monte Carlo (MCMC) framework that integrates structural and evolutionary information for protein design. RSS operates in continuous logit space, combining gradient-guided exploration with protein language model-informed jumps. Its energy function couples AlphaFold2-derived structural objectives with ESM2-derived sequence priors, balancing accuracy and biological plausibility. In an in silico protein binder design task, RSS produces 5$\times$ more designable structures and 2-3$\times$ greater structural diversity than RSO baselines, at equal computational cost. These results highlight RSS as a principled approach for efficiently exploring the protein design landscape.