EnerBridge-DPO: Energy-Aware Markov Bridge Inverse Folding for Protein Sequence Design

Designing protein sequences with favorable predicted energetic properties is an important challenge in protein inverse folding, because many existing deep learning methods are primarily trained by maximizing sequence recovery and do not explicitly incorporate energy-related preferences during generation. In this work, we propose EnerBridge-DPO, an energy-aware inverse folding framework that integrates Markov bridge sequence generation with preference optimization for protein complex design. The framework builds on the Markov bridge inverse-folding process to generate structure-compatible sequences from an informative prior sequence. It then introduces a Bridge-DPO objective that uses energy-related winner-loser preference pairs to bias the generator toward sequences favored by computational or experimental energy-related signals. In addition, we incorporate a quantitative energy-constrained loss based on mutation-induced binding free-energy changes to provide continuous ΔΔG supervision. Evaluations show that EnerBridge-DPO maintains competitive inverse-folding performance while obtaining lower predicted energy scores under selected computational scoring functions for protein complexes. On SKEMPI, EnerBridge-DPO achieves competitive ΔΔG prediction performance, with small numerical gains in several overall metrics that are not statistically conclusive under paired bootstrap analysis. These results suggest that incorporating energy-related preferences into Markov bridge inverse folding can improve computationally predicted energetic profiles, although experimental validation is required to confirm thermodynamic stability.