Inverse FoldDir: Structure-conditioned Protein Sequence Design by Dirichlet Flow Matching.

Protein engineering has important implications in the bioeconomy, enabling applications in materials, medicine, and energy. A key challenge is designing protein sequences that have a specific form and function. Protein inverse folding seeks to address this challenge by identifying amino acid sequences compatible with a desired protein backbone. This task is central to protein redesign and can provide a sequence-design capability for de novo backbones produced by structure-generation methods. Ideally, inverse folding can provide diverse sequence alternatives, fixed residues or motifs, soft biochemical preferences at selected positions, and candidates that remain experimentally useful. We developed Inverse FoldDir, a controllable inverse-folding method that performs iterative denoising on the amino acid probability simplex. Given a backbone structure, the model updates all positions jointly through a learned Dirichlet flow, supporting full sequence generation, fixed-residue inpainting, and user-defined soft residue priors. On the held-out CATH 4.2 test set, Inverse FoldDir achieved a mean TM-score of 84.5 (on a 0-100 scale) and a mean C