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

1 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 α RMSD of 1.76 Å, compared with 83.3 and 1.86 Å, respectively, for ESM-IF1, the strongest evaluated baseline on both metrics. Denoising trajectory analyses showed that positions commit at different rates and that some residues change identity late in generation, illustrating whole-sequence refinement rather than one-shot prediction or irreversible sequential decoding. We experimentally tested Inverse FoldDir in an anti-GFP nanobody redesign task, where two of 35 redesigned sequences retained reproducible sfGFP-binding signal across independent assay runs with approximately 43% sequence divergence from the native nanobody. Inverse FoldDir is a structure-conditioned protein redesign method that combines structural recovery, user control, experimental validation, and a natural route toward future property-guided sampling.