Recursive Constraint Compilation for Guided Protein Backbone Design

Many protein design problems require designing a flexible backbone region while leaving the rest of the protein structurally and functionally intact. This is especially important in tasks such as antibody-loop design, fragment inpainting, and motif-linker design, where a useful design must also connect exactly to fixed structural boundaries. Existing methods for constrained generation can enforce hard geometric constraints but typically do so by modifying the generative process itself or by repairing the structures they have generated. To address this gap, we introduce Recursive Constraint Compilation (RCC), a generator-independent framework that recursively decomposes a global hard constraint into local compatibility conditions and assembles exact local parameterizations into explicit coordinates for valid structures. For fixed-endpoint protein backbones, RCC provides exact, invertible coordinates on regular regions of the constrained space, enabling probability modeling, generation, and guidance while maintaining the geometric constraints throughout inference. We evaluate RCC across pretrained protein generators for antibody-loop design, fragment inpainting, and motif-linker design, as well as in prospective CDR-H3 design. Across these settings, RCC preserves the behavior of existing generators while enforcing exact geometry and enables effective guidance over valid backbones that is not recovered by unconstrained Cartesian optimization followed by post-hoc repair.