ADEL: Truth-Anchored Distillation with Engh-Huber-informed Strain and Linkage Chemistry for Macrocycle Design

Designing macrocyclic peptide binders requires more than generating a plausible peptide structure: the ring must close between chemically compatible atoms, and for some linkage types, the identities of these atoms depend on the sequence being designed. In this work, we propose **ADEL**, an all-atom sequence–structure co-design diffusion model that learns to satisfy this coupled geometric and chemical constraint. Our approach combines truth-anchored distillation with Engh–Huber-informed closure geometry and explicit linkage-chemistry supervision. Instead of directly distilling the projection of a sampling-time closure corrector, which we show provides a training signal redundant with the existing closure loss, we distill the model's denoising response after projection and renoising. Because this teacher is produced by the model itself, we introduce a per-atom truth gate that retains a teacher target only when it is closer to the reference structure than the student prediction, preventing the self-distillation objective from drifting during training. We further supervise the local geometry around the closing bond and the residue identities required by sequence-dependent linkages. We retrain six published methods on the same data split and evaluate all generated designs using a common type-aware protocol. On leakage-controlled CPSea targets, our model achieves a macrocycle closure rate of 47.2%, compared with 35.4% for the strongest retrained baseline, while maintaining 99.8% structural validity. Since not all baselines can explicitly represent sequence-dependent linkages, we interpret the aggregate comparison as multi-chemistry coverage rather than a fully matched constraint-solving benchmark. Across head-to-tail, isopeptide, and disulfide linkages, ADEL maintains comparable closure performance within a single co-design framework.