Multiscale Fractal Features Detect Controlled Hinge Perturbations in Protein Structures

Protein models can retain plausible global shape despite scale-specific packing distortions. Screening needs features capturing organization across distance scales. We introduce an eight-feature representation of C$\alpha$ neighbor-count scaling from 5–20 Å. We introduce Fractal Structural Conformity (FSC) as a reference-distribution score. We selected 75 RCSB X-ray entries with $\leq 2.5$ Å resolution from 30% sequence-identity clusters. We processed one 82–247-residue chain per entry with Biopython. Six four-hinge perturbations per chain generated 450 controls across $7.5^\circ$–$60^\circ$ rotations while preserving adjacent C$\alpha$ distances. Features measured effective dimension and power-law behavior plus surface–core contrast across scales. Baselines used radius of gyration plus 8 Å density and anisotropy. Five-fold PDB-grouped cross-validation used within-fold standardization and class-weighted logistic regression. Whole-PDB bootstrapping estimated uncertainty. Fractal AUROC was 0.836 (95% CI 0.804–0.867) versus 0.590 for geometry. The paired fractal-minus-geometry difference was 0.246 (95% CI 0.201–0.291). Fifty-six controls within 1 Å RMSD yielded fractal AUROC 0.587. Fractal AUPRC was 0.364 versus a 0.143 prevalence baseline. Median within-target Spearman $\rho$ between fractal classifier score and negative C$\alpha$ RMSD was 0.771 (95% CI 0.657–0.771). Correlations were positive for 73/75 targets. Multiscale features outperformed global geometry on controlled hinge perturbations, although near-reference discrimination remained modest. Using only C$\alpha$ coordinates and a reference distribution enables target-independent reranking of candidate structures. Independent decoy and predicted-structure validation remains future work.