A Universal Structural Grammar in Enzyme Fold for Predicting Drug Target Stability: Deciphering Directional Scaffolding via Multi-Stage Pearson Correlation of Asymmetric Contact Matrices

Background/Objectives: Traditional protein contact analysis often fails to distinguish between local, sequence-driven motifs and global, tertiary scaffolding, which ensures structural determinism. While deep-learning models do not fully elucidate the ‘why’, they do reveal the underlying directional rules of the stability landscape. In this study, we analyzed 475 non-redundant Protein Data Bank (PDB) structures categorized into SCOP classes (all-α, all-β, α/β, α+β) of the hydrolase superfamily. Methods: To isolate the structural anchors of the global fold, we applied a sequence separation filter of ∣i − j∣ ≥ 6 and a precise spatial cutoff of 3–5 Å between Cα-only to construct asymmetric 20 × 20 frequency matrices, both raw and normalized, then present the former using a violin diagram. We developed a Pearson Correlation (PC) framework to analyze these matrices, providing high correlation when considered as vectors and giving the directionality (N-to-C vs. C-to-N) in protein folding when considered as matrices. Results: Our results reveal a hierarchical organization of tertiary determinism. Initial visualization of Residue–Residue Contact Frequency Matrices (RRCFMs), Z-score normalization (NRRCFM), and violin plots reveal the Universal Structural Grammar (USG) of interaction. Furthermore, a near-perfect PC (r = 0.99) as determined via inter-class Z-score correlation and inter-class PC demonstrates shared statistical interaction laws. In addition, PC Stage 1 (intra-class) analysis identified high symmetry, with around 80% of contacts exhibiting a very strong to strong positive correlations, while PC Stage 2 (inter-class) analysis demonstrated that around 50% of contacts exhibited very strong to strong positive correlations. Finally, we identified universal druggable pockets for drug discovery. Conclusions: This powerful mathematical framework provides a robust analytical tool for structure-based drug design.