Lo-Shu Geometric Instability Index (GII_drug) as a Multi-Layer Pharmacological Descriptor: From TNF Inhibitor Immunogenicity to Organ-Specific irAE Prediction in Checkpoint Inhibitors

We introduce GII_drug (Geometric Instability Index), a Lo-Shu magic square-based descriptor quantifying drug-target interface contact distribution. Three datasets demonstrate its utility as an independent pharmacological information layer: (1) TNF inhibitors (N=3): GII_drug perfectly rank-orders clinical immunogenicity (infliximab 0.967 > adalimumab 0.683 > etanercept 0.350), corresponding to 2.76-fold range in anti-drug antibody rates. (2) Polypharmacology classification (N=22 drugs): GII_drug forms three distinct zones — Hub (natural products, 0.302±0.021), Calibrated (broad kinase inhibitors, 0.429±0.025), Focused (selective mAbs, 0.821±0.092; all pairwise p<0.005). Approved vs. failed oncology pilot (N=20+20): ROC AUC=0.892, optimal threshold GII≥0.643 (Specificity=1.00). (3) Checkpoint inhibitor irAE (N=10): GII_drug predicts Grade 3+ irAE (rho=+0.648, p=0.042) and skin irAE (rho=+0.818, p=0.004). Critically, pneumonitis shows no correlation (rho=+0.236, p=0.511), confirming GII_drug as a specific T-cell effector descriptor rather than a global toxicity index. Shape complementarity (Sc) predicts colitis (rho=+0.936, p=0.0001) and skin irAE (rho=+0.979, p<0.001). GII_drug constitutes an independent geometric layer complementing existing structure-based tools for biologic drug safety pre-screening.