Scaled and Weighted Laplacian Matrices as Functional Descriptors for GPCR Ligands

The G protein-coupled receptor (GPCR) pharmacology accounts for a significant field in research, clinical studies, and therapeutics. Computer-aided drug discovery is an evolving suite of techniques and methodologies that facilitate accelerated progress in drug discovery and repositioning. However, the structure-activity relationships of molecules targeting GPCRs are highly challenging in many cases since slight structural modifications can lead to drastic changes in biological functionality. Numerous molecular descriptors have been described, many of which successfully characterize the structural and physicochemical features of drug sets. Nonetheless, elucidating the structure-functionality relationships over extensive sets of drugs with multiple structural variations and known biological activity remains challenging in various biological systems. This work presents novel topological descriptors using Laplacian matrices, weighted, and scaled by atomic mass and partial charges. We tested these descriptors on three sets of GPCR ligands: muscarinic, β-adrenergic, and δ-opioid receptor ligands, evaluating their potential as functional descriptors of these receptors.