FUSED: A Functional Representation for Joint Structural and Elemental Analysis of Protein Ligand Binding Sites

Ligand binding site representations are central to the analysis of protein-ligand interactions, with applications in functional characterization, binding-site comparison, and ligand recognition. Most existing approaches characterize ligand binding sites at a single distance threshold from the ligand, despite substantial variability in how such thresholds are defined and the likelihood that relevant structural and compositional information evolves across spatial scales. We propose Functional Unification of Structural and Elemental Descriptors (FUSED), a multivariate functional rep-resentation that jointly models structural and elemental compositional information of ligand binding sites as functions of distance from the ligand. Structural information is captured through covariance-based descriptors derived from the CDPA framework, while chemical composition is represented through isometric log-ratio coordinates to appropriately account for compositional geometry. Treating distance from the ligand as a continuous functional domain allows the representation to capture evolving patterns that would be lost under fixed-threshold analyses and enables data-driven identification of informative distance ranges. We evaluate FUSED on two benchmark datasets: the Extended Kahraman dataset for multiclass ligand discrimination and the TOUGH-C1 dataset for binary binding-site classification tasks. Across both datasets, the proposed framework yields compact low-dimensional representations with clear discriminatory structure and competitive predictive performance relative to established alignment-based, sequence-based, and machine learning approaches, while maintaining interpretability and low computational cost. These results suggest that functional joint modeling of structural and compositional descriptors provides an effective and flexible framework for ligand binding site analysis.