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. Many descriptor-based approaches characterize ligand binding sites using a fixed distance threshold from the ligand, despite substantial variability in how such thresholds are defined and the possibility that relevant structural and compositional information changes across spatial scales. We propose Functional Unification of Structural and Elemental Descriptors (FUSED), a multivariate functional representation that jointly models structural and elemental compositional information on 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 account appropriately for compositional geometry. Treating distance from the ligand as a functional domain allows structural and compositional characteristics to be examined across distance thresholds rather than at a single prespecified value. The resulting representation can be used directly or combined with dimension-reduction, statistical-learning, and/or machine-learning procedures, with the distance interval tailored to the data set, analytical task, and procedure. We evaluate FUSED on three benchmark data sets spanning complementary ligand binding-site analysis tasks: the Extended Kahraman data set for multiclass ligand discrimination, TOUGH-C1 for three-class binding-site classification, and TOUGH-M1 for pairwise matching of pockets associated with drug-like ligands. FUSED supports strong discrimination in the EK and TOUGH-C1 tasks using standard statistical-learning procedures, while a supervised Siamese neural network applied to the full FUSED representation achieves a mean ROC-AUC of 0.9375 on TOUGH-M1 under repeated sequence-cluster-disjoint evaluation. Matched evaluations against leading available methods demonstrate competitive performance, with relative advantages depending on the task and comparator. Two illustrative retrieval cases identify pockets binding identical or chemically related ligands despite low global sequence and structural similarity between the proteins. These results demonstrate that FUSED provides a flexible, alignment-free representation that supports both direct examination of threshold-dependent binding-site characteristics and competitive downstream classification and pocket matching while remaining computationally practical.