HORI-EN: Atomic-level energetic profiling and higher-order network identification in protein structures

Motivation: Characterizing atomic-level stability and cooperative interaction networks is essential for understanding protein function and evolution. However, existing tools often lack the precision to integrate detailed physicochemical energies with higher-order graph-theoretic analyses. Results: We present HORI-EN, an updated implementation to the HORI framework, featuring hybrid energetic scoring (Physicochemical + Knowledge-Based) and a Normalized Interaction Score (NIS) based on cumulative distribution functions. HORI-EN identifies higher-order cliques of interacting residues, revealing cooperative stabilization networks. Validation on the SKEMPI v2 dataset demonstrates that HORI-EN shows discriminative performance in identifying mutational hotspots, achieving an ROC-AUC of 0.780 on the full dataset and 0.844 on a clean benchmark. Enrichment analysis indicates a 3.1-fold increase in precision for the top 1% of predictions. Furthermore, analysis of the residue interaction network recovers 77.4% of non-contacting hotspots by identifying one-hop bridging interactions to the partner chain. Beyond hotspot prediction, HORI-EN distinguishes native structures from decoys and captures conserved energetic signatures in evolutionary case studies of serine proteases and lipases. Availability and Implementation: The web server is freely available at https://caps.ncbs.res.in/HORI-EN and source code is available at https://github.com/thesixeyedknight/HoriPy.