Energetic networks of lone pair–π interactions in phycobiliprotein interfaces: structural organization, geometry, and cooperative stabilization

Abstract

Lone pair–π interactions represent an underexplored class of noncovalent forces in protein architecture, despite their fundamental electronic significance. Here, we present a comprehensive computational and bioinformatics analysis of lone pair–π interactions at phycobiliprotein interfaces based on 20 high-resolution X-ray crystal structures. Using defined geometric criteria and ab initio quantum-chemical calculations at the LMP2/cc-pVTZ++ level on reduced molecular models, we systematically characterized their distribution, geometry, topology, and energetic contributions. We identified 2,245 lone pair–π interactions, revealing a highly nonrandom and chemically selective interaction landscape dominated by oxygen-based lone pair donors and aromatic π acceptors, particularly Tyr and Phe. Geometric analysis showed strong distance and angular preferences, consistent with directional donor–acceptor orbital interactions rather than nonspecific packing effects. Energy calculations revealed a structured interaction potential surface, with stabilizing energies clustering in the −0.1 to −5.0 kJ mol⁻¹ range within defined geometric domains. Network analysis further demonstrated that more than half of the interactions participate in cooperative, furcated lone pair–π motifs, generating interfacial stabilization through multivalent interaction networks. Collectively, these results establish lone pair–π interactions as geometry-encoded, energetically selective, and cooperatively organized stabilizing elements that contribute to interfacial specificity, structural precision, and quaternary structure stability in phycobiliprotein assemblies.