Unraveling cooperative and competitive interactions within protein triplets in the human interactome

Knowledge about protein-protein interactions (PPIs) is crucial for our understanding of cellular functions. An important contribution to these comes from experimental high-throughput techniques such as yeast two-hybrid (Y2H), which provide evidence for direct, binary PPIs. Consequently, although protein function often emerges from interactions within multi-protein assemblies, most PPI networks focus on binary relationships. Higher-order motifs, such as protein triplets, can reflect cooperative or competitive binding events crucial for cellular function. However, distinguishing these interaction types systematically from a network of binary PPIs remains challenging. To address this issue, we present a computational framework to predict cooperative and competitive interactions among protein triplets in the human Protein Interaction Network (hPIN). By embedding the hPIN into two-dimensional hyperbolic space using the LaBNE+HM algorithm, we extracted latent geometric coordinates for each protein. Combined with topological features and biological annotations, these were used to train a Random Forest classifier on structurally validated triplets from Interactome3D. Our model achieved strong performance (AUC = 0.88), identifying angular and hyperbolic distances as two of the most predictive features. Cooperative triplets were characterized by longer common proteins and a lower frequency of paralogous partners, indicating distinct structural and evolutionary features compared to competitive cases. Structural evaluation using AlphaFold 3 confirmed that cooperative triplets exhibit distinct binding sites, whereas competitive ones share overlapping interfaces. Hyperbolic embeddings, in combination with machine learning, offer a powerful approach to characterize higher-order interaction motifs in protein networks. Our findings provide mechanistic insights into the organization of protein complexes and a predictive framework to support future studies in network biology.