Motivation: A series of recently introduced algorithms and models advocates for the existence of a hyperbolic geometry underlying the network representation of complex systems. Since the human protein interaction network (hPIN) has a complex architecture, we hypothesized that uncovering its latent geometry could ease challenging problems in systems biology, translating them into measuring distances between proteins. Results: We embedded the hPIN to hyperbolic space and found that the inferred coordinates of nodes capture biologically relevant features, like protein age, function and cellular localization. This means that the representation of the hPIN in the two-dimensional hyperbolic plane offers a novel and informative way to visualize proteins and their interactions. We then used these coordinates to compute hyperbolic distances between proteins, which served as likelihood scores for the prediction of plausible protein interactions. Finally, we observed that proteins can efficiently communicate with each other via a greedy routing process, guided by the latent geometry of the hPIN. We show that these efficient communication channels can be used to determine the core members of signal transduction pathways and to study how system perturbations impact their efficiency. Availability and implementation: An R implementation of our network embedder is available at https://github.com/galanisl/NetHypGeom. Also, a web tool for the geometric analysis of the hPIN accompanies this text at http://cbdm-01.zdv.uni-mainz.de/~galanisl/gapi. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Most functions within the cell emerge thanks to protein-protein interactions (PPIs), yet experimental determination of PPIs is both expensive and time-consuming. PPI networks present significant levels of noise and incompleteness. Predicting interactions using only PPI-network topology (topological prediction) is difficult but essential when prior biological knowledge is absent or unreliable. METHODS: Network embedding emphasizes the relations between network proteins embedded in a low-dimensional space, in which protein pairs that are closer to each other represent good candidate interactions. To achieve network denoising, which boosts prediction performance, we first applied minimum curvilinear embedding (MCE), and then adopted shortest path (SP) in the reduced space to assign likelihood scores to candidate interactions. Furthermore, we introduce (i) a new valid variation of MCE, named non-centred MCE (ncMCE); (ii) two automatic strategies for selecting the appropriate embedding dimension; and (iii) two new randomized procedures for evaluating predictions. RESULTS: We compared our method against several unsupervised and supervisedly tuned embedding approaches and node neighbourhood techniques. Despite its computational simplicity, ncMCE-SP was the overall leader, outperforming the current methods in topological link prediction. CONCLUSION: Minimum curvilinearity is a valuable non-linear framework that we successfully applied to the embedding of protein networks for the unsupervised prediction of novel PPIs. The rationale for our approach is that biological and evolutionary information is imprinted in the non-linear patterns hidden behind the protein network topology, and can be exploited for predicting new protein links. The predicted PPIs represent good candidates for testing in high-throughput experiments or for exploitation in systems biology tools such as those used for network-based inference and prediction of disease-related functional modules. AVAILABILITY: https://sites.google.com/site/carlovittoriocannistraci/home. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.