Abstract
There is an increasing accumulation of evidence supporting the existence of a hyperbolic geometry underlying the network representation of complex systems. In particular, it has been shown that the latent geometry of the human protein network (hPIN) captures biologically relevant information, leading to a meaningful visual representation of protein-protein interactions and translating challenging systems biology problems into measuring distances between proteins. Moreover, proteins can efficiently communicate with each other, without global knowledge of the hPIN structure, via a greedy routing (GR) process in which hyperbolic distances guide biological signals from source to target proteins.It is thanks to this effective information routing throughout the hPIN that the cell operates, communicates with other cells and reacts to environmental changes. As a result, the malfunction of one or a few members of this intricate system can disturb its dynamics and derive in disease phenotypes. In fact, it is known that the proteins associated with a single disease agglomerate non-randomly in the same region of the hPIN, forming one or several connected components known as the disease module (DM).Here, we present a geometric characterisation of DMs. First, we found that DM positions on the two-dimensional hyperbolic plane reflect their fragmentation and functional heterogeneity, rendering an informative picture of the cellular processes that the disease is affecting. Second, we used a distance-based dissimilarity measure to cluster DMs with shared clinical features. Finally, we took advantage of the GR strategy to study how defective proteins affect the transduction of signals throughout the hPIN.
Highlights
Regardless of whether they represent the Internet or associations between proteins, people or airports; complex networks share many topological features (Albert and Barabási 2002), which suggests that similar rules govern their formation
Topology and geometry of disease module (DM) After the construction of a high-quality human protein network (hPIN), its embedding to H2 and the evaluation of the embedding, we proceeded to analyse the topological and geometrical properties of DMs formed by the products of genes associated with 157 different diseases
The representation of the human protein interaction network in the two-dimensional hyperbolic plane has been shown to be both meaningful and useful: inferred node coordinates convey information about protein evolution and function, whereas hyperbolic distances can be used to identify potential protein interactions and simulate signalling events (Alanis-Lobato et al 2018). We report yet another scenario in which the latent geometry of the hPIN proves useful, namely the network-based analysis of disease-associated proteins
Summary
Regardless of whether they represent the Internet or associations between proteins, people or airports; complex networks share many topological features (Albert and Barabási 2002), which suggests that similar rules govern their formation. In the native representation of complex networks in the two-dimensional hyperbolic plane H2, the N network nodes are enclosed inside a circle of radius R ∼ ln N, each one lying at polar coordinates (ri, θi) (Krioukov et al 2010). These positions must ensure that connected nodes are close to each other and disconnected nodes are far apart. According to the definition of hyperbolic distance dH2 (i, j) ≈ ri + rj + 2 ln(θij/2) (AlanisLobato and Andrade-Navarro 2016; Krioukov et al 2010; Papadopoulos et al 2012), high-degree nodes are close to the centre of H2 because they need to be nearby many other nodes
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