Modelling protein-protein interaction networks

Proteins, the main motors of the cell, are in charge of performing a diverse array of biological functions. They rarely perform those functions alone, but generally work as groups of proteins that through a complex array of interactions perform a single biological function. These complex interactions between different proteins are often analysed via network theory, where a protein-protein interaction (PPI) network is created considering each protein as a node and each of their interactions as edges. Different approaches from the perspective of network analysis have been proposed to describe, analyse, and predict PPI networks. Some methods focus on the use of network summary statistics, community detection, random graph models, and machine learning procedures. However, despite the large effort invested in PPI network research, current models fail to describe well the structure of PPI networks. Small overrepresented subgraphs, which have been thought as the building blocks of networks, have been shown to be important patterns in gene regulatory networks, and there is evidence that suggests they may be evolutionarily conserved across the PPI networks of different organisms. Hence, a first step to better understand the structure of protein-protein interaction networks, is to describe how the local structure of these networks, accounted by the occurrence of small connected subgraphs, is created. We approach this problem in two stages. In the first stage, we provide a framework to statistically assess if a random graph model can describe the occurrence of different small connected subgraphs observed in PPI networks. Then, by applying this framework we find that state-of-the-art network comparison methods based on subgraph counts struggle at finding similarities between networks that have different numbers of nodes or edges. Hence, in joint work with Dr. Anatol Wegner, Dr. Robert Gaunt, Professor Gesine Reinert, and Professor Charlotte M. Deane, we propose a novel network comparison method, NetEmd, that tackles this problem indirectly by proposing a method that is invariant to translations and rescalings of subgraph count distributions, and which is better able to detect similarities across networks with different number of nodes or edges. In the second stage, we use NetEmd, along with three other state-of-the-art network comparison methods, to test the ability of several random graph models to describe the occurrence of subgraphs counts in the PPI networks of six organisms, and in multiple smaller sections of these networks. We find that the overall occurrence of small connected subgraphs could potentially be described by two network generation mechanisms operating in complementary sections of the PPI networks. In addition we find that cellular compartment-specific PPI networks can be potentially described by a single model that captures, with only two parameters, both, the common properties between the different cellular compartment networks, and their individual structural features.