Hypergraphs for predicting essential genes using multiprotein complex data

Abstract

Protein-protein interactions are crucial in many biological pathways and facilitate cellular function. Investigating these interactions as a graph of pairwise interactions can help to gain a systemic understanding of cellular processes. It is known, however, that proteins interact with each other not exclusively in pairs but also in polyadic interactions and they can form multiprotein complexes, which are stable interactions between multiple proteins. In this manuscript, we use hypergraphs to investigate multiprotein complex data. We investigate two random null models to test which hypergraph properties occur as a consequence of constraints, such as the size and the number of multiprotein complexes. We find that assortativity, the number of connected components, and clustering differ from the data to these null models. Our main finding is that projecting a hypergraph of polyadic interactions onto a graph of pairwise interactions leads to the identification of different proteins as hubs than the hypergraph. We find in our data set that the hypergraph degree is a more accurate predictor for gene-essentiality than the degree in the pairwise graph. We find that analysing a hypergraph as pairwise graph drastically changes the distribution of the local clustering coefficient. Furthermore, using a pairwise interaction representing multiprotein complex data may lead to a spurious hierarchical structure, which is not observed in the hypergraph. Hence, we illustrate that hypergraphs can be more suitable than pairwise graphs for the analysis of multiprotein complex data.

Effective epidemic containment strategy in hypergraphs

“…One is the congressional bill cosponsorship hypergraph [19,30], which has 536 nodes and 2773 hyperedges whose mean size is 16.57 and maximum size is 323. Each node represents a US congressperson, and if a set of d congresspeople cosponsored a bill in the year 2000, they are connected by a hyperedge of size d. The other is the protein interaction hypergraph [32], which has 8243 nodes and 6688 hyperedges whose mean size is 10.12 and maximum size is 421. Each node in the hypergraph represents a protein, and each hypergraph represents a type of multiprotein complex.…”

“…In a collaboration hypergraph [29,30], for instance, a hyperedge of size d encodes a d-author paper, and the nodes of the hyperedge encodes the authors of the paper. Hypergraphs have been used to describe neural and biological interactions [31,32], evolutionary dynamics [33,34], and other dynamical processes [35][36][37][38]. Recently, the simplicial susceptible-infected-susceptible (s-SIS) model [39] * jhunbk@snu.ac.kr was introduced to describe higher-order epidemic process in hypergraphs.…”

Higher-Order Networks

“…In This construction can be easily generalized to generate canonical ensembles of hypergraphs if each layer of the multiplex network construction is drawn from a canonical pure simplicial complex ensemble rather than from the pure configuration model of simplicial complexes. This model and its generalizations capturing higher-order networks formed by collections of arbitrary subgraphs [53] can be very useful to investigate the structure of real higherorder datasets [54] and to study dynamical processes. This ensemble has been recently adopted to study higher-order percolation processes [55].…”

“…Figure54 A schematic representation of the phase diagram of a contagion process on a hypergraph configuration model including pariwise interactions and 3-body interactions only. For 1 > 1c the contagion process is in an infection phase, without bistability.…”

Adaptive Neural Message Passing for Inductive Learning on Hypergraphs

“…Representing multimodal relations in the collective information generated when a user posts a tweet with an image containing multiple hashtags is infeasible using binary pairwise relations [47] or by considering tweets, users, and images as non-related channels. Hypergraphs efficiently represent multimodal objects with higher-order relations inside a channel and among channels in various domains such as visual arts [5], discussion forums [6], visual question answering systems [41], music recommender systems [14] and protein-protein interaction networks [45].…”