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 that 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. In our data set 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.

Filtering higher-order datasets

“…Proteins interact with one another to form complex molecules that are essential to cell structure and function. The specific combination of these proteins can create very different resulting molecules, and combinations of more than two proteins can form a higher-order interaction network with vastly different topology than the equivalent pairwise network [ 51 , 52 ], suggesting that the structure of protein networks may vary significantly across interaction sizes.…”

Networks beyond pairwise interactions: structure and dynamics

“…As an alternative, they have proposed an intermediate optimal solution that interpolates between graph and hypergraph approaches and allows to better capture the importance of small molecules involved in many distinct reactions. More recently, Klimm et al [688] have used hypergraphs to investigate multiprotein complex data, showing how a pairwise (network) projection produces a hierarchical structure, that is instead not observed when polyadic interactions are considered. After comparing the protein complexes with appropriate null models, the authors found that larger complexes tend to be more essential, with a hyperdegree that better correlates with gene-essentiality information than the standard graph degree.…”

Hypergraph Neural Architecture Search

“…It designs a hyperedge convolution operation to leverage the high-order correlations across data. Since then, a variety of hypergraph neural networks have been proposed for different learning tasks, including but not limited to image retrieval (Zeng et al 2023), quadratic assignment problem (Wang, Yan, and Yang 2021), biomedical science (Klimm, Deane, and Reinert 2021;Saifuddin et al 2022), keypoint matching (Kim et al 2022) and node classification (Bai, Zhang, and Torr 2021;Gao et al 2022).…”