. 2021 May 29;22(1):287.

doi: 10.1186/s12859-021-04197-2.

Hypergraph models of biological networks to identify genes critical to pathogenic viral response

Song Feng¹, Emily Heath², Brett Jefferson³, Cliff Joslyn^{3

4}, Henry Kvinge³, Hugh D Mitchell¹, Brenda Praggastis³, Amie J Eisfeld⁵, Amy C Sims⁶, Larissa B Thackray⁷, Shufang Fan⁵, Kevin B Walters⁵, Peter J Halfmann⁵, Danielle Westhoff-Smith⁵, Qing Tan⁷, Vineet D Menachery^{8

9}, Timothy P Sheahan⁸, Adam S Cockrell¹⁰, Jacob F Kocher⁸, Kelly G Stratton¹, Natalie C Heller³, Lisa M Bramer¹, Michael S Diamond^{7

11

12}, Ralph S Baric⁸, Katrina M Waters^{1

13}, Yoshihiro Kawaoka^{5

14

15

16}, Jason E McDermott^{1

17}, Emilie Purvine¹⁸

Affiliations

¹ Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA.
² Department of Mathematics, University of Illinois, Urbana-Champaign, IL, USA.
³ Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA.
⁴ Systems Science Program, Portland State University, Portland, OR, USA.
⁵ Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA.
⁶ Signature Science and Technology Division, Pacific Northwest National Laboratory, Richland, WA, USA.
⁷ Department of Medicine, Washington University School of Medicine, 63110, Saint Louis, MO, USA.
⁸ Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
⁹ Department of Microbiology and Immunology, University of Texas Medical Branch, Galveston, TX, USA.
¹⁰ KNOWBIO LLC., Durham, NC, 27703, USA.
¹¹ Department of Pathology and Immunology, Washington University School of Medicine, St. Louis, MO, USA.
¹² Department of Molecular Microbiology, Washington University School of Medicine, St. Louis, MO, USA.
¹³ Department of Comparative Medicine, University of Washington, Seattle, WA, USA.
¹⁴ Division of Virology, Department of Microbiology and Immunology, Institute of Medical Science, University of Tokyo, Tokyo, 108-8639, Japan.
¹⁵ ERATO Infection-Induced Host Responses Project, Saitama, 332-0012, Japan.
¹⁶ Department of Special Pathogens, International Research Center for Infectious Diseases, Institute of Medical Science, University of Tokyo, Tokyo, 108-8639, Japan.
¹⁷ Department of Molecular Microbiology and Immunology, Oregon Health and Science University, Portland, OR, USA.
¹⁸ Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA. emilie.purvine@pnnl.gov.

PMID: 34051754
PMCID: PMC8164482
DOI: 10.1186/s12859-021-04197-2

Hypergraph models of biological networks to identify genes critical to pathogenic viral response

Song Feng et al. BMC Bioinformatics. 2021.

. 2021 May 29;22(1):287.

doi: 10.1186/s12859-021-04197-2.

Authors

Affiliations

¹ Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA.
² Department of Mathematics, University of Illinois, Urbana-Champaign, IL, USA.
³ Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA.
⁴ Systems Science Program, Portland State University, Portland, OR, USA.
⁵ Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA.
⁶ Signature Science and Technology Division, Pacific Northwest National Laboratory, Richland, WA, USA.
⁷ Department of Medicine, Washington University School of Medicine, 63110, Saint Louis, MO, USA.
⁸ Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
⁹ Department of Microbiology and Immunology, University of Texas Medical Branch, Galveston, TX, USA.
¹⁰ KNOWBIO LLC., Durham, NC, 27703, USA.
¹¹ Department of Pathology and Immunology, Washington University School of Medicine, St. Louis, MO, USA.
¹² Department of Molecular Microbiology, Washington University School of Medicine, St. Louis, MO, USA.
¹³ Department of Comparative Medicine, University of Washington, Seattle, WA, USA.
¹⁴ Division of Virology, Department of Microbiology and Immunology, Institute of Medical Science, University of Tokyo, Tokyo, 108-8639, Japan.
¹⁵ ERATO Infection-Induced Host Responses Project, Saitama, 332-0012, Japan.
¹⁶ Department of Special Pathogens, International Research Center for Infectious Diseases, Institute of Medical Science, University of Tokyo, Tokyo, 108-8639, Japan.
¹⁷ Department of Molecular Microbiology and Immunology, Oregon Health and Science University, Portland, OR, USA.
¹⁸ Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA. emilie.purvine@pnnl.gov.

PMID: 34051754
PMCID: PMC8164482
DOI: 10.1186/s12859-021-04197-2

Abstract

Background: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems. Hypergraphs are generalizations of graphs that naturally model multi-way relationships and have shown promise in modeling systems such as protein complexes and metabolic reactions. In this paper we seek to understand how hypergraphs can more faithfully identify, and potentially predict, important genes based on complex relationships inferred from genomic expression data sets.

Results: We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges represent significantly perturbed genes, and vertices represent individual biological samples with specific experimental conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality.

Conclusions: Our results demonstrate the utility of using hypergraphs to represent complex biological systems and highlight central important responses in common to a variety of highly pathogenic viruses.

Keywords: Biological networks; Host response; Hypergraph; Influenza; MERS; SARS; Systems biology; Viral infection; Viral pathogenesis; West Nile Virus.

PubMed Disclaimer

Conflict of interest statement

RB has ongoing unrelated collaborations and/or sponsored research agreements with Moderna, VaxArt, Eli Lily, Pfizer, Takeda and Ridgeback Biosciences. MD is a consultant for Inbios, Vir Biotechnology, and Fortressa Biotech and on the Scientific Advisory Boards of Moderna and Immunome. The Diamond laboratory has received unrelated funding support in sponsored research agreements from Moderna, Vir Biotechnology, Kaleido, and Emergent BioSolutions.

Figures

**Fig. 1**
Transcriptomics example comparing graphs and hypergraphs. (Upper left) ${log}_{2}$ -fold change values for 5 genes across 4 conditions. (Lower left) Visualization of a corresponding hypergraph. (Upper right) Adjacency matrix for expression data. (Lower right) Underlying graph

**Fig. 2**
Small connected subset of the condition/gene hypergraph. Hyperedges are genes, and black circles indicate groups of vertices (conditions), with larger circles indicating larger groups

**Fig. 3**
Distributions of simple hypergraph statistics of our hypergraph. a Edge size distribution. Each edge represents a gene, the size of the edge is the number of conditions in which the gene is significantly perturbed. b Vertex degree histogram. Each vertex represents a condition, the degree of a vertex is the number of genes significantly perturbed in that condition. c Pairwise edge intersection size distribution. Each edge represents a gene. The intersection between two edges indicates the set of conditions that both genes are significantly perturbed in

**Fig. 4**
Enrichment scores of gene sets using average s-betweenness and s-harmonic closeness metrics. All results are significant with $p < 0.05$

**Fig. 5**
Comparison between different hypergraph and graph metrics

See this image and copyright information in PMC

References

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Hypergraph models of biological networks to identify genes critical to pathogenic viral response

Affiliations

Hypergraph models of biological networks to identify genes critical to pathogenic viral response

Authors

Affiliations

Abstract

Conflict of interest statement

Figures

References

MeSH terms

Substances

Grants and funding

LinkOut - more resources

Full Text Sources

Other Literature Sources

Molecular Biology Databases

Miscellaneous