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Fast Approximate Shortest Hyperpaths for Inferring Pathways in Cell Signaling Hypergraphs

Authors Spencer Krieger , John Kececioglu

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Spencer Krieger
  • Department of Computer Science, The University of Arizona, Tucson, AZ, USA
John Kececioglu
  • Department of Computer Science, The University of Arizona, Tucson, AZ, USA


We thank T.M. Murali for introducing us to the problem of shortest hyperpaths in cell-signaling hypergraphs, orienting us to the biology literature, and discussing the JUP/DSP example; Anna Ritz for discussing the NCI-PID and Reactome datasets, and providing the BioPax parser; and the anonymous referees for their helpful comments.

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Spencer Krieger and John Kececioglu. Fast Approximate Shortest Hyperpaths for Inferring Pathways in Cell Signaling Hypergraphs. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 20:1-20:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Cell signaling pathways, which are a series of reactions that start at receptors and end at transcription factors, are basic to systems biology. Properly modeling the reactions in such pathways requires directed hypergraphs, where an edge is now directed between two sets of vertices. Inferring a pathway by the most parsimonious series of reactions then corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. The state of the art for shortest hyperpaths in cell-signaling hypergraphs solves a mixed-integer linear program to find an optimal hyperpath that is restricted to be acyclic, and offers no efficiency guarantees. We present for the first time a heuristic for general shortest hyperpaths that properly handles cycles, and is guaranteed to be efficient. Its accuracy is demonstrated through exhaustive experiments on all instances from the standard NCI-PID and Reactome pathway databases, which show the heuristic finds a hyperpath that matches the state-of-the-art mixed-integer linear program on over 99% of all instances that are acyclic. On instances where only cyclic hyperpaths exist, the heuristic surpasses the state-of-the-art, which finds no solution; on every such cyclic instance, enumerating all possible hyperpaths shows that the solution found by the heuristic is in fact optimal.

Subject Classification

ACM Subject Classification
  • Applied computing → Bioinformatics
  • Applied computing → Systems biology
  • Theory of computation → Shortest paths
  • Mathematics of computing → Hypergraphs
  • Systems biology
  • cell signaling networks
  • reaction pathways
  • directed hypergraphs
  • shortest hyperpaths
  • efficient heuristics
  • hyperpath enumeration


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  1. Vicente Acuña, Paulo Vieira Milreu, Ludovic Cottret, Alberto Marchetti-Spaccamela, Leen Stougie, and Marie-France Sagot. Algorithms and complexity of enumerating minimal precursor sets in genome-wide metabolic networks. Bioinformatics, 28(19):2474-2483, July 2012. Google Scholar
  2. Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walter. Molecular Biology of the Cell. Garland Science, New York, 2007. Google Scholar
  3. Ricardo Andrade, Martin Wannagat, Cecilia C. Klein, Vicente Acuña, Alberto Marchetti-Spaccamela, Paulo V. Milreu, Leen Stougie, and Marie-France Sagot. Enumeration of minimal stoichiometric precursor sets in metabolic networks. Algorithms for Molecular Biology, 11(1):25, 2016. Google Scholar
  4. Giorgio Ausiello and Luigi Laura. Directed hypergraphs: introduction and fundamental algorithms - a survey. Theoretical Computer Science, 658:293-306, 2017. Google Scholar
  5. Pablo Carbonell, Davide Fichera, Shashi B. Pandit, and Jean-Loup Faulon. Enumerating metabolic pathways for the production of heterologous target chemicals in chassis organisms. BMC Systems Biology, 6(1):10, 2012. Google Scholar
  6. Tobias S. Christensen, Ana P. Oliveira, and Jens Nielsen. Reconstruction and logical modeling of glucose repression signaling pathways in Saccharomyces cerevisiae. BMC Systems Biology, 3(1):7, 2009. Google Scholar
  7. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. MIT Press, Cambridge, Massachusetts, 3rd edition, 2009. Google Scholar
  8. Ludovic Cottret, Paulo Vieira Milreu, Vicente Acuña, Alberto Marchetti-Spaccamela, Fábio Viduani Martinez, Marie-France Sagot, and Leen Stougie. Enumerating precursor sets of target metabolites in a metabolic network. In Proceedings of the 8th Workshop on Algorithms in Bioinformatics, pages 233-244, 2008. Google Scholar
  9. Emek Demir, Özgün Babur, Igor Rodchenkov, Bülent Arman Aksoy, Ken I Fukuda, Benjamin Gross, Onur Selçuk Sümer, Gary D Bader, and Chris Sander. Using biological pathway data with Paxtools. PLoS Computational Biology, 9(9):e1003194, 2013. Google Scholar
  10. Emek Demir, Michael P. Cary, and Suzanne Paley et al. The BioPAX community standard for pathway data sharing. Nature Biotechnology, 28(9):935-942, 2010. Google Scholar
  11. Nicholas Franzese, Adam Groce, T.M. Murali, and Anna Ritz. Hypergraph-based connectivity measures for signaling pathway topologies. PLoS Computational Biology, 15(10):1-26, October 2019. Google Scholar
  12. Giorgio Gallo, Giustino Longo, Stefano Pallottino, and Sang Nguyen. Directed hypergraphs and applications. Discrete Applied Mathematics, 42(2-3):177-201, 1993. Google Scholar
  13. H.W. Hamacher and M. Queyranne. K best solutions to combinatorial optimization problems. Annals of Operations Research, 4:123-143, 1985. Google Scholar
  14. Lenwood S. Heath and Allan A. Sioson. Semantics of multimodal network models. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 6(2):271-280, 2009. Google Scholar
  15. X Hou, J-E Liu, W Liu, C-Y Liu, Z-Y Liu, and Z-Y Sun. A new role of NUAK1: directly phosphorylating p53 and regulating cell proliferation. Oncogene, 30(26):2933-2942, June 2011. Google Scholar
  16. Zhenjun Hu, Joe Mellor, Jie Wu, Minoru Kanehisa, Joshua M. Stuart, and Charles DeLisi. Towards zoomable multidimensional maps of the cell. Nature Biotechnology, 25(5):547-554, 2007. Google Scholar
  17. Maya Huguenin, Elaine J. Müller, Sandra Trachsel-Rösmann, Beatrice Oneda, Daniel Ambort, Erwin E. Sterchi, and Daniel Lottaz. The metalloprotease meprinbeta processes E-cadherin and weakens intercellular adhesion. PLoS One, 3(5):e2153, May 2008. Google Scholar
  18. Giuseppe F. Italiano and Umberto Nanni. Online maintenance of minimal directed hypergraphs. Technical report, Department of Computer Science, Columbia University, 1989. Google Scholar
  19. G. Joshi-Tope, M. Gillespie, I. Vastrik, P. D'Eustachio, E. Schmidt, B. de Bono, B. Jassal, G.R. Gopinath, G.R. Wu, L. Matthews, S. Lewis, E. Birney, and L. Stein. Reactome: a knowledgebase of biological pathways. Nucleic Acids Research, 33:D428-432, 2005. Google Scholar
  20. Steffen Klamt, Utz-Uwe Haus, and Fabian Theis. Hypergraphs and cellular networks. PLoS Computational Biology, 5(5):e1000385, 2009. Google Scholar
  21. Susana Miravet, José Piedra, Julio Castaño, Imma Raurell, Clara Francì, Mireia Duñach, and Antonio García de Herreros. Tyrosine phosphorylation of plakoglobin causes contrary effects on its association with desmosomes and adherens junction components and modulates β-catenin-mediated transcription. Molecular and Cellular Biology, 23(20):7391-7402, 2003. Google Scholar
  22. Lars Relund Nielsen and Daniele Pretolani. A remark on the definition of a B-hyperpath. Technical report, Department of Operations Research, University of Aarhus, 2001. Google Scholar
  23. Felipe Palacios, Jogender S. Tushir, Yasuyuki Fujita, and Crislyn D'Souza-Schorey. Lysosomal targeting of E-cadherin: a unique mechanism for the down-regulation of cell-cell adhesion during epithelial to mesenchymal transitions. Molecular and Cellular Biology, 25(1):389-402, 2005. Google Scholar
  24. Emad Ramadan, Sudhir Perincheri, and David Tuck. A hyper-graph approach for analyzing transcriptional networks in breast cancer. In Proceedings of the 1st ACM Conference on Bioinformatics and Computational Biology, pages 556-562, 2010. Google Scholar
  25. Emad Ramadan, Arijit Tarafdar, and A. Pothen. A hypergraph model for the yeast protein complex network. In Proceedings of the 18th Parallel and Distributed Processing Symposium, pages 189-196, 2004. Google Scholar
  26. Anna Ritz, Brendan Avent, and T.M. Murali. Pathway analysis with signaling hypergraphs. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 14(5):1042-1055, 2017. Google Scholar
  27. Anna Ritz and T.M. Murali. Pathway analysis with signaling hypergraphs. In Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics, pages 249-258, 2014. Google Scholar
  28. Anna Ritz, Allison N. Tegge, Hyunju Kim, Christopher L. Poirel, and T.M. Murali. Signaling hypergraphs. Trends in Biotechnology, 32(7):356-362, 2014. Google Scholar
  29. Carl F. Schaefer, Kira Anthony, Shiva Krupa, Jeffrey Buchoff, Matthew Day, Timo Hannay, and Kenneth H. Buetow. PID: the Pathway Interaction Database. Nucleic Acids Research, 37:D674-679, 2009. Google Scholar
  30. Michael R. Schwob, Justin Zhan, and Aeren Dempsey. Modeling cell communication with time-dependent signaling hypergraphs. IEEE/ACM Transactions on Computational Biology and Bioinformatics, to appear 2019. Google Scholar
  31. Roded Sharan and Trey Ideker. Modeling cellular machinery through biological network comparison. Nature Biotechnology, 24(4):427-433, 2006. Google Scholar
  32. Marc Vidal, Michael E. Cusick, and Albert-Lásló Barabási. Interactome networks and human disease. Cell, 144(6):986-998, 2011. Google Scholar
  33. Wanding Zhou and Luay Nakhleh. Properties of metabolic graphs: biological organization or representation artifacts? BMC Bioinformatics, 12(1):132, 2011. Google Scholar
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