### Abstract

The accumulation of high-throughput genomic and proteomic data allows for the reconstruction of the increasingly large and complex metabolic networks. In order to analyze accumulated data and reconstructed networks, it is critical to identify network patterns and evolutionary relations between metabolic networks. But even finding similar networks is computationally challenging. Based on the property of gene duplication and function sharing in biological network, we have formulated the network alignment problem which asks the optimal vertex-to-vertex mapping allowing path contraction, vertex deletion, and vertex insertions. In this paper we present fixed parameter tractable combinatorial algorithms, which take into account the enzymes' functions and the similarity of arbitrary network topologies such as trees and arbitrary graphs wit hallowing the different types of vertex deletions. The proposed algorithms are fixed parameter tractable in the liner or square of the size of feedback vertex set respectively for the case of disallowing or allowing the deletions. We have developed the web service tool MetNetAligner which aligns metabolic networks. We evaluated our results by the randomizedP-Value computation. In the computation, we followed two standard randomization procedures and further developed two other random graph generators which keep the more stringent and consistent topology constraints. By comparing their distribution of the significant alignment pairs, we observed that the more stringent constraints in the topology the random graph generator has, the more pairs of significant alignments there exist. We also performed pair wise mapping of all pathways for four organisms and found a set of statistically significant pathway similarities. We have applied the network alignment to identifying pathway holes which are resulted by inconsistency and missing enzymes. MetNetAligner is available at http://\\alla.cs.gsu.edu:8080/MinePW/pages/gmapping/GMMain.html Two random graph generations and the list of identified pathway holes are available online.

Original language | English (US) |
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Title of host publication | Proceedings - IEEE International Conference on Data Mining, ICDM |

Pages | 679-686 |

Number of pages | 8 |

DOIs | |

State | Published - 2010 |

Event | 10th IEEE International Conference on Data Mining Workshops, ICDMW 2010 - Sydney, NSW, Australia Duration: Dec 14 2010 → Dec 17 2010 |

### Other

Other | 10th IEEE International Conference on Data Mining Workshops, ICDMW 2010 |
---|---|

Country | Australia |

City | Sydney, NSW |

Period | 12/14/10 → 12/17/10 |

### Fingerprint

### Keywords

- Feedback vertex sets
- Graph homeomorphism
- Network alignment

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings - IEEE International Conference on Data Mining, ICDM*(pp. 679-686). [5693362] https://doi.org/10.1109/ICDMW.2010.179

**Fixed-parameter tractable combinatorial algorithms for metabolic networks alignments.** / Cheng, Qiong; Wei, Jinpeng; Zelikovsky, Alexander; Ogihara, Mitsunori.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE International Conference on Data Mining, ICDM.*, 5693362, pp. 679-686, 10th IEEE International Conference on Data Mining Workshops, ICDMW 2010, Sydney, NSW, Australia, 12/14/10. https://doi.org/10.1109/ICDMW.2010.179

}

TY - GEN

T1 - Fixed-parameter tractable combinatorial algorithms for metabolic networks alignments

AU - Cheng, Qiong

AU - Wei, Jinpeng

AU - Zelikovsky, Alexander

AU - Ogihara, Mitsunori

PY - 2010

Y1 - 2010

N2 - The accumulation of high-throughput genomic and proteomic data allows for the reconstruction of the increasingly large and complex metabolic networks. In order to analyze accumulated data and reconstructed networks, it is critical to identify network patterns and evolutionary relations between metabolic networks. But even finding similar networks is computationally challenging. Based on the property of gene duplication and function sharing in biological network, we have formulated the network alignment problem which asks the optimal vertex-to-vertex mapping allowing path contraction, vertex deletion, and vertex insertions. In this paper we present fixed parameter tractable combinatorial algorithms, which take into account the enzymes' functions and the similarity of arbitrary network topologies such as trees and arbitrary graphs wit hallowing the different types of vertex deletions. The proposed algorithms are fixed parameter tractable in the liner or square of the size of feedback vertex set respectively for the case of disallowing or allowing the deletions. We have developed the web service tool MetNetAligner which aligns metabolic networks. We evaluated our results by the randomizedP-Value computation. In the computation, we followed two standard randomization procedures and further developed two other random graph generators which keep the more stringent and consistent topology constraints. By comparing their distribution of the significant alignment pairs, we observed that the more stringent constraints in the topology the random graph generator has, the more pairs of significant alignments there exist. We also performed pair wise mapping of all pathways for four organisms and found a set of statistically significant pathway similarities. We have applied the network alignment to identifying pathway holes which are resulted by inconsistency and missing enzymes. MetNetAligner is available at http://\\alla.cs.gsu.edu:8080/MinePW/pages/gmapping/GMMain.html Two random graph generations and the list of identified pathway holes are available online.

AB - The accumulation of high-throughput genomic and proteomic data allows for the reconstruction of the increasingly large and complex metabolic networks. In order to analyze accumulated data and reconstructed networks, it is critical to identify network patterns and evolutionary relations between metabolic networks. But even finding similar networks is computationally challenging. Based on the property of gene duplication and function sharing in biological network, we have formulated the network alignment problem which asks the optimal vertex-to-vertex mapping allowing path contraction, vertex deletion, and vertex insertions. In this paper we present fixed parameter tractable combinatorial algorithms, which take into account the enzymes' functions and the similarity of arbitrary network topologies such as trees and arbitrary graphs wit hallowing the different types of vertex deletions. The proposed algorithms are fixed parameter tractable in the liner or square of the size of feedback vertex set respectively for the case of disallowing or allowing the deletions. We have developed the web service tool MetNetAligner which aligns metabolic networks. We evaluated our results by the randomizedP-Value computation. In the computation, we followed two standard randomization procedures and further developed two other random graph generators which keep the more stringent and consistent topology constraints. By comparing their distribution of the significant alignment pairs, we observed that the more stringent constraints in the topology the random graph generator has, the more pairs of significant alignments there exist. We also performed pair wise mapping of all pathways for four organisms and found a set of statistically significant pathway similarities. We have applied the network alignment to identifying pathway holes which are resulted by inconsistency and missing enzymes. MetNetAligner is available at http://\\alla.cs.gsu.edu:8080/MinePW/pages/gmapping/GMMain.html Two random graph generations and the list of identified pathway holes are available online.

KW - Feedback vertex sets

KW - Graph homeomorphism

KW - Network alignment

UR - http://www.scopus.com/inward/record.url?scp=79951731906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951731906&partnerID=8YFLogxK

U2 - 10.1109/ICDMW.2010.179

DO - 10.1109/ICDMW.2010.179

M3 - Conference contribution

AN - SCOPUS:79951731906

SN - 9780769542577

SP - 679

EP - 686

BT - Proceedings - IEEE International Conference on Data Mining, ICDM

ER -