Conference Paper

Homomorphisms of Multisource Trees into Networks with Applications to Metabolic Pathways

Georgia State Univ., Atlanta
DOI: 10.1109/BIBE.2007.4375587 Conference: Bioinformatics and Bioengineering, 2007. BIBE 2007. Proceedings of the 7th IEEE International Conference on
Source: IEEE Xplore

ABSTRACT Network mapping is a convenient tool for comparing and exploring biological networks; it can be used for predicting unknown pathways, fast and meaningful searching of databases, and potentially establishing evolutionary relations. Unfortunately, existing tools for mapping paths into general networks (PathBlast) or trees into tree networks allowing gaps (MetaPathwayHunter) cannot handle large query pathways or complex networks. In this paper we consider homomorphisms, i.e., mappings allowing to map different enzymes from the query pathway into the same enzyme from the networks. Homomorphisms are more general than homeomorphism (allowing gaps) and easier to handle algorithmically. Our dynamic programming algorithm efficiently finds the minimum cost homomorphism from a multisource tree to directed acyclic graphs as well as general networks. We have performed pairwise mapping of all pathways for four organisms (E. coli, S. cerevisiae, B. subtilis and T. thermophilus species) and found a reasonably large set of statistically significant pathway similarities. Further analysis of our mappings identifies conserved pathways across examined species and indicates potential pathway holes in existing pathway descriptions.

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    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 becomes computationally challenging. Alignment of the reconstructed networks can help to catch model inconsistencies and infer missing elements. We have formulated the network alignment problem which asks for the optimal vertex-to-vertex mapping allowing path contraction, vertex deletion, and vertex insertions. This paper gives the first efficient algorithm for optimal aligning of metabolic pathways with bounded tree width. In particular, the optimal alignment from pathway P to pathway T can be found in time O(|VP| |VT|(a+1), where VP and VT are the vertex sets of pathways and a is the tree width of P. This significantly improves alignment tools since the E.coli metabolic network has tree width 3 and more than 90% of pathways of several organisms are series-parallel. We have implemented the algorithm for alignment of metabolic pathways of tree width 2 with arbitrary metabolic networks. Our experiments show that allowing pattern vertex deletion significantly improves alignment. We also have applied the network alignment to identifying inconsistency, inferring missing enzymes, and finding potential candidates for filling the holes.
    ICDMW 2010, The 10th IEEE International Conference on Data Mining Workshops, Sydney, Australia, 14 December 2010; 01/2010
  • 08/2009: pages 271 - 293; , ISBN: 9783527627981
  • [Show abstract] [Hide abstract]
    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 athttp://\alla.cs.gsu.edu:8080/MinePW/pages/gmapping/GMMain.html Two ran- - dom graph generations and the list of identified pathway holes are available online.
    ICDMW 2010, The 10th IEEE International Conference on Data Mining Workshops, Sydney, Australia, 14 December 2010; 01/2010

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