Conference Paper

Efficient Alignments of Metabolic Networks with Bounded Treewidth

DOI: 10.1109/ICDMW.2010.150 Conference: ICDMW 2010, The 10th IEEE International Conference on Data Mining Workshops, Sydney, Australia, 14 December 2010
Source: DBLP


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.

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    ABSTRACT: A general network alignment problem: a pathway forms a pattern and a cellular network (usually from another species) forms the text, and how to find the best correspondence between the text and the pattern, is investigated. A representation of metabolic network/pathway by a graph in which vertices are labeled by enzymes which they represent and each of its directed edges connects enzymes catalyzing consecutive reactions, is also discussed.
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    ABSTRACT: In this paper, we study the problem of finding a periodic attractor of a Boolean network (BN), which arises in computational systems biology and is known to be NP-hard. Since a general case is quite hard to solve, we consider special but biologically important subclasses of BNs. For finding an attractor of period 2 of a BN consisting of $n$ OR functions of positive literals, we present a polynomial time algorithm. For finding an attractor of period 2 of a BN consisting of $n$ AND/OR functions of literals, we present an $O(1.985^n)$ time algorithm. For finding an attractor of a fixed period of a BN consisting of $n$ nested canalyzing functions and having constant treewidth $w$, we present an $O(n^{2p(w+1)} poly(n))$ time algorithm.
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