MetNetAligner: a web service tool for metabolic network alignments

1. e Graph Extraction MBD Research Day Graph Layout a b 2009 e A Graph Visualization B C D c Graph searching d A X D a b Query c min(cost(ui, vj)+ λh(v,vj)) Cached Indexing Pathway Database vj A A 2.6.1.1 6.2.1.5 1.3.99.1 1. 1.1.1.82 4.2.1.2 1.5.1.5 6.3.4.3 B X d B C 1.1.1.49 2.7.1.13 1.5.1.5 1.1.1.82 4.2.1.2 6.2.1.5 6.3.4.3 2.6.1.1 1.3.99.1 B(ui, v) strongD(ui) D min(weakD(u, ui, uik) + cost(uik, vj)+ λh(v,vj)) 1.1.1.34 1.1.1.44 3.1.1.31 f uik P T A(u, v) Additional Value Service Fig 1. A portion of pentose phosphate pathway 3.5.4.9 3.5.1.10 3.5.4.9 • Enzyme-to-enzyme similarity 1) By the lowest common upper class distribution 2) By tight reaction property MetNetAligner: a web service tool for metabolic network alignments Qiong Cheng*(cscqxcx@cs.gsu.edu), Robert Harrison, Alexander Zelikovsky (alexz@cs.gsu.edu) Department of Computer Science, Georgia State University, Atlanta, GA 30303 * Partially supported by GSU Molecular Basis of Disease (MBD) and Brains & Behavior (B&B) Abstract The accumulation of high-throughput genomic, proteomic, and metabolical data allows for increasingly accurate modeling and reconstruction of metabolic networks. Alignment of the reconstructed networks can help to catch model inconsistencies and infer missing elements. In this note we present the web service tool MetNetAligner which aligns metabolic networks, taking in account the similarity of network topology and the enzymes’ functions. It can be used for predicting unknown pathways, comparing and finding conserved patterns, and resolving ambiguous identification of enzymes. The tool supports several alignment options including allowing or forbidding enzyme deletion and insertion. It is based on a novel scoring scheme which measures enzyme-to-enzyme functional similarity and a fast algorithm which efficiently finds optimal mappings from a directed graph with restricted cyclic structure to an arbitrary directed graph. MetNetAligner is available as web-server at: http://alla.cs.gsu.edu:8080/MinePW/pages/gmapping/GMMain.html Tool : MetNetAligner Problem formulation and solution cost(u,v)=Δ(u,v)+∑ min ui • Given: • 1) a metabolic pathway P =<VP, EP> (Pattern) and • 2) a metabolic network T =<VT, ET> (Text) • Find minimum cost alignment f : P  T so that • 1) Bypass deletion 2) Strong deletion 3) Week deletion fv : every vertex in VP is mapped to a vertex in VT U {b,d}; fl : every path lP across vertices in fv-1(VT) is mapped to path lT Browsers Minimize cost(f)=∑u in VP Δ(u, fv(u))+ λ∑l (|fl(l)|-1) Visualized Outputs • Alignment of two pathways • - Alignments from a single pattern pathway to all pathways in the text organism • - Alignments from every pathway in the pattern organism to every • pathway in the text organism Alignment operations and cost Matches of enzymes between pattern and text - Cost(match of u->fv(u))=0 Mismatches of enzymes - Cost(mismatch of u -> fv(u))=Δ(u, fv(u)) Insertions of text enzyme to pattern - Cost(insertion of v under fl)=λ Deletions of pattern enzyme -Cost(deletion of u under f)= Δ(u, b / d) Experiments results • Computing P-Value of homomorphism mapping Metabolic network alignments • - Random degree-conserved graph generation by reshuffling edges - Randomized P-Value computation (P-Value cutoff : 0.01 for 100 randomized graphs) • Metabolic pathway model – a directed graph in which vertices correspond to enzymes and there is a directed edge between two enzymes if the product of the reaction catalyzed by the first enzyme is asubstrate of the reaction catalyzed by the second. • All-against-all mappings among 4 species : • Identifying conserved pathways 24 pathways that are conserved across all 4 species 18 more pathways that are conserved across at least three of these species • Resolving ambiguity (see figure 2) • Discovering pathways holes (see figure 3) u Computation model for multi-source tree pattern v ui Three possibilities of the contribution of the child uito the parent u’s mapping (u->v): 1. ui is mapping to vj(vj is a descendent of v) 2. ui is strong deleted: strongD(ui) 3. ui is bypass deleted: weakD(u, ui,uik) vj uik Text T Pattern P • Mapping metabolic pathways - should capture the similarities of enzymes represented by proteins as well as topological properties. 1.2.4.- 2.3.1.- 1.2.4.2 2.3.1.61 Fig 2. Resolving ambiguity example: Mapping of glutamate degradation VII pathways from B.subtilis to T. thermophilus (p<0.01). The enlighted node reflects enzyme homology. • Topology similarity 1) Embedding - Subgraph isomorphism • 2) Gene duplication and function sharing • = vertex collapsing • 1+2=Graph homomophism • Solution • Preprocessing: • Transitive closure of text T • Pattern graph ordering • Calculate the penalties of pattern vertex strong deletion • Calculate the penalties of pattern vertex weak deletion • Dynamic Programming + Adaption of Dijkstra Fig 3. Pathway holes’ example: Mapping of formaldehyde oxidation V pathway in B. subtilis to formy1THF biosynthesis pathway in E. coli (p<0.01) (only vertices in the image of the pattern in the text are shown. • 3) Enzyme insertions • = edge subdividing • l -fine per insertion • 1+3=Approximate graph homeomorphism (Pinter et al 2005 ) References : • Q. Cheng, A. Zelikovsky, Network Mapping of Metabolic Pathways, Analysis of Complex Networks: From Biology to Linguistics, Wiley-VCH 2009 • Q. Cheng, R. Harrison, and A. Zelikovsky. "MetNetAligner: a web service tool for metabolic network alignments". Bioinformatics 2009 (To appear) • Q. Cheng, P. Berman, R. Harrison and A. Zelikovsky, "Fast Alignments of Metabolic Networks ", Proc. of IEEE International conference on Bioinformatics and Biomedicine (BIBM 2008), pp 147-152   • Q. Cheng, D. Kaur, R. Harrison, and A. Zelikovsky, "Mapping and Filling Metabolic Pathways ", RECOMB Satellite Conference on Systems Biology 2007    • Q. Cheng, R. Harrison, and A. Zelikovsky, "Homomorphisms of Multisource Trees into Networks with Applications to Metabolic Pathways", Proc. of IEEE 7-th International Symposium on BioInformatics and BioEngineering (BIBE'07)  • Ron Y Pinter, Oleg Rokhlenko, Esti Yeger-Lotem, Michal Ziv-Ukelson: Alignment of metabolic pathways. Bioinformatics. LNCS 3109. Springer-Verlag.(Aug 2005)21(16): 3401-8 • 4) Enzyme deletion • = bypass deletion : send vertex to b (Kelly et al 2005) • 1+3+4= graph homeomorphism • Runtime for DP solution with Fibonacci heaps: O(|VP|(|ET| + |VT|log|VT|)). • 5) Subpath deletion • = strong deletion : send vertex to d (Yang et al 2007) (1+5) • Handle cycles • DP does not work when pattern has cycles • “Fix” images for some pattern vertices and reduce to acyclic case • Find Minimum Feedback vertex set F(P): • - VP-F(P) is acyclic • - NP-complete but easy to be approximate • Reduce single cycle pattern graph alignment to multi-source tree pattern graph alignment • Reduce biconnected component alignment to single cycle pattern graph alignment • Reduce it to alignments of biconnected component s 1+2+3+4+5 = graph homo-homeo morphism Topologies Linear (Forst & Schulten[1999], Chen & Hofestaedt[2004];) Tree (Pinter [2005] o(|VG|2|VT|/log|VG|+|VG||VT|log|VT|) ) Arbitrary topology Mapping : Linear pattern  Graph (Kelly et al 2004) ( o(|VT|i+2|VG|2) ) Exhaustively search (Sharan et al 2005 ( o(i!) o(|VT|i+2|VG|2) ), Yang et al 2007 ( o(2|VG||VG|2) )