1. BIBM 2008 Qiong Cheng Georgia State University Joint work with Piotr Berman (Pennstate) Robert Harrison (GSU) Alexander Zelikovsky (GSU) Fast Alignments of Metabolic Networks

2. BIBM 2008 Metabolic pathway & pathways model Metabolic pathways model A portion of pentose phosphate pathway 1.1.1.49 1.1.1.34 2.7.1.13 3.1.1.31 1.1.1.44 Metabolic pathway 1.1.1.49 1.1.1.342.7.1.13 3.1.1.31 1.1.1.44

3. BIBM 2008 Alignments of metabolic pathways Enzyme Similarity Pathway topology Similarity Enzyme similarity and pathway topology together represent the similarity of pathway functionality. Mismatch/Substitute match Pattern P : query pathway Text T : pathway in database

4. BIBM 2008 Types of Pathway Alignments Pattern Text + gene duplication and function sharing = vertex collapsing embedding + enzyme insertions = edge subdividing  -fine per insertion Pinter et al 2005  e in E T (|f e (e)|-1) Δ(v, f v (v))  v in V T = + enzyme deletion = bypass deletion : send vertex to b Kelly et al 2005 + subpath deletion = strong deletion : send vertex to d Yang et al 2007 f

5. BIBM 2008 Optimal Alignment Problem Formulation Given: a metabolic pathway P = (Pattern) and a metabolic network T = (Text) Find minimum cost alignment f : P  T  Minimize cost(f)=∑ u in V P Δ(u, f v (u))+ λ∑ l in l P (|f l (l)|-1)  f v : every vertex in V P is mapped to a vertex in V T U {b,d};  f l : every path l P across vertices in f v -1 (V T ) is mapped to path l T DP solution when pattern is multisource tree Runtime for DP solution with Fibonacci heaps: O(|V P |(|E T | + |V T |log|V T |)).

6. BIBM 2008 Handling cycles ab c d e ab c d e Total Runtime : O(|V T | |F(P)| |V P | (|E T | + |V T |log|V T |)) 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): V P -F(P) is acyclic NP-complete but easy to be approximate Runtime is increased by factor O(V T |F(P)| )

7. BIBM 2008 Our software http://alla.cs.gsu.edu:8080/MinePW/pages/gmapping/G MMain.html

8. BIBM 2008 Comparison on different methods Alignment of tree pathways from different species with optimal homomorphism (HM) and optimal network alignment (NA). Average number of mismatches and gaps are reported on common statistically significant matched pathways.

9. BIBM 2008 Significant deletion Aspartate superpathway in E. coli Lysine biosynthesis in T. thermophilus Mapping result: unmatched vertices are deleted.

10. BIBM 2008 Pathway holes: find and fill Check if there is such enzyme in pattern Find the closest protein in the same group If identity is too high > 80% then we expect good filling Align to previous and next enzyme – the functions may be taken over Mapping of formaldehyde oxidation V pathway in B. subtilis to formy1THF biosynthesis pathway in E. coli Hole = missing enzyme in pathway description (in database) Finding holes is difficult task: comparison can help

11. BIBM 2008 Resolving Ambiguity Mapping of glutamate degradation VII pathways from B. subtilis to T. thermophilus (p<0.01). The shaded node reflects enzyme homology.

12. BIBM 2008 Future work Improve method of filling pathway holes Discover critical metabolic elements/modules/motifs Describe evolution of metabolic pathways Integrate with genome database

13. BIBM 2008 Acknowledgments GSU Molecular Basis of Disease (MBD) fellowship Peter Karp Oleg Rokhlenko Florian Rasche Amit Sabnis, Dipendra Kaur Kelly Westbrooks, Irina Astrovskaya, Stefan Gremalschi, Jingwu He, Dumitru Brinza, Weidong Mao,Nisar Hudewale

14. BIBM 2008 Thank you for your attention!