BIBM 2008

Qiong ChengGeorgia State University

Joint work withPiotr Berman (Pennstate) Robert Harrison (GSU)Alexander Zelikovsky (GSU)

Fast Alignments of Metabolic Networks

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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 pathway1.1.1.49

1.1.1.342.7.1.13

3.1.1.31

1.1.1.44

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Alignments of metabolic pathways

Enzyme Similarity

Pathway topology

Similarity

Enzyme similarity and pathway topology together represent the similarity of pathway functionality.

Mismatch/Substitute

match

match

match

Pattern P : query pathway Text T : pathway in database

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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

+ 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

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Optimal Alignment Problem Formulation

Given: a metabolic pathway P =<VP, EP> (Pattern) and a metabolic network T =<VT, ET> (Text)

Find minimum cost alignment f : P T

Minimize cost(f)=∑u in VP Δ(u, fv(u))+ λ∑l in lP

(|fl(l)|-1)

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

DP solution when pattern is multisource tree Runtime for DP solution with Fibonacci heaps: O(|VP|(|ET| + |VT|log|VT|)).

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Handling cycles

a bc

d

e

a bc

d

e

• Total Runtime : O(|VT| |F(P)||VP|

(|ET| + |VT|log|VT|))

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

Runtime is increased by factor O(VT |F(P)|)

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Our software http://alla.cs.gsu.edu:8080/MinePW/pages/

gmapping/GMMain.html

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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.

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Significant deletionAspartate superpathway in E. coli Lysine biosynthesis in T. thermophilus

Mapping result: unmatched vertices are deleted.

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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

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Resolving Ambiguity

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

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Future work

Improve method of filling pathway holes Discover critical metabolic

elements/modules/motifs Describe evolution of metabolic pathways Integrate with genome database

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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

BIBM 2008

Thank you for your attention!