Qiong Cheng

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Fast Alignments of Metabolic Networks

• Qiong Cheng
• Georgia State University
• Joint work with
• Piotr Berman (Pennstate)
• Robert Harrison (GSU)
• Alexander Zelikovsky (GSU)

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Metabolic pathway pathways model

• Metabolic pathway

• Metabolic pathways model

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Alignments of metabolic pathways

• Pattern P query pathway
• Text T pathway in database

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

• Enzyme Similarity

• Pathway topology
• Similarity

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Types of Pathway Alignments

• embedding

• enzyme insertions
• edge subdividing
• l -fine per insertion
• Pinter et al 2005

• gene duplication and function sharing
• vertex collapsing

Pattern

• enzyme deletion
• bypass deletion send vertex to b
• Kelly et al 2005

• subpath deletion
• strong deletion send vertex to d
• Yang et al 2007

l Se in ET (fe(e)-1)
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Optimal Alignment Problem Formulation

• Given
• a metabolic pathway P ltVP, EPgt (Pattern) and
• a metabolic network T ltVT, ETgt (Text)
• Find minimum cost alignment f P ? T

• 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

• Minimize cost(f)?u in VP ?(u, fv(u)) ??l in lP
  (fl(l)-1)

• DP solution when pattern is multisource tree
• Runtime for DP solution with Fibonacci heaps
• O(VP(ET VTlogVT)).

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Handling 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
• Runtime is increased by factor O(VT F(P))

• Total Runtime O(VT F(P)VP (ET
  VTlogVT))

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Our software

• http//alla.cs.gsu.edu8080/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 deletion
Aspartate superpathway in E. coli Lysine
biosynthesis in T. thermophilus
Mapping result unmatched vertices are deleted.
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Pathway holes find and fill

• Hole missing enzyme in pathway description (in
  database)
• Finding holes is difficult task comparison can
  help

Mapping of formaldehyde oxidation V pathway in B.
subtilis to formy1THF biosynthesis pathway in E.
coli

• Check if there is such enzyme in pattern
• Find the closest protein in the same group
• If identity is too high gt 80 then we expect good
  filling
• Align to previous and next enzyme the functions
  may be taken over

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Resolving Ambiguity
Mapping of glutamate degradation VII pathways
from B. subtilis to T. thermophilus (plt0.01). The
shaded node reflects enzyme homology.
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Future work

• Improve method of filling pathway holes
• Discover critical metabolic elements/modules/motif
  s
• 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

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Thank you for your attention!