Symmetry of metabolic network

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Symmetry of metabolic network
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KEGGMetabolic Network
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The nodes represented compound ID in KEGG
database. The nodes in different orbit are marked
with different colors and non-trivial orbits are
marked in green ellipse.
Metabolism of Cofactors and Vitamins module for
Drosophila melanogaster
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Symmetry indices

• We calculated several indices to measure the
  degree of symmetry and compared them with random
  networks
• aAut(G)
• the size of the automorphism group. Generally, a
  is very large and we use log10Aut(G) to
  represent it.
• ß a/(N!)1/N
• ß measures the symmetry relative to maximal
  possible automorphism group of a graph with N
  nodes.
• fmaxsupp(g)g?ID(G)/N
• f quantify the degree of globally symmetric for
  graph G.

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Figure 5 Comparison of the symmetry indices of
real metabolic networks with random networks
The random networks are produced by Erdos-Renyi
model utilizing Pajek . Error bar of the
symmetry index (a) a (b) ß (c) f of real
metabolic networks and corresponding randomized
networks. Conclusion symmetry in metabolic
networks is distinctly higher than that in random
networks.
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Symmetry in Metabolic Networks

• 1. Direction

• 2. Low Connectivity

Restricted network quotient considering direction
and connectivity
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Analyze orbits similarity

• We obtained all the orbits in networks which are
  defined as structurally equivalent nodes by Nauty
  algorithm.
• We use Hattoris maximal-common-subgraph based
  algorithm with loose weighting condition to do
  chemical structure comparison
• We found that compound pairs in the same orbit
  show much more similarity in function and
  chemical structures than random compound pairs in
  network.

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P-values for testing significance of the
similarity of the compounds in the orbits
Orbits denotes the number of pairs of compounds
in the orbit, compound pairs denotes the number
of pairs of compounds in the random dataset. Pt1
is the P-values of right tail t-test with equal
variance Pt2 is the P-values of right tail
t-test with unequal variance, Pr is the P-values
of Wilcoxon two-sided rank sum test.
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Compare compounds in Orbits C00158, C00311,
C00417

• Compounds similar in their chemical structure
  participated in the same pathways and were
  catalyzed by same enzymes in most cases,
  therefore show more functional similarity.

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Conclusion

• Our preliminary results showed that metabolic
  networks are generally symmetric and in
  particular locally symmetric.
• We found that symmetric compounds in the network
  showed significantly more similarity in function
  than asymmetric compounds.
• Symmetry in the metabolic network can generate
  the functional redundancy, increase the
  robustness and play an important role in network
  structure, function and evolution.