The Large Scale Organisation of Metabolic Networks

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The Large Scale Organisation of Metabolic Networks
Amit Puniyani, Physics Department Stanford
University
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Outline

• What are Metabolic Networks ?
• Questions we would like to Ask about Metabolic
  Networks
• Detour Random Graphs
• Universalities in Metabolic Networks
• Discussion

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What are Metabolic Networks ?

• Cells are complex -gt Thousands of chemical
  species
• Flow of Mass and Energy -gt Metabolism
• Different from a regulatory/signalling network
  (information transfer)
• Maps from from KEGG,WIT etc.

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Glycolysis Pathway

• Details about this topic
• Supporting information and examples
• How it relates to your audience

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Citric Acid Cycle

• Details about this topic
• Supporting information and examples
• How it relates to your audience

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Questions we would like to Ask

• Dynamics Response to perturbations ?
• Fundamental Questrions What really is
  Metabolism ?
• Is it possible to build Artificial systems which
  live
• Approach Look for Patterns
• in the Dust.

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Topology First Things First

• Represent Network by a graph
• Study properties of these graphs to see if there
  are similarities

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Graph Properties to compare ? Detour Random
Graphs
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• Summarize any actions required of your audience
• Summarize any follow up action items required of
  you

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Properties of completely Random Graphs

• Poissonian Link distribution (kconstant)
• No Clustering
• Short Average Path Lengths
• d log(N)
• Giant component if average number of links per
  node N

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Link distribution
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Small Average shortest Path

• What it means ?

• Six Degrees of Kevin Bacon

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End of Detour.

• So what really are the link distributions and
  average shortest paths of Metabolic Networks that
  have been fully mapped ?
• Answer in Jeong et al, Nature 407, 651 (2000)

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Link Distribution in Metabolic Network graphs
power law
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Power Laws

• P(k) 1/ka
• Log (P(k)) -a log(k)
• High degree (N3-2/a) nodes exist.

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Average shortest path? 3.4! For all 43
networks
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Discussion

• What are the implications of power law link
  distributions
• What does constant diameter signify ?
• Does this say anything about the common blueprint
  ?

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Some thoughts.

• Power Law Networks are more robust to random
  deletion of nodes.
• Small diameters may be desirable for efficient
  functioning
• (Fell, D., Wagner, A. (2000) The small world
  of metabolism. Nature Biotechnology 18,
  1121-1122)

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More thoughts

• Theorem If the diameter of a growing network is
  constant then it will have a power law link
  distribution with exponent between 2 and 3.
• ( A Puniyani R Lukose, in preparation)

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Conclusions

• Maybe the first step towards deciphering common
  design principles
• If not that, could at least tell something about
  evolutionary processes