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A Real-life Application of Barabasi’s Scale-Free Power-Law

A Real-life Application of Barabasi’s Scale-Free Power-Law. Presentation for ENGS 112 Doug Madory Wed, 1 JUN 05 Fri, 27 MAY 05. Background. Common property of many large networks is vertex connectivities follow a scale-free power-law distribution. Consequence of two generic mechanisms:

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A Real-life Application of Barabasi’s Scale-Free Power-Law

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  1. A Real-life Application of Barabasi’s Scale-Free Power-Law Presentation for ENGS 112 Doug Madory Wed, 1 JUN 05 Fri, 27 MAY 05

  2. Background • Common property of many large networks is vertex connectivities follow a scale-free power-law distribution. • Consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected.

  3. So what? • The objective of network theory is not network diagrams, but insight! • Application of Barabasi’s theory to bioinformatics has produced several significant biological discoveries

  4. Determining Roles of Proteins Within Metabolism • Proteins are traditionally identified on the basis of their individual actions • Modern research is trying to determine contextual or cellular function of proteins • Requires analysis of 1000’s of simultaneous protein-protein interactions – unworkable! • Must analyze as a complex network

  5. Yeast proteome

  6. Protein-Protein Interaction • Map of protein-protein interactions forms a scale-free power-law network • Few highly-connected proteins play central role in mediating interactions among numerous, less connected proteins • Consequence is tolerance to random errors • Removal of highly-connected proteins rapidly increases network diameter computationally

  7. Highly-Connected Proteins • When highly-connected proteins are removed in order of connectivity, mortality of cell increases • Highly-connected proteins paramount to survival • 93% of proteins have <5 links, 21% essential • 0.7% of proteins have >15 links, 62% essential • Conversely when proteins are removed at random, effect is negligible

  8. More Characteristics of Highly-Connected Proteins • Most hub proteins same across species • 4% of all proteins were found in all organisms of experiment • These were also the most highly connected proteins • Species-specific differences expressed in least connected proteins

  9. Small-World in Organisms • Connectivity characterized by network diameter • Shortest biochemical pathway averaged over all pairs of substrates • For all known non-biological networks average node connectivity is fixed • Implies increased diameter as new nodes added • Therefore more complex organisms should have greater network diameters – but they don’t!!!

  10. Conservation of Diameter • All metabolic networks share same diameter! • As organism complexity increases individual proteins are increasingly connected to maintain constant metabolic network diameter • Larger diameter would attenuate organism’s ability to respond efficiently to external changes

  11. Conservation of Diameter • Minitab analysis of Barabasi’s data for diameter

  12. Conservation of Gamma • All metabolic networks share power-law • a. A. Fulgidus (archae) • b. E. coli (bacterium) • c. C. Elegans (eukaryote) • d. All 43 organisms (avg) • g for all life about 2.2

  13. Conservation of g • Minitab analysis of Barabasi’s data for g

  14. Conclusions • Barabasi’s network theory offers insights into metabolic networks in cellular biology • Correlation between connectivity and indispensability of a protein confirms that robustness against lethal mutations is derived from organization of protein interactions • Metabolic networks within all living things have almost same diameter and g.

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