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Class 12: Communities

Class 12: Communities. Dr. Baruch Barzel. Network Science: Motifs March 28, 2011. A Closer Look at Networks. The bird’s eye view: . The detailed view: . A Closer Look at Networks. Intermediate view: . Motifs and Sub-graphs.

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Class 12: Communities

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  1. Class 12: Communities • Dr. Baruch Barzel Network Science: Motifs March 28, 2011

  2. A Closer Look at Networks • The bird’s eye view: • The detailed view:

  3. A Closer Look at Networks • Intermediate view:

  4. Motifs and Sub-graphs • Sub-graph: a connected graph consisting of a subset of the nodes and links of a network

  5. Motifs and Sub-graphs Motifs: Sub-graphs that have a significantly higher density in the real network than in the randomized version of the studied network • Sub-graph: a connected graph consisting of a subset of the nodes and links of a network R. Milo et al., Science 298, 824 (2002)

  6. Motifs and Sub-graphs Motifs: Sub-graphs that have a significantly higher density in the real network than in the randomized version of the studied network • Sub-graph: a connected graph consisting of a subset of the nodes and links of a network • Randomized networks: Ensemble of maximally random networks preserving the degree distribution of the original network R. Milo et al., Science 298, 824 (2002)

  7. Motifs in Realistic Networks Motifs: Sub-graphs that have a significantly higher density in the real network than in the randomized version of the studied network R. Milo et al., Science 298, 824 (2002)

  8. Motifs in Realistic Networks

  9. Motifs in Realistic Networks

  10. Motifs in Biological Networks • Protein protein • interaction network • Metabolic Network • Regulatory Network • Genes are connected if one regulates the expression of the other

  11. Motifs in Biological Networks • Activation Y X • Regulatory Network Y X • Inhibition Y X Gene x • Genes are connected if one regulates the expression of the other

  12. Motifs in Biological Networks • Regulatory Network • Feed-back loop • Auto-regulation Y X X Tong et al. Science 298, 799 (2002)

  13. The Significance of Motifs Evolutionary conservation of sub-graphs Natural selection aims to maintain function Function is typically not carried by single components, but rather by a network of interacting subunits We expect a tendency towards the evolutionary conservation of sub-networks that are capable of carrying biological function Tong et al. Science 298, 799 (2002)

  14. Auto-regulation X Mortality or Degradation could do the jobs X X X X • Auto-regulation X X X Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  15. The Auto-regulation Advantage • Auto-regulation vs. Protein Degradation X X Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  16. The Auto-regulation Advantage • Protein Degradation X Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  17. The Auto-regulation Advantage • Protein Auto-regulation • Steady state for r: X X X Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  18. The Auto-regulation Advantage • Protein Auto-regulation • Steady state for r: X X X Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  19. The Auto-regulation Advantage • Protein Auto-regulation X X X Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  20. The Auto-regulation Advantage • Auto-regulation vs. Protein Degradation X X • Auto-regulation is an efficient scheme to achieve fast response time to external stimuli Rosenfeld et al. J. Mol. Biol. 323, 785 (2002)

  21. The Auto-regulation Advantage • Auto-regulation vs. Protein Degradation Uri AlonNature Reviews8, 450 (2007)

  22. The Feed-Forward Loop X X Y Y Z Z Mangan and AlonPNAS100, 21 (2003)

  23. The Feed-Forward Loop X Y Z Arbinose system Flagella Galactose utilization Uri AlonNature Reviews8, 450 (2007)

  24. Function oFthe Feed Forward Loop Filtering of spurious spikes, and detecting persistent stimuli Uri AlonNature Reviews8, 450 (2007)

  25. Function oFthe Feed Forward Loop Sign Sensitive Delay AND – Causes a rise time delay OR – Results in turn-off delay Uri AlonNature Reviews8, 450 (2007)

  26. Function oFthe Feed Forward Loop Coherent FFL: Sign Sensitive Delay AND – Causes a rise time delay OR – Results in turn-off delay Incoherent FFL: Persistent Stimulus results in a spike of expression Uri AlonNature Reviews8, 450 (2007)

  27. Topologically Induced Motifs What determines the number of sub-graphs in biological networks? Vázquez et al. PNAS101, 52 (2004)

  28. Numerical Parameterization Numerical description of sub-graphs • Includes n nodes • A central node connected to all others • Has m edges • Denoted by: (n,m) Feed Forward Loop • (1,1) X Vázquez et al. PNAS101, 52 (2004)

  29. The Local and the Global Views Vázquez et al. PNAS101, 52 (2004)

  30. Think Global - Act Local • You need a node with a degree of at least n – 1 • You need m – (n – 1) links between its neighbors Vázquez et al. PNAS101, 52 (2004)

  31. Think Global - Act Local How frequent will the motifs (n,m) be? For a node with a degree of k: So for the whole network: Vázquez et al. PNAS101, 52 (2004)

  32. Think Global - Act Local How frequent will the motifs (n,m) be? Vázquez et al. PNAS101, 52 (2004)

  33. Interplay Between Scales • The abundance of motifs is dictated by the scaling exponents • The scaling exponents are dictated by the frequency of motifs Vázquez et al. PNAS101, 52 (2004)

  34. The Sub-graph Degree Distribution • P(T) = The probability that a node participates in exactly T triangles Vázquez et al. PNAS101, 52 (2004)

  35. Sub-graph Giant Component • At what point will the sub-graphs become sparse enough to break the network down Vázquez et al. PNAS101, 52 (2004)

  36. Sub-graph Giant Component • At what point will the sub-graphs become sparse enough to break the network down Vázquez et al. PNAS101, 52 (2004)

  37. Network Motifs Recurring sub-graphs that poses a functional benefit Shown to have functional roles in biological networks The large scale attributes and the local interaction patterns are closely related

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