Network MotifsStatisticalgraph theoretic analyses of complex biological systems

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Network MotifsStatistical/graph theoretic
analyses of complex biological systems

• Stephen Harnish
• Professor of Mathematics
• Bluffton University
• harnishs_at_bluffton.edu
• September 29, 2006
• For links and documents http//www.bluffton.edu/m
  at/seminar/

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Network Resources

• Mathematics Awareness Month Poster 2004
• http//www.mathaware.org/mam/04/2_HIV_risk.html
• Network motifs
• Milo, R. Itzkovitz, S. Kashtan, N. et. al.
  Science (2004).
• Milo, R. Shen-Orr, S. Itzkovitz, S. Kashtan, N.
  et. al. Science (2002).
• Shen-Orr, S., Milo, R., Mangan, S. Alon, U. Nat
  Genet (2002).
• Mangan, S. et. al. JMB (2003), PNAS (2003).
• www.weizmann.ac.il/mcb/UriAlon
• Computational tools
• Mdraw http//www.weizmann.ac.il/mcb/UriAlon/grou
  pNetworkMotifSW.html
• MAVisto http//mavisto.ipk-gatersleben.de/

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A social network of sexual contactsRedrawn from
the HIV data of J. J. Potterat et al, "Risk
network Structure in the early epidemic phase of
HIV transmission in Colorado Springs," Sexually
Transmitted Infections, 78 (2002). Pp. i159-i163.
From poster for Mathematics Awareness Month
April, 2004
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• Friendship network of children in a U. S. school,
  
• courtesy of James Moody.

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A visualization of the network structure of the
Internet by Hal Burch and Bill Cheswick, courtesy
of Lumeta Corporation.
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http//curriculum.calstatela.edu/courses/builders/
lessons/less/biomes/desert/hot-desert-chain.html
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http//www.chesapeakebay.net/info/ecoint6a.cfm
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http//www.calacademy.org/calwild/2003winter/stori
es/horizons.htmlA food web of predator-prey
interactions between species in a freshwater
lake, picture courtesy of Richard Williams and
Neo Martinez. Ecological Monographs, 61 (1991),
pp. 367-392.
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http//www.itk.ca/environment/tek-ecological-foodw
eb-image.php
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Small-world networks
M. E. J. Newman at Ann Arbor
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Other Graph Theoretic/Statistical Analyses of
Networks

• Small World phenomenaoften referred to as
  six-degrees of separation
• Two degrees of separation in complex food
  websWilliams, et. al. Oct. 1, 2002
• www.pnas.org/cgl/dol/10.1073/pnas.192448799

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Two degrees of separation in complex food
websWilliams, et. al. Oct. 1, 2002 www.pnas.org/
cgl/dol/10.1073/pnas.192448799
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Network Motifs
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Abstract

• Network motifs have emerged in recent years as
  key tools for the analysis of networks from
  fields as diverse as gene transcription, neuron
  connectivity, ecosystem food-chains, electronic
  circuitry and the structure of the World Wide
  Web.  
• These motifs are generally small (e.g., 3-node
  or 4-node) subgraphs which occur more frequently
  in naturally occurring networks than in
  randomized ones. 
• Some scientists assume they are the
  fundamental, functional (as well as structural)
  building-blocks of most complex hierarchical
  systems. 
• To introduce this topic we will employ
  computational software (MAVisto mfinder) to
  analyze motifs in ecological food chains and E.
  Coli gene transcription networks.

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University of Cape Town
Jameson Hall
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Drs. George and Mary Ellis
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George and Mary Ellis
Kirstenbosch Botanical Gardens
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Bisimulations and Pictures of SetsA survey of
hyperset theories, their key modeling tools, and
applications to computer science

• FACS Lab Seminar
• Prof Stephen Harnish, Visiting Researcher
• Prof. of Mathematics, Bluffton University,
  Ohio, USA
• harnishs_at_bluffton.edu
• Wednesday 5 April 2006, 15h30, M 111 (Seminar
  Room)
• Abstract
• ZFC provides a standard, robust foundation for
  modeling mathematics and its applications. Yet,
  some systems studied by computer scientists are
  most naturally modeled by self-referential sets
  with cyclic- and other infinite-element chains
  that are prohibited by ZFCs axiom of foundation.
  In recent decades the properties and applications
  of various non-well-founded (NWF) set theories
  have been developed by logicians such as Aczel,
  Scott, Finsler, Barwise and Moss. I will review
  the properties of these sets, explain one key
  modeling tool (the solution lemma), and describe
  several areas of application for computer
  science, situation theory, and linguistics.

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Structures of sets, graphs networks
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Searching for building blocks and design
principles in the genetic regulatory network of
E. coli

• Ron Milo
• Uri Alon Group
• Weizmann Institute, Israel
• November 2004
• Mathematical Biosciences InstituteOSU

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• R. Milos Definition
• Network motifs are recurring patterns that occur
  significantly more often than in randomized nets
• Note
• There are many possible distinct subgraphs

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The 13 three-node connected subgraphs
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199 4-node directed connected subgraphs
The count grows quickly 9364 5-node subgraphs
1,530,843 6-node subgraphs
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To Find Network Motifs

• Generate a suitable random ensemble (reference
  networks)
• Network motif detection process

• Count how many times each subgraph appears
• Compute statistical significance for each
  subgraph probability of appearing in random as
  much as in real network
• (P-value or Z-score)

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Ensemble of networks
Real 5 Rand 0.5 0.6
Z-score (Standard Deviations) 7.5
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Hierarchical Motif Structure
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Hierarchical Motif Structure
University of Michigan CSCSOctober 13, 2006
Emergence in Physical, Biological, and Social
Systems
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Two Tools

• Mdraw
• (Milo, et. al. at Weizmann)
• handles large networks wellsome special
  interface features
• MAVisto
• http//mavisto.ipk-gatersleben.de/
• (Java Web Start required)
• good graphical interface

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mDrawc. Elegans neural net
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ICES Journal of Marine Science
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Hermanus--Land-based whale watching
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http//www.brest.ird.fr/personnel/ppenven/publicat
ions/these/index.html
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Ecosystem structures of the South African Cape
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Predator-Prey Relations
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http//www.intarttiles.com/robertekennedy.htm
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African Penguins at Boulders Beach
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Cape Gannet

• http//www.stock-photography.co.za/stock-photograp
  hy-gannet-flying.htm

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Robben Island

• Where Nelson Mandela was a prisoner for 27 years

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Critique Network Motif Analysis

• Important issues
• What is the best model for this application?
• Do motifs play specific functional roles in the
  networks?
• Do similar kinds of networks have similar motif
  profiles?

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http//complex.upf.es/montoya/research.html
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http//cse.pdx.edu/forest/model_computer.htm
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http//oregonstate.edu/instruct/fw465/sampson/anch
ovy/anchovy09.htm
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Common Motifs
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Other motifs
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Triad (3 node) subgraph significance profile
Different Subgraphs
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Network Resources

• Mathematics Awareness Month Poster 2004
• http//www.mathaware.org/mam/04/2_HIV_risk.html
• Network motifs
• Milo, R. Itzkovitz, S. Kashtan, N. et. al.
  Science (2004).
• Milo, R. Shen-Orr, S. Itzkovitz, S. Kashtan, N.
  et. al. Science (2002).
• Shen-Orr, S., Milo, R., Mangan, S. Alon, U. Nat
  Genet (2002).
• Mangan, S. et. al. JMB (2003), PNAS (2003).
• www.weizmann.ac.il/mcb/UriAlon
• Computational tools
• Mdraw http//www.weizmann.ac.il/mcb/UriAlon/grou
  pNetworkMotifSW.html
• MAVisto http//mavisto.ipk-gatersleben.de/

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Network MotifsStatistical/graph theoretic
analyses of complex biological systems

• Stephen Harnish
• Professor of Mathematics
• Bluffton University
• harnishs_at_bluffton.edu
• September 29, 2006
• For links and documents http//www.bluffton.edu/m
  at/seminar/

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