Gene and Protein Networks I Wednesday, April 11 2006

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Gene and Protein Networks IWednesday, April 11
2006

• CSCI 4830 Algorithms for Molecular Biology
• Debra Goldberg

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Outline

1. Introduction
2. Network models
3. Implications from topology
4. Confidence assessment, edge prediction

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Outline

1. Introduction
2. Network models
3. Implications from topology
4. Confidence assessment, edge prediction

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What is a network?

• A collection of objects (nodes, vertices)
• Binary relationships (edges)
• May be directed
• Also called agraph

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Networks are everywhere
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Social networks
Nodes People Edges Friendship
from www.liberality.org
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Sexual networks
Nodes People Edges Romantic and sexual
relations
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Transportation networks
Nodes Locations Edges Roads
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Power grids
Nodes Power station Edges High voltage
transmission line
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Airline routes
Nodes Airports Edges Flights
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Internet
Nodes MBone Routers Edges Physical connection
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World-Wide-Web
Nodes Web documents Edges Hyperlinks
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Gene and protein networks
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Metabolic networks
Nodes Metabolites Edges Biochemical
reaction(enzyme)
from web.indstate.edu
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Protein interaction networks
Nodes Proteins Edges Observed interaction
from www.embl.de

• Gene function predicted

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Gene regulatory networks
Nodes Genes or gene products Edges Regulation
of expression

• Inferred from error-prone gene expression data

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Signaling networks
Nodes Molecules(e.g., Proteins or
Neurotransmitters) Edges Activation
orDeactivation
from pharyngula.org
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Signaling networks
Nodes Molecules(e.g., Proteins or
Neurotransmitters) Edges Activation
orDeactivation
from www.life.uiuc.edu
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Synthetic sick or lethal (SSL)
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SSL networks

• Gene function, drug targets predicted

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Other biological networks

• Coexpression
• Nodes genes
• Edges transcribed at same times, conditions
• Gene knockout / knockdown
• Nodes genes
• Edges similar phenotype (defects) when suppressed

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What they really look like
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We need models!
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Outline

1. Introduction
2. Network models
3. Implications from topology
4. Confidence assessment, edge prediction

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Traditional graph modeling
from GD2002
Random Regular
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Introduce small-world networks
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Small-world Networks

• Six degrees of separation
• 100 1000 friends each
• Six steps 1012 - 1018
• But

We live in communities
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Small-world measures

• Typical separation between two vertices
• Measured by characteristic path length
• Cliquishness of a typical neighborhood
• Measured by clustering coefficient

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Watts-Strogatz small-world model
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Measures of the W-S model

• Path length drops faster than cliquishness
• Wide range of phas both small-worldproperties

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Small-world measures of various graph types
Cliquishness Characteristic Path Length
Regular graph High Long
Random graph Low Short
Small-world graph High Short
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Another network property Degree distribution P
(k)

• The degree (notation k) of a node is the number
  of its neighbors
• The degree distribution is a histogram showing
  the frequency of nodes having each degree

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Degree distribution of E-R random networks
Erdös-Rényi random graphs

• Binomial degree distribution, well-approximated
  by a Poisson

Network figures from Strogatz, Nature 2001
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Degree distribution of many real-world networks

• Scale-free networks
• Degree distribution follows a power law
• P (k x) ? x -?

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Model for scale-free networks

• Growth and preferential attachment
• New node has edge to existing node v with
  probability proportional to degree of v
• Biologically plausible?

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Another scale-free network model

• Duplication and divergence
• New nodes are copies of existing nodes
• Same neighbors, then some gain/loss

Solé, Pastor-Satorras, et al. (2002)
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Other degree distributions
Amaral, Scala, et al., PNAS (2000)
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Hierarchical Networks
Ravasz, et al., Science 2002
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Properties of hierarchical networks



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C of 43 metabolic networks

• Independent of N

Ravasz, et al., Science 2002
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Scaling of the clustering coefficient C(k)

• Metabolic networks

Ravasz, et al., Science 2002
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Summary of network models
Random Poisson degree distribution
Small world high CC, short pathlengths
Scale-free power law degree distribution
Hierarchical high CC, modular, power law degree distribution
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Many real-world networks are small-world,
scale-free

• World-wide-web
• Collaboration of film actors (Kevin Bacon)
• Mathematical collaborations (Erdös number)
• Power grid of US
• Syntactic networks of English
• Neural network of C. elegans
• Metabolic networks
• Protein-protein interaction networks

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So What?
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There is information in a genes position in the
network

• We can use this to predict
• Relationships
• Interactions
• Regulatory relationships
• Protein function
• Process
• Complex / molecular machine

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Outline

1. Introduction
2. Network models
3. Implications from topology
4. Confidence assessment, edge prediction

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SSL hubs might be good cancer drug targets
Cancer cells w/ random mutations
Normal cell
Dead
Alive
Dead
(Tong et al, Science, 2004)
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Lethality

• Hubs are more likely to be essential

Jeong, et al., Nature 2001
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Degree anti-correlation

• Few edges directly between hubs
• Edges between hubs and low-degree genes are
  favored

Maslov and Sneppen, Science 2002
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Outline

1. Introduction
2. Network models
3. Implications from topology
4. Confidence assessment, edge prediction

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Confidence assessment

• Traditionally, biological networks determined
  individually
• High confidence
• Slow
• New methods look at entire organism
• Lower confidence (? 50 false positives)
• Inferences made based on this data

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Confidence assessment

• Can use topology to assess confidence if true
  edges and false edges have different network
  properties
• Assess how well each edge fits topology of true
  network
• Can also predict unknown relations

Goldberg and Roth, PNAS 2003
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Use clustering coefficient, a local property

• Number of triangles N(v) ? N(w)
• Normalization factor?

N(x) the neighborhood of node x
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Mutual clustering coefficient

• Jaccard Index Meet / Min Geometric

N(v) ? N(w) ---------------- N(v) ? N(w)
N(v) ? N(w) 2 ------------------ N(v)
N(w)
N(v) ? N(w) ------------------------ min (
N(v) , N(w) )
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Mutual clustering coefficient

• Hypergeometric
• P (intersection at least as large by chance)

-log
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Prediction

• A v-w edge would have a high clustering
  coefficient

v
w
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Interaction generality

• Confidence measure for edge based on topology
  around neighbors.

Saito, Suzuki, and Hayashizaki 2002,2003
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Confidence assessment

• Integrate experimental details with local
  topology
• Degree
• Clustering coefficient
• Degree of neighbors
• Etc.
• Used logistic regression

Bader, et al., Nature Biotechnology 2003
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The synthetic lethal network has many triangles
Xiaofeng Xin, Boone Lab
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2-hop predictors for SSL

• SSL SSL (S-S)
• Homology SSL (H-S)
• Co-expressed SSL (X-S)
• Physical interaction SSL (P-S)
• 2 physical interactions (P-P)

Wong, et al., PNAS 2004
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Multi-color motifs
Zhang, et al., Journal of Biology 2005