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Introduction to Systems Biology4. Gene (Regulatory) Networks

Toni Reverter – June 2010, Valencia, Spain.

Toni Reverter. Introduction to Systems Biology. 7 – 11 June, Valencia, Spain

4.1 Introduction to Gene Networks

When a comprehensive gene expression data set representing a large number of perturbations is made available, the reversed engineering of gene regulatory networks becomes a logical step towards the elucidation of biological pathways of interest.

While developmental (ie. Time series) experiments provide the ideal framework, Basso et al (2005; Nature Genetics, 37:382) showed that a large number of perturbations can do the trick …with the right mathematical approach.

Barabasi & Oltvai (2004) Network Biology: Understanding the cell’s functional organization. Nature Review Genetics 5:101.

“Network theory offers unforeseen possibilities to understand the cell’s internal organization and evolution, fundamentally altering our view of cell biology”.

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4.1 Introduction to Gene NetworksNetworks contain small repeating patterns of interconnections, called network Motifs .

Basic network motifs include:(1) Feed forward; (2) Single input;(3) Multiple input; (4) A combination of the above.

Think of motifs as simple building blocks of complex networks.

Much of a cell’s activity is organised as a network of interacting Modules : Sets of genes co-regulated to respond to different conditions.

Think of Modules as clusters, i.e., genes being highly connected within a cluster but sparsely (if at all) connected across modules.

Understanding this organisation is crucial for understanding cellular responses to internal and external signals.

Once a network is build, both its(1) Mathematical

and (2) Biologicalsoundness needs to be validated.

Scale-free, power-law distribution of its connectivity

Targets via essaysEffects via knock-outs



Network motifs

Patterns of inter-connections thatfrequently appearin the network

Directed graph

nodes represent genes & edges represent

transcriptional interaction

Gene regulatory networkof an organism

A transcription factor, a target gene with its binding site and

a regulatory interaction

Basic unit

Transcription factor

Target gene

Source: M. Madan-BabuMRC Laboratory of Molecular Biology, Cambridge

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4.1 Introduction to Gene NetworksConnectivity Rules

Does this map tell you which cities are important?

This one does!

The nodes with the largest number of links (connections) are most important!



Gene expression is more strongly preserved than gene connectivity. Hypothesis: Molecular wiring makes us human

Chimp vs Human

Additional Hypotheses:1. Alternative splice variants of the same gene2. The role of non-coding DNA � RNAi

Khaitovich et al. (2005)Science 309:1850.

Connectivity Rules

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Network theory used to capture Saddam Hussein!

“The intelligence background and link diagrams that we built were rooted in the concepts of network analysis. We constructed an elaborate product that traced the tribal and family linkages of Saddam Hussein thereby allowing us to focus on certain individuals who may have had (or presently had) close ties to [him],”

Major Brian J. Reedhttp://www2.asanet.org/footnotes/julyaugust05/fn3.html



http://christakis.med.harvard.edu/

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Lee et al. (2002) Science 298:799-804.

MORE TERMINOLOGY:

Nodes are Genes.

Connections (or edges or vertices or links) are Interactions.

Directed interactions (ie. having a regulatory nature) involve a Transcription Factor and its Target(s).

In the main, we’ll deal with gene co-expression networks (…a way to explore the correlation matrix).


Basic Network Motifs



Basic Network Motifs …and their relevance

Single-Input Motif

TF

G1 G2 G3

Last-In-First-Out (LIFO) Order

Temporal Order of Expression

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Feed-Forward Motif

TF1

G1 G2 G3

First-In-First-Out (FIFO) Order


TF2ACTIVATOR

REPRESSOR

� The flagella is a device made of ~30 proteins� Only built if needed (ie. if no food around)� Is an electrical motor (pumping out protons at the expense of ATP)� Capable of pushing the cell at 30 microns/sec.

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Temporal Order of ExpressionKEGG database: http://www.genome.ad.jp/kegg/kegg2.html





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Degree (or Connectivity ) of a node, k, is the No. of links this node has.

Basic Network Measures

The Degree Distribution , P(k), is the probability that a selected node has exactly k links. Networks are classified by their degree distribution.

The Clustering coefficient , C(k) = 2k/(N(N-1)), measures the amount of cohesiveness, the tendency of nodes to form clusters or modules.

Note 1 : the maximum number of connections is N(N-1)/2 (ie. Number of off-diagonals in the R matrix), in which case C(k) = 1.0. Note 2 : For many networks, C(k) ~ k-1 which is an indication of a network hierarchical character (more on this later).Note 3 : For a single node i, C(k i) = 2n i/(k i(k i-1)), where n i is the number of links connecting the k i neighbours of node i with each other and k i(k i-1)/2 is the total number of triangles that would pass through node i should all of its neighbours be connected with each other.

The Path Length = Links we need to pass to travel between two nodes. The mean path length, l tells us the average shortest pass between all pairs of nodes and offers a measure of overall navigability.



Computing Basic Network Measures

Degree Distribution:

The Clustering coefficient , C(k) = 2k/(N(N-1)):

N = 22 Genesk = 31 Connections

C = (2×31)/(22×21) = 0.1342 � 13.4%

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1. Random Network2. Scale-Free Network3. Hierarchical Network

Three Types of Networks According to their

Connectivity Structure

NB: Biological networks are reported to be Scale-Free…a bit like having an airbag in your car.


Interpreting Basic Network Measures


Each pair of nodes is connected with probability p, creating a graph with approximately [p × N(N-1)/2] randomly placed links.

The connectivity degree follows a Poisson distribution: Nodes that deviate from the average are rare and decreases exponentially.

The clustering coefficient is independent of a node’s degree of connectivity, so it appears as a horizontal line.

Mean shortest path is l ~ log(N) indicating that most nodes are connected by a short path (Small World Property).


Random Networks

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Most nodes are poorly while a few are highly connected (Hubs ).

The degree distribution approximates a power law: P(k) ~ k –γ, where γ is the degree exponent (Straight line in a Log-Log plot).

The smaller the γ, the more important is the role of the Hubs. Most biological networks have 2 < γ < 3. For γ > 3, Hubs are irrelevant and the network behaves like a random network.

The mean shortest path length is proportional to log(log(N)) (ie. Much shorter than Small World Property).

Line Random Networks, C(k) is independent of k (straight line)


Scale-Free (Power-Law) Networks


Scale-Free networks are invariant to changes in scale. Any function ofP(k) remains unchanged within a multiplicative factor P(ak) = b P(k).

This implies that scale-free networks are self-similar, i.e. any part of the network is statistically similar to the whole network and parameters are assumed to be independent of the system size.

Think of a cauliflower:


Scale-Free (Power-Law) Networks

No matter which scale is chosen the same distribution of degrees

is observed among nodes

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To accommodate modularity, clusters combine in an iterative manner, generating a hierarchical network.

The hierarchical network model seamlessly integrates a scale-freetopology with an inherent modular structure by generating a network that has a power-law degree distribution with degree exponent γ = 1 + ln4/ln3 = 2.26.

The most important signature of hierarchical modularity is the scaling of the clustering coefficient, which follows C(k) ~ k –1 a straight line of slope –1 on a log–log plot.


Hierarchical Networks


Topology

Connectivity, k

Clustering Coefficient, C(k)


Random vs Scale-Free vs Hierarchical

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In the random network (left), the five nodes with the most links (in red) are connected to only 27% of all nodes (green).

In the scale-free network (right), the five most connected nodes (red) are connected to 60% of all nodes (green)


Random vs Scale-Free Networks

Scale-free networks are resistant to random failure but vulnerable to targeted attack, specifically against hubs. This property has been held to account for the robustness of biological networks to perturbations like mutation and environmental stress. A positive correlation between essentiality and connectivity has been demonstrated linking topological centrality to functional essentiality.


Luscombe et al. (2004) Genomic analysis of regulatory network dynamics reveals large topological changes . Nature 431:308-312


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Hidalgo et al. (2009) PLoS Comp Biol 5:e1000353


Phenotypic Disease Network

Understanding and Exploiting the Flow of Information in Networks


Phenotypic Disease Network

Hidalgo et al. (2009) PLoS Comp Biol 5:e1000353



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r = 0.53; P = 0.002

r = -0.26; P = 0.146

r = -0.73; P < 0.001



A Model to Generate Networks

1. Evolution: Continuous expansion by the addition of new nodes.2. Growing schema: Starting with a small number of nodes (m0≥2),

at every time step we add a new node with m (≤2) edges that link the new node to m different nodes already present in the system.

3. Preferential-attachment (rich get richer): New nodes attach preferentially to sites that are already well connected � The probability P that a new vertex will be connected to vertex i depends on the connectivity ki of that vertex, so that P(ki) = ki/Σjkj.

Barabasi and Albert. Science (1999) 286 509-512

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Barabasi and Albert. Science (1999) 286 509-512

This network evolves into a scale-invariant state with the probability that a node has k edges, following a power law with an exponent = 2.9 +/- 0.1

This network evolves into a scale-invariant state with the probability that a node has k edges, following a power law with an exponent = 2.9 +/- 0.1




Network_Growth.mov

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4.2 Gene Co-Expression Networks

• Understand the “system” instead of reporting a list of individual parts• Describe the functioning of the engine instead of enumerating individual

nuts and bolts

• Focus on modules as opposed to individual genes• This greatly alleviates multiple testing problem

• Network terminology is intuitive to biologists

Rationale

Why?

• Genes showing higher than average co-expression are more likely to belong to the same pathway (class comparison)

• Genes controlled by the same transcription factor show higher than average co-expression (class discovery)

Wolfe CJ, Kohane IS and Butte AJ (2005) Systematic survey reveals general applicability of “guilt-by-association” within gene coexpression networks. BMC Bioinformatics, 6, 227.

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24 Normal Tissues (in dupplicate) – 3,327 Genes & 15,841 Connections

http://bioinfow.dep.usal.es/coexpression/

Prieto et al. (2009) Human gene coexpressionlandscape: confident network derived from tissue transcriptomic profiles. PLoS ONE 3:e3911



Statistics are like a bikini, what they reveal is suggestive, but what they conceal is vital (Aaron Levenstein).

The correlation coefficient is the most “bikini” of all statistics (Toni Reverter).

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Definition of “high” correlation is somewhat tricky.

Why Correlation?

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Why Correlation?



Why Correlation?

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Correlation Coefficient

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Finding significant correlations is NOT a trivial task

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Weighted Un-Weighted

All genes are connectedWidth = StrengthSoft thresholding

Some genes are connectedEqual strength

Hard thresholding

Finding significant correlations is NOT a trivial task


4.2 Gene Co-Expression NetworksThe PCIT Algorithm

=xyr

Compare Direct vs Partial Correlation

Strength of the r’ship between x and yX

Y

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Reverter and Chan (2008) Bioinformatics 21:2491

=xyr Strength of the r’ship between x and y

=xy.zr Strength of the r’ship between x and ythat is independent of z

X

Z Y





=

⋅

xy

zxy

r

rProportion of the strength of the r’shipbetween x and y that is independent of z

=xyr Strength of the r’ship between x and y

=xy.zr Strength of the r’ship between x and ythat is independent of z

X

Z Y


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PCIT: Use of Partial C orrelations and an Information T heoryapproach to establish connections in the network

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xzxy r698.0r >If

yzxy r698.0r >andConnection between X and Y




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SIMULATED DATA � RANDOM NETWORK

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The PCIT Algorithm …and the Competition

Bin Zhang and Steve Horvath (2005) "A General Framework for Weighted Gene Co-Expression Network Analysis", Statistical Applications in Genetics and Molecular Biology: Vol. 4: No. 1, Article 17.

Margolin AA et al. (2008) ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinformatics, 7, S7.

Basso K et al. (2005) Reverse engineering of regulatory networks in human B cells. Nat. Genet. 37, 382-390.

They require human interventionPCIT is completely data driven

PCIT does not force the emergence of a scale-free topoloty



PIEDMONTESE

WAGYU

PRE-NATAL POST-NATALDIETS

A/ Compute the normalized mean expression of 6,603 genes across 26 experimental conditions to generate up to six interlaced gene networks using PCIT:

1. Overall: Across the 26 conditions2. Piedmontese: Across the 10 conditions of Piedmontese samples (circles).3. Wagyu: Across the 10 conditions of Wagyu breed samples (squares).4. Pre-Natal: Across the 8 conditions of pre-natal samples (blue figures).5. Post-Natal: Across the 12 conditions of post-Natal samples (green figures).6. Diets: A network across the 6 conditions of the diet experiment (orange triangles).

B/ Select edges (connections) conserved across the 6 networks � “Always Conserved ” network.

C/ Load the Always Conserved network into Cytoscape, display organic layout algorithm and with a number of gene attributes (including regulation, pathway, etc.) incorporated in the visualization schema to enhance distinguishing among “highly conserved modules ”. Whenever possible, the genomic functionality of each module was labelled (eg. cell cycle, mitochondria, ECM, Z-disk, …).

D/ The average absolute co-expression correlation of each transcriptional regulator with the genes in each module was compute to identify the key regulators .

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The 6,603 genes (including 912 Transcription Factors)

were selected as those showing ‘good’ signals

throughout samples and ‘minimally’ variables.



The Always Conservednetwork had 3,506 genes and

6,506 connections.Up to 66 modules were

identified

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Catabolic



Cell CycleDetermines fibre number � double-muscling

TranslationProtein synthesis � double-muscling

Extracellular MatrixConnective tissue � meat quality

MitochondriaOxidative capacity �feed efficiency

Identification of “Key” Regulators

• TF included in each PCIT-derived module• TF with large average |r| with module members

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RNF14 Experimental Validation � Transfection C2C12 cells

1. Designed primers to amplify mouse RNF14 transcript. A PCR using mouse muscle cDNA template amplified two bands � 2 Transcript variants (one short, one long).

2. Both variants were engineered into an “expression construct” � CMV promoter recognised by mammalian cells as a cue to drive expression.

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4.3 Cytoscapewww.cytoscape.org

Contact UsPhone: 1300 363 400 or +61 3 9545 2176

Email: [email protected] Web: www.csiro.au

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Introduction to Systems Biology 4. Gene (Regulatory) Networksacteon.webs.upv.es › cursos › Reverter 2010 Apuntes › 5. GeneNetwor… · Introduction to Systems Biology 4. Gene