Weighted Gene Co-Expression Network Analysis of Multiple Independent Lung Cancer Data Sets Steve...
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Weighted Gene Co-Expression Network Analysis of
Multiple Independent Lung Cancer Data Sets
Steve Horvath
University of California, Los Angeles
Contents
• Mini review of weighted correlation network analysis (WGCNA)
• Module preservation statistics
• Application to multiple adenocarcinoma
Network=Adjacency Matrix
• A network can be represented by an adjacency matrix, A=[aij], that encodes whether/how a pair of nodes is connected.– A is a symmetric matrix with entries in [0,1] – For unweighted network, entries are 1 or 0
depending on whether or not 2 nodes are adjacent (connected)
– For weighted networks, the adjacency matrix reports the connection strength between node pairs
– Our convention: diagonal elements of A are all 1.
Connectivity (aka degree)
• Node connectivity = row sum of the adjacency matrix– For unweighted networks=number of direct
neighbors– For weighted networks= sum of connection
strengths to other nodes
iScaled connectivity=Kmax( )
i i ijj i
i
Connectivity k a
k
k
Density
• Density= mean adjacency• Highly related to mean connectivity
( )
( 1) 1
where is the number of network nodes.
iji j ia mean k
Densityn n n
n
How to construct a weighted gene co-expression
network?
Use power β for soft thresholding a correlation coefficient
Unsigned network, absolute value
| ( , ) |
Signed network preserves sign info
| 0.5 0.5 ( , ) |
ij i j
ij i j
a cor x x
a cor x x
Default values: β=6 for unsigned and β =12 for signed networks.Zhang et al SAGMB Vol. 4: No. 1, Article 17.
Comparing adjacency functions for transforming the correlation into a
measure of connection strength
Unsigned Network Signed Network
Advantages of soft thresholding with the power function
1. Robustness: Network results are highly robust with respect to the choice of the power β (Zhang et al 2005)
2. Calibrating different networks becomes straightforward, which facilitates consensus module analysis
3. Math reason: Geometric Interpretation of Gene Co-Expression Network Analysis. PloS Computational Biology. 4(8): e1000117
4. Module preservation statistics are particularly sensitive for measuring connectivity preservation in weighted networks
How to detect network modules?
Module Definition
• Numerous methods have been developed • We often use average linkage hierarchical
clustering coupled with the topological overlap dissimilarity measure.
• Once a dendrogram is obtained from a hierarchical clustering method, we choose a height cutoff to arrive at a clustering.
• Modules correspond to branches of the dendrogram
How to cut branches off a tree?
Langfelder P, Zhang B et al (2007) Defining clusters from a hierarchical cluster tree: the Dynamic Tree Cut library for R. Bioinformatics 2008 24(5):719-720
Module=branch of a cluster tree
Dynamic hybrid branch cutting method combinesadvantages of hierarchical clustering and pam clustering
Question: How does one summarize the expression profiles in a module?
Answer: This has been solved.Math answer: module eigengene= first principal componentNetwork answer: the most highly connected intramodular hub gene
Both turn out to be equivalent
brown
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brown
-0
.1
0.0
0.1
0.2
0.3
0.4
Module Eigengene= measure of over-expression=average redness
Rows,=genes, Columns=microarray
The brown module eigengenes across samples
Module eigengene is defined by the singular value decomposition of X• X=gene expression data of a module
gene expressions (rows) have been standardized across samples (columns)
1 2
1 2
1 2
1
( )
( )
(| |,| |, ,| |)
Message: is the module eigengene E
m
m
m
X UDV
U u u u
V v v v
D diag d d d
v
Module detection in very large data sets
• Large may mean >25k variables
R function blockwiseModules (in WGCNA library) implements 3 steps:
1. Variant of k-means to cluster variables into blocks
2. Hierarchical clustering and branch cutting in each block
3. Merge modules across blocks (based on correlations between module eigengenes)
Define 2 alternative measures of intramodular connectivity and
describe their relationship.
Intramodular Connectivity• Intramodular connectivity kIN with respect
to a given module (say the Blue module) is defined as the sum of adjacencies with the members of this module.– For unweighted networks=number of direct links
to intramodular nodes– For weighted networks= sum of connection
strengths to intramodular nodes
{ }
BlueModulei ijj BlueModule
kIN a
Eigengene based connectivity, also known as kME or module membership measure
( ) ( , )i ikME ModuleMembership i cor x ME
kME(i) is simply the correlation between the i-th gene expression profile and the module eigengene.
Very useful measure for annotating genes with regard to modules.
Module eigengene turns out to be the most highly connected gene
When dealing with a network comprised of module genes,
the scaled intramodular connectivity is determined by kME
kIM | ( , ) | | ( ) |m
" "
ax(kIM)
Group conform behavior leads to a lot of friends.
iicor x E kME i .
where | ( ) | measures group conform behavior
Derivation requires an unsigned weighted correlation network
PLoS Comput Biol 4(8): e1000117
kME i
Question
• How to measure relationships between different networks (e.g. how similar is the female liver network to the male network).
Networkof
cholesterol biosynthesis
genes
Message: female liver network (reference)Looks most similar to male liver network
Network concepts to measure relationships between networks
Numerous network concepts can be used to measure the preservation of network connectivity patterns between a reference network and a test network
• cor.k=cor(kref,ktest)
• cor(Aref,Atest)
• Cor(ClusterCoefref,ClusterCoeftest)
Is my network module preserved and reproducible?
Langfelder et al PloS Comp Biol. 7(1): e1001057.
Network module
Abstract definition of module=subset of nodes in a network.
Thus, a module forms a sub-network in a larger network
Example: module (set of genes or proteins) defined using external knowledge: KEGG pathway, GO ontology category
Example: modules defined as clusters resulting from clustering the nodes in a network
• Module preservation statistics can be used to evaluate whether a given module defined in one data set (reference network) can also be found in another data set (test network)
In general, studying module preservation is different from studying cluster preservation.
Many statistics for assessing cluster preservation e.g.Kapp AV, Tibshirani R (2007) Are clusters found in one dataset present in another dataset? Biostatistics (2007), 8, 1, pp. 9–31
But in general network modules are different from clusters (e.g. KEGG pathways may not correspond to clusters in the network).
However, many module preservation statistics lend themselves as cluster preservation statistics and vice versa
Module preservation is often an essential step in a network analysis
Construct a networkRationale: make use of interaction patterns between genes
Identify modulesRationale: module (pathway) based analysis
Relate modules to external informationArray Information: Clinical data, SNPs, proteomicsGene Information: gene ontology, EASE, IPARationale: find biologically interesting modules
Find the key drivers of interesting modulesRationale: experimental validation, therapeutics, biomarkers
Study Module Preservation across different data Rationale: • Same data: to check robustness of module definition• Different data: to find interesting modules
One can study module preservation in general networks specified by an adjacency matrix, e.g. protein-protein interaction networks.
However, particularly powerful statistics are available for correlation networks
weighted correlation networks are particularly useful for detecting subtle changes in connectivity patterns. But the methods are also applicable to unweighted networks (i.e. graphs)
Module preservation in different types of networks
Input: module assignment in reference data.
Adjacency matrices in reference Aref and test data Atest
Network preservation statistics assess preservation of
1. network density: Does the module remain densely connected in the test network?
2. connectivity: Is hub gene status preserved between reference and test networks?
3. separability of modules: Does the module remain distinct in the test data?
Network-based module preservation statistics
Several connectivity preservation statisticsFor general networks, i.e. input adjacency matrices
cor.kIM=cor(kIMref,kIMtest)
correlation of intramodular connectivity across module nodes
cor.ADJ=cor(Aref,Atest)
correlation of adjacency across module nodes
For correlation networks, i.e. input sets are variable measurements
cor.Cor=cor(corref,cortest)
cor.kME=cor(kMEref,kMEtest)
One can derive relationships among these statistics in case of weighted correlation network
Choosing thresholds for preservation statistics based on permutation test
For correlation networks, we study 4 density and 4 connectivity preservation statistics that take on values <= 1
Challenge: Thresholds could depend on many factors (number of genes, number
of samples, biology, expression platform, etc.)
Solution: Permutation test. Repeatedly permute the gene labels in the test
network to estimate the mean and standard deviation under the null hypothesis of
no preservation.
Next we calculate a Z statistic
Z=observed−mean permuted
sd permuted
Gene modules in AdiposePermutation test for estimating Z scores
For each preservation measure we report the observed value and the permutation Z score to measure significance.
Each Z score provides answer to “Is the module significantly better than a random sample of genes?”
Summarize the individual Z scores into a composite measure called Z.summary
Zsummary < 2 indicates no preservation, 2<Zsummary<10 weak to moderate evidence of preservation, Zsummary>10 strong evidence
Z=observed−mean permuted
sd permuted
Details are provided below and in the paper…
Module preservation statistics are often closely related
Red=density statistics
Blue: connectivity statistics
Green: separability statistics
Cross-tabulation based statistics
Message: it makes sense to aggregate the statistics into “composite preservation statistics”Clustering module preservation statistics based on correlations across modules
Composite statistic in correlation networks based on Z statistics
( )( ) ( )
. ( )
Permutation test allows one to estimate Z version of each statistic
. ( . | )
( . | )
Composite connectivity based statistics for correlation networks
qq q
cor Cor q
connect
cor Cor E cor Cor nullZ
Var cor Cor null
Z
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
. . . .( , , , )
Composite density based statistics for correlation networks
( , , , )
Composit
q q q q q
q q q q q
ivity cor Cor cor kME cor A cor kIM
density meanCor meanAdj propVarExpl meanKME
median Z Z Z Z
Z median Z Z Z Z
( ) ( )
( )
e statistic of density and connectivity preservation
2
q q
q connectivity densitysummary
Z ZZ
Gene modules in AdiposeAnalogously define composite statistic:
medianRank
Based on the ranks of the observed preservation statistics
Does not require a permutation test
Very fast calculation
Typically, it shows no dependence on the module size
Summary preservation• Standard cross-tabulation based statistics are intuitive
– Disadvantages: i) only applicable for modules defined via a module detection procedure, ii) ill suited for ruling out module preservation
• Network based preservation statistics measure different aspects of module preservation– Density-, connectivity-, separability preservation
• Two types of composite statistics: Zsummary and medianRank.• Composite statistic Zsummary based on a permutation test
– Advantages: thresholds can be defined, R function also calculates corresponding permutation test p-values
– Example: Zsummary<2 indicates that the module is *not* preserved– Disadvantages: i) Zsummary is computationally intensive since it is
based on a permutation test, ii) often depends on module size• Composite statistic medianRank
– Advantages: i) fast computation (no need for permutations), ii) no dependence on module size.
– Disadvantage: only applicable for ranking modules (i.e. relative preservation)
Application:Modules defined as KEGG pathways.Connectivity patterns (adjacency matrix) is defined as signed weighted co-expression network.Comparison of human brain (reference) versus
chimp brain (test) gene expression data.
Preservation of KEGG pathwaysmeasured using the composite preservation
statistics Zsummary and medianRank
• Humans versus chimp brain co-expression modules
Apoptosis module is least preserved according to both composite preservation statistics
Apoptosismodule has low valueof cor.kME=0.066
Visually inspect connectivity patterns of the apoptosis module in humans and chimpanzees
Weighted gene co-expression module. Red lines=positive correlations,Green lines=negative cor
Note that the connectivity patterns look very different.Preservation statistics are ideally suited to measure differences in connectivity preservation
Literature validation:Neuron apoptosis is known to differ between humans and chimpanzees
• It has been hypothesized that natural selection for increased cognitive ability in humans led to a reduced level of neuron apoptosis in the human brain:– Arora et al (2009) Did natural selection for increased cognitive
ability in humans lead to an elevated risk of cancer? Med Hypotheses 73: 453–456.
• Chimpanzee tumors are extremely rare and biologically different from human cancers
• A scan for positively selected genes in the genomes of humans and chimpanzees found that a large number of genes involved in apoptosis show strong evidence for positive selection (Nielsen et al 2005 PloS Biol).
Application:Studying the preservation of human brain co-expression modules in chimpanzee brain expression data.
Modules defined as clusters(branches of a cluster tree)
Data from Oldam et al 2006
Preservation of modules between human and chimpanzee brain networks
2 composite preservation statistics
Zsummary is above the threshold of 10 (green dashed line), i.e. all modules are preserved. Zsummary often shows a dependence on module size which may or may not be attractive (discussion in paper)In contrast, the median rank statistic is not dependent on module size.It indicates that the yellow module is most preserved
Application: Studying the preservation of a female mouse liver module in different
tissue/gender combinations. Module: genes of cholesterol biosynthesis pathway Network: signed weighted co-expression networkReference set: female mouse liverTest sets: other tissue/gender combinations
Data provided by Jake Lusis
Networkof
cholesterol biosynthesis
genes
Message: female liver network (reference)Looks most similar to male liver network
Note that Zsummaryis highest in the male liver network
Application:Modules defined as KEGG pathways.
Comparison of human brain (reference) versus
chimp brain (test) gene expression data.
Connectivity patterns (adjacency matrix) is defined as signed weighted co-expression network.
Preservation of KEGG pathwaysmeasured using the composite preservation
statistics Zsummary and medianRank
• Humans versus chimp brain co-expression modules
Apoptosis module is least preserved according to both composite preservation statistics
Publicly available microarray data from
lung adenocarcinoma patients
References of the array data sets
• Shedden et al (2008) Nat Med. 2008 Aug;14(8):822-7
• Tomida et al (2009) J Clin Oncol 2009 Jun 10;27(17):2793-9
• Bild et al (2006) Nature 2006 Jan 19;439(7074):353-7
• Takeuchi et al (2006) J Clin Oncol 2006 Apr 10;24(11):1679-88
• Roepman et al (2009) Clin Cancer Res. 2009 Jan 1;15(1):284-90
Array platforms 5 Affymetrix data sets
–Affy 133 A – Shedden et al ( HLM, Mich, MSKCC, DFCI)
–Affy 133 plus 2 – Bild et al
3 Agilent platforms:–21.6K custom array – Takeuchi et al–Whole Human Genome Microarray 4x44K –
Tomida et al– Whole Human Genome Oligo Microarray
G4112A – Roepman et al
Standard marginal analysisfor relating genes to survival time
(Prognostic) Gene Significance
• Roughly speaking: the correlation between gene expression and survival time.
• More accurately: relation to hazard of death (Cox regression model)
Weak relations between gene significances
Meta analysis across 8 data for select cancer stem cell related genes
Marker Gene High expression pValue High expressionpValueStemcell NANOG protective 4.3E-03 protective 3.81E-03Stemcell collagen IV protective 5.2E-03 Not Signif 3.07E-01Stemcell CD133 Not Signif 1.2E-01 protective 3.19E-02Stemcell "OCT4" Not Signif 1.5E-01 Not Signif 7.60E-01Stemcell SOX2 Not Signif 2.3E-01 Not Signif 2.58E-01Stemcell BMI1 Not Signif 3.3E-01 Not Signif 4.84E-01Stemcell CD34 Not Signif 6.2E-01 Not Signif NAStemcell N-cadherin Not Signif 8.4E-01 Not Signif 3.81E-01Stemcell CD44 Not Signif 6.5E-01 Not Signif 4.95E-01Stemcell vitronectin Not Signif 2.6E-01 Not Signif 8.50E-01Stemcell thrombospondin risk 3.5E-02 Not Signif 1.60E-01Stemcell vimentin risk 1.1E-02 Not Signif 5.73E-01Stemcell fibronectin risk 3.5E-04 Not Signif 1.24E-01TF SLUG risk 5.3E-02 risk 5.65E-02TF SIP1 risk 9.9E-05 Not Signif 2.76E-01
survival time recurrence time
Most genes are not associated with survival or recurrence
Preservation of co-expression relationships between select
cancer stem cell markers
Signed weighted co-expression network between select markers
Overall, very weak preservation. Some evidence for connectivity preservation in other Affy data
Gene co-expression module preservation
Modules found in the Shedden Michigan data set;
Zsummay
Adenocarcinoma:Network connectivity is correlated for
data from the same platform.
Affy
Agilent
Connectivity preservation often indicatesmodule preservation
Consensus module analysis
Steps for defining “consensus” modules that are shared across many networks
• Calibrate individual networks so that they become comparable– Often easier for weighted networks
• Define consensus network using quantile
• Define consensus dissimilarity based on consensus network• Define modules as clusters• Use WGCNA R function blockwiseConsensusModules or consensusDissTOMandTree
25.,...,,. 21 probAApquantileconsA ijijij
Cell cycle immune system
ProteinaceousExtracellular matrix
Consensus modules based on 8 adeno data sets
As expected, the cell cycle module eigengene is significantly (p=2E-6)
associated with survival timeCor, p-valueMeta Z, p
Cancer stem cell markers and TFs
Advantages of soft thresholding with the power function
1. Robustness: Network results are highly robust with respect to the choice of the power beta (Zhang et al 2005)
2. Calibrating different networks becomes straightforward, which facilitates consensus module analysis
3. Math reason: Geometric Interpretation of Gene Co-Expression Network Analysis. PloS Computational Biology. 4(8): e1000117
4. Module preservation statistics are particularly sensitive for measuring connectivity preservation in weighted networks
• General information on weighted correlation networks• Google search
– “WGCNA”– “weighted gene co-expression network”
R function modulePreservation is part of WGCNA package
Tutorials: preservation between human and chimp brains
www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation
Implementation and R software tutorials, WGCNA R library
Acknowledgement
(Former) Students and Postdocs: • Peter Langfelder first author & carried out lung cancer
analysis • Jason Aten, Chaochao (Ricky) Cai, Jun Dong, Tova Fuller, Ai Li,
Wen Lin, Michael Mason, Jeremy Miller, Mike Oldham, Anja Presson, Lin Song, Kellen Winden, Yafeng Zhang, Andy Yip, Bin Zhang
• Colleagues/Collaborators• Cancer: Paul Mischel, Stan Nelson• Neuroscience: Dan Geschwind, Giovanni
Coppola, Roel Ophoff• Mouse: Jake Lusis, Tom Drake
NCI: P50CA092131, P30CA16042