Steve Horvath University of California, Los Angeles Module preservation statistics.
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Transcript of Steve Horvath University of California, Los Angeles Module preservation statistics.
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
Motivational example: 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
Standard cross-tabulation based statistics have severe disadvantages
Disadvantages1. only applicable for modules defined via a
clustering procedure2. ill suited for making the strong statement
that a module is not preserved
We argue that network based approaches are superior when it comes to studying module preservation
Broad definition of a 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)
Networkof
cholesterol biosynthesis
genes
Message: female liver network (reference)Looks most similar to male liver network
Question
• How to measure relationships between different networks (e.g. how similar is the female liver network to the male network)?
• Answer: network concepts aka statistics
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
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
• E.g. Density in the test set
• cor.k=cor(kref,ktest)
• cor(Aref,Atest)
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
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
• 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.
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
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 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
Jeremy Miller, et al Dan Geschwind (2010) Divergence of human and mouse brain
transcriptome highlights Alzheimer disease pathways.
PNAS 2010
Why compare human and mouse brain transcription?
• 1) Module membership (kME) in conserved modules may be used to identify reliable markers for cell types and cellular components.
• 2) Studying differences in network organization could provide a basis for better understanding diseases enriched in human populations, such as Alzheimer’s Disease
Co-expression modules based on multiple human
and mouse gene expression data
Human Brain Modules
Mouse Brain Modules
Human modulesM7h and M9hwere enriched with AD genes
These modulescould not be found In mouse brains
Human specific modules M9h and M7h are related to AD
• Module preservation analysis identified two highly human-specific module, M9h and M7h– No clear functional annotation
• Guilt by association approaches show these modules are related to neurodegenerative dementias– M9H showed significant overlap with an Alzheimer’s
disease module that was identified using independent data sets run on different brain regions, on different platforms, and in different labs
– M7h contained two intramodular hub genes related to AD and frontotemporal dementia (FTD) in humans: GSK3β and tau
• These two modules provide key targets for furthering our understanding of neurodegenerative dementias
Genetic Programs in Human and Mouse Early Embryos Revealed
by Single-Cell RNA-Sequencing
Zhigang Xue, Kevin Huang, Xiaofei Ye,
et al
Guoping Fan
Background
• Mammalian preimplantation development is a complex process involving dramatic changes in the transcriptional architecture.
• Through single-cell RNA-sequencing (RNA-seq), we report here a comprehensive analysis of transcriptome dynamics from oocyte to morula in both human and mouse embryos.
• 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
Network Methods for Describing Sample
Relationships in Genomic Datasets: Application to
Huntington's Disease
• Michael C Oldham et al BMC Syst Biol. 2012 PMID: 22691535
Rich but complex HD data• Affymetrix microarray data from “the HD study”
– Hodges et al: Regional and cellular gene expression changes in human Huntington’s disease brain. Hum Mol Genet 2006, 15(6):965-977
• Brain samples of patients with HD (n = 44 individuals) and unaffected controls (n = 36 individuals, matched for age and sex)
• caudate nucleus (CN), cerebellum (CB), primary motor cortex (Brodmann’s area 4; BA4), and prefrontal cortex (Brodmann’s area 9; BA9)
• across five grades using Vonsattel’s neuropath criteria• Further, age, sex, the country where the experiment was
performed (samples were processed in the United States and New Zealand) and the microarray hybridization batch
Why define this sample network adjacency measure?
• Our proposed sample adjacency measure (based on β = 2) also has several other advantages. – it preserves the sign of the correlation – while any other power β could be used, the
choice of β = 2 results in an adjacency measure that is close to the correlation when the correlation is large (e.g. larger than 0.6, which is often the case among samples in microarray data).
• The adjacency measure allows one to define network concepts.
Connectivity• Gene connectivity = row sum of the adjacency matrix
– For unweighted networks=number of direct neighbors– For weighted networks= sum of connection strengths to other
nodes
– Scaled connectivity:
i ijjk a
Clustering Coefficient
Measures the cliquishness of a particular node« A node is cliquish if its neighbors know each other »
Clustering Coef of the black node = 0
Clustering Coef = 1
,
22
il lm mil i m i li
il ill i l i
a a aClusterCoef
a a
This generalizes directly to weightednetworks (Zhang and Horvath 2005)
Summary sample network• Z.k is a very useful measure for finding array outliers.• The correlation cor(K,C) between the connectivity and the
clustering coefficient (two important network concepts) is a sensitive indicator of homogeneity among biological samples. – It can distinguish biologically meaningful relationships among
subgroups of samples. – Advantage: This measure can highlight differences that cannot be
found using differential expression– Disadvantage: It requires some work to figure out which genes
lead to this effect. – Here: effect is concentrated in specific modules of genes
• Sample network approach is implemented in an R function and tutorial
Acknowledgement
Current and former lab members: • Peter Langfelder first author on many related
articles• Jason Aten, Chaochao (Ricky) Cai, Jun Dong, Tova
Fuller, Ai Li, Wen Lin, Michael Mason, Jeremy Miller, Mike Oldham, Chris Plaisier, Anja Presson, Lin Song, Kellen Winden, Yafeng Zhang, Andy Yip, Bin Zhang
• Colleagues/Collaborators• Neuroscience: Dan Geschwind,
Giovanni Coppola, Jeremy Miller, Mike Oldham, Roel Ophoff
• Mouse: Jake Lusis, Tom Drake