An Overview of Weighted Gene Co-Expression Network Analysis Contents Philosophy of Weighted Gene Co-Expression Network Analysis Network=Adjacency Matrix Steps as long as constructing a co-expression network

An Overview of Weighted Gene Co-Expression Network Analysis Contents Philosophy of Weighted Gene Co-Expression Network Analysis Network=Adjacency Matrix Steps as long as constructing a co-expression network www.phwiki.com

An Overview of Weighted Gene Co-Expression Network Analysis Contents Philosophy of Weighted Gene Co-Expression Network Analysis Network=Adjacency Matrix Steps as long as constructing a co-expression network

Zimmerman, Marcia, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal An Overview of Weighted Gene Co-Expression Network Analysis Steve Horvath University of Cali as long as nia, Los Angeles Contents How to construct a weighted gene co-expression network Why use soft thresholding How to detect network modules How to relate modules to an external clinical trait What is intramodular connectivity How to use networks as long as gene screening How to integrate networks with genetic marker data What is weighted gene co-expression network analysis (WGCNA) What is neighborhood analysis Philosophy of Weighted Gene Co-Expression Network Analysis Underst in addition to the “system” instead of reporting a list of individual parts Describe the functioning of the engine instead of enumerating individual nuts in addition to bolts Focus on modules as opposed to individual genes this greatly alleviates multiple testing problem Network terminology is intuitive to biologists

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How to construct a weighted gene co-expression network Bin Zhang in addition to Steve Horvath (2005) “A General Framework as long as Weighted Gene Co-Expression Network Analysis”, Statistical Applications in Genetics in addition to Molecular Biology: Vol. 4: No. 1, Article 17. 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 gene pairs Steps as long as constructing a co-expression network Overview: gene co-expression network analysis Microarray gene expression data Measure concordance of gene expression with a Pearson correlation C) The Pearson correlation matrix is either dichotomized to arrive at an adjacency matrix unweighted network Or trans as long as med continuously with the power adjacency function weighted network

Power adjacency function results in a weighted gene network Often choosing beta=6 works well but in general we use the “scale free topology criterion” described in Zhang in addition to Horvath 2005. Comparing adjacency functions Power Adjancy vs Step Function Comparing the power adjacency function to the step function While the network analysis results are usually highly robust with respect to the network construction method there are several reasons as long as preferring the power adjacency function. Empirical finding: Network results are highly robust with respect to the choice of the power beta Zhang B in addition to Horvath S (2005) Theoretical finding: Network Concepts make more sense in terms of the module eigengene. Horvath S, Dong J (2008) Geometric Interpretation of Gene Co-Expression Network Analysis. PloS Computational Biology

How to detect network modules Module Definition Numerous methods have been developed Here, we 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 The topological overlap dissimilarity is used as input of hierarchical clustering Generalized in Zhang in addition to Horvath (2005) to the case of weighted networks Generalized in Yip in addition to Horvath (2006) to higher order interactions

Using the topological overlap matrix (TOM) to cluster genes Here modules correspond to branches of the dendrogram TOM plot Hierarchical clustering dendrogram TOM matrix Module: Correspond to branches Genes correspond to rows in addition to columns Topological Overlap Plot Gene Functions Multi Dimensional Scaling Traditional View Different Ways of Depicting Gene Modules 1) Rows in addition to columns correspond to genes 2) Red boxes along diagonal are modules 3) Color b in addition to s=modules Idea: Use network distance in MDS

Heatmap view of module Rows=Genes Color b in addition to indicates module membership Columns= tissue samples Message: characteristic vertical b in addition to s indicate tight co-expression of module genes Module Eigengene= measure of over-expression=average redness Rows,=genes, Columns=microarray The brown module eigengenes across samples Module eigengenes can be used to determine whether 2 modules are correlated. If correlation of MEs is high-> consider merging. Eigengenes can be used to build separate networks

Consensus eigengene networks in male in addition to female mouse liver data in addition to their relationship to physiological traits Langfelder P, Horvath S (2007) Eigengene networks as long as studying the relationships between co-expression modules. BMC Systems Biology 2007 How to relate modules to external data Clinical trait (e.g. case-control status) gives rise to a gene significance measure Abstract definition of a gene significance measure GS(i) is non-negative, the bigger, the more biologically significant as long as the i-th gene Equivalent definitions GS.ClinicalTrait(i) = cor(x(i),ClinicalTrait) where x(i) is the gene expression profile of the i-th gene GS(i)=T-test(i) of differential expression between groups defined by the trait GS(i)=-log(p-value)

A SNP marker naturally gives rise to a measure of gene significance Additive SNP marker coding: AA->2, AB->1, BB->0 Absolute value of the correlation ensures that this is equivalent to AA->0, AB->1, BB->2 Dominant or recessive coding may be more appropriate in some situations Conceptually related to a LOD score at the SNP marker as long as the i-th gene expression trait GS.SNP(i) = cor(x(i), SNP). A gene significance naturally gives rise to a module significance measure Define module significance as mean gene significance Often highly related to the correlation between module eigengene in addition to trait Important Task in Many Genomic Applications: Given a network (pathway) of interacting genes how to find the central players

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Slide courtesy of A Barabasi Flight connections in addition to hub airports The nodes with the largest number of links (connections) are most important! What is intramodular connectivity Generalized 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

Gene significance versus intramodular connectivity kIN How to use networks as long as gene screening Intramodular connectivity kIN versus gene significance GS Note the relatively high correlation between gene significance in addition to intramodular connectivity in some modules In general, kIN is a more reliable measure than GS In practice, a combination of GS in addition to k should be used Module eigengene turns out to be the most highly connected gene (under mild assumptions)

Conclusions: chimp/human Gene expression is highly preserved across species brains Gene co-expression is less preserved Some modules are highly preserved Gene modules correspond roughly to brain architecture Species-specific hubs can be validated in silico using sequence comparisons Software in addition to Data Availability Sample data in addition to R software tutorials can be found at the following webpage http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork An R package in addition to accompanying tutorial can be found here: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA/ Tutorial as long as this R package http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA/TutorialWGCNApackage.doc THE END

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