Integrating Genetic and Network Analysis to Characterize ...

Integrating Genetic and Network Analysis to Characterize ...

An Overview of Weighted Gene Co-Expression Network Analysis adapted from Steve Horvath University of California, Los Angeles Contents How to construct a weighted gene coexpression network? Why use soft thresholding? How to detect network modules? How to relate modules to an external clinical trait? Philosophy of Weighted Gene CoExpression Network Analysis 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 Network terminology is intuitive to biologists How to construct a weighted gene co-expression network? 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. 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 for constructing a co-expression A) Microarray gene network expression data B) 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 transformed continuously with the power adjacency function weighted network Power adjacency function results in a weighted gene network aij | cor ( xi , x j ) | Often choosing beta=6 works well but in general we use the scale free topology criterion described in Zhang and Horvath 2005.

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 a

iu auj TOM ij aij u min(ki , k j ) 1 aij DistTOM ij 1 TOM ij Generalized in Zhang and Horvath (2005) to the case of weighted networks Generalized in Yip and 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 Genes correspond to rows and columns Hierarchical clustering dendrogram TOM matrix Module: Correspond to branches Different Ways of Depicting Gene Modules

Topological Overlap Plot Gene Functions 1) Rows and columns correspond to genes 2) Red boxes along diagonal are modules 3) Color bands=modules Multi Dimensional Scaling Idea: Use network distance in MDS Traditional View odule eigengenes can be used to determine whether 2 modu

e correlated. If correlation of MEs is high-> consider merging -0.2 0.2 -0.1 0.2 -0.1 0.2 -2.0 0.0 Martingale.Res 0.2 ME.blue

-0.2 0.08 0.2 ME.brow n 0.22 -0.2 0.19 -0.1 0.2 ME.green 0.14

0.42 0.27 0.09 0.78 0.09 -0.2 0.1 ME.grey 0.55 -0.1 0.2

ME.turquoise 0.12 0.41 0.39 0.67 0.72 0.01 -2.0 0.0

0.07 0.13 -0.2 0.2 0.08 0.04 -0.2 0.1 -0.3 0.0 ME.yellow 0.34

-0.3 0.0 Eigengenes can be used to build separate networks 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 for the ith 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)

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