1. Meta Analysis and Differential Network Analysis with Applications in Mouse Expression Data
Today you’ve heard quite a bit about weighted gene coexpression network analysis. I’ll be talking about Differential Network Analysis, one application of WGCNA.
Steve Horvath

2. Outline Standard differential expression analysis
Statistical power studies
Important network concepts
Single versus differential network analysis
Differential network construction
First I’ll be discussing the what differential network analysis is, how it differs from single network analysis, and why we would use this method.
I’ll move on to how such an analysis is implemented,
Give an example of its application along with the results achieved
And demonstrate the functional relevance of these results.

3. Standard (gene based) differential expression analysis
Many software packages and R functions calculate T tests, p-values, false discovery rates, fold changes, etc.
WGCNA R functions:
For a binary trait (e.g. case control status), use standardScreeningBinaryTrait
For a numeric trait (e.g. body weight), use standardScreeningNumericTrait
For a right censored time variable, use standardScreeningCensoredTime

4. metaAnalysis R function in the WGCNA R package

5. helpfile metaAnalysis

6. Stouffer Z statistics from metaAnalysis

7. Ranking based metaAnalysis statistics

8. Combine several gene rankings using the rankPvalue function

9. Statistical Power Studies

10. Statistical power calculations
According to google scholar, it was cited by (July 2013).

12. Network concept =network statistics

13. 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.

14. Motivational example I: Pair-wise relationships between genes across different mouse tissues and genders
Challenge:
Develop simple descriptive measures that describe the patterns.
Solution:
The following network concepts are useful:
density, centralization,
clustering coefficient, heterogeneity

15. Motivational example (continued)
Challenge: Find a simple measure for describing the
relationship between gene significance and connectivity
Solution: network concept called hub gene significance

16. Backgrounds
Network concepts are also known as network statistics or network indices
Examples: connectivity (degree), clustering coefficient, topological overlap, etc
Network concepts underlie network language and systems biological modeling.
Dozens of potentially useful network concepts are known from graph theory.

17. Review of some fundamental network concepts which are defined for all networks (not just co-expression networks) Horvath 2011 Weighted Network Analysis. Springer Book. Hardcover ISBN: Dong Horvath 2007 Understanding network concepts in modules BMC Syst Biol Horvath Dong (2008) Geometric Interpretation of Gene Co-expression network analysis. Plos Comp Biol

18. Connectivity 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

19. Density
Density= mean adjacency
Highly related to mean connectivity

20. Centralization = 1 if the network has a star topology
= 0 if all nodes have the same connectivity
Centralization = 0
because all nodes have the same connectivity of 2
Centralization = 1
because it has a star topology

21. Heterogeneity
Heterogeneity: coefficient of variation of the connectivity
Highly heterogeneous networks exhibit hubs

22. Clustering Coefficient
Measures the cliquishness of a particular node
« A node is cliquish if its neighbors know each other »
This generalizes directly to weighted
networks (Zhang and Horvath 2005)
Clustering Coef of the black node = 0
Clustering Coef = 1

23. The topological overlap dissimilarity is used as input of hierarchical clustering
Mention that Ai Li worked on it.
Generalized in Zhang and Horvath (2005) to the case of weighted networks
Generalized in Li and Horvath (2006) to multiple nodes
Generalized in Yip and Horvath (2007) to higher order interactions

24. Network Significance Defined as average gene significance
We often refer to the network significance of a module network as module significance.

25. Maximum adjacency ratio

26. Network concepts for comparing two networks

27. Differential network concepts
Node specific statistics:
Diff.ClusterCoef(i) = CC1(i) – CC2(i)
Diff.Mar(i)= MAR1(i) – MAR2(i)
Global statistics
Diff.MeanClusterCoef = Mean.CC1–Mean.CC2
Diff.MeanConnectivity=Mean.k1 – mean.k2
Diff.MeanMAR=Mean.MAR1 – mean.MAR2
Diff.MeanKME=Mean.KME
Diff.Density=Density1 – Density2
can be calculated via the modulePreservation function

28. Measuring the similarity between two networks

29. R code for computing network concepts

30. R code, help file

32. Data analysis strategies
Single network analysis versus differential network analysis

33. Goals of Single Network Analysis
Identifying genetic pathways (modules)
Finding key drivers (hub genes)
Modeling the relationships between:
Transcriptome
Clinical traits / Phenotypes
Genetic marker data

34. Single Network WGCNA 1 gene co-expression network
Validation set 1
Validation set 2
1 gene co-expression network
Multiple data sets may be used for validation

35. Goals of Differential Network Analysis
Uncover differences in modules and connectivity in different data sets
Ex: Human versus chimpanzee brains (Oldham et al. 2006)
Differing topology in multiple networks reveals genes/pathways that are wired differently in different sample populations 7
Fuller TF, Ghazalpour A, Aten JE, Drake TA, Lusis AJ, …(2007) "Weighted Gene Co-expression Network Analysis Strategies Applied to Mouse Weight", Mamm Genome. 18(6):
Oldham MC, …Geschwind DH (2006) Conservation and evolution of gene coexpression networks in human and chimpanzee brains. Proc Natl Acad Sci U S A 103,

36. Differential Network WGCNA
2+ gene co-expression networks
Identify genes and pathways that are:
Differentially expressed
Differentially wired

37. BxH Mouse Data from AJ Lusis
Single network analysis female BxH mice revealed a weight-related module (Ghazalpour et al. 2006)
Samples: Constructed networks from mice from extrema of weight spectrum:
Network 1: 30 leanest mice
Network 2: 30 heaviest mice
Transcripts: Used 3421 most connected and varying transcripts
135 FEMALES
NETWORK 1
NETWORK 2
135 female mice, 3421 most connected and varying transcripts
Ghazalpour A, Doss S, Zhang B, Wang S, Plaisier C, Castellanos R, Brozell A, Schadt EE, Drake TA, Lusis AJ, Horvath S
(2006) Integrating genetic and network analysis to characterize genes related to mouse weight. PLoS genetics 2, e130

38. Methods Compute Comparison Metrics
Difference in expression: t-test statistic
Compare difference in connectivity: DiffK
Identify significantly different genes/pathways
Permutation test
Functional analysis of significant genes/pathways
DAVID database
Primary literature

39. Computing Comparison Metrics
DIFFERENTIAL EXPRESSION
t-test statistic computed for each gene, t(i)
DIFFERENTIAL CONNECTIVITY
K1(i) = k1(i) K2(i) = k2(i)
max(k1) max(k2)
DiffK(i): difference in normalized
connectivities for each gene:
DiffK(i) = K1(i) – K2(i)

40. Sector Plot We visualize the comparison metrics via a sector plot:
x-axis: DiffK
y-axis: t statistics
We establish sector boundaries to identify regions of differentially expressed and/or connected regions
|t| = 1.96 corresponding to p = 0.05
|DiffK| = 0.4

41. Permutation test: Identifying significant sectors
NETWORK 1
NETWORK 2
no.perms: number of permutations
For each sector j, we compare the number of genes in unpermuted and permuted sectors (nobs and nperm)
PERMUTE

42. Sector Plot Results X
0.01
0.001

43. Functional Analysis
SECTOR 3
High t statistic
High DiffK
Yellow module in lean
Grey in obese
(63 genes)
SECTOR 5
Low t statistic
High Diff K
(28 genes)
Genes in these sectors have higher connectivity in lean than obese mice: ~ pathways potentially disregulated in obesity ~

44. Sector 3: Functional Analysis Results DAVID Database
“Extracellular”:
extracellular region (38% of genes p = 1.8 x 10-4)
extracellular space (34% of genes p = 5.7 x 10-4)
signaling (36% of genes p = 5.4 x 10-4)
cell adhesion (16% of genes p = 7.7 x 10-4)
glycoproteins (34% of genes p = 1.6 x 10-3)
12 terms for epidermal growth factor or its related proteins
EGF-like 1 (8.2% of genes p = 8.7 x 10-4),
EGF-like 3 (6.6% of genes p = 1.6 x 10-3),
EGF-like 2 (6.6% of genes p = 6.0 x 10-3),
EGF (8.2% of genes p = 0.013)
EGF_CA (6.6% of genes p = 0.015)

45. Sector 3: Functional Analysis Results Primary Literature
Results supported by a study on EGF levels in mice (Kurachi et al. 1993)
EGF found to be increased in obese mice
Obesity was reversed in these mice by:
Administration of anti-EGF
Sialoadenectomy
Kurachi H, Adachi H, Ohtsuka S, Morishige K, Amemiya K, Keno Y, Shimomura I, Tokunaga K, Miyake A, Matsuzawa Y, et al. (1993) Involvement of epidermal growth factor in inducing obesity in ovariectomized mice. The American journal of physiology 265, E

46. Sector 5: Functional Analysis Results DAVID Database
Enzyme inhibitor activity (p = 2.9 x 10-3)*
Protease inhibitor activity (p = 6.0 x 10-3)
Endopeptidase inhibitor activity (p = 6.0 x 10-3)
Dephosphorylation (p = 0.012)
Protein amino acid dephosphorylation (p = 0.012)
Serine-type endopeptidase inhibitor activity (p = 0.042)
* p values shown are corrected using Bonferroni correction

47. Sector 5: Functional Analysis Results Primary Literature
Itih1 and Itih3
Enriched for all categories shown previously
Located near a QTL for hyperinsulinemia (Almind and Kahn 2004)
Itih3 identified as a gene candidate for obesity-related traits based on differential expression in murine hypothalamus (Bischof and Wevrick 2005)
Serpina3n and Serpina10
Enriched for enzyme inhibitor, protease inhibitor, and endopeptidase inhibitor
Serpina10, or Protein Z-dependent protease inhibitor (ZPI) has been found to be associated with venous thrombosis (Van de Water et al. 2004)
Almind K, Kahn CR (2004) Genetic determinants of energy expenditure and insulin resistance in diet-induced obesity in mice. Diabetes 53,
Bischof JM, Wevrick R (2005) Genome-wide analysis of gene transcription in the hypothalamus. Physiological genomics 22,
Van de Water N, Tan T, Ashton F, O'Grady A, Day T, Browett P, Ockelford P, Harper P (2004) Mutations within the protein Z-dependent protease
inhibitor gene are associated with venous thromboembolic disease: a new form of thrombophilia. Bjh 127,

48. Discussion
If applicable, always report findings from a standard differential expression analysis as well.
A host of network concepts exists for describing the network topology.
Relatively few people use differential network analysis which may reflect the fact that large sample sizes are needed.
A large sample size is needed to compare two correlation coefficients
To check whether a module is preserved in another network use the modulePreservation function.

49. An R tutorial may be found at:
Acknowledgements
HORVATH LAB
Dissertation work of
Tova Fuller
Jun Dong
Peter Langfelder
Mouse data collaboration
LUSIS LAB
Jake Lusis
Anatole Ghazalpour
Thomas Drake
An R tutorial may be found at: