Peter Langfelder

WGCNA: an R package for weighted correlation network analysis

BackgroundCorrelation networks are increasingly being used in bioinformatics applications. For example, weighted gene co-expression network analysis is a systems biology method for describing the correlation patterns among genes across microarray samples. Weighted correlation network analysis (WGCNA) can be used for finding clusters (modules) of highly correlated genes, for summarizing such clusters using the module eigengene or an intramodular hub gene, for relating modules to one another and to external sample traits (using eigengene network methodology), and for calculating module membership measures. Correlation networks facilitate network based gene screening methods that can be used to identify candidate biomarkers or therapeutic targets. These methods have been successfully applied in various biological contexts, e.g. cancer, mouse genetics, yeast genetics, and analysis of brain imaging data. While parts of the correlation network methodology have been described in separate publications, there is a need to provide a user-friendly, comprehensive, and consistent software implementation and an accompanying tutorial.ResultsThe WGCNA R software package is a comprehensive collection of R functions for performing various aspects of weighted correlation network analysis. The package includes functions for network construction, module detection, gene selection, calculations of topological properties, data simulation, visualization, and interfacing with external software. Along with the R package we also present R software tutorials. While the methods development was motivated by gene expression data, the underlying data mining approach can be applied to a variety of different settings.ConclusionThe WGCNA package provides R functions for weighted correlation network analysis, e.g. co-expression network analysis of gene expression data. The R package along with its source code and additional material are freely available at http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA.

Defining clusters from a hierarchical cluster tree

SUMMARY Hierarchical clustering is a widely used method for detecting clusters in genomic data. Clusters are defined by cutting branches off the dendrogram. A common but inflexible method uses a constant height cutoff value; this method exhibits suboptimal performance on complicated dendrograms. We present the Dynamic Tree Cut R package that implements novel dynamic branch cutting methods for detecting clusters in a dendrogram depending on their shape. Compared to the constant height cutoff method, our techniques offer the following advantages: (1) they are capable of identifying nested clusters; (2) they are flexible-cluster shape parameters can be tuned to suit the application at hand; (3) they are suitable for automation; and (4) they can optionally combine the advantages of hierarchical clustering and partitioning around medoids, giving better detection of outliers. We illustrate the use of these methods by applying them to protein-protein interaction network data and to a simulated gene expression data set. AVAILABILITY The Dynamic Tree Cut method is implemented in an R package available at http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/BranchCutting.

Functional organization of the transcriptome in human brain.

The enormous complexity of the human brain ultimately derives from a finite set of molecular instructions encoded in the human genome. These instructions can be directly studied by exploring the organization of the brains transcriptome through systematic analysis of gene coexpression relationships. We analyzed gene coexpression relationships in microarray data generated from specific human brain regions and identified modules of coexpressed genes that correspond to neurons, oligodendrocytes, astrocytes and microglia. These modules provide an initial description of the transcriptional programs that distinguish the major cell classes of the human brain and indicate that cell type–specific information can be obtained from whole brain tissue without isolating homogeneous populations of cells. Other modules corresponded to additional cell types, organelles, synaptic function, gender differences and the subventricular neurogenic niche. We found that subventricular zone astrocytes, which are thought to function as neural stem cells in adults, have a distinct gene expression pattern relative to protoplasmic astrocytes. Our findings provide a new foundation for neurogenetic inquiries by revealing a robust and previously unrecognized organization to the human brain transcriptome.

Eigengene networks for studying the relationships between co-expression modules

BackgroundThere is evidence that genes and their protein products are organized into functional modules according to cellular processes and pathways. Gene co-expression networks have been used to describe the relationships between gene transcripts. Ample literature exists on how to detect biologically meaningful modules in networks but there is a need for methods that allow one to study the relationships between modules.ResultsWe show that network methods can also be used to describe the relationships between co-expression modules and present the following methodology. First, we describe several methods for detecting modules that are shared by two or more networks (referred to as consensus modules). We represent the gene expression profiles of each module by an eigengene. Second, we propose a method for constructing an eigengene network, where the edges are undirected but maintain information on the sign of the co-expression information. Third, we propose methods for differential eigengene network analysis that allow one to assess the preservation of network properties across different data sets. We illustrate the value of eigengene networks in studying the relationships between consensus modules in human and chimpanzee brains; the relationships between consensus modules in brain, muscle, liver, and adipose mouse tissues; and the relationships between male-female mouse consensus modules and clinical traits. In some applications, we find that module eigengenes can be organized into higher level clusters which we refer to as meta-modules.ConclusionEigengene networks can be effective and biologically meaningful tools for studying the relationships between modules of a gene co-expression network. The proposed methods may reveal a higher order organization of the transcriptome. R software tutorials, the data, and supplementary material can be found at the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/EigengeneNetwork.

Is my network module preserved and reproducible

In many applications, one is interested in determining which of the properties of a network module change across conditions. For example, to validate the existence of a module, it is desirable to show that it is reproducible (or preserved) in an independent test network. Here we study several types of network preservation statistics that do not require a module assignment in the test network. We distinguish network preservation statistics by the type of the underlying network. Some preservation statistics are defined for a general network (defined by an adjacency matrix) while others are only defined for a correlation network (constructed on the basis of pairwise correlations between numeric variables). Our applications show that the correlation structure facilitates the definition of particularly powerful module preservation statistics. We illustrate that evaluating module preservation is in general different from evaluating cluster preservation. We find that it is advantageous to aggregate multiple preservation statistics into summary preservation statistics. We illustrate the use of these methods in six gene co-expression network applications including 1) preservation of cholesterol biosynthesis pathway in mouse tissues, 2) comparison of human and chimpanzee brain networks, 3) preservation of selected KEGG pathways between human and chimpanzee brain networks, 4) sex differences in human cortical networks, 5) sex differences in mouse liver networks. While we find no evidence for sex specific modules in human cortical networks, we find that several human cortical modules are less preserved in chimpanzees. In particular, apoptosis genes are differentially co-expressed between humans and chimpanzees. Our simulation studies and applications show that module preservation statistics are useful for studying differences between the modular structure of networks. Data, R software and accompanying tutorials can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation.

Aging effects on DNA methylation modules in human brain and blood tissue

BackgroundSeveral recent studies reported aging effects on DNA methylation levels of individual CpG dinucleotides. But it is not yet known whether aging-related consensus modules, in the form of clusters of correlated CpG markers, can be found that are present in multiple human tissues. Such a module could facilitate the understanding of aging effects on multiple tissues.ResultsWe therefore employed weighted correlation network analysis of 2,442 Illumina DNA methylation arrays from brain and blood tissues, which enabled the identification of an age-related co-methylation module. Module preservation analysis confirmed that this module can also be found in diverse independent data sets. Biological evaluation showed that module membership is associated with Polycomb group target occupancy counts, CpG island status and autosomal chromosome location. Functional enrichment analysis revealed that the aging-related consensus module comprises genes that are involved in nervous system development, neuron differentiation and neurogenesis, and that it contains promoter CpGs of genes known to be down-regulated in early Alzheimers disease. A comparison with a standard, non-module based meta-analysis revealed that selecting CpGs based on module membership leads to significantly increased gene ontology enrichment, thus demonstrating that studying aging effects via consensus network analysis enhances the biological insights gained.ConclusionsOverall, our analysis revealed a robustly defined age-related co-methylation module that is present in multiple human tissues, including blood and brain. We conclude that blood is a promising surrogate for brain tissue when studying the effects of age on DNA methylation profiles.

Comparison of co-expression measures: mutual information, correlation, and model based indices

BackgroundCo-expression measures are often used to define networks among genes. Mutual information (MI) is often used as a generalized correlation measure. It is not clear how much MI adds beyond standard (robust) correlation measures or regression model based association measures. Further, it is important to assess what transformations of these and other co-expression measures lead to biologically meaningful modules (clusters of genes).ResultsWe provide a comprehensive comparison between mutual information and several correlation measures in 8 empirical data sets and in simulations. We also study different approaches for transforming an adjacency matrix, e.g. using the topological overlap measure. Overall, we confirm close relationships between MI and correlation in all data sets which reflects the fact that most gene pairs satisfy linear or monotonic relationships. We discuss rare situations when the two measures disagree. We also compare correlation and MI based approaches when it comes to defining co-expression network modules. We show that a robust measure of correlation (the biweight midcorrelation transformed via the topological overlap transformation) leads to modules that are superior to MI based modules and maximal information coefficient (MIC) based modules in terms of gene ontology enrichment. We present a function that relates correlation to mutual information which can be used to approximate the mutual information from the corresponding correlation coefficient. We propose the use of polynomial or spline regression models as an alternative to MI for capturing non-linear relationships between quantitative variables.ConclusionThe biweight midcorrelation outperforms MI in terms of elucidating gene pairwise relationships. Coupled with the topological overlap matrix transformation, it often leads to more significantly enriched co-expression modules. Spline and polynomial networks form attractive alternatives to MI in case of non-linear relationships. Our results indicate that MI networks can safely be replaced by correlation networks when it comes to measuring co-expression relationships in stationary data.

Genetic analysis of DNA methylation and gene expression levels in whole blood of healthy human subjects

BackgroundThe predominant model for regulation of gene expression through DNA methylation is an inverse association in which increased methylation results in decreased gene expression levels. However, recent studies suggest that the relationship between genetic variation, DNA methylation and expression is more complex.ResultsSystems genetic approaches for examining relationships between gene expression and methylation array data were used to find both negative and positive associations between these levels. A weighted correlation network analysis revealed that i) both transcriptome and methylome are organized in modules, ii) co-expression modules are generally not preserved in the methylation data and vice-versa, and iii) highly significant correlations exist between co-expression and co-methylation modules, suggesting the existence of factors that affect expression and methylation of different modules (i.e., trans effects at the level of modules). We observed that methylation probes associated with expression in cis were more likely to be located outside CpG islands, whereas specificity for CpG island shores was present when methylation, associated with expression, was under local genetic control. A structural equation model based analysis found strong support in particular for a traditional causal model in which gene expression is regulated by genetic variation via DNA methylation instead of gene expression affecting DNA methylation levels.ConclusionsOur results provide new insights into the complex mechanisms between genetic markers, epigenetic mechanisms and gene expression. We find strong support for the classical model of genetic variants regulating methylation, which in turn regulates gene expression. Moreover we show that, although the methylation and expression modules differ, they are highly correlated.

Weighted gene co-expression network analysis of the peripheral blood from Amyotrophic Lateral Sclerosis patients

BackgroundAmyotrophic Lateral Sclerosis (ALS) is a lethal disorder characterized by progressive degeneration of motor neurons in the brain and spinal cord. Diagnosis is mainly based on clinical symptoms, and there is currently no therapy to stop the disease or slow its progression. Since access to spinal cord tissue is not possible at disease onset, we investigated changes in gene expression profiles in whole blood of ALS patients.ResultsOur transcriptional study showed dramatic changes in blood of ALS patients; 2,300 probes (9.4%) showed significant differential expression in a discovery dataset consisting of 30 ALS patients and 30 healthy controls. Weighted gene co-expression network analysis (WGCNA) was used to find disease-related networks (modules) and disease related hub genes. Two large co-expression modules were found to be associated with ALS. Our findings were replicated in a second (30 patients and 30 controls) and third dataset (63 patients and 63 controls), thereby demonstrating a highly significant and consistent association of two large co-expression modules with ALS disease status. Ingenuity Pathway Analysis of the ALS related module genes implicates enrichment of functional categories related to genetic disorders, neurodegeneration of the nervous system and inflammatory disease. The ALS related modules contain a number of candidate genes possibly involved in pathogenesis of ALS.ConclusionThis first large-scale blood gene expression study in ALS observed distinct patterns between cases and controls which may provide opportunities for biomarker development as well as new insights into the molecular mechanisms of the disease.

Weighted gene coexpression network analysis: state of the art.

Weighted gene coexpression network analysis (WGCNA) has been applied to many important studies since its introduction in 2005. WGCNA can be used as a data exploratory tool or as a gene screening method; WGCNA can also be used as a tool to generate testable hypothesis for validation in independent data sets. In this article, we review key concepts of WGCNA and some of its applications in gene expression analysis of oncology, brain function, and protein interaction data.