Geometric Interpretation of Gene Coexpression Network Analysis

Abstract

The merging of network theory and microarray data analysis techniques has spawned a new field: gene coexpression network analysis. While network methods are increasingly used in biology, the network vocabulary of computational biologists tends to be far more limited than that of, say, social network theorists. Here we review and propose several potentially useful network concepts. We take advantage of the relationship between network theory and the field of microarray data analysis to clarify the meaning of and the relationship among network concepts in gene coexpression networks. Network theory offers a wealth of intuitive concepts for describing the pairwise relationships among genes, which are depicted in cluster trees and heat maps. Conversely, microarray data analysis techniques (singular value decomposition, tests of differential expression) can also be used to address difficult problems in network theory. We describe conditions when a close relationship exists between network analysis and microarray data analysis techniques, and provide a rough dictionary for translating between the two fields. Using the angular interpretation of correlations, we provide a geometric interpretation of network theoretic concepts and derive unexpected relationships among them. We use the singular value decomposition of module expression data to characterize approximately factorizable gene coexpression networks, i.e., adjacency matrices that factor into node specific contributions. High and low level views of coexpression networks allow us to study the relationships among modules and among module genes, respectively. We characterize coexpression networks where hub genes are significant with respect to a microarray sample trait and show that the network concept of intramodular connectivity can be interpreted as a fuzzy measure of module membership. We illustrate our results using human, mouse, and yeast microarray gene expression data. The unification of coexpression network methods with traditional data mining methods can inform the application and development of systems biologic methods.

Inference of Longevity-Related Genes from a Robust Coexpression Network of Seed Maturation Identifies Regulators Linking Seed Storability to Biotic Defense-Related Pathways

“…The construction of MatNet, a robust coexpression network of seed maturation, and the subsequent integration of the acquisition of longevity using trait-based gene significance measure (Horvath and Dong, 2008) led to the discovery of a gene coexpression module from which confirmed and new genes regulating seed longevity were successfully inferred. MatNet is based on the reasoning that although environmental growth conditions will affect the timing and extent of different seed traits that are (D) Transcript levels of marker genes of seed development in M. truncatula and Arabidopsis.…”

“…Here, we investigated if MatNet could be used as a tool to identify gene modules linked to longevity. According to the trait-based gene significance measure (Horvath and Dong, 2008), P50 values obtained for the five developmental time series ( Figure 3A) were used to identify transcripts with highly correlated expression profiles ( Figure 3B). Depending on the environmental growth conditions, 2560 (in the standard condition) to 20,896 probes (high temperature condition) correlated with P50 (Pearson correlation coefficient [PCC] >0.85).…”

“…Isolation of the longevity module was performed using the trait based gene significance measure, obtained by GSi ¼ corðxi; P50Þ b where the gene significance (GS) of gene i equals the absolute correlation between the gene expression profile xi and longevity expressed as P50 (days to obtain 50% germination during storage), with b = 1 (Horvath and Dong, 2008). Modulating the PCC to 0.9 or 0.8 changed the number of probes that correlated with P50, but after projection of these data lists on MatNet, the same 167 probes were identified.…”

“…Based on the so-called "guilt by association" principle, coexpression networks have been proven to be very effective to identify relevant gene interactions (Ficklin et al, 2010;Amrine et al, 2015;Li et al, 2015) and to identify sets of candidate genes underlying specific phenotypes (Lee et al, 2009;Mutwil et al, 2010). Horvath and colleagues defined a "gene significance measure" as a means to provide a simple geometric interpretation of coexpression network analysis (Horvath and Dong, 2008). A trait-based gene significance measure assesses the relationship between a quantitative trait (such as weight) and the gene expression data.…”

Transcriptome analyses reveal molecular mechanisms underlying functional recovery after spinal cord injury

“…Both MN datasets (42 samples, including M region injury data and normal/uninjured controls) and RCN-LC datasets (45 samples, including R and C region lesion control/LC samples together with normal/uninjured controls) were independently constructed for WGCNA (18,19). Details are provided in SI Materials and Methods.…”