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Open Access Highly Accessed Research article

Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory

Feng Luo15, Yunfeng Yang1, Jianxin Zhong23, Haichun Gao17, Latifur Khan4, Dorothea K Thompson16 and Jizhong Zhou17*

  • * Corresponding author: Jizhong Zhou

  • † Equal contributors

Author Affiliations

1 Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

2 Computer Science & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

3 Department of Physics, Xiangtan University, Hunan 411105, PR China

4 Department of Computer Science, University of Texas at Dallas, Richardson, TX 75083, USA

5 School of Computing, Clemson University, Clemson, SC, 29634, USA

6 Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907, USA

7 Insitute for Environmental Genomics, and Department of Botany and Microbiology, University of Oklahoma, Norman, OK, 73019, USA

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BMC Bioinformatics 2007, 8:299  doi:10.1186/1471-2105-8-299

Published: 14 August 2007



Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory.


Application of random matrix theory to microarray data of S. oneidensis, E. coli, yeast, A. thaliana, Drosophila, mouse and human indicates that there is a sharp transition of nearest neighbour spacing distribution (NNSD) of correlation matrix after gradually removing certain elements insider the matrix. Testing on an in silico modular model has demonstrated that this transition can be used to determine the correlation threshold for revealing modular co-expression networks. The co-expression network derived from yeast cell cycling microarray data is supported by gene annotation. The topological properties of the resulting co-expression network agree well with the general properties of biological networks. Computational evaluations have showed that RMT approach is sensitive and robust. Furthermore, evaluation on sampled expression data of an in silico modular gene system has showed that under-sampled expressions do not affect the recovery of gene co-expression network. Moreover, the cellular roles of 215 functionally unknown genes from yeast, E. coli and S. oneidensis are predicted by the gene co-expression networks using guilt-by-association principle, many of which are supported by existing information or our experimental verification, further demonstrating the reliability of this approach for gene function prediction.


Our rigorous analysis of gene expression microarray profiles using RMT has showed that the transition of NNSD of correlation matrix of microarray profile provides a profound theoretical criterion to determine the correlation threshold for identifying gene co-expression networks.