Methodology article

Modeling gene expression regulatory networks with the sparse vector autoregressive model

André Fujita^1,2 , João R Sato¹ , Humberto M Garay-Malpartida^2,3 , Rui Yamaguchi⁴ , Satoru Miyano⁴ , Mari C Sogayar² and Carlos E Ferreira¹

¹Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010 – São Paulo, 05508-090, SP, Brazil

²Chemistry Institute, University of São Paulo, Av. Lineu Prestes, 748 – São Paulo, 05513-970, SP, Brazil

³School of Arts, Science and Humanities, University of São Paulo, Av. Arlindo Bettio, 1000 – São Paulo, 03828-000, SP, Brazil

⁴Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo, 108-8639, Japan

author email corresponding author email

BMC Systems Biology 2007, 1:39doi:10.1186/1752-0509-1-39

Published:	30 August 2007

Abstract

Background

To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems.

Results

We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets.

Conclusion

The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.