Abstract
BackgroundTo 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.ResultsWe 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.ConclusionThe 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.
Highlights
To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required
In order to measure the performance of sparse vector autoregressive model (SVAR), intensive simulations were carried out
The number of genes was kept at n = 100 and we varied the sample size, i.e., the time-series length
Summary
To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. 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 genegene networks. Several methods to model genetic networks were proposed in the last few years, such as the Bayesian networks [4,5,6,7,8], Structural Equation Models [9], Probabilistic Boolean Networks [10,11,12], Graphical Gaussian Models [13], Fuzzy controls [14], and Differential Equations [15] These methods allow modeling several regulatory networks for which biological information is available, it is difficult to determine the flow of information when there is no a priori knowledge
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