A comparative study of covariance selection models for the inference of gene regulatory networks.

Motivation: The inference, or 'reverse-engineering', of gene regulatory networks from expression data and the description of the complex dependency structures among genes are open issues in modern molecular biology.

Results: In this paper we compared three regularized methods of covariance selection for the inference of gene regulatory networks, developed to circumvent the problems raising when the number of observations n is smaller than the number of genes p. The examined approaches provided three alternative estimates of the inverse covariance matrix: (a) the 'PINV' method is based on the Moore-Penrose pseudoinverse, (b) the 'RCM' method performs correlation between regression residuals and (c) 'ℓ(2C)' method maximizes a properly regularized log-likelihood function. Our extensive simulation studies showed that ℓ(2C) outperformed the other two methods having the most predictive partial correlation estimates and the highest values of sensitivity to infer conditional dependencies between genes even when a few number of observations was available. The application of this method for inferring gene networks of the isoprenoid biosynthesis pathways in Arabidopsis thaliana allowed to enlighten a negative partial correlation coefficient between the two hubs in the two isoprenoid pathways and, more importantly, provided an evidence of cross-talk between genes in the plastidial and the cytosolic pathways. When applied to gene expression data relative to a signature of HRAS oncogene in human cell cultures, the method revealed 9 genes (p-value<0.0005) directly interacting with HRAS, sharing the same Ras-responsive binding site for the transcription factor RREB1. This result suggests that the transcriptional activation of these genes is mediated by a common transcription factor downstream of Ras signaling.

Availability: Software implementing the methods in the form of Matlab scripts are available at: http://users.ba.cnr.it/issia/iesina18/CovSelModelsCodes.zip.