Differential analysis of gene regulatory networks modeled with structural equation models

Abstract

A gene regulatory networks (GRN) is composed of a set of genes as well as the regulatory relationships between them. Under different conditions, GRNs with the same gene set usually have similar but not exactly the same structure. The differential analysis of GRNs under different conditions is of great significance to understand gene functions and biological mechanisms. In a naive approach, GRNs under different conditions can be separately inferred via existing GRN inference algorithms, and then the difference between them can be identified by comparing the estimated structures. However, such an approach does not consider the commonality of the pairwise GRNs, which may decrease the predictive accuracy of the differential GRN. In this paper, we model GRNs with the structural equation models (SEMs) to integrate gene expression data and genetic perturbations, and propose a joint differential analysis algorithm named differential sparse SEM (DiffSSEM) to identify the topology structures of GRNs under different conditions as well as the difference between them. The DiffSSEM algorithm simultaneously consider the sparsity of separate GRNs and differential GRN. Simulations were run on synthetic data and the results demonstrated that the DiffSSEM algorithm outperforms the naive approach based on a state-of-the-art sparse SEM inference algorithm. Finally, a real data set of 15 lung genes from 42 tumor tissues and normal tissues was analyzed with the DiffSSEM algorithm to identify the differential GRN.