Inference of Gene Regulatory Networks with Sparse Structural Equation Models Exploiting Genetic Perturbations

Integrating genetic perturbations with gene expression data not only improves accuracy of regulatory network topology inference, but also enables learning of causal regulatory relations between genes. Although a number of methods have been developed to integrate both types of data, the desiderata of efficient and powerful algorithms still remains. In this paper, sparse structural equation models (SEMs) are employed to integrate both gene expression data and cis-expression quantitative trait loci (cis-eQTL), for modeling gene regulatory networks in accordance with biological evidence about genes regulating or being regulated by a small number of genes. A systematic inference method named sparsity-aware maximum likelihood (SML) is developed for SEM estimation. Using simulated directed acyclic or cyclic networks, the SML performance is compared with that of two state-of-the-art algorithms: the adaptive Lasso (AL) based scheme, and the QTL-directed dependency graph (QDG) method. Computer simulations demonstrate that the novel SML algorithm offers significantly better performance than the AL-based and QDG algorithms across all sample sizes from 100 to 1,000, in terms of detection power and false discovery rate, in all the cases tested that include acyclic or cyclic networks of 10, 30 and 300 genes. The SML method is further applied to infer a network of 39 human genes that are related to the immune function and are chosen to have a reliable eQTL per gene. The resulting network consists of 9 genes and 13 edges. Most of the edges represent interactions reasonably expected from experimental evidence, while the remaining may just indicate the emergence of new interactions. The sparse SEM and efficient SML algorithm provide an effective means of exploiting both gene expression and perturbation data to infer gene regulatory networks. An open-source computer program implementing the SML algorithm is freely available upon request.Author Summary: Deciphering the structure of gene regulatory networks is crucial for understanding gene functions and cellular dynamics, as well as system-level modeling of individual genes and cellular functions. Computational methods exploiting gene expression and other types of data generated from high-throughput experiments provide an efficient and low-cost means of inferring gene networks. Sparse structural equation models are employed to: i) integrate both gene expression and genetic perturbation data for inference of gene networks; and, ii) develop an efficient sparsity-aware inference algorithm. Computer simulations corroborate that the novel algorithm markedly outperforms state-of-the-art alternatives. The algorithm is further applied to infer a real human gene network unveiling possible interactions between several genes. Since gene networks can be perturbed not only by genetic variations but also by other means such as gene copy number changes, gene knockdown or controlled gene over-expression, this paper's method can be applied to a number of practical scenarios.