Modeling and identification of gene regulatory networks: A Granger causality approach

Abstract

It is of increasing interest in systems biology to discover gene regulatory networks (GRNs) from time-series genomic data, i.e., to explore the interactions among a large number of genes and gene products over time. Currently, one common approach is based on Granger causality, which models the time-series genomic data as a vector autoregressive (VAR) process and estimates the GRNs from the VAR coefficient matrix. The main challenge for identification of VAR models is the high dimensionality of genes and limited number of time points, which results in statistically inefficient solution and high computational complexity. Therefore, fast and efficient variable selection techniques are highly desirable. In this paper, an introductory review of identification methods and variable selection techniques for VAR models in learning the GRNs will be presented. Furthermore, a dynamic VAR (DVAR) model, which accounts for dynamic GRNs changing with time during the experimental cycle, and its identification methods are introduced.

Gene regulatory network discovery using pairwise Granger causality

“…AR model: GC can be extended to multivariate case [2,18], where the system has a number of variables n ≥ 3. Suppose there are n time series, one for each variable.…”

“…Computational analysis of genomic data is cheaper and faster than laboratory work, yielding information that may help decipher biological mechanisms which are crucial to scientific and medical advances [1][2][3]. An important problem is the discovery (or reconstruction) of gene regulatory network (GRN) from gene expression data, where gene-gene interactions are identified.…”

“…Previously, a number of reconstruction methods have been applied to the GRN discovery problem, such as correlation-based methods, Bayesian networks, Boolean networks, differential equation models, etc. [1][2][3][4][5][6][7]. More recently, Granger causality (GC) [8] has emerged as a potent tool for identifying causal relations among multivariate time series [9][10][11][12][13][14][15][16].…”

“…However, their implementations only modelled causal relations of one unit time lag, which is not realistic because interactions with longer time lags are very common [3]. Hence, later studies usually allow higher order models [2,11,[13][14][15][16]. In [14,15], partial and complex GC were proposed to handle situations with exogenous inputs and gene modules.…”

“…Since GRN structure may be time-varying, Fujita et al [13] attempted dynamic modelling with GC, where the number of genes involved was only 3 or 4. Zhang et al [2] mentioned that dynamic modelling of GRN remained an open problem, mainly because of the curse of dimensionality in gene expression data. That is, the number of genes is much larger than the data length, so that a full model cannot be applied to all genes simultaneously.…”