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Understanding the relationships between transcription factors (TFs) and genes in plants under abiotic stress responses, tolerance and adaptation to adverse environments is very important in developing resilient crop varieties. While experimental methods to characterize stress responsive TFs and their targets are highly accurate, identification and characterization of the role of a given gene in a given stress response event are often laborious and time consuming. Computational approaches, on the other hand, offer a platform to identify new knowledge by integrating high throughput omics data and mathematical methods/models. In this research, we have developed a generic linear model of transcriptional regulatory networks (TRNs) and a companion algorithm to identify and to characterize stress responsive genes and their roles in a given stress response event. The proposed methodology was applied to plants, by using Arabidopsis thaliana as an example, under abiotic stress. Well known interactions were inferred as well as putative novel ones that may play important roles in plants under abiotic stress conditions as confirmed by statistical and literature evidences.