Motivation: Gene regulatory networks (GRNs) of the same organism can be different under different conditions, although the overall network structure may be similar. Understanding the difference in GRNs under different conditions is important to understand condition-specific gene regulation. When gene expression and other relevant data under two different conditions are available, they can be used by an existing network inference algorithm to estimate two GRNs separately, and then to identify the difference between the two GRNs. However, such an approach does not exploit the similarity in two GRNs, and may sacrifice inference accuracy. Results: In this paper, we model GRNs with the structural equation model (SEM) that can integrate gene expression and genetic perturbation data, and develop an algorithm named fused sparse SEM (FSSEM), to jointly infer GRNs under two conditions, and then to identify difference of the two GRNs. Computer simulations demonstrate that the FSSEM algorithm outperforms the approach that estimates two GRNs separately. Analysis of a gene expression and SNP dataset of lung cancer and normal lung tissues with FSSEM inferred a GRN largely agree with the known lung GRN reported in the literature, and it identified a differential GRN, whose genes with largest degrees were reported to be implicated in lung cancer. The FSSEM algorithm provides a valuable tool for joint inference of two GRNs and identification of the differential GRN under two conditions.
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