NJGCG: A node-based joint Gaussian copula graphical model for gene networks inference across multiple states

Inferring the interactions between genes is essential for understanding the mechanisms underlying biological processes. Gene networks will change along with the change of environment and state. The accumulation of gene expression data from multiple states makes it possible to estimate the gene networks in various states based on computational methods. However, most existing gene network inference methods focus on estimating a gene network from a single state, ignoring the similarities between networks in different but related states. Moreover, in addition to individual edges, similarities and differences between different networks may also be driven by hub genes. But existing network inference methods rarely consider hub genes, which affects the accuracy of network estimation. In this paper, we propose a novel node-based joint Gaussian copula graphical (NJGCG) model to infer multiple gene networks from gene expression data containing heterogeneous samples jointly. Our model can handle various gene expression data with missing values. Furthermore, a tree-structured group lasso penalty is designed to identify the common and specific hub genes in different gene networks. Simulation studies show that our proposed method outperforms other compared methods in all cases. We also apply NJGCG to infer the gene networks for different stages of differentiation in mouse embryonic stem cells and different subtypes of breast cancer, and explore changes in gene networks across different stages of differentiation or different subtypes of breast cancer. The common and specific hub genes in the estimated gene networks are closely related to stem cell differentiation processes and heterogeneity within breast cancers.