In many applications, such as gene co-expression network analyses, data arises with a huge number of covariates while the size of sample is comparatively small. To improve the accuracy of prediction, variable selection is often used to get a sparse solution by forcing coefficients of variables contributing less to the observed response variable to zero. Various algorithms were developed for variable selection, but LASSO is well known for its statistical accuracy, computational feasibility and broad applicability to adaptation. In this project, we applied LASSO to the gene co-expression network of rice with salt stress to discover key gene interactions for salt-tolerance related phenotypes. The dataset we have is a high-dimensional one, having 50K genes from 100 samples, with the issue of multicollinearity for fitting linear regression - the expression level of genes in the same pathway tends to be highly correlated. The property of LASSO with sparse parameters is naturally suitable to identify gene interactions of interest in this dataset. After biologically functional modules in the co-expression network was identified, the major changed expression patterns were further selected by LASSO regression to establish a linear relationship between gene expression profiles and physiological responses, such as sodium/potassium condenses, with salt stress. Five modules of intensively co-expressed genes, from 45 to 291 genes, were identified by our method with significant P-values, which indicate these modules are significantly associated with physiological responses to stress. Genes in these modules have functions related to ion transport, osmotic adjustment, and oxidative tolerance. For example, LOC_Os7g47350 and LOC_Os07g37320 are co-expressed gene in the same module 15. Both are ion transporter genes and have higher gene expression levels for rice with low sodium levels with salt stress.
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