A Novel Method to Efficiently Highlight Nonlinearly Expressed Genes

For precision medicine, there is a need to identify genes that accurately distinguish the physiological state or response to a particular therapy, but this can be challenging. Many methods of analyzing differential expression have been established and applied to this problem, such as t-test, edgeR, and DEseq2. A common feature of these methods is their focus on a linear relationship (differential expression) between gene expression and phenotype. However, they may overlook nonlinear relationships due to various factors, such as the degree of disease progression, sex, age, ethnicity, and environmental factors. Maximal information coefficient (MIC) was proposed to capture a wide range of associations of two variables in both linear and nonlinear relationships. However, with MIC it is difficult to highlight genes with nonlinear expression patterns as the genes giving the most strongly supported hits are linearly expressed, especially for noisy data. It is thus important to also efficiently identify nonlinearly expressed genes in order to unravel the molecular basis of disease and to reveal new therapeutic targets. We propose a novel nonlinearity measure called normalized differential correlation (NDC) to efficiently highlight nonlinearly expressed genes in transcriptome datasets. Validation using six real-world cancer datasets revealed that the NDC method could highlight nonlinearly expressed genes that could not be highlighted by t-test, MIC, edgeR, and DEseq2, although MIC could capture nonlinear correlations. The classification accuracy indicated that analysis of these genes could adequately distinguish cancer and paracarcinoma tissue samples. Furthermore, the results of biological interpretation of the identified genes suggested that some of them were involved in key functional pathways associated with cancer progression and metastasis. All of this evidence suggests that these nonlinearly expressed genes may play a central role in regulating cancer progression.