Mixed Distribution Models Based on Single-Cell RNA Sequencing Data

Progress in single-cell RNA sequencing (scRNA-seq) has yielded a lot of valuable data. Analysis of these data can provide a new perspective for studying the intratumoral heterogeneity and identifying gene markers. In this paper, the scRNA-seq data of colorectal cancer (CRC) are analyzed, and it is found that the shape of the gene expression difference (GED) data shows certain distribution regularity. To study the distribution regularity, mixed stable-normal distribution (MSND) model and mixed stable-exponential distribution (MSED) model are constructed to fit the GED data. And the estimated parameters of MSND and MSED are used to describe some characteristics of their distribution. Through the comparison of root mean square error and the chi-squared goodness of fit test, it is found that the fitting effect of MSED and MSND are both better than that of stable distribution and Cauchy distribution. Considering the given quantile thresholds, MSND and MSED can be used to identify tumor-related genes. The results of functional analysis indicate that the selected genes are highly correlated with CRC. In addition, the parameters of MSND and MSED exhibit a certain trend with the development of CRC. To explore the association, Gene-set enrichment analysis (GSEA) is performed. The results of GSEA reveal that the trend can well characterize the intratumoral heterogeneity of CRC. In addition, the application of MSED model on hepatocellular carcinoma shows that our model can analyze other cancers. Overall, MSND model and MSED model can well fit the GED data in different disease stages, the parameters of the two models can characterize the heterogeneity of CRC tumor cells, and the two models can be used to identify genes highly correlated with tumors.