SOMSC: Self-Organization-Map for High-Dimensional Single-Cell Data of Cellular States and Their Transitions

Abstract

Measurement of gene expression levels for multiple genes in single cells provides a powerful approach to study heterogeneity of cell populations and cellular plasticity. While the expression levels of multiple genes in each cell are available in such data, the potential connections among the cells (e.g. the cellular state transition relationship) are not directly evident from the measurement. Classifying the cellular states, identifying their transitions among those states, and extracting the pseudotime ordering of cells are challenging due to the noise in the data and the high-dimensionality in the number of genes in the data. In this paper we adapt the classical self-organizing-map (SOM) approach for single-cell gene expression data (SOMSC), such as those based on single cell qPCR and single cell RNA-seq. In SOMSC, a cellular state map (CSM) is derived and employed to identify cellular states inherited in the population of the measured single cells. Cells located in the same basin of the CSM are considered as in one cellular state while barriers among the basins in CSM provide information on transitions among the cellular states. A cellular state transitions path (e.g. differentiation) and a temporal ordering of the measured single cells are consequently obtained. In addition, SOMSC could estimate the cellular state replication probability and transition probabilities. Applied to a set of synthetic data, one single-cell qPCR data set on mouse early embryonic development and two single-cell RNA-seq data sets, SOMSC shows effectiveness in capturing cellular states and their transitions presented in the high-dimensional single-cell data. This approach will have broader applications to analyzing cellular fate specification and cell lineages using single cell gene expression data