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

Measurements of gene expression levels for multiple genes in single cells provide 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 lineage relationship) are not directly evident from the measurement. Classifying cellular states and identifying transitions among those states are challenging due to many factors, including the small number of cells versus the large number of genes collected in the data. In this paper we adapt a classical self-organizing-map approach to single-cell gene expression data, such as those based on qPCR and RNA-seq. In this method (SOMSC), a cellular state map (CSM) is derived and employed to identify cellular states inherited in a population of measured single cells. Cells located in the same basin of the CSM are considered as in one cellular state while barriers between the basins provide information on transitions among the cellular states. Consequently, paths of cellular state transitions (e.g. differentiation) and a temporal ordering of the measured single cells are obtained. Applied to a set of synthetic data, two single-cell qPCR data sets and two single-cell RNA-seq data sets for a simulated model of cell differentiation, and systems on the early embryo development, haematopoietic cell lineages, human preimplanation embryo development, and human skeletal muscle myoblasts differentiation, the SOMSC shows good capabilities in identifying cellular states and their transitions in the high-dimensional single-cell data. This approach will have broad applications in studying cell lineages and cellular fate specification.