Laplacian eigenmaps and principal curves for high resolution pseudotemporal ordering of single-cell RNA-seq profiles

Advances in RNA-seq technologies provide unprecedented insight into the variability and heterogeneity of gene expression at the single-cell level. However, such data offers only a snapshot of the transcriptome, whereas it is often the progression of cells through dynamic biological processes that is of interest. As a result, one outstanding challenge is to infer such progressions by ordering gene expression from single cell data alone, known as the cell ordering problem. Here, we introduce a new method that constructs a low-dimensional non-linear embedding of the data using laplacian eigenmaps before assigning each cell a pseudotime using principal curves. We characterise why on a theoretical level our method is more robust to the high levels of noise typical of single-cell RNA-seq data before demonstrating its utility on two existing datasets of differentiating cells.