Abstract
During embryonic development, cells undertake a series of cell fate decisions to form a complete organism, epitomising a branching process. In some instances, these decisions are reversible, particularly during the onset of disease. Single cell transcriptomics provides a rich resource to explore the temporal progression of bifurcations in gene activity and are there-fore useful for elucidating the mechanisms of cell fate decisions, provided that the cells can be suitably ordered over a developmental axis. Most methods for inferring this ordering have been developed for heterogeneous populations of cells collected at single time points, with few approaches specifically designed with structured data in mind, such as single cell time-series data. Recent advances based on Gaussian process latent variable models (GPLVMs) address this by allowing the incorporation of prior information, such as capture time, to yield more accurate ordering of cells. However, such ap-proaches do not allow the ordering of cells over developmental processes with more than one branch. Here we develop a pseudotime approach that allows the ordering of cells over developmental trajectories with arbitrary numbers of branches, in the form of branch-recombinant Gaussian process latent variable models (B-RGPLVM). We use first demonstrate the advantage of our approach compared to existing pseudotime algorithms. Subsequently, we use B-RGPLVMs to infer cell ordering that occurs during early human development as primordial germ cells (PGCs), the precursors of sperm and egg, and somatic cells diverge in the developing embryo. Using our approach, we identify known master regulators of human PGC development, and predict roles for a variety of signalling pathways, as well as transcription factors and epigenetic modifiers. By concentrating on the earliest branched signalling events, we identified an antagonistic role for FGF receptor (FGFR) signalling pathway in the acquisition of competence for human PGC fate. We experimentally validate our predic-tions using pharmacological blocking of FGFR or its downstream effectors (MEK, PI3K and JAK), and demonstrate en-hanced competency for PGC fate in vitro. Thus, B-RGPLVMs represent a powerful and flexible data-driven approach for dissecting the temporal dynamics of cell fate decisions, providing unique insights into the mechanisms of early embryo-genesis. Software is available from: https://github.com/cap76/BranchingGPs