Lineage and state dynamics in stem cell differentiation*

High-dimensional single cell measurements allow capturing snapshots of dynamic transitions in biological systems. Over the past few years, measurements such as single cell RNA-Sequencing (RNA-Seq) have come to be routinely used in stem cell biology. However, as single cell measurements necessarily destroy cells, they do not definitively reveal long-term dynamic behaviors. Various theoretical models have been invoked to link static snapshots to dynamics, all necessarily making assumptions. I will describe the assumptions underlying one such model of a Fokker-Planck type, and its limitations. I will then show how the combination of lineage data in single cell transcriptomes allows explicitly testing dynamic inference models on single cell RNA-Seq data. Our results show the successes but also failures of dynamic inference, and provide a test demonstrating the existence of "hidden variables" underlying cellular dynamics as measured by RNA-Seq. The results and methods are applied to the lineage hierarchy of hematopoiesis.