Oscillatory differentiation dynamics fundamentally restricts the resolution of pseudotime reconstruction algorithms

The challenge to understand differentiation and cell lineages in development has resulted in many bioinformatics software tools, notably those working with gene expression data obtained via single-cell RNA sequencing obtained at snapshots in time. Reconstruction methods for trajectories often proceed by dimension reduction, data clustering and then computation of a tree graph in which edges indicate closely related clusters. Cell lineages can then be deduced by following paths through the tree. In the case of multi-potent cells undergoing differentiation, this trajectory reconstruction involves the reconstruction of multiple distinct lineages corresponding to commitment to each of a set of distinct fates. Recent work suggests that there may be cases in which the cell differentiation process involves trajectories that explore, in a dynamic and oscillatory fashion, propensity to differentiate into a number of possible cell fates before commitment finally occurs. Here, we show theoretically that the presence of such oscillations provides intrinsic constraints on the quality and resolution of the trajectory reconstruction process, even for idealized noise-free data. These constraints point to inherent common limitations of current methodologies and serve both to provide additional challenge in the development of software tools and also may help to understand features observed in recent experiments.