Abstract
Differentiation of multipotential progenitor cells is a key process in the development of any multi-cellular organism and often continues throughout its life. It is often assumed that a bi-potential progenitor develops along a (relatively) straight trajectory until it reaches a decision point where the trajectory bifurcates. At this point one of two directions is chosen, each direction representing the unfolding of a new transcriptional programme. However, we have lacked quantitative means for testing this model. Accordingly, we have developed the R package TrajectoryGeometry. Applying this to published data we find several examples where, rather than bifurcate, developmental pathways branch. That is, the bipotential progenitor develops along a relatively straight trajectory leading to one of its potential fates. A second relatively straight trajectory branches off from this towards the other potential fate. In this sense only cells that branch off to follow the second trajectory make a 'decision'. Our methods give precise descriptions of the genes and cellular pathways involved in these trajectories. We speculate that branching may be the more common behaviour and may have advantages from a control-theoretic viewpoint.