Abstract
Understanding the process of fate specification, i.e. how multipotent stem cells are able to transition into one of several different cell types, is a central question in developmental biology. In our previous work we proposed a mathematical model for this transition which, perhaps surprisingly, appeared generically to include an oscillatory regime in the path from multipotent cells to fate-specified states. Here we carry out a detailed mathematical analysis of two variants of a generic gene regulatory network (GRN). We show how symmetry organizes many aspects of the model behaviour and reveal the role of a specific codimension-two bifurcation point as an organizing centre. The central role of symmetry implies that qualitatively equivalent results would be obtained regardless of the modelling details. The model-independent nature of our results makes them of substantial wider interest and is supported by numerical work. We conclude that the overall sequence of bifurcations that create and destroy the oscillations is generically and robustly organized by this codimension-two point. In the stem cell context the persistence of the oscillatory regime augments the perspective suggested by Waddington's epigenetic landscape by highlighting the potentially dynamic nature of cell fate transitions.