Dr Saeed Farjami

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.

Neural crest cells are crucial in development, not least because of their remarkable multipotency. Early findings stimulated two hypotheses for how fate specification and commitment from fully multipotent neural crest cells might occur, progressive fate restriction (PFR) and direct fate restriction, differing in whether partially restricted intermediates were involved. Initially hotly debated, they remain unreconciled, although PFR has become favoured. However, testing of a PFR hypothesis of zebrafish pigment cell development refutes this view. We propose a novel ‘cyclical fate restriction’ hypothesis, based upon a more dynamic view of transcriptional states, reconciling the experimental evidence underpinning the traditional hypotheses.

Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically motivated mathematical models for cell differentiation that generically generate oscillations and hence suggest alternatives to the standard framework based on Waddington's epigenetic landscape. The models allow us to suggest two generic dynamical scenarios that describe the differentiation process. In the first scenario, gradual variation of a single control parameter is responsible for both entering and exiting the oscillatory regime. In the second scenario, two control parameters vary: one responsible for entering, and the other for exiting the oscillatory regime. We analyse the standard repressilator and four variants of it and show the dynamical behaviours associated with each scenario. We present a thorough analysis of the associated bifurcations and argue that gene regulatory networks with these repressilator-like characteristics are promising candidates to describe cell fate selection through an oscillatory process.

Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence suggest alternatives to the standard framework based on Waddington's epigenetic landscape. The models allow us to suggest two generic dynamical scenarios that describe the differentiation process. In the first scenario gradual variation of a single control parameter is responsible for both entering and exiting the oscillatory regime. In the second scenario two control parameters vary: one responsible for entering, and the other for exiting the oscillatory regime. We analyse the standard repressilator and four variants of it and show the dynamical behaviours associated with each scenario. We present a thorough analysis of the associated bifurcations and argue that gene regulatory networks with these repressilator-like characteristics are promising candidates to describe cell fate selection through an oscillatory process.