Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles. (21st September 2022) - Wedgwood, Kyle C.A.; Ashwin, Peter
Graphical abstract: The left panel displays the critical manifold for our pattern forming model, which describes the establishment of a morphogenetic gradient and its influence on intracellular cell state dynamics over a growing tissue. The system trajectories, shown in grey, display two types of behaviour corresponding to the acquisition of one of two cell fates. One type of trajectory remains always on the upper (attracting) surface of the critical manifold, whilst the other type "fall off" onto the lower surface. The stable manifold of a folded saddle (green line) acts as a separatix between regions of tissue adopting the cell fates corresponding to the upper and lower surfaces, which is confirmed in the numerical simulations shown on the right. Highlights: We present a two-stage model of cell differentiation in a growing domain We find sufficient conditions for robust patterning of the domain in terms of parameters that determine timescales within the model We show that the success of patterning in the model can be understood in terms of a folded singularity for system with two slow and one fast variable. Abstract: One of the fundamental mechanisms in embryogenesis is the process by which cells differentiate and create tissues and structures important for functioning as a multicellular organism. Morphogenesis involves diffusive process of chemical signalling involving morphogens that pre-pattern the tissue. These morphogens influence cell fate through a highly nonlinear process of transcriptional signalling. In this paper, we consider this multiscale process in an idealised model for a growing domain. We focus on intracellular processes that lead to robust differentiation into two cell lineages through interaction of a single morphogen species with a cell fate variable that undergoes a bifurcation from monostability to bistability. In particular, we investigate conditions that result in successful and robust pattern formation into two well-separated domains, as well as conditions where this fails and produces a pinned boundary wave where only one part of the domain grows. We show that successful and unsuccessful patterning scenarios can be characterised in terms of presence or absence of a folded saddle singularity for a system with two slow variables and one fast variable; this models the interaction of slow morphogen diffusion, slow parameter drift through bifurcation and fast transcription dynamics. We illustrate how this approach can successfully model acquisition of three cell fates to produce three-domain "French flag" patterning, as well as for a more realistic model of the cell fate dynamics in terms of two mutually inhibiting transcription factors.