Periodic pattern formation in developmental biology : a study of the mechanisms underlying somitogenesis
Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. The principal aim of this thesis is to develop a series of mathematical models for somite formation. We begin by reviewing the current models for somitogenesis in the light of new experimental evidence regarding the presence of a segmentation clock and graded expression of FGF8. We conduct a preliminary investigation into the wavefront of FGF8 along the antero-posterior axis and integrate this model into the framework of an existing model for a signalling process. We demonstrate that this new “Clock and Wavefront” model can produce coherent series’ of somites in a manner that is tightly regulated in both space and time, and that it can also mimic the effects seen when FGF8 expression is perturbed locally. We then use the model to make some experimentally testable predictions. The latter part of the thesis concentrates on building more biologically accurate model for the FGF8 gradient. We move to consider a model for the FGF8 gradient which involves a complex network of biochemical interactions with negative feedback between FGF8 and retinoic acid. The resulting system of seven coupled non-linear equations, including both ordinary and partial differential equations, is difficult to analyse. To facilitate our understanding of the non-linear interactions between FGF8 and retinoic acid, we finally consider a reduced model which can display travelling wavefronts of opposing FGF8 and retinoic acid concentrations moving down the antero-posterior axis. The model allowed us to calculate a minimum wave speed for the wavefronts as a function of key model parameters such as the rate of FGF8 and retinoic acid decay; strong dependence on the values of these parameters is a result that is hypothesised to occur in vivo.