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The clock and wavefront paradigm is arguably the most widely accepted modelfor explaining the embryonic process of somitogenesis. According to this model,somitogenesis is based upon the interaction between a genetic oscillator, knownas segmentation clock, and a differentiation wavefront, which provides thepositional information indicating where each pair of somites is formed. Shortlyafter the clock and wavefront paradigm was introduced, Meinhardt presented aconceptually different mathematical model for morphogenesis in general, andsomitogenesis in particular. Recently, Cotterell et al. rediscovered anequivalent model by systematically enumerating and studying small networksperforming segmentation. Cotterell et al. called it a progressive oscillatoryreaction-diffusion (PORD) model. In the Meinhardt- PORD model, somitogenesis isdriven by short-range interactions and the posterior movement of the front is alocal, emergent phenomenon, which is not controlled by global positionalinformation. With this model, it is possible to explain some experimentalobservations that are incompatible with the clock and wavefront model. Howeverthe Meinhardt-PORD model has some important disadvantages of its own. Namely,it is quite sensitive to fluctuations and depends on very specific initialconditions (which are not biologically realistic). In this work, we propose anequivalent Meinhardt-PORD model, and then amend it to couple it with awavefront consisting of a receding morphogen gradient. By doing so, we get ahybrid model between the Meinhardt-PORD and the clock-and-wavefront ones, whichovercomes most of the deficiencies of the two originating models.

Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock