The clock and wavefront model is one of the most accepted models for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a moving wavefront, which provides the positional information indicating where each pair of somites is formed. Recently, Cotterell et al. (2015) reported a conceptually different mathematical model for somitogenesis. The authors  called it a progressive oscillatory reaction-diffusion (PORD) model. In this model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With the PORD model, it was possible to explain some experimental observations that are incompatible with the clock and wavefront model. However the PORD model has the disadvantage of being quite sensitive to fluctuations  . In this work, we propose a modified version of the PORD modelin order to overcome this and others inconveniences. By means of numerical simulations and a numerical stability analysis, we demonstrate that the modified PORD model achieves the robustness characteristic of somitogenesis, when the effect of the wavefront is included .
The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a moving wavefront, which provides the positional information indicating where each pair of somites is formed. Shortly after the clock and wavefront paradigm was introduced, Meinhardt presented a conceptually different mathematical model for morphogenesis in general, and somitogenesis in particular. Recently, Cotterellet al. rediscovered an equivalent model by systematically enumerating and studying small networks performing segmentation. Cotterellet al. called it a progressive oscillatory reaction-diffusion (PORD) model. In the Meinhardt-PORD model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With this model, it is possible to explain some experimental observations that are incompatible with the clock and wavefront model. However the Meinhardt-PORD model has some important disadvantages of its own. Namely, it is quite sensitive to fluctuations and depends on very specific initial conditions (which are not biologically realistic) . In this work, we propose an equivalent Meinhardt-PORD model, and then amend it to couple it with a morphogen wavefront. By doing so, we get a hybrid model between the Meinhardt-PORD and the clock-and-wavefront ones, which overcomes most of the deficiencies of the two originating models .
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