Sustained vs. oscillating expressions of Ngn2, Dll1 and Hes1: A model of neural differentiation of embryonic telencephalon

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• We study a model of neural differentiation for two cells consistent with the experimental results.
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• The model is robust against fluctuations.
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• We introduce the neighbor cells in a self-consistent way.

Neural progenitor cells show oscillatory expression of the Notch ligand Delta-like1 (Dll1), the Notch target Hes1 and the proneural gene Neurogenin 2 (Ngn2) during embryonic development of the mammalian telencephalon. On the other hand, expression of these genes is sustained in postmitotic neurons (upregulated for Ngn2 and Dll1, down regulated for Hes1). These facts suggest that a switch from oscillatory to sustained expression of proneural and other genes is critical in neural fate decisions. Moreover, despite controversies over the role of Numb in determining the neural fate in mammals, there is evidence that inheritance of Numb during neurogenic cell division is involved in neural differentiation. It is also known that mNumb activates Notch1 receptor degradation. The arrest of oscillations in a given cell may be due to increasing degradation of Notch1 brought about by mNumb during neurogenic division. We introduce a modification in a previous model of the gene network for two cells coupled by the Delta-Notch pathway (Wang et al., 2011). We analyze the consequences of an asymmetry between two neighbor cells in the rate of degradation of Notch (mimicking the effect of asymmetric inheritance of mNumb during the neurogenic division). The results show that a slight difference in Notch degradation between the two cells keeps oscillation going in one of them while oscillation stops in the other. Moreover, when Delta-Notch coupling is canceled, both cells show sustained expression (upregulated levels for Ngn2 and Dll1, downregulated for Hes1). We show that the model is stable against parameter variations. Moreover, to take into account the possible influence of the environment on both cells, neighboring cells are included in a mean field approximation. Both, parameter fluctuations and effects of the environment lead to asynchronous oscillations of Hes1/Ngn2 in different progenitor cells.