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

Abstract

During embryonic development of the mammalian telencephalon, expressions of the Notch ligand: Delta like1 (Dll1), Hes1 and the proneural gene Neu- rogenin 2 (Ngn2) are oscillating in neural progenitors, being sustained in postmitotic neurons (upregulated for Ngn2 and Dll1 and downregulated for Hes1), suggesting a sustained vs. oscillating behavior in proneural genes is critical in neural fate dicitions. Moreover, beyond the controversies over the role of mNumb in determining neural fate in mammals, there is evidence that their heritage during the neurogenic division is involved in neural specification. It is also known that mNumb activates Notch1 receptor degradation. A suggested mechanism that unifies two experimental lines, is the arresting the oscillations in the cell specified by the Notch1 receptor degradation by mNumb during neurogenic division. We introduce a modification in a previous model of the gene network for two coupled cells by Delta - Notch(Wang et al., 2011). We analyze the consequences of an asymmetry in the rate of degradation of Notch between two neighbor cells (mimicking a possible effect of Numb in asymmetric neurogenic division). The model shows that a slight difference in Notch degradation between two cells maintains the oscillations in one of them while it and arrests them in the neighbor, thus describing the phenomenon of the oscillating vs. sustained expression in the neural differentiation (neural progenitors vs. postmitotic neurons). In addition, when canceling the coupling Delta - Notch, both cells show subtained expressions with levels of Ngn2 and Dll1 upregulated and Hes1 downregulated. These results are consistent with a role of Numb in inducing the differentiation by inhibiting the oscillations in the Notch signaling as well as the function of this pathway in the maintenance of neural progenitors. The model is stable against fluctuations in the values of the parameters. Moreover, given the spatially localized character of mitosis, we introduce the effect of neighboring cells in a self-consistent approximation. Both, parameters fluctuations as will as the effect of the environment, lead to asynchronous character of oscillations of Hes1/Ngn2 in progenitor cells.