During development of multicellular organisms, multiple signalling systems play important roles. However, it is very hard to understand the interplays between many signalling pathways using conventional methods of molecular biology, biochemistry and genetics. Mathematical modelling should be combined with these biological methods to solve biological problem.
The waves of differentiation in visual system development are key examples of the complex interplays between multiple signalling systems. In this study, we focus on a wave of differentiation called the proneural wave, which occurs in the developing fly brain and accompanies Notch-mediated lateral inhibition and EGF-mediated neural differentiation. During proneural wave progression, the sheet-like neuroepithelial cells (NEs) sequentially differentiate to neural stem cells called neuroblasts (NBs). The proneural wave is an ideal model system to investigate the roles and dynamics of the interplay between important signalling pathways such as Notch and EGF.
Notch-mediated lateral inhibition regulates binary cell-fate choice, resulting in salt-and-pepper patterns during various developmental processes. The proneural wave accompanies Notch activity that is propagated without the formation of a salt-and-pepper pattern. However, mathematical modelling and genetic analysis clearly demonstrated that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signalling causes the formation of salt-and-pepper pattern, it is most likely that EGF diffusion cancels salt-and-pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a novel function of Notch signalling that regulates propagation of the wave of differentiation.
In our previous results, Notch signalling is activated only once at the wave front. However, Notch signalling is actually activated again behind the wave front forming twin peaks in vivo. The results of our parameter search show that the twin peaks of Notch activity can be reproduced by elevating the coefficient of cis-inhibition, by which Notch activity is autonomously repressed by Delta ligand. Moreover, the formation of the twin peaks could be stabilized by introducing strong non-linearity to cis-inhibition. The result of our in vivo experiment is consistent with the non-linear behaviour of cis-inhibition. The possible molecular mechanisms of non-linearity in cis-inhibition will be discussed.