Abstract
Hes genes are transcriptional repressors activated by Notch. In the developing mouse neural tissue, HES5 expression oscillates in neural progenitors (Manning et al. 2019 Nat. Commun. 10, 1-19 (doi:10.1038/s41467-019-10734-8)) and is spatially organized in small clusters of cells with synchronized expression (microclusters). Furthermore, these microclusters are arranged with a spatial periodicity of three-four cells in the dorso-ventral axis and show regular switching between HES5 high/low expression on a longer time scale and larger amplitude than individual temporal oscillators (Biga et al. 2021 Mol. Syst. Biol. 17, e9902 (doi:10.15252/msb.20209902)). However, our initial computational modelling of coupled HES5 could not explain these features of the experimental data. In this study, we provide theoretical results that address these issues with biologically pertinent additions. Here, we report that extending Notch signalling to non-neighbouring progenitor cells is sufficient to generate spatial periodicity of the correct size. In addition, introducing a regular perturbation of Notch signalling by the emerging differentiating cells induces a temporal switching in the spatial pattern, which is longer than an individual cell's periodicity. Thus, with these two new mechanisms, a computational model delivers outputs that closely resemble the complex tissue-level HES5 dynamics. Finally, we predict that such dynamic patterning spreads out differentiation events in space, complementing our previous findings whereby the local synchronization controls the rate of differentiation.