Travelling waves in somitogenesis: Collective cellular properties emerge from time-delayed juxtacrine oscillation coupling

Abstract

The sculpturing of the vertebrate body plan into segments begins with the sequential formation of somites in the presomitic mesoderm (PSM). The rhythmicity of this process is controlled by travelling waves of gene expression. These kinetic waves emerge from coupled cellular oscillators and sweep across the PSM. In zebrafish, the oscillations are driven by autorepression of her genes and are synchronized via Notch signalling. Mathematical modelling has played an important role in explaining how collective properties emerge from the molecular interactions. Increasingly more quantitative experimental data permits the validation of those mathematical models, yet leads to increasingly more complex model formulations that hamper an intuitive understanding of the underlying mechanisms. Here, we review previous efforts, and design a mechanistic model of the her1 oscillator, which represents the experimentally viable her7;hes6 double mutant. This genetically simplified system is ideally suited to conceptually recapitulate oscillatory entrainment and travelling wave formation, and to highlight open questions. It shows that three key parameters, the autorepression delay, the juxtacrine coupling delay, and the coupling strength, are sufficient to understand the emergence of the collective period, the collective amplitude, and the synchronization of neighbouring Her1 oscillators. Moreover, two spatiotemporal time delay gradients, in the autorepression and in the juxtacrine signalling, are required to explain the collective oscillatory dynamics and synchrony of PSM cells. The highlighted developmental principles likely apply more generally to other developmental processes, including neurogenesis and angiogenesis.

Multistability and transitions between spatiotemporal patterns through versatile Notch-Hes signaling

“…The model could recapitulate a wide spectrum of spatiotemporal behaviors that has been reported over last decades using distinct classes of theoretical models of lateral inhibition. Lateral inhibition itself is a notorious mechanism to generate diverse, and eventually multistable, inhomogeneous fine-grained patterns (Collier et al, 1996;Owen et al, 2000;Hadjivasiliou et al, 2016;Hunter et al, 2016), but can also give rise to diverse coherent and synchronization states through timedelayed juxtacrine coupling between oscillatory cells (Lewis, 2003;Morelli et al, 2009;Murray et al, 2011;Wang et al, 2011;Jörg et al, 2015;Tomka et al, 2018). Furthermore, repulsive coupling between synthetic oscillators has been shown to generate a wide range of collective regimes including synchronization states and inhomogeneous stationary states (Ullner et al, 2008;Koseska et al, 2010).…”

“…This seminal model has been further refined to illustrate how positive feedback, protrusions, signaling crosstalks or cell division can modulate the relative stability or occurence of diverse -periodic or aperiodic-spatial patterns (Wearing et al, 2000;Hunter et al, 2016;Hadjivasiliou et al, 2016). In developmental contexts where Notch-Hes signals contribute to cellular oscillations, various models, using a discrete or continuous description of tissues and using a phase-like or biochemical description of oscillators, have been used to capture the emergence of patterns such as traveling waves (Murray et al, 2011(Murray et al, , 2013Jörg et al, 2015;Tomka et al, 2018), antiphase synchrony (Lewis, 2003;Wang et al, 2011) or dynamic clusters (Biga et al, 2021).…”

Time and space in segmentation

“…This has been discussed in the context of the vertebrate segmentation clock, which combines direct her / hes autorepression and indirect autorepression via Notch signalling. Modelling suggests that the time delays in the two feedback loops should scale similarly along the SAZ, to avoid the oscillations being extinguished [ 200 , 221 ]. For other cross-regulating processes, altered phase relationships along the SAZ have been clearly documented, and the phenomenon appears to be functionally important for segment patterning [ 214 , 222 , 223 ].…”

Positional information encoded in the dynamic differences between neighbouring oscillators during vertebrate segmentation

“…PSM cells communicate with their neighbors via Notch/Delta signaling, and Notch signaling has been shown to control Mesp2, which is required to initiate somite segmentation (Takahashi et al, 2000; Morimoto et al, 2005; Yasuhiko et al 2006). It is possible that as long as the differences in amplitude and period are small between oscillators, communication between neighboring cells maintains oscillations synchronized (Riedel-Kruse et al, 2007; Delaune et al, 2012; Jiang et al, 2000; Tomka et al, 2018). However, once the differences exceed a critical value, entrainment breaks.…”