Modelling Oscillator Synchronisation During Vertebrate Axis Segmentation

Abstract

The somitogenesis clock regulates the periodicity with which somites form in the posterior pre-somitic mesoderm. Whilst cell heterogeneity results in noisy oscillation rates amongst constituent cells, synchrony within the population is maintained as oscillators are entrained via juxtracine signalling mechanisms. Here we consider a population of phase-coupled oscillators and investigate how biologically motivated perturbations to the entrained state can perturb synchrony within the population. We find that the ratio of mitosis length to clock period can influence levels of desynchronisation. Moreover, we observe that random cell movement, and hence change of local neighbourhoods, increases synchronisation.

Modularity of the segmentation clock and morphogenesis

“…Therefore our results represent a lower bound on the effect of mitosis on the clock. Using the estimated values of T G and T M for zebrafish (see methods for calculation), we find that the presence of cell division creates asynchrony as reported previously ( Murray et al (2013 )), and has no identifiable effect on frequency (figure 6B-C). Fixing T G + T M = 187.5 mins and varying T M shows a T M -dependent trend where synchrony decreases with increasing T M (figure 6E).…”

“…As previous models of mitosis and the segmentation clock have been two-dimensional and therefore may not quantitatively recapture the cell mixing and geometry present in zebrafish ( Murray et al (2013 , 2019)), we sought to investigate the effect of mitosis in the presence of the more accurate three-dimensional geometry and cell mixing. To do so, we simulated cell division by assigning each cell a cell cycle phase τ that increases at a constant rate of 1 min −1 , and spawning a new cell adjacent to that cell once that its τ ≥ T G + T M , where T G denotes the total time in minutes to complete G1, S, and G2 phases of the cell cycle, and T M denotes the time spent in M phase, in minutes.…”

“…During M phase of the cell cycle segmentation clock gene expression in zebrafish is known to arrest ( Horikawa et al (2006 )), causing a lag in nascent daughter cells relative to their neighbours ( Delaune et al (2012 )). If cell divisions are asynchronous, as appears to be the case in zebrafish ( Kanki and Ho (1997 ); Steventon et al (2016 )), then such lags can create asynchrony of oscillations in the tissue ( Murray et al (2013 )).…”

“…During M phase of the cell cycle segmentation clock gene expression in zebrafish is known to arrest(Horikawa et al (2006)), causing a lag in nascent daughter cells relative to their neighbours(Delaune et al (2012)). If cell divisions are asynchronous, as appears to be the case in zebrafish(Kanki and Ho (1997); Steventon et al(2016)), then such lags can create asynchrony of oscillations in the tissue(Murray et al (2013)). As previous models of mitosis and the segmentation clock have been 2D and may not quantitatively recapture the cell mixing and geometry present in zebrafish(Murray et al (2013(Murray et al ( , 2019)), we sought to investigate the effect of mitosis in the presence of the more accurate 3D geometry and cell mixing in the present model.…”

“…If cell divisions are asynchronous, as appears to be the case in zebrafish(Kanki and Ho (1997); Steventon et al(2016)), then such lags can create asynchrony of oscillations in the tissue(Murray et al (2013)). As previous models of mitosis and the segmentation clock have been 2D and may not quantitatively recapture the cell mixing and geometry present in zebrafish(Murray et al (2013(Murray et al ( , 2019)), we sought to investigate the effect of mitosis in the presence of the more accurate 3D geometry and cell mixing in the present model. To do so, we simulated cell division by assigning each cell a cell cycle phase 𝜏 that increases at a constant rate of 1 min −1 , and spawning a new cell adjacent to that cell once that its 𝜏 ≥ 𝑇 𝐺 + 𝑇 𝑀 , where 𝑇 𝐺 denotes the cumulative time to complete G1, S, and G2 phases of the cell cycle, and 𝑇 𝑀 denotes the time spent in M phase.…”