Random cell movement promotes synchronization of the segmentation clock

Abstract

In vertebrate somitogenesis, the expression of segmentation clock genes oscillates and the oscillation is synchronized over nearby cells. Both experimental and theoretical studies have shown that the synchronization among cells is realized by intercellular interaction via Delta-Notch signaling. However, the following questions emerge: (i) During somitogenesis, dynamic rearrangement of relative cell positions is observed in the posterior presomitic mesoderm. Can a synchronized state be stably sustained under random cell movement? (ii) Experimental studies have reported that the synchronization of cells can be recovered in about 10 or fewer oscillation cycles after the complete loss of synchrony. However, such a quick recovery of synchronization is not possible according to previous theoretical models. In this paper, we first show by numerical modeling that synchronized oscillation can be sustained under random cell movement. We also find that for initial perturbation, the synchronization of cells is recovered much faster and it is for a wider range of reaction parameters than the case without cell movement. When the posterior presomitic mesoderm is rectangular, faster synchronization is achieved if cells exchange their locations more with neighbors located along the longer side of the domain. Finally, we discuss that the enhancement of synchronization by random cell movement occurs in several different models for the oscillation of segmentation clock genes.zebrafish | somitogenesis | Delta-Notch | mathematical models I n vertebrate development, somites bud off from the anterior end of the tissue not yet differentiated to somites, called the presomitic mesoderm (PSM), one by one moving posteriorly. The time interval between the formation of one somite and the next is almost constant during somitogenesis, and it is species-specific. In the PSM, there are segmentation clock genes with oscillating expression, and the timing of segmentation is considered to be controlled by the oscillatory expression of these genes because their period of oscillation is very close to the period of segmentation (1-5).The oscillatory expression of the segmentation clock genes is known to be caused by the negative feedback regulation by their own products (6-8). Neighboring cells are in contact with each other (9, 10). In the PSM, oscillatory expressions are synchronized among neighboring cells. This synchronized oscillation is necessary for normal segmentation, and disruption of the synchronization results in a defective somite boundary (11-13).Theoretical models of segmentation in vertebrates have been developed to explain the spatiotemporal periodicity of the segmentation process (14-18), the oscillatory expression of segmentation clock genes (19)(20)(21)(22)(23)(24), and the wave-like gene expression observed in the anterior PSM (23,(25)(26)(27)(28)(29). Previous theoretical studies have also addressed mechanisms of synchronization of the segmentation clock between cells (13,24,25,30). In zebrafish, the synchronization of the segment...

Superdiffusion, large-scale synchronization, and topological defects

“…This leads to the emergence of spin-waves in one dimension [29,30] and topological defects [31] in two dimensions. These facts, that relate synchronization theory and statistical mechanics, were often overlooked in studies of motile oscillators [32][33][34][35][36][37][38]. Here, we discuss how the motion of these topological excitations and the corresponding annihilation dynamics is affected by the motion of the oscillators.…”

Systems biology and the integration of mechanistic explanation and mathematical explanation

“…From experimental studies it is known that individual oscillating cells move so as to change their relative positions, and that synchronization is recovered upon perturbation that initially destroy synchrony. Uriu et al (2010) mathematically show that synchronization can be maintained under random cell movement, and that such movement actually reduced the timespan of reestablishing synchrony following perturbation.…”

Modelling Oscillator Synchronisation During Vertebrate Axis Segmentation

“…Bénazéraf et al [6] have recently quantified random cell motion in the mouse PSM while, in a theoretical study, Uriu et al [7] have demonstrated that random cell movement enhances synchronisation of neighbouring molecular oscillators. We now investigate the effects of random cell movement on the mitosis-perturbed phase dynamics introduced in Sect.…”

“…Random cell movement has also been quantified in zebrafish [1], although spatial variation in motility rates along the AP axis has not, to the best of our knowledge, been documented. A recent computational study has indicated that random cell movement should increase synchronisation in a population of locally coupled oscillators [7].…”