Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Abstract

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.

The tissue mechanics of vertebrate body elongation and segmentation

“…As cells move from the dorsal to ventral posterior tailbud, this flow loses coherence resulting in an increase in cell mixing (Figure 1A) [15••,16••]. Computer simulations suggest that this cell mixing may help synchronize the segmentation clock that generates the segmental prepattern in the PSM [17•]. As mesodermal progenitors enter the posterior PSM, cell motion declines concomitantly with the assembly of an extracellular matrix (ECM) composed of Fibronectin and Laminin [15••,18].…”

Collective gradient sensing and chemotaxis: modeling and recent developments

“…First is Iyengar and Rao [120], who predict that rearrangement at the receptor level can help observe a time-varying signal; the ideal time-dependent configuration switches between active clustering, stationary lattices, and passive diffusion. Secondly, Uriu and Morelli [121, 122] propose that synchronization between cells can be improved by tissue rearrangement, using a self-propelled particle model with cells also having phase oscillators that couple between neighbors. These suggest interesting places of potential contact to gradient sensing at the collective level.…”

Mobility-induced persistent chimera states

“…The stochastic exchange of positions is modeled as a Poisson process. We introduce a mobility rate λ such that each pair of neighboring oscillators exchange positions with a probability λ/2 per unit time [14,15,23]. With this modeling, the waiting time for the next exchange event for each oscillator is stochastic and its statistics obey an exponential distri- bution with mean 1/λ.…”

“…Mobility of oscillators sets the timescale for how often single oscillators exchange neighbors, which is particularly relevant in locally coupled systems. Mobility has been shown to reduce the time the system needs to achieve synchronization [14,15,22,23], by extending the effective range of the coupling [15] or through coarsening [24]. Thus, both coupling delay and mobility independently have distinct effects on the dynamics of coupled oscillators.…”