Waves in cell monolayer without proliferation: density determines cell velocity and wave celerity

Collective cell migration contributes to morphogenesis, wound healing or tumor metastasis. Culturing epithelial monolayers on a substrate is an in vitro configuration suitable to quantitatively characterize such tissue migration by measuring cell velocity, density and cell-substrate interaction force. Inhibiting cell division, we limit cell density increase and favor steady cell migration, while by using long narrow strips we stabilise the migrating front shape, so that we observe migration over a day or more. In the monolayer bulk, the cell velocity is a function of the cell density, namely it increases as a linear function of the cell radius. At least ten periods of propagating velocity waves are detected with a high signal-to-noise ratio, enabling for their quantitative spatio-temporal analysis. Cell density displays waves, in phase opposition with the velocity, as predicted by mass conservation; similarly, cell-substrate force appear to display small amplitude waves, in phase quadrature with respect to velocity, compatible with predictions for an elastic monolayer. The wave phase celerity is of order of ten micrometers per minute, i.e. ten times the monolayer migration velocity; wave celerity and frequency too decrease with cell density. We propose an experiment-inspired bottom-up biochemical model of these waves, where motility forces in the bulk of the monolayer are oriented by a dynamic pulling on cell-cell junctions. We find that parameters values close to the instability limit where waves appear yield predictions of wave characteristics close to experimentally observed values. These results lead to the determination of biomechanical parameters, strongly constrain possible theoretical models of waves propagation, and provide a new insight in the link between cell-level biomechanics or biochemistry and tissue-level collective cell migration. Insert Received for publication Date and in final form Date. Correspondence: [email protected], [email protected]