Collective cell migration without proliferation: density determines cell velocity and wave velocity

Collective cell migration contributes to morphogenesis, wound healing or tumor metastasis. Culturing epithelial monolayers on a substrate enables to quantify such tissue migration. By using narrow strips, we stabilise the front shape; by inhibiting cell division, we limit density increase and favor steady migration; by using long strips, we observe a confined cell monolayer migrating over days. A coherent collective movement propagates over millimeters; cells spread and density decreases from the monolayer bulk toward the front. Cell velocity ([~]micrometer per minute) increases linearly with cell radius, and does not depend explicitly on the distance to the front. Over ten periods of backwards propagating velocity waves, with wavelength [~]millimeter, are detected with a signal-to-noise ratio enabling for quantitative spatio-temporal analysis. Their velocity ([~]ten micrometers per minute) is ten times the cell velocity; it increases linearly with the cell radius. Their period ([~]two hours) is spatially homogeneous, and increases with the front density. When we inhibit the formation of lamellipodia, cell velocity drops while waves either disappear, or have a smaller amplitude and slower period. Our phenomenological model assumes that both cell and wave velocities are related with the activity of lamellipodia, and that the local stretching in the monolayer bulk modulates traction stresses. We find that parameter values close to the instability limit where waves appear yield qualitative and quantitative predictions compatible with experiments, including the facts that: waves propagate backwards; wave velocity increases with cell radius; lamellipodia inhibition attenuates, slows down or even suppresses the waves. Together, our experiments and modelling evidence the importance of lamellipodia in collective cell migration and waves.