  Collective cell migration contributes to embryogenesis, wound healing and
tumor metastasis. Cell monolayer migration experiments help understanding what
determines the movement of cells far from the leading edge. Inhibiting cell
proliferation limits cell density increase and prevents jamming; we observe
long-duration migration and quantify space-time characteristics of the velocity
profile over large length- and time-scales. Velocity waves propagate backwards
and their frequency depends only on cell density at the moving front. Both cell
average velocity and wave velocity increase linearly with the cell effective
radius regardless of the distance to the front. Inhibiting lamellipodia
decreases cell velocity while waves either disappear or have a lower frequency.
Our model combines conservation laws, monolayer mechanical properties and a
phenomenological coupling between strain and polarity: advancing cells pull on
their followers which then become polarized. With reasonable values of
parameters, this model agrees with several of our experimental observations.
Together, our experiments and model disantangle the respective contributions of
active velocity and of proliferation in monolayer migration, explain how cells
maintain their polarity far from the moving front, and highlight the importance
of strain-polarity coupling and density in long-range information propagation.
