  Single and collective cellular oscillations involving the actomyosin
cytoskeleton have been observed in numerous biological systems. We show here
that a generic model of a contractile material, which is turning over and
contracts against an elastic element, exhibits spontaneous oscillations. Such a
model can thus account for shape oscillations observed in amnioserosa cells
during dorsal closure of the Drosophila embryo. We investigate the collective
dynamics of an ensemble of such oscillators and show that the relative
contribution of viscous and friction losses yield different regimes of
collective oscillations. Taking into account the diffusion of contractile
elements, our theoretical framework predicts the appearance of traveling waves
which might account for the propagation of actomyosin contractile waves
observed during morphogenesis.
