Spontaneous oscillations from turnover of an elastic contractile material

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.