Active behavior of the Cytoskeleton

This review presents some of our recent results on active polar gels. Active polar gels are viscoelastic materials formed by polar filaments which are maintained in a non-equilibrium state by constant consumption of energy. This non-equilibrium state is characterized by the existence of internal stresses and spontaneous flows. A defining example of an active polar gel is provided by the acto-myosin cytoskeleton of eukaryotic cells. It is formed by actin filaments interacting with myosin molecular motors which are driven by the hydrolysis of adenosine-tri-phosphate (ATP).We first present a hydrodynamic theory of active polar gels. The hydrodynamic equations are generic as they only rely on symmetry arguments. We then use the hydrodynamic approach to study the spontaneous generation of flow in an active polar film and the formation of vortex defects. The last part of this review is devoted to an analysis of the active gel theory in situations which are reminiscent of structures formed by the cytoskeleton in living cells.