Spontaneous flow transition in active polar gels

– We study theoretically the effects of confinement on active polar gels such as the actin network of eukaryotic cells. Using generalized hydrodynamics equations derived for active gels, we predict, in the case of quasi one-dimensional geometry, a spontaneous flow transition from a homogeneously polarized immobile state for small thicknesses, to a perturbed flowing state for larger thicknesses. The transition is not driven by an external field but by the activity of the system. We suggest several possible experimental realizations. Introduction and statement of the problem. – Active materials are a challenging class of systems driven out of equilibrium by an internal or an external energy source. Many examples of active systems are provided by the biological world such as self–propelled particle assemblies in bacterial colonies, or the membrane or the cytoskeleton of eukaryotic cells [1]. The cell cytoskeleton is a complex network of long filamentary proteins (mostly F-actin, microtubules and intermediate filaments) interacting with a variety of smaller proteins [2] which can, among other things, crosslink or cap the filaments. A well studied class of proteins interacting with actin and microtubules are motor proteins, myosin, kinesin or dyneins. These proteins use the chemical energy of Adenosinetriphosphate (ATP) hydrolysis to " walk " along the filaments, and exert stresses that deform the filament network [3,19]. The active properties of the cytoskeleton play a crucial role in most for cell functions such as intracellular transport, motility and cell division. Many efforts towards understanding the mechanical properties of the cytoskeleton have focused on the description of its passive visco-elastic properties which are well understood in terms of a gel built by cross-linked semi-flexible polymers [17, 18]. More recently, Kruse et al. [15, 16] have proposed a generalized hydrodynamic theory based on conservation laws and symmetry considerations, to describe macroscopically active polar gels. A typical example is given by the network of actin cytoskeletal filaments in the presence of myosin II motor proteins which generate active processes by hydrolyzing ATP. Since cytoskeletal filaments are structurally polar (with a + and-end), each filament locally defines a unit vector. The filamental structure gives rise on large scales to a macroscopic polarity if the filaments are on average aligned.