Steady-state directional flow in active model cytoskeletal network

Mesoscopic flow of cytoskeletal actin networks in eukaryotic cells, driven by active motor processes, is crucial in a wide variety of cellular dynamics, including intracellular transport, positioning of nuclei, cell migration and division. It remains unclear how such collective dynamics, involving subtly balanced spatiotemporal interactions of many molecular components with transient networks of polymeric actin are regulated and maintained in steady states. We here use a model system of water-in-oil emulsion droplets composed of Xenopus egg extract that contains all the ingredients for active cytoskeletal assembly. We observe conspicuous 3D radially convergent stationary flow patterns of F-actin networks driven by non-muscle myosin motors. Actin intensity and velocity profiles maintain steady-state gradients from the droplet periphery to its center while actin constantly polymerizes and depolymerizes. The contracting actin network drives a mechanical phase separation and forms of a central inclusion. In order to elucidate the mechanisms that lead to the observed patterns and to a precise and stable positioning of the steady-state inclusion in the center of the droplet, we model the network as an isotropic active gel. This model allow us to compute the steady-state actin velocity and concentration profiles as well as the magnitude of the centering force acting on the inclusion.