Self-organization and hydrodynamics of active rods on fluid membranes

The transport and self-organization of active self-propelled rod-like proteins and biopolymers on the cell membrane and other fluid interfaces is key to many biological processes and functions. Such systems are shown to exhibit a complex range of collective behaviors, including aggregation, polar and nematic ordering, and complex dynamics of topological defects. Here, we use a continuum description of active polar rods to study the collective dynamics of a dilute suspension of pusher and puller rods in a fluid membrane submerged in a bulk fluid on the interior and exterior. This serves as a simplified model for the assembly of cytoskeletal biopolymers on the cell membrane. The behavior is determined by two dimensionless quantities: (1) the ratio of active to thermal stresses, and (2) the ratio of the rod’s length (L) to Saffman-Delbruck length (l0), where l0 is the ratio of the 2D membrane viscosity to 3D bulk viscosity. Using stability analysis and numerical simulations, we show that the coupling between the membrane’s tangential flows to 3D bulk flows introduces several novel features that are absent in active suspensions in free space 3D and 2D geometries. Specifically, we show that pusher rods undergo a finite wavelength nematic order transition at sufficiently high activities. The wavelength of the ordered domains decreases with increasing L/l0. Furthermore, we show that in addition to ordering, the pusher suspensions undergo phase transition in density (aggregation) above some critical swimming velocity, which depends on L/l0.