Pattern Formation In Active Fluids

Motivated by the dynamics of the actomyosin cell cortex in which stress generation is under biochemical regulation, we develop a hydrodynamic theory for pattern formation in active fluids. Nonhomogeneous active stress profiles drive fluid motion which transports diffusing stress regulators by advection. Based on this principle, we present a mechanism for pattern formation in which a single diffusing species up-regulates active stress, resulting in steady nonhomogeneous flow and concentration profiles. We also investigate general pattern-forming behaviors of reaction diffusion systems embedded in active fluids. In particular, we find that the presence of active stress-driven flow greatly expands the region of parameter space in which patterns may form in classic Turing-type systems.  The theory is applied to the polarization of the one-cell C. elegans embryo.