Pattern Formation In the Acto-Myosin Cortex: An Active Reaction-Diffusion-Advection Process

The acto-myosin cortex, which resides immediately below the eukaryotic cell membrane, is a thin network of crosslinked actin filaments on which myosin motors exert stress though active processes involving ATP hydrolysis.  The cortex is continuously remodeled, so that on long time scales it may be treated as a viscous fluid.  Regulators of myosin activity and actin dynamics, and therefore active stress, are also present in the cortex.  To capture this biochemical and mechanical coupling, we have developed a general hydrodynamic description of the cortex as a thin film of an active viscous fluid in which active stresses are under regulation of biochemical species which undergo diffusion and chemical reactions.  The coupling of active mechanical stresses with a reaction-diffusion system results in biochemical pattern formation with steady viscous flow.  In many cases, active fluid motion promotes patterns in systems which would otherwise remain homogeneous.  Such patterns are prevalent in embryonic development, cell motility, and polarization, and this theory provides a simple, general framework in which they may be understood.  We apply the theory to the dynamics of the polarization of the one-cell C. elegans embryo, a system for which mechanical and chemical coupling is essential.