In the bacterium Escherichia coli, the Min proteins oscillate between the cell poles to select the cell center as division site. This dynamic pattern has been proposed to arise by self-organization of these proteins, and several models have suggested a reaction-diffusion type mechanism. Here, we found that the Min proteins spontaneously formed planar surface waves on a flat membrane in vitro. The formation and maintenance of these patterns, which extended for hundreds of micrometers, required adenosine 5'-triphosphate (ATP), and they persisted for hours. We present a reaction-diffusion model of the MinD and MinE dynamics that accounts for our experimental observations and also captures the in vivo oscillations.
We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel generates a non equilibrium state characterized by the generation of flows and stresses. Our theory can be applied to experiments in which cytoskeletal patterns are set in motion by active processes such as those which are at work in cells.
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