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.