Nonequilibrium fluctuations, travelling waves, and instabilities in activemembranes

The stability of a flexible fluid membrane containing a distribution of mob ile, active proteins (e.g.. proton pumps) is shown to depend on the structu re and functional asymmetry of the proteins. A stable active membrane is in a nonequilibrium steady state with height fluctuations whose statistical p roperties are governed by the protein activity. Disturbances are predicted to Gravel as waves at sufficiently long wavelength, with speed set by the n ormal velocity of the pumps. The unstable case involves a spontaneous, pump -driven undulation of the membrane, with clumping of the proteins in region s of high activity.