Dynamics of active membranes with internal noise

– We study the time-dependent height fluctuations of an active membrane containing energy-dissipating pumps that drive the membrane out of equilibrium. Unlike previous investigations based on models that neglect either curvature couplings or random fluctuations in pump activities, our formulation explores two new models that take both of these effects into account. In the first model, the magnitude of the nonequilibrium forces generated by the pumps is allowed to fluctuate temporally. In the second model, the pumps are allowed to switch between " on " and " off " states. We compute the mean squared displacement of a membrane point for both models, and show that they exhibit distinct dynamical behaviors from previous models, and in particular, a superdiffusive regime specifically arising from the shot noise. Introduction. – While the physics of biomembranes in equilibrium is fairly developed [1], recent studies focus on active membranes that contain proteins, such as ion channels, ion pumps, and photo-active proteins like bacteriorhodopsin. These proteins consume the chemical energy of ATP, dissipate it into the medium, and thus drive the membrane out of equilibrium [2, 3]. The importance of active processes has been demonstrated in an experiment showing that the fluctuations in the shape of red blood cells depend on the viscosity of the environment and on ATP concentrations [4]. In in vitro experiments, nonequilibrium forces arising from ion pumps embedded in a membrane are shown to enhance its fluctuations [5, 6, 7]. There are currently two theoretical models for active membranes [3]. The Prost-Bruinsma (PB) model takes nonequilibrium forces in the form of active noises that include diffusion and the stochastic nature (shot noise) of the pumps, but ignores the coupling between the pumps and membrane curvature [8, 9, 10]. The other model proposed by Ramaswamy, Toner and Prost (RTP) incorporates this coupling but ignores the random nature of the protein activity [11, 12]. For steady state measurements of active membranes, the RTP model agrees quite well with experiments [6, 7]. In this Letter, we further explore the dynamical properties of the RTP model, argue that it is important to include the shot noise for dynamical measurements, and present two new models that include both curvature effects and pump stochasticity. In the first model, which may be an appropriate description for light-activated pumps such as