Membrane undulations driven by force fluctuations of active proteins

We analyze the height undulations of a membrane due to fluctuations in the force generated by membrane-bound proteins that induce normal motion or bending. We compare our results to the results of experiments on red blood cells and vesicles with incorporated active proton pumps. We treat these proteins as having an intrinsic time scale for the force generation or conformational change, leading to nonthermal membrane fluctuations. We find that the active fluctuations are inversely proportional to the viscosity of the surrounding fluid. This highlights some universal features of active membrane undulations.