Biological membranes are subjected to many nonequilibrium phenomena that are essential for living cells. In order to get a more complete physical description of these membranes, we have studied both theoretically and experimentally the effect of two nonequilibrium processes on the properties and dynamics of membranes. In a first part, we propose a general theory, completely covariant, of fluid membranes which are subjected to exchanges of biological materials (e.g. lipid vesicles, enzymes or membrane proteins). Using this phenomenology to study fluctuations of such membranes, we have shown that under certain conditions these develops an instability and shoots out a long thin tubule which bear a morphological resemblance to membranes of eukaryotic organelles. We have also applied successfully this model to describe the fusion phenomenon experimentally observed between small and giant charged vesicles mimicking endocytosis phenomena described in living cells. In a second part, we have considered the modification of fluctuations spectrum of membranes induced by transmembrane proteins activity. A theoretical model developed in labs, taking into account the non-equilibrium activity predicts that the shape fluctuations should be amplified in presence of an additional nonequilibrium noise source. To test experimentally these predictions, we have developed a new general method for the reconstitution of transmembrane proteins as the ATP-driven pump, Calcium-ATPase into giant unilamellar vesicles. Using micropipet technique, we have measured both a bending rigidity decrease due to the presence of proteins into the membrane, and an enhanced fluctuation level in active membranes.
