Statistique et dynamique des membranes complexes

Lipid bilayers, which form the basis of biological membranes, are self-assembled structures that belong to the field of soft matter. They feature very rich physical properties. While each of the two monolayers of the membrane is a two-dimensional fluid, the membrane resists bending and stretching: it is elastic. Biological membranes are composed of different lipid species and contain various inclusions, in particular membrane proteins. These inclusions interact with the lipid bilayer and with each other through the lipid bilayer. In addition, a biological membrane is surrounded by a heterogeneous and constantly changing environment, which can influence and perturb it. This thesis deals with the statistics and dynamics of complex biological membranes. We focus on some generic effects of the presence of one or two membrane inclusions, or of a local chemical change of the environment of the membrane. In Part I, we study the Casimir-like interaction between two membrane inclusions, which arises from the constraints imposed by the inclusions on the thermal fluctuations of the shape of the membrane. We calculate the fluctuations of the Casimir-like force between two point-like inclusions, showing the quantitative importance of these fluctuations, and studying their dependence on the distance between the inclusions. We then investigate the differences between two definitions of the force exerted by a correlated fluid on an inclusion, in a microstate of the fluid. This force plays a key part in studies of the Casimir-like force beyond its thermal equilibrium value. Finally, we study Casimir-like interactions between rod-shaped membrane inclusions, for different types of rigid rods, and for rods with finite outof-plane bending rigidity. In Part II, we examine membrane elasticity at the nanoscale, which is involved in local membrane thickness deformations in the vicinity of proteins. We put forward the importance of an energetic term that is neglected in existing models. We reanalyze numerical and experimental data, obtaining some clues for the presence of this term. In Part III, we present a theoretical description of the dynamics of a membrane submitted to a local chemical perturbation of its environment, starting from first principles. We compare our theoretical predictions to new experimental results regarding the dynamical deformation of a biomimetic membrane submitted to a local pH increase, and we obtain good agreement between theory and experiments. Finally, we show that investigations of dynamical local perturbations provide more information on the response of the membrane than the standard studies that restrict to static and global perturbations of the membrane environment. iv te l-0 07 67 94 3, v er si on 1 20 D ec 2 01 2