This thesis deals with biological membranes, studied from the point of view of theoretical physics. We focus on some generic effects of the presence of one or two membrane inclusions, e.g., proteins, or of a local chemical change of the environment of the membrane. First, 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. We clarify the definition of the force exerted by a correlated fluid on an inclusion, in a microstate of the fluid. This definition plays a key art in studies of the Casimir-like force beyond its thermal equilibrium value. We also study the Casimir-like interaction between rod-shaped membrane inclusions. Then, we investigate 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. Finally, 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.
