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Shape matters in protein mobility within membranes David Lacoste , Laboratoire de Physico-Chimie Théorique Lateral Brownian diffusion of proteins in lipid membranes has been predicted by Saffman and Delbrück to depend only on protein size and on the viscosity of the membrane and of the surrounding medium. Using a single-molecule tracking technique on two transmembrane proteins that bend the membrane differently and are reconstituted in giant unilamellar vesicles, we show that the mobility of a membrane protein is crucially dependent on the local membrane deformation self-generated around the protein, which can be tuned by adjusting membrane tension [1]. The feedback between membrane shaping and mobility is well explained by analytical and numerical models that include the friction of the deformed membrane patch with the surrounding medium and the friction internal to the bilayer. Extensions of this framework to other types of coupling between the membrane and the protein will be discussed [2]. [1] F. Quemeneur, J.K. Sigurdsson, M. Renner, P.J. Atzberger, P. Bassereau and D. Lacoste, PNAS 111, 5083 (2014) [2] V. Démery and D. Lacoste, chapter in book "Physics of biological membranes", published by Springer Netherlands