Shape matters in protein mobility within membranes

The lateral mobility of proteins within cell membranes is usually thought to be dependent on their size and modulated by local heterogeneities of the membrane. Experiments using single-particle tracking on reconstituted membranes demonstrate that protein diffusion is significantly influenced by the interplay of membrane curvature, membrane tension, and protein shape. We find that the curvature-coupled voltage-gated potassium channel (KvAP) undergoes a significant increase in protein mobility under tension, whereas the mobility of the curvature-neutral water channel aquaporin 0 (AQP0) is insensitive to it. Such observations are well explained in terms of an effective friction coefficient of the protein induced by the local membrane deformation.Brownian motion plays an essential role in biological processes. Since the pioneering experiments of Perrin (1), the observation of diffusing objects has emerged as a mean to extract the rheological properties of the surrounding medium or the probe particle size. The theoretical investigation of diffusion of proteins within membranes has been studied widely going back to P. G. Saffman and M. Delbrück (SD). They investigated the hydrodynamic drag acting on a membrane inclusion when the membrane is described as a 2D fluid sheet of viscosity embedded within a less viscous fluid of viscosity η (2). In this theory, the diffusion coefficient D₀ in the limit of a large viscosity contrast between the membrane and bulk fluid is given by:The length is the length scale over which flow is generated within the bilayer by the inclusion, k_BT is the thermal energy, and γ is Euler’s constant. This model predicts a logarithmic dependence of D₀ on the protein radius a_p, which has been confirmed for some in vitro experiments on membranes containing transmembrane proteins (see ref. 3 and references therein). In contrast, the experiments of Gambin et al. (4) showed significant deviations from the SD theory.A possible origin for the discrepancy observed by Gambin et al. (4) is the significant local membrane deformation due to the interaction between the inclusion and the lipid bilayer (5). Naji et al. suggested in ref. 6 that inclusions experience additional dissipation, either due to internal flows within the membrane or to additional fluid flows produced by the deformed membrane. This work triggered a number of theoretical studies investigating the coupling of inclusion proteins with the membrane that had been pioneered by the Seifert’s group (see ref. 7 and references therein). Such studies have systematically gone beyond the SD model by including additional effects (8–12). So far, a thorough verification of these ideas has not been attempted. To investigate the effect of the protein–lipid coupling on the protein mobility, we study its dependence on membrane tension, because this parameter affects the local membrane deformation.In this work, we compare the mobility of two transmembrane proteins with the same lateral size, aquaporin 0 (AQP0) and a voltage-gated potassium channel (KvAP), reconstituted in giant unilamellar vesicles (GUVs). Whereas AQP0 does not deform locally the bilayer, KvAP locally bends the membrane (13). Using single-particle tracking (SPT), we demonstrate that the curvature-coupled protein KvAP undergoes a significant increase in mobility under tension, whereas the mobility of the curvature-neutral water channel AQP0 is insensitive to it. This difference, which goes beyond the SD model, is explained by an approach that includes the interplay between membrane deformation and friction with the surrounding medium and within the bilayer. This is compelling evidence that the Brownian motion of a shaping-membrane protein is not simply dependent on the inclusion size but also related to the lateral extension of the deformed membrane patch, which depends on tension.