Curvature-coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.Comment: 16 pages, 8 figure

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes

Programmed Bending Reveals Dynamic Mechanochemical Coupling in Supported Lipid Bilayers

In living cells, mechanochemical coupling represents a dynamic means by which membrane components are spatially organized. An extra-ordinary example of such coupling involves curvature-dependent polar localization of chemically-distinct lipid domains at bacterial poles, which also undergo dramatic reequilibration upon subtle changes in their interfacial environment such as during sporulation. Here, we demonstrate that such interfacially-triggered mechanochemical coupling can be recapitulated in vitro by simultaneous, real-time introduction of mechanically-generated periodic curvatures and attendant strain-induced lateral forces in lipid bilayers supported on elastomeric substrates. In particular, we show that real-time wrinkling of the elastomeric substrate prompts a dynamic domain reorganization within the adhering bilayer, producing large, oriented liquid-ordered domains in regions of low curvature. Our results suggest a mechanism in which interfacial forces generated during surface wrinkling and the topographical deformation of the bilayer combine to facilitate dynamic reequilibration prompting the observed domain reorganization. We anticipate this curvature-generating model system will prove to be a simple and versatile tool for a broad range of studies of curvature-dependent dynamic reorganizations in membranes that are constrained by the interfacial elastic and dynamic frameworks such as the cell wall, glycocalyx, and cytoskeleton