Bending Stiffness and Curvature Coupling of Ternary Lipid Mixtures

There exists a wide range of curvature gradients within and between cellular organelles. Differences between membrane morphologies play important roles in cell homeostasis, for example, in the sorting and trafficking of membrane components, as well as in controlling the activities of membrane associated proteins. To better understand the mechanisms by which curvature regulates cellular functions, here, we investigate membrane curvature coupling to membrane composition and mechanical properties.We find that bending stiffness depends on membrane curvature of micro-scale homogeneous ternary lipid mixtures. Curvature gradients were generated by lipid tethers with controllable radius pulled from giant vesicles, and bending stiffness was obtained from tether radius and membrane tension measurements. As curvature increases, bending energy overcomes mixing entropy such that highly flexible lipid groups are sorted into the tube from the flat membrane. The sorting is enhanced as composition approaches the neighborhood of the mixing-demixing critical point, through two trajectories: parallel and perpendicular to the phase boundary. An expression that predicts bending stiffness to be a quadratic function of curvature in ternary mixture is derived, from which curvature sorting efficiency is obtained. We then interpret the sorting efficiency to be the ratio of a driving force for and a resistance to sorting. In addition, we estimate the bending stiffness of ternary mixtures at zero curvature, finding consistency with our measurements from the micropipette aspiration method.