Curvature-driven lateral segregation of membrane constituents in Golgi cisternae

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Abstract
Lateral segregation of mobile membrane constituents (e.g. lipids, proteins or membrane domains) into the regions of their preferred curvature relaxes stresses in the membrane. The equilibrium distribution of the constituents in the membrane is thus a balance between the gains in the membrane elastic energy and the segregation-induced loss of entropy. The membrane in the Golgi cisternae is particularly susceptible to the curvature-driven segregation because it possesses two very different curvatures-the highly curved membrane in the cisternal rims and the flat membrane in the cisternal sides. In this work, we calculate the extent of lateral segregation in the Golgi cisternae in the case where the segregation is driven by the Helfrich bending energy. It is assumed that the membrane bending constant and spontaneous curvature depend on the local membrane composition. A simple analytical expression for the extent of the lateral segregation is derived. The results show that the segregation depends on the ratio between the bending constant and the thermal energy, the difference of the preferred curvatures of the constituents and the sizes of the constituents. Applying the model to a typical Golgi cisterna, it was found that entropy can effectively limit the extent of the curvature-driven lateral segregation.