Coupling between vesicle shape and lateral distribution of mobile membrane inclusions

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Abstract
Membrane inclusions such as membrane-embedded peptides or proteins exhibit a curvature-dependent interaction with the surrounding lipid matrix due to the mismatch between their intrinsic curvature and the local membrane curvature. This interaction causes an inhomogeneous lateral distribution of the inclusions and a corresponding adjustment of the vesicle shape. We have studied theoretically the axisymmetric equilibrium shapes of lipid vesicles with mobile inclusions, taking into account that the membrane free energy includes the elastic energy of the lipid bilayer and a contribution due to an inclusion-membrane interaction. Equations describing the shape are derived by minimizing the total free energy at fixed membrane area, enclosed volume, and number of inclusions and are then solved numerically. It is shown that vesicle shape may assume a symmetry that differs from that of the vesicle with no inclusions. If the inclusion-membrane interaction exceeds a certain value, there is no axisymmetric solution of the equations with a continuous and derivable lateral density of inclusions over the whole area of the vesicle. When approaching the critical vesicle shape, the shapes obtained differ qualitatively from those described by the area difference elasticity model of the elastic properties of lipid membranes. In general, vesicle shapes adjust to the presence of inclusions by increasing regions with favorable curvature and decreasing regions of unfavorable curvature in a way such that the lateral distribution of inclusions becomes inhomogeneous.