Stresses in lipid membranes and interactions between inclusions
This study is devoted to a theoretical model of the membrane-mediated interactions between inclusions (proteins) incorporated into lipid bilayers. The interactions are due to the overlap of the bilayer deformations around each of two approaching inclusions. To determine the resulting stresses in the membrane we have developed an appropriate model of the lipid bilayer, which has been described as an elastic layer (the hydrocarbon-chain region) sandwiched between two Gibbs dividing surfaces (the two headgroup regions). Expressions for the membrane stretching and bending elastic moduli have been derived in terms of the lipid monolayer tension and elastic constants. The interaction between two cylindrical inclusions have been calculated by using both force and energy approaches. The range of this interaction turns out to be of the order of several inclusion radii. The results, which are in qualitative agreement with the experimental observations, can be applied to the interpretation of membrane processes and mechanisms, such as protein aggregation in lipid membranes, as well as to any process affected by the membrane stretching and bending elastic properties.