Dependence of protein-induced lipid bilayer thickness deformations on protein shape

Structural biology has shown that membrane proteins come in a great variety of shapes, with distinct membrane proteins, and even different conformational states of the same membrane protein, often showing distinct hydrophobic thicknesses deviating from the unperturbed thickness of the surrounding lipid bilayer. The resulting protein-induced bilayer thickness deformations can be captured quantitatively by membrane elasticity theory, and have been found to play an important role in membrane protein regulation. Physical models of protein-induced bilayer thickness deformations usually focus on idealized, cylindrical membrane protein shapes. We describe here a boundary value method for the straightforward calculation of protein-induced bilayer thickness deformations for arbitrary protein shapes. We find that the deviations of protein shape from rotational symmetry suggested by structural biology can have a large effect on the energy of protein-induced bilayer thickness deformations. Intriguingly, our calculations suggest that the elastic coupling of lipid bilayer properties and membrane protein conformational state may provide a generic physical mechanism for temperature sensing through ion channels.