Inclusion induced bilayer deformations: The lipid tilt degree of freedom,
submitted to Eur.Biophys.J
The theory of protein induced lipid bilayer deformations is reinvestigated. We present a general phenomenological description of the lipid layer perturbation around a single, cylindrically symmetric inclusion in a symmetric, tension free bilayer. Two oder parameters are included, one describes the chain stretching and the other one is the tilt of the lipid director. The elastic moduli are expressed through the interaction constants of a molecular lipid model. Assuming strong hydrophobic coupling and incompressibility of the hydrocarbon chains, we estimate typical membrane deformation energies and the corresponding spring constants for single gramicidin A channels with and without the lipid tilt degree of freedom taken into account. We argue that lipid tilt relaxation may lead to a severalfold reduction in the spring constant and should thus not be neglected. The model is also used to calculate the change the bilayer deformation energy upon a change in the electrostatic energy of charged bilayers.