A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness dP, embedded in a lipid bilayer of unperturbed thickness doL. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when dP > doL) in order to bridge over the lipid-protein hydrophobic mismatch (dP-doL). The bilayer's hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isometric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy delta F is calculated as a function of dP-doL. Most calculations are for C14 amphiphiles which, in the absence of a protein, pack at an average area per head-group ao approximately equal to 32 A2 (doL approximately 24.5 A), corresponding to the fluid state of the membrane. When dP = doL, delta F > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When dP > doL, the interaction free energy is further increased due to the enhanced stretching of the tails. When dP < doL, chain flexibility (entropy) increases, but this contribution to delta F is overcounted by the increase in the interfacial free energy. Thus, delta F obtains a minimum at dP-doL approximately 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the discussion.