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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 d(P), embedded in a lipid bilayer of unperturbed thickness d(L)o. 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 d(P) > d(L)o) in order to bridge over the lipid-protein hydrophobic mismatch (d(P) - d(L)o). 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 isomeric 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 DELTAF is calculated as a function of d(P) - d(L)o. Most calculations are for C-14 amphiphiles which, in the absence of a protein, pack at an average area per head-group a0 congruent-to 32 angstrom2 (d(L)o congruent-to 24.5 angstrom), corresponding to the fluid state of the membrane. When d(P) = d(L)o, DELTAF > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When d(P) > d(L)o, the interaction free energy is further increased due to the enhanced stretching of the tails. When d(P) < d(L)o, chain flexibility (entropy) increases, but this contribution to DELTAF is overcounted by the increase in the interfacial free energy. Thus, DELTAF obtains a minimum at d(P) - d(L)o congruent-to 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.

Last updated on 02/28/2017