A statistical-mechanical treatment of the molecular binding into lipid membrane is presented in combination with molecular simulation. The membrane solution is viewed as an inhomogeneous, mixed solvent system, and the free energy of solvation of a solute in membrane is computed with a realistic set of potential functions by the method of energy representation. Carbon monoxide, carbon dioxide, benzene, and ethylbenzene are adopted as model solutes to analyze the binding into 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) membrane. It is shown that the membrane inside is more favorable than bulk water and that the solute distribution is diffuse throughout the membrane inside. The membrane-water partition coefficient is then constructed with the help of the Kirkwood-Buff theory from the solvation free energy obtained separately in the hydrophobic, glycerol, headgroup, and aqueous regions. To discuss the role of repulsive and attractive interactions, the solvation free energy is partitioned into the DMPC and water contributions and the effect of water to stabilize the benzene and ethylbenzene solutes within the membrane is pointed out.

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77.
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78.
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79.
The contributions to Kx from regions V–VI are 0.09%, 0.7% , 0.04%, and 0.001% in weight for CO, CO2, benzene, and ethylbenzene, respectively.
80.
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83.
The “excluded-volume” region can be identified over the energy coordinate ϵ as ϵ>ϵc, where ϵc is rather arbitrary and is typically 1020kcal/mol. When the integral over ϵ in Eqs. (24) and (25) is restricted to the ϵ domain corresponding to the excluded-volume region, the integral value is larger in the order of bulk water, region IV, and region II.
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