A neutral protein "carrier" may help an ion to transfer into and cross a lipid membrane. (a) What is the electrostatic free-energy change when a monovalent ion is transferred from water at $25^{\circ} \mathrm{C}$ to a hydrocarbon solvent with dielectric constant $D=2 ?$ The radius of the ion is $0.2 \mathrm{nm}$ (b) Comment on the ability of the ions to diffuse through lipid bilayers. How has nature solved this problem? How do ions manage to get across? (Adapted from Problem 22.11 of K. Dill and S. Bromberg, Molecular Driving Forces, 2nd ed. Garland Science, 2011.)
Added by Ignacio C.
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Given that the ion is monovalent, we can take q = e, the elementary charge, which is approximately 1.6 x 10^-19 C. The permittivity of free space ε₀ is approximately 8.85 x 10^-12 C²/N·m². The radius of the ion r is given as 0.2 nm, or 0.2 x 10^-9 m. The Show more…
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