Cholesterol-Dependent Bending Energy Is Important in Cholesterol Distribution of the Plasma Membrane

We consider the plasma membrane that contains a cholesterol molar fraction of 0.4 and ask how that cholesterol is distributed between the two leaves. Because of the rapid flip-flop of cholesterol between leaves, we assume that its distribution is determined by the equality of its chemical potentials in the two leaves. When we consider only the contributions of entropy and interactions to the cholesterol chemical potential in our model system, we find, not surprisingly, that the cholesterol is mostly in the outer leaf because of the strong attraction between cholesterol and sphingomyelin (SM), which is predominantly in that leaf. We find 72% there. We then include the contribution from the bending energy in each leaf that must be overcome to join the leaves in a flat bilayer. The product of bending modulus and spontaneous curvature is obtained from simulation. We find that the addition of cholesterol to the outer leaf reduces the spontaneous curvature, which is initially positive, until it passes through zero when the molar fraction of cholesterol in the outer leaf is 0.28. Additional cholesterol is driven toward the inner leaf by the sphingomyelin phosphatidylcholine mixture. This is resisted by the bending energy contribution to the inner leaf. We find, again by simulation, that the addition of cholesterol monotonically increases the magnitude of the spontaneous curvature of the inner leaf, which is negative. This increases its bending energy. We conclude that, as a result of these competing effects, the percentage of cholesterol in the outer leaf is reduced to similar to 63 +/- 6%.