Cholesterol-Dependent Bending Energies in Both Leaves Play a Significant Role in Determining the Cholesterol Distribution in the Plasma Membrane

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We consider a plasma membrane that contains a cholesterol mol 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 due to the strong attraction between cholesterol and sphingomyelin, which is predominantly in the outer leaf, the cholesterol is mostly in that leaf. We find 74% of the total cholesterol there. The explicit interaction energy does not include the bending energy, which we consider next. Simulations indicate that the bending energy of cholesterol-sphingomyelin mixtures varies non-linearly with composition. This energy is obtained from the product of bending modulus and spontaneous curvature that is available from simulation. We find that the addition of cholesterol to the outer leaf reduces the spontaneous curvature, which is initially positive. It passes through zero when the mol fraction of cholesterol in the outer leaf is 0.28. Additional cholesterol is driven toward the inner leaf by the sphingomyelin. 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 percent of total cholesterol that is in the outer leaf is reduced to about 62% ±4%.