Nonadditive Compositional Curvature Energetics of Lipid Bilayers

The unique properties of the individual lipids that compose biological membranes together determine the energetics of the surface. The energetics of the surface, in turn, govern the formation of membrane structures and membrane reshaping processes, and thus they will underlie cellular-scale models of viral fusion, vesicle-dependent transport, and lateral organization relevant to signaling. The spontaneous curvature, to the best of our knowledge, is always assumed to be additive. We describe observations from simulations of unexpected nonadditive compositional curvature energetics of two lipids essential to the plasma membrane: sphingomyelin and cholesterol. A model is developed that connects molecular interactions to curvature stress, and which explains the role of local composition. Cholesterol is shown to lower the number of effective Kuhn segments of saturated acyl chains, reducing lateral pressure below the neutral surface of bending and favoring positive curvature. The effect is not observed for unsaturated (flexible) acyl chains. Likewise, hydrogen bonding between sphingomyelin lipids leads to positive curvature, but only at sufficient concentration, below which the lipid prefers negative curvature.

Figure 1

The derivative of the free energy (per unit area) with respect to curvature versus the cholesterol mole fraction.

Figure 2

(Left panel) The area compressibility modulus versus the cholesterol mole fraction from simulation. Selected points are labeled with their chain extension values $x$, as defined in the text. (Right panel) The number of independent effective polymer segments, $n_s$, versus the cholesterol mole fraction. Values for DPPC past 0.25 mole fraction cholesterol are dimmed because the Gaussian approximation for the free energy is likely no longer valid in these highly constrained environments.

Figure 3

The derivative of the free energy (per unit area) with respect to curvature. The 100% PSM point indicated by the circle (taken from a previous study [42]) was run at 321 K, while the others were run at 318 K.