Spontaneous Curvature, Differential Stress, and Bending Modulus of Asymmetric Lipid Membranes

Abstract

On time scales shorter than lipid flip-flop time, lipid bilayers in cells assume asymmetric non-equilibrium steady states in which the physical characteristics of the two leaflets are different. The most notable difference is in lipid composition, but it can also involve different lateral stresses in each leaflet that add up to an overall (usually vanishing) tension. We explore the interplay between these two sources of asymmetry using theoretical modeling and coarse-grained simulation. By minimizing total elastic energy, we find a preferred spontaneous curvature that balances torques between bending moments and differential stress, which can at times lead to unexpected consequences. For example, compositionally asymmetric flat bilayers whose area per lipid in each leaflet is matched with corresponding symmetric tensionless flat bilayers, still exhibit residual differential stress, demonstrating that the conditions of zero area strain and zero bending moment are not identical. Furthermore, we observe that the bending modulus can significantly increase if differential stress exceeds a certain minimum threshold, but that compositional asymmetry alone cannot cause this. We attribute this effect to a stiffening in the compressed leaflet, which seems to be related to its gel transition, but not exactly coinciding with it. Finally, we show that the presence of rapidly flip-flopping lipid species (such as cholesterol) will not necessarily lead to total elimination of differential stress, but may in fact even induce it, depending on whether the partitioning energy prefers one leaflet over the other.