Calculating Elastic Constants and the Effects of Curvature on the Binding of Lipid Chain Anchors to DPPC/DOPC/Cholesterol Model Lipid Bilayers

Abstract

Using a theoretical model of a bilayer membrane containing cholesterol, dipalmitoyl-phophatidylcholine (DPPC), and dioleoylphosphatidylcholine (DOPC) that qualitatively reproduces phase diagrams of giant unilaminar vesicles (GUVs) of the same three components [R. Elliott, I. Szleifer, and M. Schick, Phys. Rev. Lett., 96, p.098101 (2006)], we calculate the bending and saddle-splay force constants in Gel, liquid-ordered (lo), and liquid-disordered (ld) phases. The molecular theory employed in our study allows us to determine the effects of the mode of membrane bending deformation on the value of the elastic constants for different phases. The effect of “blocked” vs “free” exchange of lipids across the two monolayers on the values of the bending constant is as high as 50 kbT in the ld phase to as high as 200 kbT in the lo phase. These results show that one must strongly consider the mode of deformation in regard to the mechanical properties of lipid bilayers. For example, if cholesterol is allowed to flip-flop and the other lipid species are “blocked”, then the bending elastic constant is 20-40 kbT larger then the case where all of the lipid species are allowed to be exchanged from leaflet to leaflet.We will also present results on how the curvature of lipid vesicles determines the amount of binding of molecules with lipid tail anchors. By explicitly determining the chemical potential difference of species across a curved bilayer under different modes of deformation, we are able to calculate the equilibrium binding concentrations of lipid tail anchors as a function of membrane curvature, concentration of lipids, and local electrostatic environment.