(57a) Mode Specific Elastic Constants and the Effects of Curvature On the Binding of Lipid Chain Anchors to DPPC/DOPC/Cholesterol Model Lipid Bilayers

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 constants for gel, liquid-ordered (lo), and liquid-disordered (ld) phases.  By proper expansion of the free energy, the molecular theory enables us to determine the effects of the mode of membrane bending deformation on the value of the elastic constants for different phases. In particular, we refer to the ability of the molecules to arrange the composition between the two monolayers upon deformation. 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 k_bT in the ld phase to as high as 200 k_bT in the lo phase.  These results show that one must strongly consider the mode of deformation in determining the mechanical properties of lipid bilayers, as has been shown in previous work by several authors.

We also calculate 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 in both liquid-ordered and liquid-disordered phases, we are able to calculate the equilibrium binding concentrations of lipid tail anchors as a function of membrane curvature, concentration of lipids, and solution environment.  Our results are in excellent agreement with recent experiments [N. S. Hatzakis et. al., Nature Chem. Bio., 5, 835, 2009].