Mode specific elastic constants for the gel, liquid-ordered, and liquid-disordered phases of DPPC/DOPC/cholesterol model lipid bilayers

Abstract

Using a microscopic molecular theory, we determine the bending and saddle-splay constants of three-component lipid bilayers. The membrane contains cholesterol, dipalmitoyl-phophatidylcholine (DPPC), and dioleoylphosphatidylcholine (DOPC) and the predictions of the theory have been shown to qualitatively reproduce phase diagrams of giant unilamellar vesicles (GUVs) of the same three components. The bending and saddle-splay constants were calculated 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 bending and saddle-splay constants obtained from the free energy expansion can be expressed in terms of moments of the local lateral pressures and their derivatives all evaluated for a symmetric planar bilayer. 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 determining the mechanical properties of lipid bilayers. We discuss how the different contributions to the lateral pressures affect the values of the elastic constants including the effects of cholesterol concentration and temperature on the membrane elastic constants. We also calculate the equilibrium binding concentrations of lipid tail anchors as a function of membrane curvature by explicitly determining the chemical potential difference of species across a curved bilayer. Our results are in excellent agreement with recent experimental results.

Introductory Lecture: Basic quantities in model biomembranes

“…It is well recognized, as evidenced in papers at this Discussion , 3–8 that the bending modulus K C is a most important quantity for describing the flexibility of membranes at a mesoscopic, supramolecular level. Other material quantities are the Gaussian curvature modulus K G , 7,8 important for membrane fusion, 9 and the isothermal area compressibility modulus K A .…”

“…Other material quantities are the Gaussian curvature modulus K G , 7,8 important for membrane fusion, 9 and the isothermal area compressibility modulus K A . 10 Nevertheless, the centrality of the bending modulus is indicated, in the case of the Gaussian curvature, by the fact that it is the ratio K G / K C that is usually reported rather than K G alone, and the compressibility modulus K A is also often closely related to K C ( vide infra ).…”

“…Even the relatively biologically irrelevant, but physically interesting, gel phase continues to play a role in that the phase transition into the fluid phase is an easy measure of the effect of additives 90 and this phase is a valuable testing ground for techniques. 8,47 The hexagonal II phase 83 and the cubic phase 6 are used in discussing membrane fusion. 97,98 Other structures, such as tubules 3,51 or fibers, 96 are relevant biologically in that membranes undergo morphological transformation required for cell function.…”

Membrane Curvature and Lipid Composition Synergize To Regulate N-Ras Anchor Recruitment

“…The equilibrium state of a given system is calculated through functional minimization with respect to the system's free variables, and is represented by the system's thermodynamic free energy (34,35). There is only one free parameter in the model.…”

Phospholipid/cholesterol/decanethiol mixtures for direct assembly of immunosensing interfaces

“…A binary mixture of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC)/cholesterol (Chol) (70:30) was employed. The phase diagram for this mixture shows that at the lipid molar proportions used the system is in the liquid ordered phase [20][21][22][23], which presents high mechanical resistance [24] and molecular packing but at the same time is fluid. This fluidity will not only allow for the proper functional dynamics of the biosensing proteins but also facilitate the formation of a planar and continuous lipid bilayer from lipid vesicles.…”