Density functional theory approach for coarse-grained lipid bilayers.

Lipid bilayers are important inhomogeneous fluid systems that mediate the environment of cells and the interaction of cells with their environment. A variety of approaches have been taken to model the lipid molecules in bilayers, from all atom molecular dynamics to rigid body liquid crystals. In this paper we discuss the application of a density functional theory approach that treats the lipid molecules at the coarse-grained level of a freely jointed chain. This approach allows for compressibility effects, and can therefore be used to study not only the long range structure in lipid bilayers, but also the nanoscale structure induced in the bilayer when the lipids crystallize or when an inclusion (e.g., an embedded protein) is present. This paper presents a detailed analysis of fluid bilayers and lamellae predicted by the theory. In particular we locate solutions with zero surface tension. We calculate the phase diagram for all possible phases with planar symmetry, including uniform macrophases. Surprisingly, we find a first-order phase transition from the lamellar phase to an isolated bilayer phase on lowering the temperature. This transition appears to be driven by solvent packing effects. A further lowering of the temperature leads to a set of highly ordered bilayers.

Comparison of density functional theory and simulation of fluid bilayers.

We compare results of classical density functional theory (DFT) to molecular dynamics (MD) simulations of coarse-grained models of lipids in solvent. We find that the DFT captures the liquid structure of coarse-grained lipids both near surfaces and in bilayers adequately. In contrast we find that the MD simulations do not predict ordering in bilayers as is observed in low temperature DFT calculations. The mechanical properties of the fluid DFT bilayers are qualitatively similar to those of the MD bilayers; in particular the shapes of the lateral stress profiles are similar. Values of the area compressibility modulus are in reasonable agreement with previous work on coarse-grained lipids.

Toward Quantitative Coarse-Grained Models of Lipids with Fluids Density Functional Theory.

We describe methods to determine optimal coarse-grained models of lipid bilayers for use in fluids density functional theory (fluids-DFT) calculations. Both coarse-grained lipid architecture and optimal parametrizations of the models based on experimental measures are discussed in the context of dipalmitoylphosphatidylcholine (DPPC) lipid bilayers in water. The calculations are based on a combination of the modified-iSAFT theory for bonded systems and an accurate fundamental measures theory (FMT) for hard sphere reference fluids. We furthermore discuss a novel approach for pressure control in the fluids-DFT calculations that facilitates both partitioning studies and zero tension control for the bilayer studies. A detailed discussion of the numerical implementations for both solvers and pressure control capabilities are provided. We show that it is possible to develop a coarse-grained lipid bilayer model that is consistent with experimental properties (thickness and area per lipid) of DPPC provided that the coarse-graining is not too extreme. As a final test of the model, we find that the predicted area compressibility moduli and lateral pressure profiles of the optimized models are in reasonable agreement with prior results.

Computational investigations of pore forming peptide assemblies in lipid bilayers.

This Letter presents the first application of a three-dimensional numerical molecular theory based modeling approach to study the structure and energetics of assemblies of peptides embedded in lipid bilayers. Coarse-grained models were used for both the peptides and lipids. Both barrel-stave and toroidal pore morphologies for the lipids near the peptide assemblies are found, but at different assembly sizes. The free energy of the assembly is found to have a global free energy minimum for a solution with a membrane-spanning toroidal pore. A pairwise approximation to this free energy is found to underpredict the free energy minimum associated with the membrane-spanning pores.

Alcohols reduce lateral membrane pressures: predictions from molecular theory.

We explore the effects of alcohols on fluid lipid bilayers using a molecular theory with a coarse-grained model. We show that the trends predicted from the theory in the changes in area per lipid, alcohol concentration in the bilayer, and area compressibility modulus, as a function of alcohol chain length and of the alcohol concentration in the solvent far from the bilayer, follow those found experimentally. We then use the theory to study the effect of added alcohol on the lateral pressure profile across the membrane, and find that added alcohol reduces the surface tensions at both the headgroup/solvent and headgroup/tailgroup interfaces, as well as the lateral pressures in the headgroup and tailgroup regions. These changes in lateral pressures could affect the conformations of membrane proteins, providing a nonspecific mechanism for the biological effects of alcohols on cells.