Phospholipid component volumes: determination and application to bilayer structure calculations.

We present a new method for the determination of bilayer structure based on a combination of computational studies and laboratory experiments. From molecular dynamics simulations, the volumes of submolecular fragments of saturated and unsaturated phosphatidylcholines in the liquid crystalline state have been extracted with a precision not available experimentally. Constancy of component volumes, both among different lipids and as a function of membrane position for a given lipid, have been examined. The component volumes were then incorporated into the liquid crystallographic method described by Wiener and White (1992. Biophys. J. 61:434-447, and references therein) for determining the structure of a fluid-phase dioleoylphosphatidylcholine bilayer from x-ray and neutron diffraction experiments.

Molecular dynamics simulation of unsaturated lipid bilayers at low hydration: parameterization and comparison with diffraction studies.

A potential energy function for unsaturated hydrocarbons is proposed and is shown to agree well with experiment, using molecular dynamics simulations of a water/octene interface and a dioleoyl phosphatidylcholine (DOPC) bilayer. The simulation results verify most of the assumptions used in interpreting the DOPC experiments, but suggest a few that should be reconsidered. Comparisons with recent results of a simulation of a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer show that disorder is comparable, even though the temperature, hydration level, and surface area/lipid for DOPC are lower. These observations highlight the dramatic effects of unsaturation on bilayer structure.

Determination of component volumes of lipid bilayers from simulations.

An efficient method for extracting volumetric data from simulations is developed. The method is illustrated using a recent atomic-level molecular dynamics simulation of L alpha phase 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayer. Results from this simulation are obtained for the volumes of water (VW), lipid (V1), chain methylenes (V2), chain terminal methyls (V3), and lipid headgroups (VH), including separate volumes for carboxyl (Vcoo), glyceryl (Vgl), phosphoryl (VPO4), and choline (Vchol) groups. The method assumes only that each group has the same average volume regardless of its location in the bilayer, and this assumption is then tested with the current simulation. The volumes obtained agree well with the values VW and VL that have been obtained directly from experiment, as well as with the volumes VH, V2, and V3 that require certain assumptions in addition to the experimental data. This method should help to support and refine some assumptions that are necessary when interpreting experimental data.

Length scales of lipid dynamics and molecular dynamics.

Following a brief overview of length scales and system size in computer simulation, it is demonstrated that a simulation sized lipid bilayer (typically a 50 x 50 A2 patch) is in the regime where stretching dominates undulation, while the reverse holds for a flaccid macroscopic membrane. Then it is estimated that current system sizes of membrane simulations must be increased by at least a factor of 10 before thermodynamic limits are approached for quantities such as surface tension.

On simulating lipid bilayers with an applied surface tension: periodic boundary conditions and undulations.

As sketched in Fig. 1, a current molecular dynamics computer simulation of a lipid bilayer fails to capture significant features of the macroscopic system, including long wavelength undulations. Such fluctuations are intrinsically connected to the value of the macroscopic (or thermodynamic) surface tension (cf. Eqs. 1 and 9; for a related treatment, see Brochard et al., 1975, 1976). Consequently, the surface tension that might be evaluated in an MD simulation should not be expected to equal the surface tension obtained from macroscopic measurements. Put another way, the largest of the three simulations presented here contained over 16,000 atoms and required substantial computer time to complete, but modeled a system of only 36 lipids per side. From this perspective it is not surprising that the system is not at the thermodynamic limit. An important practical consequence of this effect is that simulations with fluctuating area should be carried out with a nonzero applied surface tension (gamma 0 of Fig. 2) even when the macroscopic tension is zero, or close to zero. Computer simulations at fixed surface area, which can explicitly determine pressure anisotropy at the molecular level, should ultimately lend insight into the value of gamma 0, including its dependence on lipid composition and other membrane components. As we have noted and will describe further in separate publications (Feller et al., 1996; Feller et al., manuscript in preparation), surface tensions obtained from simulations can be distorted by inadequate initial conditions and convergence, and are sensitive to potential energy functions, force truncation methods, and system size; it is not difficult, in fact, to tune terms in the potential energy function so as to yield surface tensions close to zero. This is why parameters should be tested extensively on simpler systems, for example, monolayers. The estimates of gamma 0 that we have presented here should be regarded as qualitative, and primarily underscore the assertion that the surface tension of a microscopically flat, simulation-sized patch is significantly greater than zero. As the simulation cell length increases, the surface tension that would be evaluated (or should be applied) decreases; in the limit of micrometer-sized simulation cells, gamma would approach zero or its appropriate thermodynamic value. The theories presented here also imply that the estimation of bilayer surface tension from monolayer data should take the degree of flatness into account. These conclusions are independent of the precise values of parameters such as bending constants. In conclusion, from the simulator's perspective, the question "What is the surface tension of a bilayer?" is better phrased as "What is the value of the applied surface tension necessary to simulate a particular experimental system with a given number of lipids?". As we have shown, the answer to the second question varies, but it should not be assumed a priori to equal zero.