Bilayer Simulations

Recently, a molecular dynamics study of the phospholipid DLPE was reported by Damodaran et al. using a united atom model. The model was built from the crystal structure of DLPE reported by Elder et al. The fully hydrated DLPE bilayer has an interlamellar water layer of 5 A. The bilayer was solvated by 553 SPCE waters ( 11 water molecules/lipid) in the head group region. This lipid has a gel-to-liquid-crystalline transition temperature of 

This bilayer—water system was simulated at 315 K, well above the gel-to-liquid-crystalline phase transition temperature. An MD trajectory of 150 ps was generated and analyzed from a 50 ps equilibrated starting structure.  

The dynamics of the water molecules as analyzed by categorizing them as being bound (i.e., closely associated with the bilayer surface) and bulk according to their distance from the lipid head groups. Water molecules within 

4 A from any lipid head group atom were considered to be bound, and any water more than 4 A away from all lipid head groups was considered to be bulk. Because the bound/bulk status of waters can change during the course of a simulation, the nonbonded atom list was updated every picosecond. Of the 553 waters used in the simulation, on average there were only 160 bulk waters. The velocity autocorrelation functions (VAF), the mean square displacements (MSD), and the orientational correlational functions (OCF) for the bound and bulk waters were calculated. VAFs were calculated as  

In these equations v and r refer to the center-of-mass velocity and position and M refers to the orientation of the C2 axis of the water molecules. 

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The snapshot from a fluid bilayer simulation shown in Figure 2 reveals that the bilayer/ water interface is quite rough and broad on the scale of the diameter of a water molecule. 

Whereas the main challenge for the first bilayer simulations has been to obtain stable bilayers with properties (e.g., densities) which compare well with experiments, more and more complex problems can be tackled nowadays. For example, lipid bilayers were set up and compared in different phases (the fluid, the gel, the ripple phase) [67,68,76,81]. The formation of large pores and the structure of water in these water channels have been studied [80,81], and the forces acting on lipids which are pulled out of a membrane have been measured [82]. The bilayer systems themselves are also becoming more complex. Bilayers made of complicated amphiphiles such as unsaturated lipids have been considered [83,84]. The effect of adding cholesterol has been investigated [85,86]. An increasing number of studies are concerned with the important complex of hpid/protein interactions [87-89] and, in particular, with the structure of ion channels [90-92]. 

Trent JO, Wang ZX, Murray JL, Shao W, Tamamura H, et al. 2003. Lipid bilayer simulations of CXCR4 with inverse agonists and weak partial agonists. J Biol Chem 278(47) 47136-47144. 

Sands, Z.A., Sansom, M.S. How does a voltage sensor interact with a lipid bilayer Simulations of a potassium channel domain. Structure 2007,15, 235-44. 

Notman, R., den Otter, W.K., Noro, M.G., Briels, W.J., Anwar, J. The permeability enhancing mechanism of DMSO in ceramide bilayers simulated by molecular dynamics. Biophys. J. 2007,93, 2056-68. 

Density profile for water, trehalose, and phospholipid headgroups (nitrogen and phosphorous) for a fully hydrated DPPC bilayer. Simulations at 50°C indicate that trehalose concentration is higher near phospholipid head groups than in the bulk (FaUer et al., 2003). The concentration of trehalose in the aqueous phase is 4% by weight. 

Fig. 33. Directions of the principal axes of the l3C chemical shift tensor of the C=0 group, helical axis, and static magnetic field, B0, and 13C NMR spectral patterns of the C=0 carbons corresponding to the orientation of the a-helix with respect to the surface of the magnetically oriented lipid bilayers. Simulated spectra were calculated using 5, =241 ppm, 22 =189 ppm, and < 33 =96 ppm for the rigid case (a), rotation about the helical axis (slow MAS) (b), fast MAS (c), magnetic orientation parallel to the magnetic field (d), an angle 8 with the magnetic field (e), and the direction perpendicular to the magnetic field (f).11 Reproduced with permission from the Biophysical Society.

Watanabe and Klein have reported MD simulations of the hexagonal mesophase of sodium octanoate in water with hexagonal symmetry. The singlet (i.e., one atom) probability distribution functions of the carbon atoms on the hydrocarbon chains show close similarity to those in the micelle. The dynamics of water molecules close to the head groups shows lower mean square displacements, and their orientational correlation function decays more slowly than those of waters farther from the head groups, as was seen in a recent bilayer simulation.6 ... 

Stern, H.A., Feller, S.E. Calculation of the dielectric permittivity profile for a nonuniform system Application to a lipid bilayer simulation. J. Chem. Phys. 2003,118,3401-12. 

Once the computer resources advanced far enough to allow their atomic-level simulation, few interfacial phenomena have attracted more attention from researches in the field of molecular modeling as the transport of small molecules in lipid bilayers. Simulation of unassisted transport of water (11) and ions (12) study of energetic and structural effects... 

In the case of lipid bilayer simulation, it is just necessary to build a bilayer from the left side to the right side of the box. With the PBC convention, the images of the bilayer included in the eentral box will ensure continuity through the different boxes (see Figure 9.8). 

Brandt EG, Edholm O (2010) Stretched exponential dynamics in lipid bilayer simulations. J Chem Phys 133 115101... 

Brandt EG, Braun AR, Sachs JN, Nagle JF, Edholm O (2011) Interpretation of fluctuation spectra in lipid bilayer simulations. Biophys J 100 2104-2111... 

Wang ZJ, Desemo M (2010) A systematically coarse-grained solvent-free model for quantitative phospholipid bilayer simulation. J Phys Chem B 114(34) 11207-11220... 

This is the main argument to use a surface tension of zero in bilayer simulations. Volume changes in lipid-water systems are minimal, even across the liquid-crystalline/gel phase transition and the number of water and lipid molecules remains constant. 

The early simulations of bilayer systems with explicit solvent provided a wealth of information and in a way defined a set of standard analyses for lipid bilayer simulations. Since the position of all atoms is known at any time during the simulation, it is simple to extract density profiles for different atoms or molecules. Electron density profiles can be compared with data from X-ray diffraction and nuclear density profiles with neutron diffraction, giving a first indication of the correcmess of the distribution of atoms. A convenient framework to discuss the overall structure of the lipid bilayer is the four-region model (Figure 3) proposed by Marrink et al. ... 

Looking back at the work done on lipid bilayer simulations it is clear that substantial progress has been made since the mid-1980s. At the same time, the limitations of the current simulations are becoming more obvious. Innovation can be expected in many aspects of lipid bilayer simulation, and we will mention a few. 

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