1. Molecular Dynamics simulation of Cholesterol Maze Pattern at High Cholesterol Concentration Using Coarse-Grained Force Field Yu Mao, Xin Chen, Mohammad Alwarawrah, Jian Dai, FazleHussain and Juyang Huang Department of Physics and Astronomy, Texas Tech University, Lubbock, Texas C= C=
ABSTRACT
After initial energy minimization and equilibrium runs, simulations were performed with a 30 fs time step at the temperature of 310 K. A semi-isotropic pressure of 1 bar was maintained with a Parrinello-Rahmanbarostat. As illustrated in Figure 3, each system was first run for 10 µs. Then a temperature annealing procedure was used: The temperature was increased to 348 K for 5 µs. After that, the temperature was cooled down linearly to 310K in 2 µs, and finally a 3 µs simulation at 310 K was followed.
Temperature ( K )
348
Line Formation and Hexagonal Pattern
Figure 6 shows the distribution of number of cholesterol neighbors for a cholesterol. Majority of cholesterol molecules have two cholesterol molecules as the nearest neighbors, i.e., they have line formation. We also calculated the angel between the direction of neighbor molecules, acyl chains and the x-direction of the simulation box, as shown in Figure 7. Six peaks in each system indicates neighboring cholesterol molecules and the acyl chains having hexagonal packing.
Cholesterol and phosphatidylcholine (PC) are major components in many cell membranes. According to the Umbrella Model [1], the lateral packing of cholesterol and PC molecules in a lipid membrane with the lowest energy at the cholesterol mole fraction of 0.67 is that cholesterol and lipid acyl chains form alternating straight lines as shown in Figure 1a. However, this packing pattern has a small entropy, thus a large overall free-energy. So the equilibrium formation (i.e., the one with the lowest free-energy) is the so-called “maze pattern”, as shown in Figure 1b. The maze pattern was first predicted in a lattice model Monte Carlo simulation with a simple force-field based on the Umbrella Model [1]. The pattern has not yet been confirmed experimentally due to technical challenges. In this study, using more advanced coarse-grained Molecular Dynamics simulation with no assumption of any conceptual model, we show that cholesterol and PC molecules in deed form the predicted maze pattern. We systematically characterized the maze pattern in nano-meter scale and directly tested some essential predictions by the Umbrella model. Some cell membranes, such as lens membrane in human eye, have extremely high cholesterol content (50% - 65%). This study will help us understand the unique properties of such biomembranes.
310 10 15 17 20
Time (µs)
Figure 3. The Simulations were performed usinga temperature annealing method as shown above.
RESULTS
The Maze Pattern in Hexagonal Packing
Some researchers have proposed that cholesterol and PC molecules form hexagonal packing in a lipid bilayer, and others suggested that cholesterol and acyl chains of phospholipids form hexagonal packing. We used the maze patterns to test these hypotheses. We computed the 2D density map (averaged for3 ns) for the three systems. We consider the whole cholesterol molecule and the acyl chains of PC as the basic packing units. Figure 4 clearly shows the maze pattern for all three systems. We can conclude that the hexagonal neighbors are cholesterol molecule and acyl chains of PC. The results strongly support the assumption and prediction of the Umbrella model.
Figure 7. Distribution of angle between neighboring molecules and x-direction. The six peaks reflect hexagonal packing.
Figure 6. The distribution of number of cholesterol neighbors for a cholesterol. The peak number of 2 indicates that majority of cholesterol are in line formation.
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(b)
Figure 1. (a) The packing of cholesterol and PC acyl chains with the lowest energy. Black dots: cholesterol; white dots: PC acyl chains. (b)The predicted equilibrium packing pattern, the “maze pattern”, that has the lowest overall free-energy [1].
CONCLUSION
For the first time, without using a conceptual model, the existence of cholesterol maze pattern is confirmed by coarse-grained MD simulation with standard force field.
Our results support the hypothesis that cholesterol molecule and acyl chains of PC form a hexagonal packing in a lipid bilayer. Other packing hypotheses were ruled out.
3) This study confirmed three major predictions of the Umbrella model. The Umbrella model has become the only correct model describing key cholesterol-lipid interactions. Our result will help us to understand some unique properties of biomembranes containing high cholesterol.
METHODS
In this study, the Martini biomolecular CG model was used (Figure 2). Simulations were executed using the GROMACS simulation package version with the standard Martini v2.1 simulation settings [2, 3, 4, 5]. All simulations were built using the INSANE (INSertmembrANE) CG building tool, available at the Martini portal [6]. Each bilayer simulation (i.e., 66% Cholesterol in POPC, 66% Cholesterol in DPPC or 66% Cholesterol in DOPC ) has 440 phosphatidylcholine and 855 cholesterol molecules in each leaflet and ~43500 CG water beads, totaling over molecules. Systems were solvated with ample water ( >15 CG waters per lipid, corresponding to >60 real water molecules per lipid) [7]. In order to suppress bilayer undulations, a position restraint, with a force constant of 2 kJ mol-1 nm-2, was added to the phosphate (PO4) bead of the predominant PC lipid species on the upper leaflet with respect to the Z-direction [7].
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Figure 4. 2D density map of cholesterol and acyl chains of phospholipids clearly show the predicted maze pattern. (A) 66% cholesterol in DPPC. (B) 66% cholesterol in POPC. (C) 66% cholesterol in DOPC. Black dots: cholesterol; green dots: DPPC acyl chains; blue dots: POPC acyl chains; red dots: DOPC acyl chains.
The Umbrella Effect
Figure 5 illustrates the distributions of headgroups and acyl chains of DPPC, POPC and DOPC around cholesterol in pure PCs and PCs/66%cholesterol bilayers. The position of a headgroup was taken as the midpoint of its P−N vector and the center of mass of two acyl chains from the same PC above the double bond was used as the position of PC chains. From the figure we can see that the phosphor lipid head groups which is the polar part try to shield the non polar cholesterol molecules from water, as predicted by the Umbrella model[1].
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Martini tutorials: lipids (
H.I. Ingólfsson, M.N. Melo, F.J. van Eerden, C. Arnarez, C.A. López, T.A. Wassenaar, X. Periole, A.H. De Vries, D.P. Tieleman, S.J. Marrink. Lipid organization of the plasma membrane. JACS, 136: , 2014
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Figure 5. 2D radial distribution functions confirm the umbrella effect. (A) 66% cholesterol in DPPC. (B) 66% cholesterol in POPC. (C) 66% cholesterol in DOPC.
Figure 2. Coarse-grained Martini models of cholesterol and 3 PCs.