Molecular dynamics simulations of DPPC bilayers using "LIME", a new coarse-grained model

Abstract

A new intermediate resolution model for phospholipids, LIME, designed for use with discontinuous molecular dynamics (DMD) simulations is presented. The implicit-solvent model was developed using a multiscale modeling approach in which the geometric and energetic parameters are obtained by collecting data from atomistic simulations of a system composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecules and explicit water. In the model, 14 coarse-grained sites that are classified as 1 of 6 types represent DPPC. DMD simulations performed on a random solution of DPPC resulted in the formation of a defect-free bilayer in less than 4 h. The bilayer formed quantitatively reproduces the main structural properties (e.g., area per lipid, bilayer thickness, bond order parameters) that are observed experimentally. In addition, the bilayer transitions from a liquid-crystalline phase to a tilted gel phase when the temperature is reduced. Transbilayer movement of a lipid from the bottom leaflet to the top leaflet is observed when the temperature is increased.

Figure 1

(a) United atom and (b) coarse-grained representation of DPPC. The color scheme is; purple (choline entity – type I for site 1); yellow (phosphate group – type II for site 2); red (ester group – type III for site 3); orange (ester group – type IV for site 9); cyan (alkyl tail groups – type V for sites 4–7 & 10–13); green (terminal tail groups – type VI for sites 8&14). The coarsegrained site size does not represent the actual size of each site.

Figure 2

A schematic of the approach used to calculate the LIME interaction energies for two coarse-grained types: (a) the radial distribution function is calculated (b) the one-step Boltzmann inversion scheme is used to calculate the potential of mean force by inverting the RDF; ε is chosen as the minimum U(r) value (blue line); the depth of the square well potential or the interaction energy is assigned the ε value (red line)

Figure 3

A radial distribution function for sites 1 & 1 obtained during a LIME simulation. The first non-zero value is located at the hard sphere diameter (4.75 Å) and the small discontinuity is located at the square-well width (12.55 Å). The shape of the radial distribution function differs significantly from the shape of a distribution function associated with a more traditional Lennard Jones potential.

Figure 4

(a) The intermolecular radial distribution functions, hard-sphere diameters (σ_HS) and square-well diameters (λ) for coarse-grained types 1 & 1, 1 & 2, and 5 & 5.

Figure 5

The intramolecular bond distribution functions, minimum bond lengths (σ_MIN) and maximum bond lengths (σ_MAX) for coarse-grained types 1 & 2, 3 & 5, and 5 & 6

Figure 6

Snapshots of the areal view of a DPPC bilayer formed from 256 lipids in a box with dimensions of 100Å × 100Å × 100Å (a) and in a box with dimensions of 90Å × 90Å × 90Å (b)

Figure 7

Snapshots from a simulation of DPPC spontaneous bilayer formation. The figures were created with VMD.[] The color scheme is: purple (choline entity – type I); orange (phosphate group – type II); red (ester groups – type III and type IV); cyan (alkyl tail groups – type V and type VI). (a) – (f) = 0, 15, 50, 100, 125 and 150 million collisions, respectively. The system is started from a random configuration (a) and aggregates in only 50 million collisions (d). An additional 100 million collisions are required for the aggregate to adopt the conformation of a defect-free bilayer (h).

Figure 8

Comparison of the orientational bond order parameter S_BOND for intra-molecular bonds in LIME/DMD (green line) and GROMACS simulations (blue line) versus the bond number: the latter is defined in the inset.

Figure 9

Snapshots of a lipid bilayer in DMD/LIME as the system temperature is cooled from (a) a liquid-crystalline phase at T* = 0.77, (b) a tilted gel phase at T* = 0.30 and (c) a cross-tilted gel phase which is only observed in some simulations. The snapshots were generated in VMD.[]

Figure 10

Snapshots of a lipid (spherical representation) as it flips from the bottom leaflet of a bilayer to the top leaflet. The tail beads of the lipid that flips are highlighted in yellow and the head beads are highlighted in lime. The images were created with VMD. (a) – (c) = 866, 883, 885 million collisions, respectively.

Figure 11

Mass density distribution of coarse-grained sites in DMD/LIME simulations (dotted lines) and GROMACS simulations (solid lines) versus the distance from the bilayer center (z = 0 Å).