Solvent-Free, Highly Coarse-Grained Models for Charged Lipid Systems

Abstract

We present a methodology to develop coarse-grained lipid models such that electrostatic interactions between the coarse-grained sites can be derived accurately from an all-atom molecular dynamics trajectory and expressed as an effective pairwise electrostatic potential with appropriate screening functions. The reference nonbonded forces from the all-atom trajectory are decomposed into separate electrostatic and van der Waals (vdW) forces, based on the multiscale coarse-graining method. The coarse-grained electrostatic potential is assumed to be a general function of unknown variables and the final site-site interactions are obtained variationally, where the residual of the electrostatic forces from the assumed field is minimized. The resulting electrostatic interactions are fitted to screened electrostatics functions, with a special treatment for distance-dependent dielectrics and screened dipole-dipole interactions. The vdW interactions are derived separately. The resulting charged hybrid coarse-graining method is applied to various solvent-free three-site models of anionic lipid systems.

Figure 1

Flowchart showing the steps involved in the charged hybrid coarse-grained (cHCG) modeling protocol.

Figure 2

Three-site cHCG models of (a) DOPC, (b) DOPS, and (c) PIP₃ lipid molecules in this study.

Figure 3

Pairwise effective (electrostatic and vdW) interactions using the cHCG method between the headgroup sites in a 1:1 DOPC:DOPS system: (a) PC–PC effective electrostatic interactions, (b) PC–PS effective electrostatic interactions, (c) PS–PS effective electrostatic interactions, and (d) nonbonded vdW interactions between the head groups sites in 1:1 DOPC:DOPS system (error bar is on the order of 0.1–0.2 kcal/mol).

Figure 4

(a) z-density profile for 1:1 DOPC:DOPS three CG sites from the atomistic simulation (black) and the CG simulation (red). (b) The accumulated average number of lipids in one of the membrane leaflets with total 5000 lipids. The figure shows the lateral organization of the lipids for 1:1 DOPC:DOPS and 3:1 DOPS system. The y-axis denotes the number of lipids around a central lipid and the results indicate almost perfect mixing. The dashed black line overlaps the black line (complete mixing), and the blue and red lines (1:1 systems) also overlap, since PC and PS lipids have almost identical lateral organization.

Figure 5

Fluctuations in area per lipid with time in CG simulations with the 1:1 DOPC:DOPS cHCG model. The average area per lipid is shown as dashed lines, and the compressibility modulus is calculated using the average area per lipid and its fluctuations.

Figure 6

MSD of DOPC:DOPS bilayer system with 5000 lipids calculated using center of mass diffusion. The MSD for 1:1 DOPC:DOPS is denoted in black, and the MSD for 3:1 DOPC:DOPS is shown in red.

Figure 7

(a) Lateral pressure profile for the 1:1 DOPC:DOPS bilayer system with 5000 lipids. (b) Surface tension evolution with time for the same system.

Figure 8

Snapshots of the CG simulations on a vesicle with 1:1 DOPC:DOPS composition (the vesicle size is ∼40 nm diameter (∼20 000 lipids) and simulated for 100 ns): (a) initial system with a cross-section across the center; (b) the configuration after 5 ns; (c) cross-sectional view after ∼50 ns; and (d) final converged simulation after the length of the simulation. The test was performed to examine the resilience of the model to high-curvature systems.

Figure 9

Snapshot of CG simulations on tubule with ∼40 000 lipids and simulated for 150 ns: (a) initial configuration showing the front view; (b) initial configuration showing the top view; (c) snapshot after 20 ns, showing the closing in of the open-end tops; and (d) fully converged sphere after 150 ns of simulation time.

Figure 10

(a) PH-domain protein with CG sites in black and dipole moment vectors on CG sites shown as small arrows; the overall dipole orientation of the protein is shown with the long gray arrow. (b) PIP₃ lipid, with the arrow depicting the headgroup dipole orientation (the headgroup orientation is defined as in ref (77)). (c) Snapshots of CG simulation of PH domain on DOPC:DOPS–PIP₃ membrane. The protein CG sites are shown in gray; the DOPC, DOPS, and PIP₃ headgroup sites on the top leaflet are shown in blue, red, and green, respectively. The orange arrow indicates the dipole vector direction on the PIP₃ headgroup as defined in ref (75).

Figure 11

(a) Distribution of the PIP₃ lipid dipole angle in the native bilayer environment on the bottom leaflet. (b) Time evolution of the angle between the protein and PIP₃ dipole vectors on the top leaflet.