Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites

Abstract

Despite the central role of lipids in many biophysical functions, the molecular mechanisms that dictate macroscopic lipid behavior remain elusive to both experimental and computational approaches. As such, there has been much interest in the development of low-resolution, implicit-solvent coarse-grained (CG) models to dynamically simulate biologically relevant spatiotemporal scales with molecular fidelity. However, in the absence of solvent, a key challenge for CG models is to faithfully emulate solvent-mediated forces, which include both hydrophilic and hydrophobic interactions that drive lipid aggregation and self-assembly. In this work, we provide a new methodological framework to incorporate semiexplicit solvent effects through the use of virtual CG particles, which represent structural features of the solvent-lipid interface. To do so, we leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to construct our virtual-site CG (VCG) models. As a proof-of-concept, we focus our efforts on two lipid species, 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl- sn-glycero-3-phosphocholine (DPPC), which adopt a liquid-disordered and gel phase, respectively, at room temperature. Through our analysis, we also present, to our knowledge, the first direct comparison between the MS-CG and REM methods for a complex biomolecule and highlight each of their strengths and weaknesses. We further demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings suggest that the VCG framework is a powerful approach for investigation into macromolecular biophysics.

Figure 1

Schematic of the coarse-grained mapping procedure for DOPC and DPPC. (a) The CG model consists of six sites that together represent all lipid atoms, while the virtual SL site represents local structural features of solvent near lipid head groups. (b) The red path indicates conventional implicit-solvent CG mapping procedures, while the green path indicates the procedure used in this work: water is first mapped to single-site particles and used to construct virtual SL sites. Explicit details on mapping can be found in Table S1 and Figure S1.

Figure 2

Radial distribution function (RDF) for coarse-grained single-site water around lipid HG (i.e., headgroup) sites. The dashed line indicates the radial distance cutoff that is used to construct the virtual SL sites. The inset shows a representative snapshot of water coordinating between two lipid phosphate groups through hydrogen bonding interactions, which corresponds to the first peak of the RDF.

Figure 3

Flowchart depicting the parametrization strategy used to construct each of the coarse-grained lipid models, which rely on two variational methods: multiscale coarse-graining (MS-CG) and relative entropy minimization (REM). The right block shows the REM optimization subprocedure based on Newton–Raphson minimization, in which a two-part strategy is adopted: initially, stochastically chosen subsets of parameters are refined for each iteration, followed by refinement of all parameters at each iteration.

Figure 4

Coarse-grained DOPC interactions. (a) Comparison between seven-site (DOPC-7V) and six-site (DOPC-6) pair potentials for a representative subset of all nonbonded interactions. Models generated using multiscale coarse-graining (MS-CG) and relative entropy minimization (REM) are also denoted by solid and dashed lines, respectively, yielding a total of four different models. Note the emergence of the SL-MG attraction in the DOPC-7V model, which appears to mediate MG-MG attraction (i.e., to maintain surface tension). (b) Bond and angle potentials were computed using MS-CG in the DOPC-7V case (solid) and DOPC-6 case (diamond symbols). For simplicity, the DOPC-6 bonded potentials were used for the two REM models.

Figure 5

Comparison of structural correlations in coarse-grained DOPC lipid bilayers between mapped all-atom trajectories, multiscale coarse-graining models (MS-CG), and relative entropy minimization (REM) models; here, both DOPC-7V (solid lines) and DOPC-6 (dashed lines) models are shown. The left and right panels are lateral (i.e., xy-direction) and perpendicular (i.e., z-direction) number density profiles between the listed sites. Each of the profiles was averaged over both leaflets and used a bin size of 0.01 nm.

Figure 6

Molecular snapshots of self-assembled MSCG-7V for DOPC starting from random configurations at the listed concentrations with colors consistent with Figure 1(a). As concentration increases, the DOPC-7V model adopts morphologies that range between vesicles, tubules, bilayers, and tubule networks. The top row of panels depicts interiors of the same configurations shown in the bottom row of panels through the use of a clipping plane.

Figure 7

Coarse-grained DPPC interactions. (a) Comparison between seven-site (DPPC-7V) and six-site (DPPC-6) pair potentials for a representative subset of all nonbonded interactions. Models generated using multiscale coarse-graining (MS-CG) and relative entropy minimization (REM) are also denoted by solid and dashed lines, respectively, yielding a total of four different models. Similar to the DOPC-7V case, note the emergence of the SL-MG attraction, which appears to mediate MG-MG attraction for lipid aggregation. (b) Bond and angle potentials were computed using MS-CG in the DPPC-7V case (solid) and DPPC-6 case (diamond symbols). For simplicity, the DPPC-6 bonded potentials were used for the two REM models.

Figure 8

Comparison of structural correlations in coarse-grained DPPC lipid bilayers between mapped all-atom trajectories, multiscale coarse-graining models (MS-CG), and relative entropy minimization (REM) models; here, only DPPC-7V results are shown. The left and right panels are lateral (i.e., xy-direction) and perpendicular (i.e., z-direction) number density profiles between the listed sites. Each of the profiles was averaged over both leaflets and used a bin size of 0.01 nm.

Figure 9

(a) Lateral view snapshots of DPPC-7V from the mapped all-atom (AA) configuration, the MSCG-7V model, and the REM-7V model. Colors are consistent with Figure 1. (b) Comparison of amplitudes from the fast Fourier transform of the bilayer surface morphologies (taken with reference to the MG bead [red] height) generated by each model.