Multiscale simulation of ternary stratum corneum lipid mixtures: Effects of cholesterol composition

Abstract

Molecular dynamics simulations of mixtures of the ceramide N-(tetracosanoyl)-sphingosine (NS), cholesterol, and a free fatty acid are performed to gain a molecular-level understanding of the structure of the lipids found in the stratum corneum layer of skin. A new coarse-grained force field for cholesterol was developed using the multistate iterative Boltzmann inversion method (MS-IBI). The coarse-grained cholesterol force field is compatible with previously developed coarse-grained force fields for ceramide NS, free fatty acids, and water, and validated against atomistic simulations of these lipids using the CHARMM force field. Self-assembly simulations of multilayer structures using these coarse-grained force fields are performed, revealing that a large fraction of the ceramides adopt extended conformations, which cannot occur in the single bilayer in water structures typically studied using molecular simulation. Cholesterol fluidizes the membrane by promoting packing defects and an increase in cholesterol content is found to reduce the bilayer thickness, due to an increase in interdigitation of the C₂₄ lipid tails, consistent with experimental observations. Using a reverse-mapping procedure, a self-assembled coarse-grained multilayer system is used to construct an equivalent structure with atomistic resolution. Simulations of this atomistic structure are found to closely agree with experimentally derived neutron scattering length density profiles. Significant interlayer hydrogen bonding is observed in the inner layers of the atomistic multilayer structure that are not found in the outer layers in contact with water or in equivalent bilayer structures. This work highlights the importance of simulating multilayer structures, as compared to the more commonly studied bilayer systems, to enable more appropriate comparisons with multilayer experimental membranes. These results also provide validation of the efficacy of the coarse-grained force fields and the framework for multiscale simulation.

Graphical Abstract

Introduction

The visible, outermost skin layer, called the stratum corneum (SC), is essential for skin’s role as a barrier to water loss from the body and invasion of toxic chemicals and infectious agents into the body. The SC is organized into a brick-and-mortar like arrangement in which corneocytes (the bricks) are surrounded by a dense, lamellar-structured lipid matrix (the mortar). This lipid matrix is a complex mixture of ceramides (CERs), cholesterol (CHOL), and free fatty acids (FFAs), with a distribution of carbon chain lengths in both the CERs and FFAs. CERs are two-tailed lipids in which a fatty acid chain is connected by an amide bond to a sphingoid base. At least 22 different subclasses of CERs have been identified in human SC with those combining a nonhydroxy (N) or alpha hydroxy (A) fatty acid chain with either a 6-hydroxy-sphingosine (H) or phytosphingosine (P) chain, designated as CERs NH, NP, AH, and AP,¹ being most common.^2–4 The structure and composition of this lipid matrix are crucial for a properly functioning skin barrier.⁵ Small angle X-ray diffraction (SAXD) studies of healthy human SC reveal two coexisting crystalline lamellar phases with repeat distances of ~13 nm for the long periodicity phase (LPP) and ~6 nm for the short-periodicity phase (SPP).^6,7 Compared with healthy skin, the SC lipids in many skin diseases, such as psoriasis and atopic dermatitis, exhibit altered compositions, abnormal lamellar arrangements, and an impaired skin barrier.^5,8–10

Various experimental models with well-defined compositions of a limited number of lipid molecules have been used to study the relationships between SC lipid composition, structure and barrier function.^11–16 Compositions of the experimental synthetic lipid model that has been studied most, called the SC substitute (SCS), are based on porcine SC lipids, in which CER nonhydroxy sphingosine (CER NS) is the most abundant CER. One of these, which forms the SPP without the LPP (SCS_SPP), can closely mimic the phase behavior and lateral organization of the SPP in human SC.^17–19 This SCS_SPP mixture contains five CERs (NS C₂₄, NP C₂₄, AS C₂₄, and AP C₂₄ and C₁₆, where C₂₄ and C₁₆ designate fatty acid chain lengths of 24 and 16 carbons, respectively), although predominantly (60 mole %) CER NS C₂₄, combined with equimolar amounts of CHOL and a mixture of FFAs with tail lengths ranging from C₁₆-C₂₆.^17,18 Even simpler mixtures containing as few as three components (CER NS C₂₄, CHOL, and FFA C₂₄), can mimic characteristic behaviors of the SCS_SPP.^20,21 For example, the lamellar repeat distance of the equimolar version of this three-component mixture, identified here as the SCS_SPP,min is the same (5.4 nm) as observed for the SCS_SPP.^17,22

Several insights into the formation and structure of the SPP as well as the role of CHOL specifically have been derived from studies of these synthetic lipid mixtures. For instance, using SAXD and Fourier Transform Infrared (FTIR) spectroscopy of SCS_SPP samples prepared with varying amounts of CHOL, Mojumdar et al.¹⁹ observed that (i) CHOL is required to form the SPP and to enhance formation of the dense orthorhombic lateral packing, (ii) phase separated crystalline CHOL is present, and (iii) the repeat distance for the SPP is constant for CHOL/CER mole ratios between 0.2 and 1. Likewise, in comparisons of SCS_SPP,min mixtures prepared with CER:CHOL:FFA mole ratios of 1:0.45:1 and 1:1:1, the repeat distances were the same, and phase separated CHOL was only detected in the high CHOL mixture.^20,21 In neutron diffraction studies of the SCS_SPP formulated with selectively deuterated molecules, CERs were determined to be arranged symmetrically, the CHOL headgroups were found to lie slightly inward from the unit cell boundary, and the FFA headgroups were located at the unit cell boundary with the tips of their tails interdigitating in the unit cell center.¹⁹ Using FTIR and selectively deuterated molecules in the SCS_SPP,min mixture, Skolova et al.²⁰ identified the presence of fully extended CER with its sphingosine and fatty acid tails associated preferentially with CHOL and FFA, respectively.

Experimental identification of lamellar and lateral lipid arrangements and molecular organization for even these simplified lipid systems is difficult, time consuming and costly. Increasingly, researchers have turned to molecular dynamics (MD) simulations as a useful tool for analyzing membrane properties at the atomistic level, and for relating microscopic details of the system with macroscopic properties observed in experiments. For example, in simulations of bilayers containing an equimolar mixture of CER NS C₂₄ and FFA C₂₄, both Das et al.²³ and Gupta et al.²⁴ observed a decrease in bilayer thickness with a corresponding increase in interdigitation of FFA and CER’s fatty acid tails when CHOL was added. Adding CHOL also increased the area compressibility indicating a more rigid bilayer,^23,24 while decreasing lipid tail order as indicated by a decrease in the nematic order parameter, which decreased further when FFA was reduced by half.²⁴ Schmitt et al. examined mixtures of CER NS C24, CER AP C24, CHOL and FFA C24 in 0.67:0.33:0.7:1 and 0.33:0.67:0.7:1 ratios using both experimental neutron scattering as well as atomistic molecular dynamics simulations.²⁵ The simulations revealed trends in the lipid tilt angle and axial position, which matched experimental results. In simulations of an equimolar mixture of CER NS C₂₄, CHOL and FFA C₂₄, Gupta et al.²⁴ found that CER hydrogen bonds with both other CERs and other lipids, while CHOL only hydrogen bonds with CERs and FFAs. In a related system, Moore et al.²⁶ found that increasing CHOL content in bilayers of CER NS C₂₄ and CHOL increased interdigitation, with a corresponding decrease in bilayer thickness and increased density in the center of the tail region, and resulted in fewer hydrogen bonds between lipids. Adding FFA C₂₄ to the equimolar CER NS C₂₄:CHOL system increased the bilayer thickness with a further decrease in the number of hydrogen bonds. Moore et al. also measured the in-plane lipid-lipid coordination number, a measure of the number of molecules within the first coordination shell (i.e. nearest neighbors). FFA molecules in bilayers containing equimolar CER NS C₂₄, CHOL and FFA C₂₄ were observed to have a higher in-plane lipid-lipid coordination number (2.3) with other FFA tails than for the randomly mixed system (1.5), suggesting that FFA molecules prefer to neighbor other FFA molecules.²⁶ In a study of high and low hydration (30 compared with 2 water molecules per lipid) of CER NS C₂₄, CHOL, and FFA C₂₄ bilayers with 1:1:1 and 1:1:0.5 mole ratios, Del Regno and Notman²⁷ observed formation of CHOL-rich regions, which were absent in the low hydration systems where water formed disconnected flattened pools in the headgroup region.

The simulation results described above illustrate the power of this tool for studying SC lipids. However, MD simulations of atomistic models, which calculate interactions between all atoms in the system, have a high computational cost that limits the size and timescales that can be reasonably studied. In addition, lipid mobility in the rigid gel-phase organization of the SC lamellae requires much longer simulation times to reach equilibrium than in more commonly studied fluid-phase membranes. As a consequence, almost all atomistic simulations thus far have used preassembled membrane configurations, rather than self-assembling membranes from isotropic mixtures, and, unless careful equilibration procedures are used, the final configuration of the simulation may not be able to adequately decorrelate from the initial configuration, thereby biasing the results.^26,28

To date most atomistic simulation studies have focused almost exclusively on hydrated bilayer structures, in which lipid conformations are dictated by the lipid-water interface, whereas, lipid lamellae in the SC include many layers and are largely dehydrated with minimal water contact.¹⁷ Furthermore, in these bilayer simulations, CER molecules are restricted to the hairpin conformation (Figure 1f and 1g). This is not the case for the SPP in experimental multilayer systems, which exhibit a mixture of hairpin and extended conformations.^17,20 While atomistic simulations of larger, multilayer structures, which include lipid-lipid interfaces, are possible, lipid conformation and in-plane morphological arrangement will tend to remain close to their initial pre-assembled configurations²⁶ because transitions between hairpin and extended conformations, and movement from one leaflet (defined as half a bilayer) to another, or from well-mixed systems to lipid clusters are unlikely to occur over the currently feasible timescales for these systems. Given these potential limitations, self-assembly is a possible route toward examining lipid membrane configurations that arise naturally, rather than an assumed pre-assembled structure, similar to the experiments using model SC lipid systems.^11–16 However, the computational cost associated with self-assembly of SC lipids is unrealistic for atomistic models at present.

Figure 1:

a) CG mapping scheme for CHOL, where the A, B, C, and D rings of the skeletal structure are labeled, c) FFA C₂₄, and d) CER NS C₂₄. In all cases, CG beads are spherically symmetric. CG representation of d) CHOL, e) FFA C24, f) CER NS C24 in a hairpin configuration, and e) CER NS C24 in an extended configuration. CG mappings are colored to be consistent with simulation renderings in this work: CHEAD is black, CBODY (i.e., RING1–4, CHME, CTAIL, CTERM beads) yellow, FHEAD is purple, TAIL and TER2 are gray, OH1 and OH2 are red, MHEAD2 is cyan, and AMIDE is blue.

MD simulations of coarse-grained (CG) models, which group 2–5 atoms and their bonded hydrogen atoms into a single interaction site (a CG bead), can be used to study longer timescales and larger system sizes than simulations of atomistic models. This is enabled by the reduced number of interactions that need to be computed at each timestep and the softening of those interactions relative to the atomistic system.^29–32 As a result, CG simulations can be used to study self-assembly of mixed lipid lamellae once reliable CG models have been developed.

While numerous CG studies have been performed of phospholipids, similar studies for SC lipids, and CERs in particular, are in their infancy. The popular CG MARTINI model has been applied to a few SC lipids (CER NS^29,33–36, CER AP³⁰, CER NP³⁷, CHOL^38,39, and FFA³⁸). However, the generic nature of the MARTINI force field parameters, which circumvents the need for extensive optimization, also limits MARTINI’s ability to accurately reproduce experimental and atomistic SC lipid membrane structures. ^{29,30,33–39}

Hadley and M^cCabe developed the first CG model specifically optimized for SC lipids.^40–42 Using the iterative Boltzmann inversion method (IBI), they optimized a CG force field to accurately reproduce the structure of pure atomistic systems of FFA and CHOL as well as mixtures thereof. A limitation of these models is that multiple force fields are required to reproduce fluid and ordered states in order to compensate for the poor state transferability of IBI-derived force fields.⁴² To address this issue, M^cCabe and co-workers subsequently developed CG force fields for CER NS,⁴³ FFA,⁴³ water,⁴⁴ and the corresponding cross-interactions,³² using the multistate iterative Boltzmann inversion (MS-IBI) method. The MS-IBI approach, combined with a simulated wetting procedure to properly describe hydrophobic interactions, was found to enable the development of transferable force fields. Simulations using these CG force fields were shown to be in close agreement with their atomistic targets in terms of both bulk fluid and ordered structural properties, while also capturing the correct balance between hydrophobic and hydrophilic interactions necessary for the self-assembly of lamellar structures. Furthermore, these force fields have been used to study the self-assembly of SC lipids into bilayer and multi-lamellar structures.^32,43 The multilayer results enable examination of inner bilayers (i.e., layers without bulk water contact) that are more representative of experiment and allow assessment of the preferred conformation of CERs, either extended or hairpin, in the lipid lamella.^32,43 For example, in multilayer simulations performed using the MS-IBI optimized force fields, approximately 15% of the CERs adopted extended conformations in the inner layers in pure CER NS systems, which increased to approximately 25% for systems with a 1:1 mole ratio of CER NS C₂₄ and FFA C₂₄.^32,43

By the nature of their construction, CG models are simpler than their atomistic counterparts and thus quantities that depend on atomistic level detail, such as hydrogen bonding or electron density, cannot be directly measured. Methods have thus been proposed to reverse-map CG systems to the atomistic level in order to generate atomistic configurations.^26,27,45 So far, these methods have primarily been applied to fluid membranes, with only limited application to gel-phase membranes and models of the SC,^30,46 likely due to the challenges associated with generating stable atomistic configurations for dense, highly ordered membranes. The development and implementation of such reverse-mapping algorithms for gel-phase membranes is essential for combining the ability to self-assemble large multilayer membranes using CG models with the accuracy of results obtained from atomistic simulations.

Here, we present a MS-IBI based CG model for CHOL using the mapping scheme for CHOL proposed by Hadley and M^cCabe,⁴¹ optimized to be compatible with MS-IBI models for water, CER NS, and FFA.^32,43,44 The model is tested and validated through the study of a minimal model of the SPP phase containing CER NS, CHOL and FFA C₂₄. We then explore the effects of CHOL concentration on self-assembled multilayer structures containing equimolar mixtures of CER NS C₂₄ and FFA C₂₄. In particular, we examine the tendency of CER NS to form hairpin rather than extended conformations in multilayer lipid lamella, along with analyses of the three-dimensional structural arrangements of the individual lipids within the multilayer structures. Finally, an atomistic multilayer system that mimics the CG conformations was constructed from the CG simulation results using a simple reverse-mapping approach and then used in atomistically detailed examinations of hydrogen bonding and the localization of atomic species.

Materials and Methods

To simulate a model SPP phase, a minimal 3-component system containing ceramide N-(tetracosanoyl)-sphingosine (NS) with a saturated acyl chain of C₂₄, designated CER NS C₂₄ mixed with CHOL, and FFA C₂₄ has been studied. Although CER NS is not the most abundant CER in human SC, it is chosen here for the availability of experimental data for CER NS containing systems. In experiments, this mixture formed lamellar phases resembling the SPP at molar ratios of 1:1:1 and 1:0.45:1 for CER NS C₂₄:CHOL:FFA C₂₄, although we note that at the 1:1:1 ratio, a separate CHOL-rich domain is formed and thus the amount of CHOL in the SPP phase is lower than the nominal ratio.²¹ CG models for CER NS, FFA, and water were developed in previous work.^32,43,44 The schemes for mapping atoms in CER NS C₂₄ and FFA C₂₄ to CG beads are shown in Figure 1; a CG water bead represents 4 water molecules.⁴⁷ CER NS C₁₆ and FFA C₁₆ were also studied by eliminating the TER2 and two TAIL beads of the C₂₄ fatty acid chain.

CHOL CG Model

The CG model for CHOL is shown in Figure 1a,d.⁴¹ In this mapping, proposed by Hadley and M^cCabe,⁴¹ nonbonded interactions of the CHOL molecule are described by nine separate interaction sites (i.e., beads), five of them unique. The CHOL head bead (CHEAD) represents the hydroxyl group and two of the carbon atoms in the A ring of the 4-ring structure denoted as A-D in Figure 1a. The remaining carbon atoms in the A ring and rings B-D are allocated into four RING beads. The CHOL tail attached to the D ring is divided into two distinct beads, CTAIL and CTERM. To capture the molecular roughness of one face of the CHOL molecule, the methyl groups attached to rings are each mapped to a CHME bead (i.e., chiral methyl).⁴¹ For the remainder of the discussion, the RING, CTAIL, CTERM, and CHME beads are collectively referred to as CBODY.

MS-IBI Optimization

The MS-IBI method,⁴⁸ which is an extension of the commonly used IBI methodology,⁴⁹ was used to optimize the CG CHOL force field and cross interactions with other lipids.^48,49 In its usual implementation, IBI performs self-consistent optimization of a CG interaction potential, whereby the CG interactions are modified at each step by comparing the radial distribution function (RDF) of the CG simulation to the RDF of the “target,” typically from an atomistic simulation of the system being reproduced. MS-IBI uses the same general procedure, but instead allows the CG interaction potential to be optimized based upon the agreement with multiple distinct targets; these targets may be for the same molecules or different molecules with a subset of shared chemical topologies, at distinct thermodynamic state points/structures, and/or at the same state point but simulated using different ensembles. For example, constant volume (NVT) and constant pressure (NPT) states are often both utilized simultaneously in optimizing a force field to enable it to capture the pressure-density relationship of the system.⁴³ This is accomplished by considering the correction to the CG interaction potential to be the normalized sum of the deviations between RDFs for the multiple targets, as shown in Equation 1,

$$V^{i+1}\left(r\right)=V^i\left(r\right)-N_{states}^{-1}\sum _s{\alpha }_s\left(r\right)k_B{T}_s\ln \left[\frac{g_s^{target}\left(r\right)}{g_s^i\left(r\right)}\right]$$ (1)

where Vⁱ(r) and Vⁱ⁺¹(r) are the potential energy functions at the current and next iterations, respectively, for a given pair of atom types; $g_s^{target}\left(r\right)$ and $g_s^i\left(r\right)$ are the radial distribution functions between a given pair of atom types for state s, calculated respectively from the target atomistic system mapped to the CG level and the current iteration; α_s(r) is a weighting factor for state s; N_states is the total number of states; T_s is the temperature of target state s; and k_B is the Boltzmann constant. For the case of a single state point, equation 1 reduces to the standard IBI procedure.

The relative weight (α_s(r)) of each of the states allows more emphasis to be placed on matching targets deemed to be of greater importance for the desired application (e.g., in our case, greater emphasis placed upon ordered state points). The α_s parameters also act as damping factors to stabilize the optimization procedure by preventing large updates that can slow down the rate of convergence. Additionally, for MS-IBI, the weighting functions are defined such that they decrease linearly from their maximum value, α_max, at r = 0, to zero at r = r_max to suppress artifacts in the interaction potential that can arise due to intermediate and long-range correlations in the RDF, following the work in reference ⁵⁰. The values of α_max (listed in Table S2) are chosen via guidance from prior optimization work and refined via guess and check iteration to arrive at the final set used in the optimization of the model presented here. In general, ordered states are provided with a higher α_max than disordered states; e.g., monolayer, bilayer, and multilayer states have a value of α_max = 0.5 and α_max = 0.05 for the bulk fluid for interactions between FFA TAIL and CHOL CBODY.

The nonbonded interactions for CG CHOL were parametrized using the MS-IBI approach to match several target states from atomistic simulations in order to improve state transferability of the model as compared to the original parameters determined by Hadley and M^cCabe using single-state IBI.^51,52 To capture a range of behaviors, the target states for optimizing the CHOL force field included the bulk fluid, a monolayer, hydrated bilayer, and dehydrated stacked bilayers (i.e., no water in between the bilayer leaflets at all). Surface wetting simulations were also performed for select interactions to measure contact angles and aid in gauging the accuracy of the strength of the hydrophobic interactions in the CG model and tuning these strengths as necesary.⁴³ Complete details of the target states and the force field optimization process are provided in the supporting information (§S1.1 and §S2.1).

Simulation Methodology

Atomistic simulations were performed for three purposes: (i) to generate target data (bulk fluid, monolayer, hydrated bilayer, dehydrated stacked bilayers; Table S1) for the MS-IBI optimization of the CHOL CG model, (ii) to calculate structural properties from hydrated bilayers of CER NS, CHOL and FFA mixtures for validating the CG model, and (iii) to interrogate atomistic level details recovered by ‘reverse mapping’ the 6-leaflet self-assembled CG simulations to the atomistic level. All atomistic simulations employed the CHARMM36 force field⁵¹ with additional parameters from Guo et al.⁵² for CER NS and from Cournia et al.⁵³ for CHOL. Atomistic simulations were performed using the GROMACS simulation engine version 2018⁵⁴ with a 1 fs timestep. Van der Waals interactions were truncated at 12 Å with a smooth switching function applied between 10 and 12 Å. Short-range electrostatics were truncated at 12 Å and long-range electrostatics calculated using the particle-mesh Ewald (PME) method. NVT and NPT simulations employed the Nose-Hoover thermostat with a coupling constant of 1 ps.⁵⁵ For hydrated bilayers, separate but identical thermostats were applied to the water and the lipids. NPT simulations used a Parrinello-Rahman barostat⁵⁶ with a coupling constant of 10 ps. Semi-isotropic coupling (in the xy-dimensions, along the bilayer plane) were used for bilayer systems, whereas isotropic coupling was used for the bulk fluid systems. For ordered systems, such as bilayers, the random walk MD (RWMD) procedure²⁶ was used to allow lipids to decorrelate from their initial orientation and in-plane morphology. The exact simulation protocol is detailed in the supporting information (§S1). For target and validation data, four replicate simulations were performed, each differing by the seed given to the RWMD temperature sequence.

The CG simulations were performed using the HOOMD-Blue simulation engine, version 2.9.3.⁵⁷ A timestep of 10 fs was used in all of the CG simulations. Full details of the simulation parameters used and the accuracy of the individual CG RDFs as compared to their atomistic targets mapped to the CG level are provided in the supporting information (§S2 and §S4). Simulations of the self-assembly of CG model membranes were initialized by randomizing the configuration and orientation of the lipids in the center of the simulation box and hydrating this lipid region with a randomized arrangement of water using the Molecular Simulation and Design Framework (MoSDeF)^58–60 mBuild software.⁶¹ The initial configuration of the lipid systems starts with the water and lipids phase separated; while this phase separation happens very rapidly for a fully mixed, isotropic system, initializing the system in phase separated configurations ensures that membranes form with their interface normal to one of the principle axes of the system, for ease of analysis. Self-assembled bilayer systems contained 1,000 lipid molecules and 4- and 6-leaflet systems contained 2,000 lipid molecules. All systems contained 10 water beads per lipid (10,000 and 20,000 water beads respectively in total for the bilayer and multilayer systems), which translates to 40 water molecules per lipid. Four independent replicates, each starting from randomized initial configurations, were simulated for each self-assembled CG system studied. To accelerate self-assembly, the box annealing protocol described in Moore et al.³² was employed. Finally, production runs for the self-assembled systems were carried out in the NPT ensemble for 200 ns at 1 bar and 305K using the Martyna-Tobias-Klein thermostat-barostat with the same coupling constants as the atomistic simulations.⁶² Data from at least the final 100 ns of the simulations was used for analysis. Additional details of the CG system set up and simulations are provided in the supporting information (§S2).

Analysis

Analysis of the lipid systems was performed utilizing the MDTraj,⁶³ Freud,⁶⁴ and Voro++⁶⁵ software packages. Structural properties of the systems were characterized using the area per lipid (APL) and/or normalized lipid area (NLA), bilayer thickness, interdigitation, tilt angle, and nematic order parameter (S₂). We introduce the NLA in this work as a new metric that allows systems with lipids containing different numbers of tails and different cross-sectional areas to be compared on a more equivalent basis than APL. NLA is calculated by normalizing the APL by the average effective number of tails, where FFA is counted as 1 tail, CER NS acyl and sphingosine chains as 1 tail each (i.e., a hairpin CER would be counted as 2 and an extended would be 1 in an individual leaflet), and CHOL as 1.9 tails. The effective number of CHOL tails was determined by considering the cross sectional area of CHOL to be ~38 Ų (reported in experiment to be between 37–39 Ų)^66,67 and the cross-sectional area of a saturated carbon chain to be ~20 Ų (20.7 Ų for steric acid,⁶⁸ ~20.6 Ų for behenic acid,⁶⁹ and 20 Ų per chain from prior simulations of dehydrated CER NS bilayers using CHARMM⁴³). A discussion of the impact of the choice of the number of effective tails for CHOL is included in the supporting information (§S3.2).

The fraction of CERs in the hairpin and extended conformations and the number and location of water beads were measured separately for outer leaflets (defined as those in contact with the water interface) and the inner leaflets (those not in contact with the water interface) of the multilayer systems. To further describe in-plane morphology, the in-plane coordination number between CHOL with itself and with the other lipid types was determined along with the Voronoi tessellation to examine local packing as described in the supporting information (§S6). For atomistic systems, neutron scattering length density profiles and hydrogen bonds were also calculated as described in the supporting information (§S3.6 and §S3.7).

Unless specified differently, results derived from both the atomistic and CG simulations are reported in tables and figures as the mean ± the pooled standard deviation from four replicate simulations initialized in different randomized configurations. For quantities derived from all lipids combined (e.g., NLA, APL, bilayer thickness, interdigitation, S₂, and hydrogen bonding), the standard deviation for each replicate is calculated from the single observation determined at each time frame of the final production simulation (typically 2,000 frames). For quantities derived from individual lipids (e.g., tilt angle, cluster size, and Voronoi tessellation results), the standard deviation for each replicate is the pooled standard deviations of the multiple observations from each time frame. As a result, standard deviation values reported for quantities like tilt angle, which include the variability for each time frame (i.e., the thermal fluctuations), are larger than the standard deviation of the time averaged value for these quantities (e.g., a few degrees compared with less than a degree for tilt angle).

Results and Discussion

CHOL force field validation

Given that the optimization process of CHOL closely follows the procedures developed and used in our prior studies that optimized CG force fields for water, CER NS and FFA^32,43,44, we refer the reader to the supporting information (§S1.1 and §S2.1) for further details, and here focus on the validation of the new force field. All of the potentials and RDFs from the MS-IBI derivation of the CHOL CG force field and its cross interactions with other SC lipids are provided in the supporting information (§S4). Machine readable tabulated force field files are available on GitHub.⁷⁰ The CG CHOL force field obtained from the MS-IBI optimization is found to accurately describe pure CHOL. The atomistic and CG simulations are in good agreement for bulk fluid properties; for example, the density of pure CHOL at 550 K and 1 atm is reproduced with high accuracy (0.73 ± 0.01 g/mL (CG) versus 0.73 ± 0.01 g/mL (atomistic)), as is that for an equimolar mixture of CHOL and FFA C₂₄ at 1 atm and 500 K (0.81 ± 0.03 g/mL (CG) versus 0.79 ± 0.01 g/mL (atomistic)). High temperatures were chosen for these systems to ensure that the lipids remain in a fluid state. Good agreement is also obtained between the atomistic target and CG RDFs (Figure 2). CHOL-CER NS and CHOL-FFA RDFs are in close agreement for ordered states but deviate more for bulk states, where the CG model predicts stronger association between the headgroups than is seen in the atomistic simulations (Figures S4 and S5). Because the focus of this work is on the formation of ordered phases, which are given a higher weighting factor in the MS-IBI optimization, these bulk phase deviations are considered acceptable

Figure 2:

RDFs and pair potentials from the pure CHOL force field optimization. Top: target and CG RDFs at the 550K NPT state; middle: target and CG RDFs from the 400K NVT state; bottom: pair potential that yields the CG RDFs above. Each column corresponds to the pair interaction listed at the top of the column.

In hydrated bilayer simulations of two or three lipids, the CG force field reproduces with good accuracy the structural properties of the pre-assembled atomistic bilayers in both pre-assembled and self-assembled CG simulations at 305K (Table 1). Three systems of equimolar mixtures were studied: CER NS C₂₄:CHOL allowing the CHOL-CER NS cross interactions to be tested, CHOL:FFA C₁₆ allowing the CHOL-FFA interactions to be tested, and CER NS C₂₄:CHOL:FFA C₂₄, the system of particular interest in this study. Because the pre-assembled CG simulations were initialized using the final configuration of the atomistic simulation mapped to the CG level, the differences between the CG and atomistic structure for pre-assembled bilayers is primarily driven by the CG force field rather than the equilibration procedure used to form the self-assembled systems.

Table 1:

Structural properties of hydrated bilayers in the atomistic and CG systems studied at 305K. Results shown are the mean ± pooled standard deviation of four simulations.

System	APL (Å2)	Bilayer Thickness (Å)	S 2	Tilt (°)
CER NS C24:CHOL 1:1
Atomistic preassembled	38.8 ± 0.3	47.8 ± 0.1	0.958 ± 0.007	9 ± 5
CG preassembled	39.74 ± 0.06	48.0 ± 0.1	0.931 ± 0.003	10. ± 6
CG self-assembled	38.71 ± 0.16	48.33 ± 0.08	0.947 ± 0.014	10. ± 6
CHOL:FFA C16 1:1
Atomistic preassembled	29.92 ± 0.09	35.9 ± 0.2	0.951 ± 0.004	11 ± 6
CG preassembled	30.58 ± 0.08	33.22 ± 0.05	0.908 ± 0.004	13 ± 6
CG self-assembled	30.33 ± 0.13	35.77±0.03	0.929 ± 0.014	11±6
CER NS C24:CHOL:FFA C24 1:0.5:1
Atomistic preassembled	30.38 ± 0.05	52.7 ± 0.18	0.977 ± 0.014	8 ± 4
CG preassembled	33.08 ± 0.17	50.7 ± 0.2	0.96 ± 0.03	8 ± 5
CG self-assembled	33.32 ± 0.16	50.82 ± 0.02	0.96 ± 0.02	8 ± 5

Focusing first on the comparison between pre-assembled bilayers, systems composed of CER NS C₂₄:CHOL and CHOL:FFA C₁₆, both in 1:1 ratios, the CG APL is within 2.5% of the atomistic APL, demonstrating that the CG model captures the in-plane packing of the lipids, similar to prior results for pure CER NS and CER NS:FFA mixtures.²⁶ The thickness of the CG CER NS C₂₄:CHOL bilayer shows almost perfect agreement with the atomistic bilayer, while the CG model of CHOL:FFA C₁₆ underpredicts the atomistic bilayer thickness by ∼7.5%. In both the CER NS C₂₄:CHOL and CHOL:FFA C₁₆ equimolar systems, the nematic order (S₂) of the lipid tails indicates that they are highly ordered, although the CG model slightly underpredicts the atomistic results. The CG model reproduces tilt angle well with a small over prediction that is well within the observed standard deviation. CG simulations from pre-assembled bilayers of CER NS C₂₄, CHOL, and FFA C₂₄ with a 1:0.5:1 mole ratio are also reported in Table 1. These show good agreement with the results from atomistic simulations, although the CG force field predicts an APL that is ~10% larger, with ~4% smaller thickness. Significantly, these three component lipid simulations provide an unbiased validation of the CG force field because target states from the three component systems were not included in the target optimization; only two component lipid systems were used as targets.

In general, close agreement is observed between the self-assembled CG and atomistic simulations in terms of structural properties, supporting the accuracy of the CG model (Table 1). For the CER NS C₂₄: CHOL:FFA system, the self-assembled CG simulations slightly over predict the APL and underpredict the thickness, but these deviations are well within the accuracy expected for the CG force field, as observed in prior work.^32,43 We note that for this composition, the structural properties of both the pre- and self-assembled CG simulations are not statistically different; this agreement suggests that the CG simulations reached the same energy minimum regardless of the procedure for the bilayer formation. Similar agreement between pre- and self-assembled configurations is observed for the CER NS C₂₄:CHOL composition as well. The slight deviations seen when comparing pre- and self-assembled CG configurations for the CHOL:FFA C₁₆ composition suggests that the pre-assembled systems may simply be stuck in a low energy, metastable configuration (here, demonstrating increased tilt and an associated reduced bilayer thickness, as these two measures cannot typically vary independently). However, the close agreement of the CG self-assembled and atomistic results for CHOL:FFA C₁₆ again supports the accuracy of the CG model and highlights the importance of using self-assembly to initialize configurations. Furthermore, agreement between the atomistic and self-assembled configurations provides additional self-consistent validation of the efficacy of the RWMD procedure²⁶ used in the atomistic simulations to relax and decorrelate the lipids from their initial configurations and morphologies.

In experimental studies of equimolar CHOL:FFA C16 mixtures, Lafleur and co-workers^71,72 observed the appearance of a bilayer phase at 326.5 K. To allow comparison of the MS-IBI CG force fields with these experiments, additional self-assembly simulations were performed at 330K for CHOL:FFA C₁₆. The 35.7 Å bilayer thickness observed for these simulations is 9% smaller than the 39 Å repeat distance observed by X-ray diffraction at 328K.⁷³ However, the fraction of CHOL in the experimental bilayer may be greater than 50% due to phase separation of FFA into a second isotropic phase.⁷² The APL of 30.9 Ų from the CG model at 330K is ~8% lower than the 33.3 Ų obtained for the same system via atomistic simulation at 333K in a previous study.⁴⁰ Also, the change in APL for the equimolar CHOL-FFA C₁₆ system from 305 to 330K was much smaller for the CG model (30.33 to 30.9 Å) than the atomistic model (29.92 to 33.3 Å). This suggests that the temperature dependence of the CG model is much weaker than the atomistic model, which is expected given that IBI optimized models, like the ones used herein, are typically not optimized to reproduce thermotropic behavior.^74,75 In prior work, Hadley and M^cCabe also used their IBI-derived CG force field to self-assemble equimolar mixtures of CHOL and FFA C₁₆.⁴⁰ From this model at 333 K, the bilayer thickness was 30 Å, which is slightly lower than the experimental value, and the APL was 33.3 Ų, which is in near perfect agreement with atomistic simulations. The latter result is expected because the Hadley-M^cCabe IBI model used the equimolar CHOL and FFA bilayer at 333K as the only target state for the CHOL/FFA cross-interactions, whereas the MS-IBI CHOL model derived in this work did not consider this state. However, despite these small deficiencies, the CG force field derived herein overall provides good agreement with the corresponding atomistic simulations and can capture self-assembly of the lipids into ordered phases.

We can further compare the collective behavior of the CG MS-IBI models to the CG MARTINI-based model developed by Podewitz, et al.,³⁶ for a 1:0.5:1 mole ratio mixture of CER NS C24:CHOL:FFA C24 at 300K. Their MARTINI model produced an APL of 34.4Ų that is ~13% larger than the atomistic result compared to the ~10% over-estimate of the MS-IBI model. The 53.0 Å bilayer thickness reported for the MARTINI model was calculated from the distance between the water interfaces on either side of the bilayer (defined as the position where water density decreased to half of the bulk density), which differs from the bilayer calculations reported in Table 1. For comparison, the bilayer thicknesses for the atomistic and MS-IBI simulations calculated using the water-interface method are 57.0 Å and 54.4 Å, respectively, showing closer agreement than MARTINI with atomistic simulation. A more significant difference between the MS-IBI and the MARTINI models is the absence of tilt in the MARTINI simulations.

Self-assembled lamellar structures

Simulations of the self-assembly of lipid membranes have been performed using the validated MS-IBI CG force fields described above for 3-component mixtures of CER NS C₂₄, CHOL and FFA C₂₄ to explore the effect of varying the CHOL composition on structural properties. Differences in the properties of a bilayer sandwiched between bulk water layers compared with those obtained from leaflets in the middle of a multilayer structure are also explored via the self-assembly of membranes with 2- (i.e., bilayer), 4- and 6-leaflets.

Comparison of bilayer and multilayer structures

As noted earlier, experimental SC lipid membrane systems exhibit multilayer structures, which, for a typical lipid deposition of between 0.9 and 1.5 mg/cm²,^18,76,77 produce lipid membranes that are more than 10 μm thick. This corresponds to a stack of more than a thousand ~6 nm SPP-type bilayers. Thus, almost all lipids in these systems reside in interior bilayers without direct contact to bulk water. Experimental measurements of these systems, such as X-ray scattering profiles, and FTIR and NMR spectra, therefore represent the behavior of interior lipids, which, with much lower hydration, behave differently from the single hydrated bilayers that have been examined in many other simulation studies. Specifically, the interior lipids in experimental lipid systems have only 1–2 water molecules per lipid in the headgroup region, compared with the large amounts of water surrounding the headgroups in simulations of hydrated bilayers (typically 20 to 40 waters per lipid^23,26,45). Less water leads to more interactions between headgroups,¹⁷ and allows the CERs to adopt an extended conformation, which is not seen in hydrated bilayer systems because contact between water and CER tails is highly unfavorable.

To investigate the differences between bilayer and multilayer systems, mixtures of CER NS C₂₄:CHOL:FFA C₂₄ in a 1:0.5:1 molar ratio were self-assembled into 2-, 4-, and 6-leaflet structures (Figure 3a, b, and e). In the following analysis, the headgroups of the ‘outer’ leaflets are in contact with the bulk water interface, whereas headgroups of the ‘inner’ leaflets are in contact with headgroups of an adjacent leaflet. The inner leaflets of the self-assembled multilayer systems contained small amounts of water: 2.20 ± 0.05 water molecules per lipid for the 4-leaflet system and 2.8 ± 0.2 for the 6-leaflet system. This is in good agreement with the ~2 waters per lipid based on neutron scattering measurements¹⁷ observed in the aforementioned experimental model of SPP systems containing an equimolar mixture of CERs, CHOL, and FFAs of varying tail lengths. In addition, a significant fraction of the inner CERs adopt an extended conformation (~35–36%) in the simulated structures.

Figure 3:

Simulation snapshots of self-assembled mixtures of CER NS C₂₄:CHOL:FFA C₂₄ A) in bilayer (2-leaflet) and B) 4-leaflet configuration with a 1:0.5:1 molar ratio; C-F are 6-leaflet configurations with mole ratios of C) 1:0:1, D) 1:0.2:1, E) 1:0.5:1, and F) 1:1:1. Water is represented as transparent volumes determined using the QuickSurf representation in VMD. For clarity lipid backbones are represented as a stick model, with headgroup beads rendered as spheres, following the color scheme described in Figure 1.

The combination of low hydration and the presence of extended CERs in the inner layers of the multilayer systems affects structural properties as shown in Table 2, which reports the average across all leaflets, except for the fraction of extended CERs and the number of water molecules per lipid, which were calculated from only the inner leaflets. The decrease in APL for the 4- and 6-leaflet systems compared to the 2-leaflet systems can be attributed to the increase in extended CERs, which pack more efficiently. At the same time, the tilt angle for the 6-leaflet system is slightly larger than for the 2- or 4-leaflet systems. The average bilayer thickness increased by ~2–3 Å as the number of inner leaflets increases, which is consistent with reduced lipid interdigitation in the inner leaflets. The average bilayer thickness of 53.81 Å for the 6-leaflet system closely agrees with the experimentally measured 53–54 Å repeat distances for the SPP phase in the SCS_SPP synthetic lipid mixture (described in the Introduction), likely because lipid hydration and the presence of extended CERs in the 4 inner leaflets more closely matches the experimental system.^17,18

Table 2:

Average structural properties of 2-, 4-, and 6-leaflet systems of CER NS C₂₄/CHOL/FFA C₂₄ with a molar ratio 1:0.5:1. Results are the average across all leaflets (the mean ± pooled standard deviation of four simulations), except for the fraction of extended CERs and the water molecules per lipid, which are calculated from the inner leaflets that do not contact bulk water.

	2-leaflet	4-leaflet	6-leaflet
APL (Å2)	33.7 ± 0.2	33.40 ± 0.13	33.14 ± 0.08
Tilt Angle (°)	8 ± 5	8 ± 5	9 ± 5
Interdigitation (Å)	10.7 ± 0.2	10.13 ± 0.14	9.2 ± 0.3
Average Bilayer Thickness (Å)	50.82 ± 0.02	52.94 ± 0.06	53.81 ± 0.10
% CERs extended in inner leaflets	--	36.3 ± 1.9	35.3±0.7
Water molecules/lipid in inner leaflets	--	2.20 ± 0.05	2.8 ± 0.2

Influence of CHOL content on self-assembled CG systems

To examine the role of CHOL in the SC, the mole ratio of CHOL in the minimal SPP systems containing equimolar CER NS C₂₄ and FFA C₂₄ was varied from 0 to 1 relative to CER NS in self-assembled simulations of the 6-leaflet system, which consists of an inner bilayer sandwiched between two outer bilayers (Figure 3c-f). Figure 4 shows the trends in the structural properties of the inner and outer bilayers as a function of CHOL concentration. If adding CHOL does not change lipid packing, then NLA should be constant. This appears to be the case in the outer layers for CHOL/CER molar ratios of 0 to 0.5, with only a small decrease in NLA at CHOL/CER mole ratio of 1. In contrast, NLA values for the inner layers decrease as CHOL is added, suggesting more efficient packing at higher CHOL composition. Also, NLA is consistently greater for the inner layers compared to the outer layers, indicating that the lipids in the inner layers pack less efficiently compared to those in the outer layers. The choice of 1.9 effective tails for CHOL, which is based, as described above, on experimental measurements of cross-sectional area, does not substantially impact the observed trends (see Fig. S1 and the surrounding discussion). Because CHOL is relatively short (approximately the same length as FFA C₁₆), increasing its concentration causes a roughly proportional increase in the interdigitation of the FFA C₂₄ tails and C₂₄ (fatty acid) tails of CER NS C₂₄. The number of extended CER NS molecules, which are abundant in the four inner leaflets and absent in the outer leaflets, increased from ~32% to 38% as the CHOL/CER mole ratio is increased from 0.2 to 1 (Figure 4a). This might occur because the extended conformation packs more efficiently around the CHOL, or, alternatively, because CHOL interaction with one type of CER tail (fatty acid or sphingosine) is preferred over the other tail.

Figure 4:

Average structural properties for the inner and outer bilayers of the 6-leaflet system with varying CHOL:CER molar ratio in an equimolar mixture of CER NS C₂₄:FFA C₂₄. a) % CERs in an extended conformation (calculated from the four inner leaflets), b) NLA, c) tilt angle, d) S₂, e) bilayer thickness, and f) interdigitation. Results shown are the mean ± pooled standard deviation of four simulations. In some cases, the error bars are smaller than the symbol size. Experimental bilayer thicknesses are repeat distance measurements for the SCS_SPP system from Mojumdar et al.¹⁸ (this mixture of 5 different CERs combined with equimolar amounts of CHOL and an FFA mixture with tail length varying from C₁₆ to C₂₆ is described in the introduction and the text discussing Figure 6).

Adding as little as 0.2 CHOL per CER NS disrupts the ordering of the hydrocarbon tails for both the inner and outer bilayers, as indicated by the significant decrease in S₂; however, further increases in the CHOL content have no effect. Like tail order, the tilt angle of the inner bilayer is roughly the same when CHOL is present but deviates when CHOL is absent. In contrast, the outer bilayer tilt is the same whether CHOL is or is not present. Because bilayer thickness is affected by both interdigitation and tilt angle (i.e., bilayer thickness decreases with increased interdigitation and increases with decreased tilt angle), the inner bilayer thickness is unchanged when the mole ratio of CHOL/CER is increased from 0 to 0.2, after which the thickness decreases proportional to the increase in CHOL amount; also, therefore, the thickness of the outer bilayers decreases proportional to CHOL amount starting with no CHOL.

Repeat distances measured by SAXD of the SCS_SPP mixture with varying amounts of CHOL are quantitatively similar to bilayer thicknesses calculated from simulation. However, unlike the simulation bilayer thicknesses, which decrease with increasing CHOL/CER mole ratio, the experimental repeat distances are constant, indicating that interdigitation (assuming constant tilt angle) did not change with increasing CHOL. The different lipid compositions of the experiments and simulations, especially the presence of FFAs with multiple tail lengths instead of only FFA C₂₄ as in the simulations, is a likely cause of these different observations. In the SCS_SPP mixture, CHOL may be able to offset gaps caused by the variation of the FFA tail lengths, which it cannot do when there is no variation in FFA tail lengths. Another possibility is that the amount of CHOL in the simulated bilayers is larger than in the experimental bilayers, because experimentally at CHOL/CER mole ratios of 1 and possibly lower, some of the CHOL resides in a separate CHOL phase.¹⁸

The effect of CHOL content on the preferential arrangement and aggregation of lipid tails in the inner bilayer was examined using three different methods: cluster analysis quantifying the formation of nearest neighbor networks with the same lipid tail type, coordination number calculation for CHOL with each lipid tail type, and Voronoi analysis of the number of adjacent neighbors for each lipid type in the inner four leaflets (see supporting information §S3 and §S6 for calculation details). The mean cluster size, defined as the average number of lipid tails of the same type in a cluster, are reported in Figure 5A. When CHOL is absent, the cluster sizes for the FFA and CER NS lipid tails are almost the same. Increasing the CHOL/CER mole ratio from 0.2 to 1 causes an expected approximately proportional increase in the size of the CHOL cluster. The surprising result is that when the CHOL/CER ratio is small (0.2), FFA exhibits a strong preference for being a neighbor with other FFA molecules. With further increases in the CHOL molar ratio, this preference for FFA molecules to neighbor each other diminishes, perhaps because more FFA molecules are needed to fill the larger number of packing defects introduced by more CHOL.

Figure 5:

A) Mean cluster size (defined as the number of each lipid type in a cluster) for lipid tails in the inner leaflets; sphingosine and fatty acid tails of CER NS C₂₄ are designated respectively as FA and SPH. B) CHOL-X coordination numbers, where X is either CHOL, FFA C₂₄, the sphingosine chain of CER NS C₂₄ (SPH), or the fatty acid chain of CER NS C₂₄ (FA). Results shown are the mean ± pooled standard deviation of four simulations.

The coordination numbers of the CHOL tails with each of the lipid tail types are presented for the 1:0.2:1, 1:0.5:1, and 1:1:1 CER NS C₂₄:CHOL:FFA C₂₄ systems in Figure 5B. It is evident from the coordination numbers that for all three systems, CHOL is most likely to have FFA C₂₄ neighbors. Among the CER tails, CHOL is more likely to have CER sphingosine tails as neighbors rather than CER fatty acid tail. This is most easily seen for the CHOL/CER mole ratio of 0.2 where the coordination numbers are 2.6 (FFA), 2 (sphingosine tail), 1.3 (CER fatty acid tail) and 0.5 (CHOL) compared with the values expected if the likelihood was based on the number of each tail type in the mixture; i.e., 2 for all lipid tails except CHOL, which is 0.4. The relative magnitude of these preferences decrease with increasing CHOL content; at a CHOL molar ratio of 1, CHOL is a neighbor with itself and the other types of lipid tails in almost equal amounts with FFA being a neighbor to CHOL slightly more often than the others.

These results are consistent with experimental Fourier transform infrared (FTIR) spectra, which suggest that the CER sphingosine tail is a more likely than the CER fatty acid tail to neighbor CHOL molecules in an equimolar mixture of CER NS C₂₄, CHOL, and FFA C₂₄ plus 5 wt % cholesterol sulfate (in which the FFA and/or the fatty acid chain of the CER were deuterated).²⁰ The authors of this study also concluded that CER NS C₂₄ favors an extended conformation, and FFA C₂₄ prefers to associate with the fatty acid tail of CER NS C₂₄ but not with CHOL. This last conclusion does not necessarily contradict the coordination numbers in Figure 5B because an increased likelihood for FFA molecules to neighbor CHOL does not require CHOL to be a more frequent neighbor to FFA. For example, a single CHOL molecule surrounded by six FFA molecules would have six FFA neighbors but each of those FFAs might have only one CHOL neighbor. Although the extent of these neighbor preferences cannot be quantified from their experimental measurements, the authors proposed a model that assumes all CERs are extended, CHOL is a neighbor to only CER sphingosine tails, and FFA C₂₄ is only a neighbor to CER fatty acid tails or itself.²⁰ This model and a similar model from Iwai et al.⁷⁸ are inconsistent with the results in Figure 5B indicating that FFA C₂₄ is a common neighbor of CHOL. These differences could be related to the conformation of the CER NS C₂₄ molecules, where we observe that roughly 1/3 are in an extended conformation; a larger fraction of extended molecules could alter the in-plane structure due to localization of the molecular interactions in the membrane and changes to hydrogen bonding (as discussed below in the context of recovering atomistic details).

The Voronoi analysis (Figures S8 and S9 in the supporting information) shows that CHOL molecules in a mixture with smaller and similarly sized FFA and CER tails (cross-sectional area of ~38 Ų for CHOL compared with about 20 Ų for hydrocarbon tails from above) most often have seven nearest neighbors with an average of more than 6.5. In the absence of CHOL, FFA and the CER NS tails each have exactly six nearest neighbors. To accommodate CHOL and its seven nearest neighbors, many of the FFA and CER NS tails adjacent to CHOL have only five nearest neighbors. Because the average number of nearest neighbors for CHOL is independent of CHOL content, there are more FFA and CER tails with only five nearest neighbors in mixtures with more CHOL. Overall, the average number of nearest neighbors is slightly smaller for FFA than for either CER NS tail, suggesting that a few more FFA molecules may squeeze around CHOL.

Recovering atomistic details

As previously discussed, the CG model and force field used in this work is capable of reproducing, with good accuracy, many of the key structural metrics of the corresponding atomistic bilayers. However, the loss of atomistic level details in the CG model prohibits comparisons with experimental neutron scattering length density (NSLD) measurements as well as accurate calculations of quantities such as hydrogen bonding. Here, a simple procedure is used to reintroduce atomistic level details into the CG multilayer configurations generated via self-assembly. In this approach, the morphology (i.e., in-plane arrangement of lipids) and CER conformations (i.e., hairpin or extended) are determined from the self-assembled CG structure and the atomistic lipids are arranged accordingly. With this configuration generated, the same general procedures used for the pre-assembled atomistic bilayers are employed to relax the system. Since morphology is derived from the unbiased self-assembled simulation, RWMD is not required. The main goal is to allow lipids to perform a local energy minimization while retaining the configuration dictated by the self-assembled system in a process that is akin to the reverse-mapping of Wassenaar et al.⁷⁹ However, unlike the method of Wassenaar et al.,⁷⁹ this simplified reverse mapping method does not need to use constrained simulations or lengthy energy minimization steps to relieve the system of overlapping atoms, which would be abundant in the large and dense multilayer systems studied in this work.

Here, we focus on an atomistic configuration generated for the system shown in Figure 3e, namely 6 leaflets of the 1:0.5:1 CER NS C₂₄ :CHOL:FFA C₂₄ mixture containing 2,000 total lipids sandwiched between two water layers containing 26,666 molecules (13.3 water molecules/lipid which is equivalent to 40 water molecules/lipid in the outermost leaflets). The small number of water molecules associated with the headgroups of the inner leaflets in the CG configuration (Table 2) were not included in this analysis. As is typical for initializing atomistic bilayers, the in-plane area of the initial configuration is set larger than the anticipated equilibrium area to avoid overlaps between the lipids; in this case, the initial in-plane box dimensions are larger than the final dimensions by a factor of ~1.2. All lipids in the atomistic multilayer have their in-plane rotational orientation randomized, similar to the bilayer simulations above and in prior work,²⁶ with the individual lipid tilt angle set to match the average value from the CG simulation. The pre-assembled structure is then hydrated. To relax this configuration, a steepest-descent energy minimization is performed to remove high energy states, followed by a 10 ns NVT step at 305K to relax the molecular structure. Next an NPT step is performed for 100 ns at 305K and 1 atm to allow the box shape (i.e., the in-plane area) to relax and for lipids to further minimize their energy. A final 20 ns NPT production step at 305K and 1 atm is performed to gather 2,000 frames of simulation data spaced in even 10 ps intervals for analysis. Data for the reverse-mapped systems are from a single replicate reported as the mean and standard deviations from each of the frames of the final production simulation, as discussed previously.

A simulation snapshot of the relaxed atomistic multilayer configuration for CER NS C₂₄:CHOL:FFA C₂₄ mixture with a 1:0.5:1 molar ratio at 305K and 1 atm is shown in Figure 6a, with the extended and hairpin CERs designated in different colors (Figure 6b) to highlight their presence. The composition of the leaflets with and without water contact deviate by a small amount from the overall molar ratio of CER NS C₂₄:CHOL:FFA C₂₄, namely, 1:0.52:1.09 (131:68:144 molecules/leaflet) for the two leaflets with water contact (indicating CER NS is depleted) and 1:0.49:0.95 (134.5:66:128 molecules/leaflet) for the 4 leaflets without water contact (indicating CHOL is depleted); 35% of the CERs (46.8 molecules/leaflet) in the inner bilayer are in an extended conformation. The tilt of the atomistic system is on average 9.9 ± 8.2° compared to 9.2 ± 5.3° for the corresponding CG systems. We note that average tilt angle from the CG system was used to set the initial tilt angle of the lipids in atomistic system, and thus we might expect such agreement; however, due to starting with a configuration that was expanded by a factor of ~1.2 in the in-plane dimensions, lipids were provided with sufficient freedom to adjust this angle if the initial value was unfavorable. The average NLA for the atomistic system is calculated to be 20.35 ± 0.03 Ų, which is slightly smaller than 20.96 ± 0.04 Ų for the corresponding CG systems.

Figure 6:

a) Simulation snapshot of a reverse-mapped atomistic 1:0.5:1 CER NS C₂₄:CHOL:FFA C₂₄ 6-leaflet system with lipids colored according to the images in b). A 1-nm thick slice is highlighted in a) and shown in detail in Figure 7a. c) Protiated NSLD profiles for the inner bilayer (i.e., inner 2 leaflets) from the atomistic multilayer simulation shown in a) compared with experimental results for the SCS_SPP system from Groen et al.¹⁷ (see text for system composition) and an equivalent composition atomistic bilayer simulation used to validate the CG force field (see Table 1).

As a means of validating the atomistic configuration, the NSLD profile calculated for the inner 2 leaflets of the 6-leaflet system in Figure 6a is compared in Figure 6c to an experimental NSLD for the SCS_SPP system with a nominal bin size value of 0.25Å (see §S3.6). We recall that the experimental SCS_SPP system, which is described in the Introduction contains a CER mixture (NS C₂₄, AP C₂₄, AS C₂₄, and AP C₁₆ and C₂₄) combined with equimolar amounts of CHOL and a FFA mixture ranging from C₁₆ to C₂₆.²⁶ We expect the experimental system, despite its more complex composition and larger amount of CHOL, to be relevant to the simpler simulated systems. First, at 60 mol %, CER NS C₂₄ is the dominant CER species in the experimental system. Second, as much as half of the CHOL in the experimental system is located in a separate crystalline CHOL phase, which reduces the amount in the lamallae.¹⁹ Finally, similar phase behavior, including formation of the SPP, has been demonstrated for simplifications of the experimental composition including FFA C₂₄ instead of the FFA mixture and/or CER NS C₂₄ instead of the CER mixture.⁸⁰ There is good agreement between the NSLD calculated from the simulated multilayer system and experiment in terms of the position and shape of the main peaks, suggesting the reverse-mapped atomistic system captures the same 53.9 Å repeat distance seen experimentally.¹⁷ However, there is a slight difference in the thicknesses of the secondary peaks located at ±15 Å for the experimental and reverse-mapped atomistic NSLD profile. This may be attributed to the difference in lipid composition as well as truncation error in the experimental measurement. Comparing to the NSLD profile calculated for an equivalent composition single hydrated bilayer (one of the replicates used to validate the CG force field, as reported in Table 1), the main peaks are considerably narrower because there is a lipid-water interface, rather than a lipid-lipid interface, as in the simulated multilayer system or experiment.

Moore et al.²⁶ and Wang and Klauda⁴⁵ also compared their simulations of equimolar amounts of CER NS C₂₄, CHOL, and FFA C₂₄ in a single hydrated bilayer to the same NSLD experimental data; the results of Moore et al.²⁶ and Wang and Klauda⁴⁵ are similar to each other with repeat distances smaller than the 53.9 Å reported experimentally (~50 Å from Moore et al. and ~49 Å from Wang and Klauda). This reduced repeat distance is expected given that the larger concentration of shorter length CHOL molecules enables increased interdigitation compared with the 1:0.5:1 CER NS C₂₄:CHOL:FFA C₂₄ composition; this was shown previously in the CG simulations as a function of CHOL concentration (Figure 4). As was seen in the hydrated single bilayer system in Figure 6c, the main peaks in the simulations from Moore et al.²⁶ and Wang and Klauda⁴⁵ are also significantly narrower than those seen in experiment and the multilayer simulation, since the peaks in the hydrated bilayers represent a water-lipid interface, not lipid-lipid interface.

To highlight the ordering of the lipids, Figure 7a renders a slice of the system located between the two highlighted planes in Figure 6a using the color scheme shown in Figure 6b. To quantify the distribution of the species in Figure 7a, Figures 7b and 7c plot the density histogram of the lipid components of this system. The z-distance from the center (i.e., x-axis) in Figures 7b and 7c correspond to the spatial dimensions shown in 7a. Consistent with the experimental observations,¹⁹ the FFA chains show increased density within the central region of a leaflet pair (as seen at z-positions of ~ −60, 0, and 60 Å in Figure 7b) due to interdigitation of the chains. Also consistent with experiment, CHOL appears to sit deeper in the leaflet, away from the CER and FFA headgroups. Experimentally, this distance has been measured to be ~4 Å from the edge of the unit cell, at position ±22.9 Å;¹⁹ examination of the density profile of the headgroup oxygen in CHOL, labeled as CHOL O in Figure 7b, a peak location at ±22.8 Å is identified, in close agreement with experiment. Figure 7c shows the overall density histogram of all CER NS, along with separate histograms for molecules in the hairpin and extended conformations. At approximately ±25 Å, the hairpin CERs show two small peaks (one is slightly larger than the other), corresponding to the two layers formed by opposing CER headgroups. The histogram for the extended conformation shows only a single peak located roughly at the center between these two headgroup peaks, rather than aligning with the position of either layer of the hairpin headgroups.

Figure 7:

a) Slice from the center of the simulation cell for the 1:0.5:1 molar ratio of CER NS C₂₄:CHOL:FFA C₂₄ 6-leaflet system shown in Figure 6a using the color scheme specified in Figure 6b. b) Density profile of CER NS, CHOL, FFA. The density profile of the oxygen in the CHOL headgroup is also plotted, with the numerical values scaled by a factor of 10 to make them visible on this plot. c) Density profile for CER NS showing the hairpin and extended conformations separately.

Headgroups in lipid membranes form a network of intermolecular hydrogen bonds that affects membrane stability and permeability.^81,82 It is important therefore to measure hydrogen bonding between different lipid components within and between leaflets. Table 3 reports the average number of hydrogen bonds between each pair of lipid types in the 6-leaflet system measured separately for the leaflets with and without bulk water contact (i.e., outer leaflets represent the two leaflets in contact with the bulk water, inner leaflets represent the 4 leaflets that do not contact the bulk water). Considering first the overall number of hydrogen bonds scaled by the number of lipids in each leaflet type (i.e. inner or outer leaflets), we observe that lipids in the inner leaflets, which can participate in both intra-and inter-leaflet bonding, have approximately 3 times the number of lipid-lipid hydrogen bonds than the outer leaflets, which have only intra-leaflet bonding due to the interface with water; each lipid in the outer leaflet has 2.00 ± 0.04 hydrogen bonds with water. Intra-layer lipid-lipid hydrogen bonding of the inner leaflets (0.584 ± 0.023 bonds per lipid) is about half of all hydrogen bonding in these leaflets and slightly larger than in the outer leaflets (0.396 ± 0.020). We note that the inner leaflets in this analysis were dehydrated, preventing hydrogen bonding with water. How the small number of water molecules associated with the headgroups of the inner leaflets, as observed experimentally and in the CG configuration, affect hydrogen bonding is an interesting question that we reserve for separate investigation.

Table 3:

Normalized number of lipid-lipid hydrogen bonds in the reverse-mapped atomistic structure for the 6-leaflet system of CER NS C₂₄:CHOL:FFA C₂₄ with a 1:0.5:1 molar ratio. Results are shown for CERs, CHOL, and FFA in the inner and outer leaflets, as well as specifically the extended (exCER) and hairpin (hpCER) CERs in the inner leaflets. The values reported are the mean ± standard deviation, normalized by the number of the designated lipid type or pairs of lipid types in the specified leaflets. Raw data are provided in Table S5 of the supporting information.

Lipid Pair	Inner Leaflets	Outer Leaflets	Normalization
CER-CER	1.149 ± 0.034	0.500 ± 0.036	# CERs
CER-CHOL	0.267 ± 0.016	0.123 + 0.018	# CERs
CER-FFA	0.897 ± 0.024	0.299 + 0.024	# CERs
CHOL-CHOL	0.004 ± 0.004	0.003 ± 0.005	# CHOLs
CHOL-FFA	0.289 ± 0.029	0.105 ± 0.021	# CHOLs
FFA-FFA	0.442 ± 0.011	0.052 + 0.016	# FFAs
FFA-CHOL	0.149 ± 0.015	0.050 ± 0.010	# FFAs
ALL-ALL	1.178 ± 0.020	0.396 ± 0.020	# All lipids
exCER-exCER	0.144 ± 0.082	--	# CER-CER pairs
exCER-hpCER	0.443 ± 0.058	--	# CER-CER pairs
hpCER-hpCER	0.413 ± 0.053	--	# CER-CER pairs
exCER-CHOL	0.345 ± 0.139	--	# CER-CHOL pairs
hpCER-CHOL	0.655 ± 0.099	--	# CER-CHOL pairs
exCER-FFA	0.345 ± 0.067	--	# CER-FFA pairs
hpCER-FFA	0.655 ± 0.043	--	# CER-FFA pairs

Del Regno and Notman examined hydrogen bonding in simulations of 1:1:1 and 2:2:1 mole ratios of CER NS C₂₄:CHOL:FFA C₂₄ systems at two levels of hydration: (i) fully hydrated, akin to the outer leaflets, and (ii) low hydration with only two waters per lipid, similar to the inner leaflets.²⁷ In their work, the intra-lipid (i.e., lateral) hydrogen bonding did not depend on the water content, which disagrees with the findings presented here.²⁷ This difference in behavior may arise from the different compositions considered, the presence of a small amount of water in the Del Regno and Notman system, or from other subtle aspects (e.g., the use of a different force field). It is also possible that the presence of extended CER NS conformations, which were not included in the Del Regno and Notman study, is a crucial difference between the outer (hydrated) and inner (dehydrated) leaflets observed in this work.²⁷ Therefore, to further explore these questions, we examined the number of hydrogen bonds as a function of the different lipid types and CER NS conformations.

On average each CER in the inner leaflets hydrogen bonds with one other CER and one FFA, whereas in the outer leaflet only one out of every two CERs hydrogen bonds with another CER and only 1/3 hydrogen bond with FFA. Far fewer hydrogen bonds exist between CER and CHOL: only 1 in 4 CERs hydrogen bond with CHOL in the inner leaflets, and in the outer leaflets, the number is just 1 in 8. Virtually no CHOL-CHOL hydrogen bonding is observed anywhere in the system. Hydrogen bonds are found between FFA and CHOL, where, again, the outer leaflets have fewer bonds (~1/3) than the inner leaflets. There are virtually no FFA-FFA hydrogen bonds in the outer leaflets but approximately 1 hydrogen bond for every 2 FFA lipids in the inner leaflets, with two-thirds of these occurring between separate leaflets. CER conformation appears to have no effect on its hydrogen bonding with either CHOL or FFA: 35% of the hydrogen bonds between both CHOL and FFA are with the extended CER conformation (Table 3), which matches the fraction of CERs in the extended conformation. The situation is different for hydrogen bonding of CER with itself, where bonding between CERs that are both extended is lower by a factor of more than five than hydrogen bonding of the hairpin conformation with either another hairpin or the extended conformation (which occur in approximately equal amounts). This behavior may be linked to the relative amount of each conformation in the system and how CERs distribute themselves spatially, rather than an intrinsic difference in the ability of the extended CERs to hydrogen bond with each other.

Given the importance of hydrogen bonding on membrane barrier properties, the large differences in the amount of hydrogen bonding within the inner leaflets compared with the outer leaflets are likely to produce corresponding differences in permeability. One would expect, therefore, that permeability measurements derived from simulations of a bilayer sandwiched between bulk water layers would be different than from simulations of multilayer systems containing extended CER conformations without large amounts of water between the layers. Because of this, simulated permeability measurements of bilayers in contact with bulk water, or stacked upon each other without extended conformations, should be interpreted cautiously, especially when compared with experimental permeability measurements across either the SC or model SC lipid membranes.

Conclusions

In this work, we present a novel CG force field for CHOL, derived using the MS-IBI method,⁴⁸ that is compatible with our previously developed MS-IBI-based CG force fields for CER NS, FFA and water.^32,43,44 Together these provide a set of force fields that can be used to examine SC lipid systems exhibiting SPP-like ordering. In this work, the CHOL-CHOL self-interactions and CHOL-CER and CHOL-FFA cross interaction potentials were optimized using a diverse set of atomistic target states ranging from bulk fluids to pure bilayers and mixed bilayers. The resulting force fields enable close agreement between the structural properties of the CG and atomistic systems studied. The CHOL force field was further validated by comparing bilayer structural properties of preassembled atomistic, preassembled CG, and self-assembled CG structures for mixtures of CHOL with CER NS and FFA that were not used as target states for optimization; agreement was again good indicating that the CG model accurately reproduces atomistic bilayer structures. To probe multilayer structures that should be more representative of experiments (e.g., Mojumdar, et al.¹⁸), self-assembled bilayer and 4- and 6-leaflet systems were simulated and compared for mixtures of CER NS C₂₄:CHOL:FFA C₂₄ with 1:0.5:1 molar ratios. Differences between the inner and outer leaflets in the average APL, tilt angle, S₂ order parameter, and bilayer thickness are relatively small even though a significant number of extended CERs (~35–36% of total CERs in interior layers) are present in the inner layers of the multilayer structures, which affects the morphology and arrangement of lipids in-plane as well as lipid-lipid interactions spanning adjacent layers. Because experimental studies, such as neutron scattering and FTIR, average properties over dozens of lamellae, the results are largely dependent on the structure of interior layers, and thus the inner bilayer of the 6-leaflet structures provides the best comparison to experimental measurements. Simulations of self-assembled 6-leaflet CER NS C₂₄:CHOL:FFA C₂₄ 1:X:1 systems, where the CHOL molar ratio, X, ranged from 0 to 1, demonstrated that interdigitation, fluidity, and the number of packing defects increase with increasing CHOL content. The results also indicate that the size of FFA and CER clusters reduces with increasing CHOL, suggesting that CHOL may improve the miscibility of these two components.

To further compare with experiment and examine atomistic level properties, a simple reverse-mapping procedure was used to generate an atomistic 6-leaflet containing CER NS C₂₄:CHOL:FFA C₂₄ with a 1:0.5:1 molar ratio, using the corresponding CG self-assembled structure as reference. This reverse-mapped structure preserved the conformation of CERs (i.e., hairpin or extended) and in-plane morphology of the associated self-assembled structure. Compared to previous work,^26,45 which used only pre-assembled bilayer systems, the simulated NSLD curves using the inner layer of the reverse mapped structure showed much closer agreement with experimental NSLD curves for a model SPP system,¹⁷ highlighting the importance of considering multilayer structures. Furthermore, it was observed that approximately half of the lipid-lipid hydrogen bonds in the inner portion of the multilayer system exist between lipids in separate leaflets (i.e., inter-layer hydrogen bonding), which may differentiate barrier properties through the inner layers from the outer layers or bilayer structures. This multiscale approach allows for the exploration of atomistic self-assembled multilayer configurations that capture both hairpin and extended CER conformation and unbiased morphologies rather than arbitrarily arranged pre-assembled configurations, which makes the simulation of systems that are more representative of experimental studies possible. Given the significant impact of extended CERs on the observed properties, this work highlights the need for further study into the role of the different amounts of extended CERs on system properties. With the parameterization of additional CER headgroups for the CG model, this approach can be applied to other experimentally realized model systems^12,83,84 and provide molecular-level explanations for the observed experimental behavior.