Phospholipid Chain Interactions with Cholesterol Drive Domain Formation in Lipid Membranes

Abstract

Cholesterol is a key component of eukaryotic membranes, but its role in cellular biology in general and in lipid rafts in particular remains controversial. Model membranes are used extensively to determine the phase behavior of ternary mixtures of cholesterol, a saturated lipid, and an unsaturated lipid with liquid-ordered and liquid-disordered phase coexistence. Despite many different experiments that determine lipid-phase diagrams, we lack an understanding of the molecular-level driving forces for liquid phase coexistence in bilayers with cholesterol. Here, we use atomistic molecular dynamics computer simulations to address the driving forces for phase coexistence in ternary lipid mixtures. Domain formation is directly observed in a long-timescale simulation of a mixture of 1,2-distearoyl-sn-glycero-3-phosphocholine, unsaturated 1,2-dilinoleoyl-sn-glycero-3-phosphocholine, and cholesterol. Free-energy calculations for the exchange of the saturated and unsaturated lipids between the ordered and disordered phases give insight into the mixing behavior. We show that a large energetic contribution to domain formation is favorable enthalpic interactions of the saturated lipid in the ordered phase. This favorable energy for forming an ordered, cholesterol-rich phase is opposed by a large unfavorable entropy. Martini coarse-grained simulations capture the unfavorable free energy of mixing but do not reproduce the entropic contribution because of the reduced representation of the phospholipid tails. Phospholipid tails and their degree of unsaturation are key energetic contributors to lipid phase separation.

Introduction

Lipid mixing is a fundamental problem in cellular biology. How lipids self-associate and interact with membrane proteins is crucial for the function of cell membranes. The lipid raft hypothesis was initially conceived to explain the difference in membrane sorting between the apical and basal sides of epithelial cells (1), although membrane domains had been suggested earlier (2). The idea of membrane sorting, with cholesterol-sphingomyelin interactions as an organizing principle, changed the way lipid membranes had been traditionally viewed with a much-enhanced bioactive role. “Lipid raft” has become a broadly used term, but lipid rafts are generally thought to be small (10–100 nm), dynamic domains in cell membranes enriched in cholesterol, sphingomyelin (or other saturated lipids), and specific membrane proteins (3). There has been considerable research and debate on the existence and characterization of rafts because of their implicated role in cellular signaling and signaling related disease (3). Stimulated emission depletion nanoscopy has been used to observe inhomogeneity in living cells (4) and point to the importance of sphingolipids and the cytoskeleton in domain formation (5). The composition and nanometer resolution accessible by high-resolution secondary ion mass spectrometry has called into question a central tenant of the current raft hypothesis, locally enriched regions of cholesterol, although sphingomyelin domains have been observed (6, 7, 8, 9). It is becoming clear that cells have dynamic nanoscale domains, likely enriched in different lipids and membrane associated proteins depending on organism, cell type, and organelle. We are gaining an appreciation for the complexity and intricacies of cell membranes and their molecular-level interactions, and the role of lipids in transmembrane protein function is still being characterized.

A major bottleneck to studying cellular membranes is their diversity, with thousands of types of lipids, membrane proteins, and active processes such as enzyme catalysis, vesicle fusion and fission, and lipid-transport proteins. Eukaryotic membranes display a gradient in the structure and lipid composition from the endoplasmic reticulum to the plasma membrane: from low (0–5 mol%) to high (25–50 mol%) cholesterol content (10). There is also a high concentration of transmembrane proteins and interactions with the cytoskeleton, which has been implicated in cellular membrane sorting and clustering (11). Because of the many hurdles for characterizing in vivo lipid domains, model vesicles have been used extensively (12, 13, 14, 15, 16, 17, 18, 19). It has been observed that cholesterol induces phase separation in model giant unilamellar vesicle (GUV) mixtures with saturated and unsaturated lipids (20), with a liquid-ordered (l_o) phase coexistence with a liquid-disordered (l_d) phase. Great effort has been made in characterizing the phase diagrams for cholesterol-containing lipid bilayers and monolayers (21). Ternary and quaternary phase diagrams have been determined for many lipids with cholesterol using NMR, fluorescence spectroscopy, and many other methods (22, 23, 24, 25, 26). Stimulated emission depletion nanoscopy recently showed that many fluorescently labeled lipid analogs mispartition between l_o and l_d domains in GUVs compared to their native counterparts, and, importantly, GUVs composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine/sphingomyelin/cholesterol are probably not good models for cell membranes (27).

The fundamental basis for membrane domains is lipid-lipid and lipid-protein interactions, which are difficult to probe experimentally at the single-molecule level. Computer simulations provide a unique view of membrane systems that complements experimental data, and have been used to study membrane phase behavior (28). Coarse-grained (CG) simulations have been used extensively to study membrane domain formation (28, 29, 30), including a recent simulation mimicking a real cell’s plasma membrane (31). Given the prevalent use of CG models to study lipid mixing, it is crucial to assess their possible limitations. Neglecting lipid chain entropy is a necessary part of coarse-graining and may be a relevant choice for a great number of problems but limits the thermodynamic resolution of Martini and models of similar detail. Atomistic simulations were only very recently shown to observe phase separation in a 10-μs simulation on a small bilayer patch (15 × 15 nm patch) (32). Atomistic simulations of smaller model bilayers have shown many critical details regarding the properties of cholesterol-containing bilayers. The condensing effect of cholesterol was shown in early simulations of 10s of nanoseconds (33, 34). There have been many atomistic simulations characterizing cholesterol interactions in lipid bilayers, with favorable packing between the flat face of cholesterol and saturated lipid tails (35, 36). Polyunsaturated lipid tails have been shown to pack poorly with cholesterol (37). Long-timescale simulations with the all-atom CHARMM36 force field have shown hexagonal packing of lipids in the l_o phase, consistent with NMR measurements (38). Free energies for lipid processes are difficult to calculate because of slow dynamics, strong electrostatic interaction for the head groups, water ordering and “binding” at the interface, and collective interactions between neighboring lipids. Using umbrella sampling, cholesterol has been shown to have a lower free energy in ordered bilayers (39, 40, 41). We determined the free energy for removing a single 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid from bilayers with (up to 40 mol%) and without cholesterol (42). Contrary to conventional thinking that cholesterol and a saturated lipid interact favorably, we found that DPPC had a lower free energy in the bilayer without cholesterol. This idea that cholesterol is “pushing” lipids, in addition to the attraction between cholesterol and the saturated lipid, has been suggested using nearest-neighbor recognition measurements (43). What is cholesterol’s role in lipid bilayer phase behavior?

We have addressed the thermodynamics for the mixing of saturated and unsaturated PC lipids with cholesterol using atomistic and CG computer simulations. Atomistic molecular dynamics simulations were used to observe domain formation during a 10-μs simulation from a random mixture. We used thermodynamic integration (TI) calculations to determine the free energy for exchanging an unsaturated and saturated lipid between the l_d and l_o phases. The free energy transformation was designed to get accurate statistics by applying a minimal chemical change to the system, i.e., changing four double bonds to single bonds. The free energy for changing a 1,2-dilinoleoyl-sn-glycero-3-phosphocholine (DLiPC) to a 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) lipid in any l_d bilayer is favorable by ∼20 kJ/mol, irrespective of the composition or temperature, even in a DLiPC bilayer with 40 mol% cholesterol. In a gel phase, the free-energy difference is more favorable (∼45 kJ/mol), with enthalpically favorable packing of the lipid tails. In the l_o phase, we find a free-energy difference of ∼35–40 kJ/mol, which is strongly temperature- and concentration-dependent and has a large unfavorable entropy change. Martini CG simulations show that the total free energy of lipid exchange is similar to the atomistic value, but the contributions are different. We discuss the implications of our results on membrane phase behavior and cell biology.

Methods

All-atom simulations

Simulations were conducted using GROMACS version 4.5 (44). The v-rescale method was used to maintain the temperature with a coupling constant of 0.1 ps (45). Semiisotropic pressure coupling with the Berendsen weak coupling method (46), a compressibility of 4.5 × 10⁻⁵ bar⁻¹, a coupling constant of 2.5 ps, and a 1-bar reference pressure was used. The reaction-field method (47) was used for long-range interactions with a 1.4-nm cutoff, with 62 for the dielectric constant of bulk water. A 7-fs time step was used by adding an additional bond from the hydrogen on the hydroxyl of cholesterol to the carbon adjacent to the oxygen, thus constraining the fast-angle bending of the light hydrogen. Additionally, the mass of the water hydrogens was set to 4 amu at the expense of the oxygen (reduced to 12 amu) as suggested in (48). The LINCS algorithm (49) was used to constrain bonds and angles, and SETTLE for water (50). The united atom Berger lipid parameters were used for DSPC and DLiPC (51), with the double-bond dihedrals from (52). The cholesterol model was based on the GROMOS force field (53). The simple point change water model was used (54).

We tested the effect of the 7-fs time step and reaction-field long-range electrostatics on the thermodynamics of lipid mixing by conducting TI calculations with particle mesh Ewald for electrostatics and a 2-fs time step. The free energies are within the statistical error (Table 2), and because we are concerned with thermodynamic properties, this should not be a problem. The kinetic properties, particularly for the heavy water, would be influenced somewhat by the longer time step and shifted mass (48).

Table 2.

Atomistic ΔG_un-sat Values

Bilayer (Phase)	Temperature (K)	ΔGun-sat (kJ/mol)
DLiPC	300	−20.2 ± 1.0
DLiPC	310	−19.9 ± 0.7
DLiPC	320	−20.3 ± 0.6
DLiPC	335	−20.4 ± 0.5
DLiPC (2fs, PME)	300	−19.8 ± 1.4
DLiPC-40%CHOL	300	−21.9 ± 0.8
DSPC (liq.)	335	−21.4 ± 0.8
DSPC (gel)	300	−44.6 ± 3.2
DSPC-40%CHOL	300	−39.9 ± 1.3
DSPC-40%CHOL	310	−37.8 ± 1.7
DSPC-40%CHOL	320	−29.8 ± 1.9
Stripe-Ord	300	−35.3 ± 2.6
Stripe-Dis	300	−21.0 ± 2.2

Martini simulations

GROMACS 4.5 (44) was used to run Martini 2.0 lipid CG simulations (55). We also tested the Martini 2.2 cholesterol model (31). We used a 20-fs time step for the simulations. Electrostatic interactions were truncated at 1.2 nm and treated with a switch function from 0 to 1.2 nm. A dielectric constant of 15 is used for the electrostatic interactions. Lennard-Jones interactions were cut off at 1.2 nm, and a switch function was used between 0.9 and 1.2 nm. The Berendsen thermostat and barostat were used with coupling constants of 0.4 and 1.1 ps, and a compressibility of 6.5 × 10⁻⁵ was used for the semiisotropic pressure coupling (46).

Systems

A large (∼16 × 16 nm) box with 352:352:320 DLiPC:DSPC:CHOL lipids was first built with the Martini model. The system was equilibrated at 350 K to create a homogeneously mixed membrane. This structure was converted back to atomistic detail using the method in (56). This large bilayer was simulated for 10 μs at 300 K with atomistic parameters as described above.

Using the Martini CG model, we ran a 5-μs simulation of a rectangular bilayer system with a 168:252:180 DLiPC:DSPC:CHOL (cholesterol) ratio of lipids and observed phase separation into l_o and l_d. As Martini dynamics are roughly four times faster than atomistic, this is ∼20 μs, and therefore this was long enough to observe phase separation in this system. Because of periodic boundary conditions, we have infinitely long stripes of each phase. The system phase separated into an l_o and l_d phase, as expected from previous simulations (57). We then converted the CG structures to atomistic representation (56), and the simulation was continued with atomistic parameters.

Thermodynamic integration

We ran TI calculations to determine the free energy for changing a saturated DSPC into a polyunsaturated DLiPC. Both lipids have 18-carbon tails and therefore the same number of particles in the united-atom Berger force field. For the conversion, we change four single bonds into four cis-double bonds, changing the bond lengths, angles, dihedrals, and Lennard-Jones parameters. Because the Berger model is united-atom, we do not have to change the number of atoms, simply changing the CH2 atom types to CH. This was accomplished in two steps: the force constant for the improper dihedral (which keeps the double bonds planar) was first reduced from 100 to 15. For this transformation we used 11 evenly spaced λ windows, and each simulation was 140 ns. The rest of the parameters including removing the improper dihedral and changing the Lennard-Jones parameters, and the bond angles were alchemically changed from DLiPC parameters to DSPC parameters in a second calculation. We note that for the second transformation, state A (DLiPC) already had a reduced improper force constant of 15. As mentioned above, a second set of thermodynamic integration calculations that reduce the improper force constant from 15 to 0 was also calculated. For this transformation, we used 18 λ values and 140 ns for each simulation. Changing all the parameters in one step led to instabilities at high λ values because of the harmonic improper term. By adding together both free energies, we obtain the total free energy for mutating DLiPC to DSPC. The error in dH/dλ was estimated using the block averaging procedure (58) for each λ simulation, and error propagation was used to estimate the total error for ΔG_un-sat.

For the Martini model, we calculated the free energy for converting a saturated four-bead DSPC molecule into a four-bead DLiPC. Because of the 4-to-1 mapping in Martini, lipid tails represent a range of atomistic carbons, and we note that the four-bead saturated tail is normally referred to as DPPC. A comparison of five-bead lipids could be of future interest. TI calculations with the Martini model for the DLiPC to DSPC transformation had only changes in the central tail bead’s Van der Waal parameters and the bond angles.

Centered difference—entropy/enthalpy decomposition

From the basic definition of entropy (Eq. 1), the entropy difference between two states can be estimated from the free-energy difference at two different temperatures (Eq. 2).

$$S=-{\left(\frac{\partial G}{\partial T}\right)}_{N,P}$$ (1)

$$\mathit{\Delta }{S}_{B-A}=-\frac{\mathit{\Delta }{G}_{B-A}^{TI}\left(T+\mathit{\Delta }T\right)-\mathit{\Delta }{G}_{B-A}^{TI}(T-\mathit{\Delta }T)}{2\mathit{\Delta }T}\text{.}$$ (2)

The difference in enthalpy can then be calculated using the difference in free energy and entropy (i.e., from ΔG = ΔH−TΔS).

Results

Atomistic domain formation

Starting from a random lateral distribution of cholesterol, DLiPC, and DSPC, we ran a 10-μs simulation and directly observed demixing of the bilayer (Fig. 1). At the start, we observe a more homogenous distribution in the lateral composition. During the simulation, the number of DSPC-DSPC contacts increases, the DLiPC-DSPC contacts decrease, and the number of DSPC-cholesterol contacts increases marginally. This indicates phase separation with preferential DSPC-DSPC interactions. Because of the small box size, we do not expect full phase separation to occur, with most lipids near an interface between the ordered and disordered domains. The total potential energy of the system decreases as the domain forms (Fig. 1). The drop in energy is due to more favorable Lennard-Jones interactions and bonded interactions, whereas the short-ranged electrostatic energy remains relatively constant despite large fluctuations. These results show that atomistically these lipids will undergo phase separation, but much larger simulations and longer timescales would be needed to observe bulk phase separation. Further research is needed to assess how long simulations should run and how large systems need to be to study atomistic lipid phase separation.

Figure 1.

(A) Top view of the large DSPC (red):DLiPC (blue):cholesterol (yellow) at the start of the simulation. The periodic box is shown as a white square. (B) A snapshot after 10 μs of simulation, showing domain formation, is given. (C) Energetic contributions during bilayer phase separation in the large DSPC:DLiPC:cholesterol bilayer are shown. Each component was set to 0 kJ/mol at the start of the simulation. (D) The number of contacts between each type of lipid and DSPC during phase separation is shown. A distance cutoff of 1.0 nm between the central carbon in the glycerol backbone for the PC lipids and the oxygen of cholesterol was used. To see this figure in color, go online.

Martini lipid free energies

By determining the free energy to convert one lipid to another in both phases, we can determine the relative concentration of each phase or the excess chemical potential difference. The total chemical potential of a lipid (μ) is a combination of its excess chemical potential (μ_ex) and the ideal gas contribution (μ_ideal), which is directly related to its concentration, or mole fraction in that phase (X).

$${\mu }_{DSPC}={\mu }_{ex}+{\mu }_{ideal}={\mu }_{DSPC,ex}+RTln{X}_{DSPC}\text{.}$$ (3)

At equilibrium, the total chemical potential for each type of lipid must be equal in all phases of the system:

$${\mu }_{DSPC,ORD,ex}+RTln{X}_{DSPC,ORD}={\mu }_{DSPC,DIS,ex}+RTln{X}_{DSPC,DIS}\text{.}$$ (4)

Fig. 4 illustrates the thermodynamic cycle, in which the excess chemical potential difference (Δμ_ex) is calculated from simulations of a single molecule in a specific phase. The excess chemical potential accounts for all the energetic contributions except for the concentration effects. Rearranging Eq. 4, the change in excess chemical potential is equal to the free energy due to the concentration difference in each phase.

$$\mathit{\Delta }{\mu }_{DSPC,ORD-DIS,ex}=RTln\frac{X_{DSPC,ORD}}{X_{DSPC,DIS}}\text{.}$$ (5)

Figure 4.

Thermodynamic cycle for exchanging a single DSPC in the l_o phase for a DLiPC in the l_d phase. We computed the free energy for the top and bottom steps, the difference of which is also the difference between the two sides of the cycle. Combining these two components gives the total free energy for exchange (ΔΔG_exchange) of 14 kJ/mol. To see this figure in color, go online.

The right side of Eq. 5 is DSPC’s contribution to the mixing entropy of the system, which is zero when the concentration is equal in both phases, meaning the chemical potential is the same in both phases as well. Because of the thermodynamic cycle in Fig. 4, we can equate the sides with the top and bottom arms in the cycle.

$$\mathit{\Delta \Delta }{G}_{exchange}={}_{}\mathit{\Delta }{\mu }_{DSPC-DLiPC,ORD,ex}+\mathit{\Delta }{\mu }_{DLiPC-DSPC,DIS,ex}=\mathit{\Delta }{\mu }_{DSPC,ORD-DIS,ex}+\mathit{\Delta }{\mu }_{DLiPC,DIS-ORD,ex}\text{.}$$ (6)

With atomistic models, it is easier to calculate the sides of the thermodynamic cycle (i.e., μ_{DSPC−DLiPC, ORD, ex}). Another approach is to calculate the free energy for moving a lipid from one phase to the other, but this is also technically challenging. A more accessible approach for atomistic simulations is to mutate one lipid to the other in each phase. By calculating the free energy for exchange (ΔΔG_exchange), we equate it to the excess chemical potential difference of DSPC and DLiPC in the two phases.

To first illustrate that our free-energy calculations correspond to the excess chemical potentials, we have used the Martini CG model. With this model, we are able to directly observe bulk phase separation, thereby obtaining the concentrations for the right-hand side of Eq. 5. We also calculate the free energy for mutating a single lipid from unsaturated to saturated (ΔG_un-sat) in both phases, which should be the left-hand side of Eq. 5. Fig. 2 illustrates the connection between the chemical potential difference and concentration using the Martini model. We first ran a 5-μs simulation and observed domain formation in a long rectangular box, which creates a phase-separated stripe because of periodic boundary conditions. From the number density of each lipid in the l_d and l_o phase (Fig. 2 A), we determined ΔΔG_exchange to be 16.7 kJ/mol. We then restrained a single lipid in each phase and used TI to determine ΔG_un-sat, which we then used to determine a ΔΔG_exchange of 14.3 kJ/mol. The agreement between these two methods for calculating ΔΔG_exchange shows that TI can be used to study lipid mixing with the benefit of reduced sampling.

Figure 2.

Calculating ΔΔG_exchange using lipid densities and TI calculations with the Martini model. (A) The phase-separated bilayer of DSPC (red), DLiPC (blue), and cholesterol (yellow), looking down on the top of the bilayer, is shown. (B) The average lipid densities across the bilayer, calculated after the bilayer phase separated, are given. To see this figure in color, go online.

We determined ΔG_un-sat for small lipid systems with the Martini model. First, we built small bilayers for the l_d and l_o phases based on the lipid densities in the stripe-domain system, 84:4:12 and 2:59:39 ratios of DLiPC:DSPC:CHOL, respectively. Table 1 shows that these systems have very similar values for ΔG_un-sat as the stripe bilayer, 6.1 kJ/mol (l_d) and −9.6 kJ/mol (l_o). Combining these two numbers using Eq. 6 gives a ΔΔG_exchange of 15.7 kJ/mol, which is in better agreement with the ΔΔG_exchange from the lipid densities, likely due to better sampling and possible artifacts from restraining the lipid in the stripe phase. ΔG_un-sat values were also calculated for one- and two-component mixtures (Table 1). In the disordered, pure DLiPC bilayer, ΔG_un-sat was 9.5 kJ/mol, and it was −3.2 kJ/mol in the pure DSPC bilayer. A higher ΔG_un-sat of −13.8 kJ/mol was calculated in a DSPC-40 mol% cholesterol mixture, because this system is more ordered than the l_o system.

Table 1.

Martini ΔG_un-sat Values

Bilayer	Temperature (K)	ΔGun-sat (kJ/mol)
DLiPC	300	9.5 ± 0.1
DSPC	300	−3.5 ± 3.0
DSPC-40%CHOL	300	−21.4 ± 2.1
Stripe-Ld	300	7.3 ± 0.9
Stripe-Lo	300	−13.2 ± 3.1
DSPC-40%CHOL – v2.2	300	−13.8 ± 1.5
Small-Ld – v2.2	300	6.1 ± 1.6
Small-Lo – v2.2	300	−9.6 ± 1.9
Stripe-Ld – v2.2	300	5.8 ± 2.1
Stripe-Lo –v2.2	300	−8.5 ± 2.4

An improved Martini cholesterol model was recently shown to reduce the solid nature of l_o bilayers in better agreement with experiments and simulations (31). We tested the effect of the Martini v2.0 compared to Martini v2.2 cholesterol in a DSPC-40 mol% cholesterol bilayer (Table 1). As expected, the newer cholesterol resulted in a lower ΔG_un-sat (−13.8 kJ/mol compared to −21.4 kJ/mol), because the bilayer is less ordered. The stripe-domain bilayers ΔG_un-sat showed this same trend (Table 1).

Atomistic lipid free energies

Based on the Martini simulations, we are confident that we can use TI calculations to determine the free energy of lipid mixing. We determined the free energy to alchemically convert DLiPC to DSPC in a number of atomistic membrane systems. Fig. 3 shows the systems studied: pure DLiPC and DSPC (at 335 K) l_d bilayers, a 3:2 DSPC:CHOL mixture in the l_o phase, and a gel DSPC bilayer. In all membrane environments, we find a favorable free energy for converting DLiPC to DSPC. Table 2 lists the free energy in various membranes at a number of different temperatures and phases. The free energy is favorable for changing DLiPC to DSPC in all cases and more favorable for the gel DSPC and the l_o phase. ΔG_un-sat is ∼−20 kJ/mol in the l_d phase, both in the DLiPC bilayer at 300 K and in the DSPC bilayer at 335 K and the DLiPC bilayer with 40% cholesterol. We find the lowest free energy of −45 kJ/mol in the DSPC bilayer at 300 K, which is in the gel state. In the l_o phases, we find intermediate values for the free energy that are dependent on the amount of cholesterol and the temperature of the system.

Figure 3.

Atomistic free energies for the alchemical transformation of DLiPC to DSPC in different membrane environments. The colors are the same as in Fig. 2, with water colored white. To see this figure in color, go online.

We determined ΔΔG_exchange for exchanging DLiPC and DSPC between l_d and l_o phases in a stripe domain by computing the top and bottom portion of the thermodynamic cycle shown in Fig. 4. As was shown with the CG model, the free energies for mutating the two lipids in either phase is equal to the free energy for moving each lipid to the opposite phase (the side edges of the thermodynamic cycle in Fig. 4). The agreement with the Martini model is within the error, with a ΔΔG_exchange of 14 kJ/mol for both atomistic and for Martini. We note that these domains may not reflect the equilibrium lipid composition, as they were constructed from Martini phase-separated systems. But the fact that we find very similar ΔG_un-sat for the different phases as for the small bilayer patches shows that qualitatively, the agreement is good (Table 2). For the l_d domain, we find a free energy of −21 kJ/mol in close agreement with all other liquid phase systems. The free energy of −35 kJ/mol for the l_o phase is close to the −39 kJ/mol for the small 40% cholesterol system. The discrepancy is likely due to the different lipid compositions between the small system and the l_o stripe phase, which likely had less cholesterol and some DLiPC. Overall, ΔΔG_exchange is unfavorable by 14 kJ/mol, which is expected given that they phase separate (Fig. 3). It is important to note that although the agreement between Martini and atomistic systems for ΔΔG_exchange is good, the contributions are completely opposite.

Atomistic entropy and lipid conformational freedom

By determining ΔΔG_exchange for the atomistic model at different temperatures, we can estimate the change in entropy using the centered difference method (see Methods). The centered difference method that we have used to estimate the entropy and enthalpy contributions is prone to large errors, so we stress the large difference between the two phases, not the specific values. For the atomistic model, in the l_d phase, we find a near-zero change in entropy compared to an unfavorable change of −TΔS_un-sat of ∼156 kJ/mol in the l_o phase (Table 3). We note that this is the entropy change for the entire system, not just the configurational entropy of the perturbed lipid. In the l_o bilayer, the exchange results in a favorable enthalpy of −194 kJ/mol. The packing of saturated lipids in the l_o phase results in large favorable enthalpy change but is opposed by an unfavorable entropy change. This matches our expectations from the reduced potential energy in the large system that phase separates (Fig. 1). Adding the contributions together, −TΔΔS_exchange (the entropy change for exchanging lipids) for the atomistic model is −158 kJ/mol, and the enthalpy change, ΔΔH_exchange, is 176 kJ/mol. For the Martini model, we find a −TΔΔS_exchange of −21 kJ/mol, and the ΔΔH_exchange is 38 kJ/mol (Table 3). Compared to the atomistic model, the Martini model has the same trends in the entropy and enthalpy contributions but much-reduced magnitudes.

Table 3.

Entropy and Enthalpy Decomposition for Unsaturated to Saturated Lipid Alchemical Transformations

Bilayer (Temperature (K))	Negative TΔS (kJ/mol)	ΔH (kJ/mol)
AA DLiPC (310)	−2	−18
AA DSPC-CHOL (310)	156	−194
CG – Small-Ld – v2.2	19	−12
CG – Small-Lo – v2.2	40	−50

AA, all-atom.

We aligned the molecular conformations of a single DLiPC and DSPC in the l_o and l_d phases (Fig. 5). Both lipids adapt to the local environment of the bilayer, with restricted conformations in the l_o domain and more varied molecular conformations in the l_d phase. In the l_d phase, we find that both DLiPC and DSPC sample a large distribution of different conformations, although the distribution for DLiPC is noticeably broader than DSPC. Although not quantitative, these figures strongly suggest that the large entropic contribution is not solely from changes in configurational entropy of the single exchanging lipid.

Figure 5.

Single lipid conformations in the different domains of the stripe bilayer. Each structure was aligned using a root mean-square deviation fit. To see this figure in color, go online.

Discussion

Cholesterol-induced domain formation

We have used molecular dynamics simulations to explore the atomic level details for cholesterol mixed with saturated and polyunsaturated phospholipids. Free-energy calculations that, to our knowledge, are novel are used to determine the thermodynamic basis for phospholipid partitioning between l_d and l_o phases. In general, our results support the traditional view of the ordering effect of cholesterol on saturated phospholipids. This behavior is often explained to be due to the chemical structure of cholesterol, with a small head group and rigid sterol body, that interacts favorably with saturated lipid tails. Our results show that a major driving force for domain formation is due to the unfavorable entropy of a polyunsaturated phospholipid residing in the ordered domain. Previously, we showed that saturated DPPC molecules prefer disordered bilayers compared to ordered, cholesterol-rich bilayers (42). This suggests that domain formation is largely due to unfavorable interactions between the unsaturated lipid in an ordered lipid environment in addition to favorable enthalpic interactions between the saturated lipids with cholesterol.

The Martini model has been used extensively to study membrane domain formation (28, 57) because of the slow dynamics and computational cost of atomistic simulations (59). We observed the start of domain formation in a ternary lipid mixture of cholesterol, DLiPC, and DSPC using atomistic molecular dynamics computer simulations. The system is too small (15 × 15 nm bilayer) to observe true phase separation, in which interfacial interactions would dominate over the bulk behavior of the lipids in our small bilayer patch. This result shows that the Berger lipid parameters can qualitatively reproduce the experimental phase diagrams of model membranes with cholesterol, both saturated and unsaturated (phospholipids) (15, 60). This is in agreement with a previous study comparing Berger and Martini parameters for equilibrium domain formation in a cholesterol:DLiPC:DPPC mixture (32). In-depth analysis showed that Martini can reproduce the general structural mechanism for domain formation but is 40 times faster than the atomistic model (32). Many other previous atomistic simulations have shown preferential interactions of cholesterol with saturated lipids (33, 34). From our energy decompositions (Fig. 1), we show that domain formation is enthalpically favorable due to more trans bond conformations and Van der Waals interactions when cholesterol interacts with the saturated lipid tails. But the enthalpic gain is offset by a large and unfavorable entropic contribution, which we determined with free-energy calculations.

Atomistic free-energy calculations can address the underlying driving forces for domain formation. We use the Martini model to show that our free-energy calculations are directly related to the difference in concentration for each lipid in either phase. The advantage of using free-energy calculations is that we can use smaller bilayers and obtain adequate statistics because of the small perturbation of changing four double bonds to single bonds. From the atomistic simulations, the most favorable environment for the transformation of DLiPC to DSPC is in the gel-DSPC phase, followed by the l_o phase. There is a trend that more cholesterol makes the transformation more favorable: there was more local cholesterol in the 3:2 DSPC:CHOL bilayer than in the l_o phase in the stripe-domain system, and a lower ΔG_un-sat in the 3:2 system. The favorable free energy of the saturated lipid is due to the formation of stronger enthalpic interactions at the expense of considerable entropy. In all the l_d bilayers we studied, we found very similar values for the ΔG_un-sat because of slightly more favorable enthalpic interactions for the saturated lipid. In the l_d phase, there is a near-zero change in entropy for changing the unsaturated to saturated lipid, because the disordered liquid state does not restrict lipid tail conformations. Interestingly, ΔG_un-sat in the 40 mol% cholesterol mixed with DLiPC was the same as the l_d phase bilayers, suggesting that polyunsaturated lipids cannot pack into an l_o phase.

We could directly compare our ΔΔG_exchange values to the concentration differences in the two phases determined from the tie lines of experimental phase diagrams. Quantitative comparison is not possible because we are unaware of a DSPC:DLiPC:Cholesterol phase diagram, and the tie lines from experimental diagrams are difficult to obtain accurately (61). Qualitatively, our results match experimental studies predicting enrichment of the saturated phospholipid in the l_o phase and the unsaturated lipid in the l_d phase. Direct comparison is also not possible because of our use of the CG stripe bilayers to construct the atomistic phase-separated bilayers. In this work, we are more interested in the clear trends, which are supported by the small bilayer results, and not qualitative comparison. The similarity of ΔΔG_exchange for CG and atomistic models also supports this methodology, but the difference in the components of ΔΔG_exchange suggests this will not always be the case, and care is needed when obtaining atomistic bilayer starting structures from CG simulations.

Models: when do chemical details matter?

The Martini model has been used extensively to study lipid bilayer domains (28). By determining thermodynamic parameters for the process of lipid mixing, we are able to address the molecular driving forces. We find that although Martini does semiquantitatively match the atomistic ΔΔG_exchange, the underlying components are different. For the atomistic model, we find that converting the unsaturated lipid to saturated in the l_d phase is favorable, whereas for Martini this is unfavorable. The entropy/enthalpy decomposition shows that Martini had the same trends as atomistic but much lower total contributions. This is most likely due to the reduced representation in the Martini model, in which a large portion of the lipid’s entropy has been replaced by enthalpic interactions. This was previously noted in the first version of the Martini model (62). Whether either model is correct remains to be settled with experimental evidence, but the difference is striking.

The success of Martini in modeling lipid phase behavior (28, 30, 57) and other models of similar detail (63) suggests that some degrees of freedom can be neglected and still observe many interesting phenomena. Even more simple continuum models, phenomenological models, and lattice models have reproduced many aspects of lipid mixing and added to our understanding of lipid phase behavior (64, 65, 66, 67, 68). But our results call into question using Martini—and likely other CG models of similar and lower resolution—to obtain quantitative thermodynamic analysis for lipid mixing at the molecular level. One may obtain accurate free energies of transfer and the distribution of all the molecules in an entire plasma membrane patch (31), but the underlying molecular-level physical mechanism and thermodynamics are not necessarily correct. This is not to deny the utility of such models but to set boundaries on the types of problems that can be solved with a particular model. We show that the recently updated Martini cholesterol parameters improve the agreement with atomistic free energies for DLiPC-DSPC lipid exchange. This is due to the earlier cholesterol molecule forming a too-rigid l_o phase, noted in (31). Similar free-energy calculations may prove useful for parameterizing and validating lipid models, especially if linked to experimental thermodynamic data in the future.

Biomembrane implications

Our results show that phase separation in simple model systems is a complex process, and illustrates the importance of phospholipid conformations and double bonds on the molecular level energetics. Although the total free energy is relatively small, we find very high entropy and enthalpy contributions. Enthalpy-entropy compensation is a well-known phenomenon in many other biological problems, such as drug binding and protein-protein interactions (69). It has been suggested that the magnitude for the entropy is much too large to be attributed to conformation of the macromolecule and therefore must include solvation contributions (69). Based on our root mean-square deviation fit for DLiPC and DSPC shown in Fig. 5, we suggest that the conformational entropy change for the single exchanging lipid would be extremely small. We speculate that the large entropy change could be due to the “solvation” of the exchanging lipid by the surrounding lipids in the bilayer.

The large enthalpic and entropic contributions could be a convenient way for the cell to control lipid localization: with a high-fidelity switch between ordered-disordered. For example, being near a membrane protein or cytoskeleton may shift this balance. The large entropic contribution means that subtle changes in temperature could also be used to “activate” this lipid “switch.” It will be interesting to run similar free-energy calculations on membrane-protein-bound phospholipids. Most biologically relevant phospholipids have one saturated tail and one unsaturated tail, so investigating monounsaturated lipids using the same protocol would be of interest.

The phase behavior of simple lipid mixtures and the molecular-level details for lipid mixing have many biological applications. The complexity of a real cell membrane—with actin cytoskeleton, membrane proteins, ion gradients, and thousands of lipid types—makes simple model systems necessary to characterize the molecular details. Understanding the physicochemical properties of membranes at the molecular level will allow critical advances in personalized medicine, including drug delivery; membrane protein localization and function; new druggable sites on G-protein coupled receptors, ion channels, and multidrug transporters; and peptide aggregation such as amyloid peptides and cationic penetrating peptides. Methods similar to ours may help in many future investigations.

Conclusions

Phase separation in cholesterol, saturated, and unsaturated phosphatidylcholine lipid bilayers is described with molecular-level details. We show that lipid domain formation results in more favorable enthalpic interactions for the saturated lipid in the l_o phase but is accompanied by a large unfavorable shift in entropy. Both saturated and unsaturated lipids have similar conformations in each phase, suggesting the unfavorable entropy change is not simply due to conformational differences. The reduced number of degrees of freedom of the Martini model’s tails means the free energy for domain formation has little conformational entropy contribution. This suggests that although Martini can reproduce the general distribution of lipids in l_o and l_d phases, the molecular driving forces are different than atomistic models. Important atomistic details for lipid mixing are presented with implications for cellular-membrane-domain formation.

Author Contributions

W.F.D.B. and D.P.T. designed the research. W.F.D.B. performed the research and analyzed the data. W.F.D.B., D.P.T., and J.-E.S. wrote the manuscript.

Editor: Tobias Baumgart.