An Improved Highly Mobile Membrane Mimetic Model for Investigating Protein-Cholesterol Interactions

Abstract

Cholesterol (CHL) plays an integral role of modulating the function and activity of various mammalian membrane proteins. Due to the slow dynamics of lipids, conventional computational studies of protein-CHL interactions rely on either long-timescale atomistic simulations or coarse-grained approximations to sample the process. The highly mobile membrane mimetic (HMMM) has been developed to enhance lipid diffusion and thus used to facilitate the investigation of lipid interactions with peripheral membrane proteins and, with customized in silico solvents to replace phospholipid tails, with integral membrane proteins. Here, we report an updated HMMM model that is able to include CHL, a non-phospholipid component of the membrane, hence called HMMM-CHL. To this end, we had to optimize the effect of the customized solvents on CHL behavior in the membrane. Furthermore, the new solvent is also compatible with simulations using force-based switching protocols. In HMMM-CHL, both improved CHL dynamics and accelerated lipid diffusion are integrated. To test the updated model, we have applied it to characterization of protein-CHL interactions in two membrane protein systems, the human ${\beta }_2$-adrenergic receptor (${\beta }_2\text{AR}$) and the mitochondrial voltage-dependent anion channel 1 (VDAC-1). Our HMMM-CHL simulations successfully identified CHL binding sites and captured detailed CHL interactions in excellent consistency with experimental data as well as other simulation results, indicating the utility of the improved model in applications where an enhanced sampling of protein-CHL interactions is desired.

Graphical Abstract

Introduction

Membrane protein dynamics and function are influenced and even regulated by the heterogeneous lipid environment of biological membranes.^1,2 Among various lipids in mammalian cell membranes, cholesterol (CHL) is a unique sterol that can alter membrane physical properties such as thickness, fluidity, and curvature.^3,4 Such CHL-induced membrane effects have been suggested to cause indirect CHL modulations of protein structure and dynamics.^5–7 With the rapid developments in proteomics and structural biology, CHL binding proteins and putative CHL binding sites in membrane proteins have been discovered suggesting the possibility of direct CHL modulation of protein function.^8–10 Several CHL binding motifs have been defined based on protein sequence analysis and structural information.^11–13 Molecular docking studies and free energy calculations have provided support for some of these binding motifs in proteins such as G-protein coupled receptors (GPCRs).^14–16 Nevertheless, there is currently still no consensus as to whether CHL modulates protein functions through indirect membrane effects, direct binding to specific binding sites/motifs, or a combination of the two. Molecular dynamics (MD) simulations can address this question to some degree.^17–22 In support of CHL’s indirect influence on membrane proteins, the membrane thickening and ordering effects induced by a high CHL content can be directly obtained from MD simulations. Given sufficient time and sampling, MD simulations can also capture direct CHL binding to a membrane protein, thus allowing one to investigate how such a binding affects the protein’s structure, dynamics, and function.

A common challenge faced by MD simulations aiming at studying CHL-protein interactions is the relatively slow dynamics of lipids, which together with the limited timescales accessible to MD simulations, results in inadequate lateral motion and insufficient mixing of lipids during the simulations. Both from experiments^23,24 and from conventional atomistic simulations,^25,26 the lateral diffusion coefficients of phospholipids and CHL are estimated to be on the order of 10⁻⁸ to 10⁻⁷ cm²/s (0.1–1 Ų/ns), in membranes with CHL concentrations ranging from 0 to 50%. Based on this rate, a lipid molecule will need to, on the average, spend at least microseconds to travel across an average membrane protein simulation box with a typical lateral dimension of 100 Å. To achieve sufficient lipid mixing and sampling, microsecond-long atomistic simulations have been performed to successfully characterize lipid mixing,²⁷ as well as CHL binding and interactions with membrane proteins^28–34 However, without access to specialized (and limited) computational resources such as Anton,^35,36 it is still prohibitively expensive to routinely perform microsecond simulations. Coarse-grained (CG) simulations.^37,38 offer an alternative approach frequently used for better sampling of the slow lipid diffusion. Specifically for CHL, the CG methods have been used for mapping CHL binding sites,^39–43 or studying its effects on, e.g., the oligomerization of membrane proteins.^44–48 In CG models, several atoms are grouped and represented by one bead, thereby resulting in softer potentials and the ability of using longer timesteps, which in turn translate into more sampling compared to atomistic simulations. Nevertheless, CG models achieve this at the cost of losing detailed atomic descriptions, e.g., at the protein-CHL interface. Other efforts to enhance lipid mixing in simulations include accelerated MD (aMD),⁴⁹ surface-tension replica-exchange MD ($\gamma$-REMD),⁵⁰ replica exchange with solute tempering (REST),⁵¹ an alchemical approach based on Monte Carlo exchanges (MDAS),⁵² and hydrogen mass repartitioning (HMR),⁵³ although their application to membrane protein-CHL systems has been quite limited thus far.

The highly mobile membrane mimetic (HMMM) has been developed as an alternative approach for enhanced sampling of protein-lipid interactions.^54–58 In the original design of HMMM, the acyl tails of phospholipids are truncated and replaced by an organic solvent, 1,1-dichloroethane (DCLE), to represent the hydrophobic core of the bilayer.⁵⁴ This model has proven effective in increasing lipid lateral diffusion while recapitulating the energetics of amino acids membrane partitioning at the lipid-water interface,⁵⁹ and thus proven fruitful to capture membrane binding and interactions of a number of peripheral proteins.^54,60–73 Due to the polar nature of DCLE used in the original HMMM model, however, solvent molecules can cause undesirable intercalation as well as penetration between the helices of transmembrane proteins, an artifact that limited the application of the model to only single-pass transmembrane proteins.^74,75 To overcome this limitation, in silico solvents inspired by united-atom lipid force fields,^76–79 i.e., single carbon solvent ethane (SCSE) and single carbon solvent methane (SCSM), have been custom-parameterized to provide a less problematic representation for the membrane interior.⁵⁸ In particular, the solvent SCSE has been demonstrated to minimize solvent intercalation while maintaining membrane properties compared to conventional membranes, allowing the extension of the HMMM model to multi-pass transmembrane proteins.⁵⁸

The philosophy behind the previous parameterization of the in silico solvents to substitute lipid acyl chains lies in designing solvents that are small, nonpolar, and liquid. Its implementation relies on employing Lennard-Jones (LJ) particles with tunable LJ parameters to control their intra- and inter-species interactions.⁵⁸ A major problem in the previous implementation of the in silico solvents is the choice of LJ switching scheme⁸⁰ used in the MD algorithms, specifically the one in NAMD.^81,82 The previous model was parameterized for a potential-based LJ switching scheme, while the force-based LJ switching scheme is shown to be preferred with the CHARMM36 lipid force field⁸³ and generates more consistent bilayer properties.⁸⁰ As a result, the previously developed SCSE solvent exhibits unstable behaviors beyond 304 K when the force-based LJ switching scheme is used, due to its liquid-gas phase transition (see Results). Another problem associated with the previous solvent parameterization is neglecting the strength of its interactions with proteins and lipids, especially in membrane systems containing CHL. A too strong inter-species interaction for the original SCSE leads to its intercalation within the protein and disfavors protein-CHL interactions, while a too weak inter-species interaction will cause excessive clustering of CHL and its aggregation around the protein. Therefore, it is imperative, though nontrivial, to reparameterize the solvent both for compatibility with the force-based LJ switching scheme, and for recapitulating CHL dynamics and interactions with transmembrane proteins in the HMMM model.

In this work, we use extensive atomistic simulations to calibrate the interaction terms of SCSE by comparing membrane properties and CHL dynamics of HMMM simulations with those obtained from $\mu$s-long, full-length (FL) membrane simulations. The updated HMMM model with improved CHL dynamics, named HMMM-CHL, along with its reparameterized solvent SCSE2, is then applied to two representative test cases to examine its capability of identifying CHL interaction sites. The test cases chosen here include a multi-span $\alpha$-helical transmembrane protein, the human ${\beta }_2$-adrenergic receptor (${\beta }_2\text{AR}$) (PDB: 3D4S),¹³ and a $\beta$-barrel transmembrane protein, the mitochondrial voltage-dependent anion channel 1 (VDAC-1) (PDB: 2K4T).⁸⁴ These two integral membrane proteins with distinct folds have been extensively studied both experimentally^84–89 and with MD simulations,^31–33,44 specifically with regard to their CHL binding and modulation. In this paper, we first report the systematic reparameterization of the improved in silico solvent for HMMM membranes, SCSE2. Subsequently, the HMMM-CHL models, comprising various ratios of CHL and phosphatidylcholine (PC), are compared with conventional FL membrane simulations regarding structural and kinetics properties of the membranes. Lastly, the two test cases are discussed in the context of other relevant studies with respect to the strength and weakness of our HMMM-CHL model in characterizing protein-CHL interactions.

Methods

Here, we first describe the general simulation protocols used in the study. Then, the parameterization process for the new solvent, SCSE2, is explained. Next, we detail the comparison of the HMMM-CHL membranes with conventional FL membrane simulations. Finally, we will introduce the simulation of the two integral membrane proteins with HMMM-CHL and characterization of protein-CHL interactions.

MD simulation details

All MD simulations were performed with NAMD 2.12⁸¹ using the CHARMM36 force field for PC lipids,⁸³ the CHARMM36c force field for CHL,⁹⁰ CHARMM36m for proteins,⁹¹ and customized parameters for SCSE/SCSE2 (Table 1). In the HMMM-CHL simulations, NBFIX terms were used to reproduce CHL’s lateral atomic distribution in FL membrane simulations at three different CHL concentrations (Fig. S5). Constant temperature at 310 K, unless otherwise noted, and constant pressure at 1 atm were enforced by Langevin dynamics with a damping coefficient of 1 ps⁻¹ and Langevin piston Nosé-Hoover methods,⁹² respectively. A constant $xy$ plane dimension ratio was used for all membrane simulations to allow fluctuations in membrane surface area. Long-range electrostatics were calculated every 2 fs using the particle mesh Ewald (PME) method⁹³ with a grid spacing of 1 Å. All simulations were carried out with a time step of 2 fs and used SETTLE⁹⁴ to constrain bond lengths involving hydrogens, a cutoff of 12 Å for LJ interactions, and a force-based switching scheme starting at 10 Å, except for simulations at 310 K with the original SCSE solvent model where a potential-based switching scheme was used to keep SCSE in liquid phase.

Table 1:

SCSE and SCSE2 parameters

	intra-species (NBFIX)		inter-species
	$ϵ(\text{kcal}/\text{mol})$	$r_{\text{min}}(\AA )$	$ϵ(\text{kcal}/\text{mol})$	$r_{\text{min}}(\AA )$
SCSE58	−0.274	3.150	−0.1120	4.160
SCSE2	−0.344	3.511	−0.2184	4.160

Parameterization of SCSE2

Searching for SCSE2 intra-species LJ terms

We followed the same parameterization procedures and kept the same bonded parameters as in the previous work⁵⁸ in search of the SCSE2 intra-species potential which was added in the form of NBFIX terms to the standard parameters. An initial set of 1,000 randomly generated pairs of LJ parameters, $ϵ$ and $r_{\text{min}}$, were used to simulate 10,000 SCSE2 particles at 310 K for 200 ps. The initial parameter space was split into a liquid, a gas, and a metastable state (Fig. 1). A second set of simulations with 5,000 randomly generated pairs of LJ parameters at the liquid phase were carried out to compute the solvent’s bulk properties, the volume per CH₂, and the isothermal compressibility.⁵⁸ Based on the resulting data points, the intra-species NBFIX parameters were determined by the least-squares method to fit the properties of cyclohexane determined by experiments⁹⁵ (Fig. S1C,D). The final NBFIX parameters were validated by additional 100 independent simulations performed to collect statistics for the bulk properties shown in Table 2.

Figure 1:

Phase diagram for the SCSE and SCSE2 in silico solvents at 310 K. The color represents the average volume per molecule for each simulation, which distinguishes liquid (blue/magenta points) and gas (red/orange points) phases. The black crosses represent cases where simulations crashed prior to completion due to a large decrease in volume, which might represent metastable states. Green and magenta stars represent SCSE and SCSE2 solvents, respectively.

Table 2:

Comparison of bulk properties of SCSE and SCSE2

system	T(K)	volume per CH2 (Å3)	compressibility (TPa−1)
cyclohexane95	298	30.10	1,120
SCSE	298	29.38 ± 0.06	8,242 ± 2,014
SCSE2	298	29.78 ± 0.02	1,048±216
cyclohexane95	308	30.47	1,219
SCSEa	310	30.53 ± 0.10	11,343 ± 3,482
SCSE2	310	30.44 ± 0.02	1,226 ± 249

^aForce-based LJ switching was used to keep SCSE in liquid phase.

Membrane construction

Conventional full-length (FL) membranes containing a mixture of POPC and CHL were constructed and solvated with TIP3P water⁹⁶ at 150 mM NaCl using the CHARMM-GUI Membrane Builder.^97,98 Three CHL concentrations were simulated with a total of 100 lipids in each leaflet, at CHL:POPC ratios of 5:95, 20:80, and 50:50, respectively. The FL membranes were then converted to HMMM-CHL by replacing every two carbons, along with their hydrogens, after the sixth carbons in the phospholipid acyl tails with a SCSE2 molecule using an in-house Tcl script. HMMM-CHL and FL membrane simulations were carried out at 298 K with a constant $x/y$ membrane plane ratio for 50 ns and 1 $\mu$s, respectively, after energy minimization and standard steps of short equilibration in the CHARMM-GUI HMMM simulation protocol.⁵⁶ During the HMMM-CHL simulations, a half-harmonic restraint of 0.05 kcal mol⁻¹ Å⁻² was applied to the C26 and C36 atoms in the short-tailed PC lipids to prevent lipid diffusion into the aqueous phase. A half-harmonic restraint of 1 kcal mol⁻¹ Å⁻² was applied to the $z$ coordinates (along membrane normal) of C3-C17 atoms in each CHL molecule to prevent excessive CHL tilting (Fig. S4).

Tuning SCSE2 inter-species LJ terms

In order to achieve a good balance between SCSE2 self-interaction and its interactions with other molecular species, we aimed to reproduce the lipid atomic distribution by scaling the inter-species interaction term $ϵ$ (Fig. S2). The optimal scaling factor was chosen by comparing the atomic probability density profiles of CHL molecules in HMMM-CHL simulations to those in FL membrane simulations. The atomic probability density profiles for CHL heavy atoms were taken from the last 40 ns of the HMMM-CHL simulations and from the last 800 ns of the FL membrane simulations when membranes were considered equilibrated and steady. To compare the atomic probability density profiles of CHL in both membranes, statistical distances/divergences were calculated to measure the difference of CHL distribution across membranes (Fig. S3). The final scaling factor was determined when a minimum difference was observed between HMMM-CHL and FL membranes.

Solvation free energy

The solvation free energies of SCSE and SCSE2 were estimated using alchemical free energy perturbation (FEP), specifically using the double-annihilation or double-decoupling approach,^99,100 where the solute molecule is decoupled from the solvent and from the vacuum, and the solvation free energy is computed as the difference between the decoupling free energies of the solvent and the vacuum. Here, we adapted the double-decoupling approach and assumed no differences in the intramolecular energies for SCSE and SCSE2 between vacuum and the solvent during the creation/coupling process. Therefore, the decoupling free energies of the solute molecule is zero in the vacuum. Since the transfer free energy from vacuum to any solvent is also zero for the solute in the annihilated/decoupled state, the solvation free energy in a solvent is equivalent to the creation free energy of the solute in that solvent. This creation process was simulated by growing the solute in a pre-equilibrated solvent box of size 80 Å × 80 Å × 80 Å, a process stratified into 20 windows. A soft-core LJ potential was used to improve stability.¹⁰⁰ The backward process of annihilating the solute was also computed to assure reversibility and convergence.¹⁰⁰ For each window, 220 ps simulation was performed in each window and the last 200 ps was used for the free energy calculations. The convergence of the solvation free energy was examined using ParseFEP in VMD.¹⁰¹

Analysis of HMMM-CHL and FL membrane simulations

We used 50-ns HMMM-CHL simulations and 1-$\mu$s FL membrane simulations to quantify various membrane properties, including atomic probability density profiles, $S_{\text{CH}}$ order parameters, area compressibility modulus $\left(K_{\mathrm{A}}\right)$, area per lipid (APL), and lipid lateral diffusion coefficients $\left(D_{\mathrm{L}}\right)$.

The atomic probability density profiles of PC and CHL heavy atoms were calculated as described previously in the solvent parameterization section. The carbon-hydrogen order parameters, $\left|S_{\text{CH}}\right|$, measure the order profile of CHL and lipid acyl chains. The $S_{\text{CH}}$ is defined as

$$\left|S_{\text{CH}}\right|=⟨\frac{1}{2}\left(3{\text{cos}}^2\theta -1\right)⟩$$ (1)

where $\theta$ represents the angle of the carbon-hydrogen vector with respect to the membrane normal. The $K_{\mathrm{A}}$ measures the stiffness of the membrane and was calculated as

$$K_{\mathrm{A}}=\frac{k_{\mathrm{B}}T⟨A⟩}{⟨(A-⟨A⟩{)}^2⟩}$$ (2)

where $A$ is the membrane area. The APL was estimated using Membplugin¹⁰² in VMD,¹⁰³ in which the C2, C21, and C31 atoms of each PC lipid and the O3 atom of each CHL molecules were used for Voronoi tessellation. The $D_{\mathrm{L}}$ was calculated according to the Einstein relation as

$$D_{\mathrm{L}}=\underset{t\to \infty }{\text{lim}}\frac{1}{4t}⟨{\left(r\left(t_0+t\right)-r\left(t_0\right)\right)}^2⟩$$ (3)

where $r\left(t_0+t\right)$ and $r\left(t_0\right)$ are the center of mass of a lipid molecule at time $t_0+t$ and $t_0$, respectively, projected to the membrane plane.

Test membrane protein systems: ${\beta }_2\text{AR}$ and VDAC-1

The structures of ${\beta }_2\text{AR}$ (PDB: 3D4S) and VDAC-1 (PDB: 2K4T) were obtained from the Protein Data Bank.¹⁰⁴ We followed the same protocol as Cang, et al. to revert the engineered modifications introduced during the crystallization of ${\beta }_2\text{AR}$.³¹ In VDAC-1, the membrane-facing residue E73 was kept deprotonated due to the role of its charged state in cation binding and dynamics of VDAC-1.^105–107 Both termini of ${\beta }_2\text{AR}$ were capped with neutral patches, while the termini of VDAC-1 (resolved in its full-length form) were kept in their native charged states.

Both proteins were embedded in conventional FL membranes and solvated with TIP3P water⁹⁶ and 150 mM NaCl using CHARMM-GUI.^97,98 The lipid composition for each membrane was adopted from previous computational studies.^31,32 The ${\beta }_2\text{AR}$ was embedded in a membrane composed of 33% CHL and 67% POPC, while the VDAC-1 was simulated in a membrane containing 10% CHL and 90% DOPC. Three independent replicas were generated for each system with distinct initial lipid placements. For ${\beta }_2\text{AR}$, one of the three replicas was constructed with the two co-crystallized CHL molecules (CHL-bound), whereas in the other two replicas the co-crystallized CHL molecules were removed (CHL-unbound). The FL membrane systems were then converted to HMMM-CHL, as mentioned earlier, using an in-house Tcl script that replaces the phospholipid tails with a liquid solvent.

All six HMMM-CHL systems were minimized and equilibrated following the standard CHARMM-GUI HMMM simulation protocol,⁵⁶ and then subjected to 300-ns production runs. During the production runs, a harmonic restraint of 0.05 kcal mol⁻¹ Å⁻² was applied to the protein $\mathrm{C}\alpha$ atoms to ensure that the PDB structure of the protein is preserved. A grid potential was used to prevent SCSE2 diffusion into the water phase.¹⁰⁸ NBFIX terms were used to mitigate excessive CHL aggregation. Half-harmonic restraints were applied to both PC and CHL lipids as described earlier.

Results and Discussion

Parameterizing the in silico solvent SCSE2

In the original design of in silico solvents for HMMM,⁵⁸ LJ particles were used to substitute methylene (–CH2–) groups present in phospholipid acyl tails.⁵⁸ The van der Waals (vdW) parameters for intra-species interaction terms of these particles, specifically the $ϵ$ and $r_{\text{min}}$ in the NBFIX terms, were adjusted such that they reproduced bulk properties of cyclohexane, which is entirely composed of methylene units. The volume per CH₂ and the isothermal compressibility were the two bulk properties used as the target observables for this purpose. In particular, the solvent SCSM, which is composed of only one LJ particle, was parameterized to match both the volume per CH₂ and the compressibility of cyclohexane, and the solvent SCSE, composed of two LJ particle, was only parameterized against the volume per CH₂ of cyclohexane.⁵⁸

Furthermore, the previous parameterization was performed at 310 K using a potential-based LJ switching scheme. When we used those parameters with a force-based LJ switching scheme (at a temperature range of 298–310 K) we observed a liquid-gas phase transition at 304 K (Fig. S1A). This observation indicates that the first generation of SCSE would evaporate and not be compatible with the force-based LJ switching scheme at 310 K.

In order to reparameterize SCSE2 solvent in a compatible manner with the force-based LJ switching scheme, the parameter space was explored thoroughly at 310 K. The phase diagram showed similar patterns to the previous parameterization, where liquid and gas phases are observed along with a metastable state (Figs. 1, S1B). The prior SCSE parameters were found at the border between the liquid and gas phases, which explains why the phase transition was observed when the force-based LJ switching scheme was employed. Further exploration of the phase space identified a local region where the parameters for SCSE2 are determined by the least-squares method to fit both the volume per CH₂ and the compressibility of cyclohexane (Fig. S1C,D). The new parameters for SCSE2 are tabulated in Table 1. The solvent SCSE2 remains liquid up to 370 K with its volume per CH₂ reaching 35.14 ± 0.35 ų, indicating its stability across a wide range of commonly used temperatures. From the validation simulations, the bulk properties of SCSE2 were found to agree well with those of cyclohexane at both 298 K and 310 K (Table 2). In addition, the isothermal compressibility of SCSE2 also matches the target values compared to the prior SCSE, which we believe is an important feature to allow membrane simulations with a variable $xy$ plane area.

The interactions between SCSE2 and other species are specified by its inter-species LJ terms, i.e., $ϵ$ and $r_{\text{min}}$ used in the vdW mixing rule. A good balance between SCSE2 self-interaction and its interactions with other molecular species, especially lipids and proteins, is of crucial importance in characterizing protein-lipid/CHL interactions. Protein-CHL interactions are highly system-dependent and difficult to describe quantitatively. In order to achieve transferability of our model to different protein systems, we decided to take an indirect approach by tuning the inter-species parameters for SCSE2 in protein-free membrane systems containing different ratios of PC and CHL. One major concern of using the SCSE2 solvent as a substitute for conventional lipids is that it may interfere with protein-CHL interactions and lipid-CHL interactions. Here, we aimed to searching for optimal inter-species parameters that will cause minimum interference to the PC-CHL interactions, which are reflected by membrane structural properties such as PC/CHL distribution.

Starting with the previously developed inter-species potential terms for SCSE, which are provided in Table 1 ($ϵ$ and $r_{\mathit{\text{min}}}$ are, respectively, the sum of $ϵ$ from methylene building blocks of the solvent and the effective radius of a methylene group⁵⁸), we noticed that the behavior of the HMMM-CHL membranes and PC/CHL distribution can be directly affected by scaling the $ϵ$ term alone (Fig. S2A,B). CHL molecules tend to aggregate due to excessive SCSE2 self-interactions when the $ϵ$ is too weak, while CHL molecules immerse into the in silico solvent layer when the $ϵ$ is too strong (Fig. S2A,B). The optimal scaling factor for $ϵ$ was determined such that the CHL atomic probability density profiles in HMMM-CHL simulations matched those in FL membrane simulations (Fig. S3). The final scaling factor was determined to be 1.95, and the corresponding $ϵ$ is listed in Table 1.

During the parameterization of inter-species terms, two additional types of restraints and one parameter fix were considered for HMMM-CHL simulations. (1) Half-harmonic restraints were applied to the terminal carbons of the short-tailed PC lipids to maintain their $z$ positions overlapping with the SCSE2 solvent and prevent PC lipids’ dissociation from the membrane. These restraints, when compared with the harmonic restraints imposed on the $z$ positions of lipid carbonyl atoms in previous HMMM models,⁵⁶ provide better mobility of lipid head groups particularly for interaction with transmembrane proteins.¹⁰⁸ (2) Half-harmonic restraints were also applied to the $z$ positions of C3 and C17 atoms in each CHL molecule. These restraints effectively maintain CHL tilt angle distribution while allowing it to fluctuate in the $z$ dimension (Fig. S4). (3) NBFIX was used to adjust CHL self-interaction and aggregation. To ameliorate the CHL lateral distribution in HMMM-CHL, NBFIX terms for a select set of CHL carbon and hydrogen atoms, namely CRL1, CRL2, HGA1, and HGA2, were tuned downed by 10% from the C36c force field⁹⁰ to replicate the radial distribution functions (RDF) of CHL in FL membrane simulations (Fig. S5, Table 3). Due to the difference in the rough side, where two angular methyl groups are located, and the smooth side of CHL rings, two types of CHL dimerization have been reported in NMR experiments.¹⁰⁹ In good agreement, we have identified two populations of CHL dimers in both FL and HMMM-CHL membranes, indicated by the double peaks in their RDF especially for the two angular methyl carbons, C18 and C19.

Table 3:

NBFIX terms for tuning CHL self-interaction.

	ϵ (kcal/mol)	rmin (Å)
CRL1-CRL1	−0.0324	4.02
CRL1-CRL2	−0.0418	4.03
CRL1-HGA1	−0.0362	3.35
CRL1-HGA2	−0.0319	3.35
CRL2-CRL2	−0.0540	4.04
CRL2-HGA1	−0.0468	3.36
CRL2-HGA2	−0.0412	3.36
HGA1-HGA1	−0.0405	2.68
HGA1-HGA2	−0.0357	2.68
HGA2-HGA2	−0.0315	2.68

Using the new parameters for SCSE2, we calculated and compared its solvation free energy with the original SCSE (Table 4). The new SCSE2 is slightly more hydrophobic and shows a higher free energy to solvate in water compared to SCSE. This difference might account for the improved water behaviors observed in the case of the VDAC-1 system discussed later. It is energetically less unfavorable to solvate SCSE2 into water, while it is energetically less favorable to desolvate SCSE2 from its bulk solvent. For both SCSE and SCSE2, the overall free energy to transfer the in silico solvent molecule from its bulk into water is unfavorable and comparable. These results indicate that our new solvent satisfies the hydrophobic property required to mimic the membrane interior.

Table 4:

Comparison of solvation free energies^a.

system	T (K)	$\Delta G_{\text{water}\text{in}\text{SCSE}}$ (kcal/mol)	$\Delta G_{\text{SCSE}\text{in}\text{water}}$ (kcal/mol)	$\Delta G_{\text{SCSE}\text{in}\text{SCSE}}$ (kcal/mol)	$\Delta G_{\text{SCSE}\to \text{water}}^{\mathit{b}}$ (kcal/mol)
SCSE	298	1.14 ± 0.02	3.21 ± 0.04	−1.73 ± 0.02	4.94
SCSE2	298	1.76 ± 0.02	1.64 ± 0.04	−2.74 ± 0.02	4.38
SCSEc	310	1.00 ± 0.02	3.23 ± 0.04	−1.72 ± 0.02	4.95
SCSE2	310	1.73 ± 0.02	1.81 ± 0.04	−2.69 ± 0.02	4.50

^a$\Delta G_{\text{water}\text{in}\text{SCSE}}$ denotes the free energy of solvating a water molecule in SCSE solvent, likewise for $\Delta G_{\text{SCSE}\text{in}\text{water}}$ and $\Delta G_{\text{SCSE}\text{in}\text{SCSE}}$

^bThe free energy to transfer an in silico solvent molecule from its bulk solvent into water, $\Delta G_{\text{SCSE}\to \text{water}}$, is equivalent to $\Delta G_{\text{SCSE}\text{in}\text{water}}-\Delta G_{\text{SCSE}\text{in}\text{SCSE}}$.

^cForce-based LJ switching was used to keep SCSE in liquid phase.

Comparing HMMM-CHL with FL membranes

Following the reparameterization of SCSE2, we examined lipid distributions and dynamics in HMMM-CHL simulations and compared them with those in $\mu$s-long FL membrane simulations at three different CHL concentrations, i.e., 5%, 20%, and 50%. As shown in Fig. 2, the atomic probability density profiles of both PC and CHL show good agreement with those in FL membranes. Additionally, the membrane thickening effect of CHL was also captured in HMMM-CHL simulations. This becomes especially apparent in 50% CHL/50% PC membranes where the interdigitation of CHL tails diminishes in both HMMM-CHL and FL membrane simulations, resulting in a double-peaked distribution for the CHL tails (Fig. 2A,B). Compared to the FL membranes, short-tailed PC lipids show a slightly narrower distribution in HMMM-CHL at 5% and 20% CHL concentrations. We attribute this behavior to the half-harmonic restraints (0.05 kcal mol⁻¹ Å⁻²) imposed on the terminal carbons of the short-tailed PC lipids, which slightly dampens the fluctuations of PC lipids. In practice, these restraints could be weakened or removed to recover phospholipid fluctuations.

Figure 2:

Atomic probability density profiles of CHL and PC in FL (A) and HMMM-CHL (B) membrane simulations. The selected CHL and PC atoms with their color code notations are labeled in (C) and (D), respectively. The colored dashed lines in (A) and (B) correspond to the PC atoms (C21/C31 and C26/C36) in different tails. The black dashed lines in (D) indicate where the lipid acyl tails are shortened in HMMM-CHL.

Similarly, the membrane ordering effect of CHL was observed in HMMM-CHL simulations as indicated by the $\left|S_{\text{CH}}\right|$ order parameters (Figs. 3, S6). The order parameters agree well with those in FL membranes, particularly for CHL rings, while the CHL isooctyl tails are more disordered (Fig. 3). As expected, PC lipids become much more disordered in HMMM-CHL due to its shortened acyl tails (Fig. S6), even though their fluctuation is slightly affected by the restraints imposed on the tail terminal carbons (Fig. 2). We believe that instead of being an artifact, the disordering effect of the HMMM-CHL model on CHL and PC lipid tails might be beneficial to sampling protein-lipid interactions.

Figure 3:

CHL $\left|S_{\text{CH}}\right|$ order parameters at different CHL concentrations. $X$-axis represents the atom name for each hydrogen atom, except for C–H bonds present in the methyl groups where the average values are used, e.g., angular methyl groups with H18 and H19, and methyl groups in the tail with H21, H26, and H27.

In HMMM-CHL simulations, we used a constant ratio to control the membrane plane rather than a constant area usually used in HMMM simulations.^54,56,58 The intention was to examine to what degree the new solvent, SCSE2, might affect the membrane surface tension and thus lipid lateral mobility. As shown by the area compressibility modulus, HMMM-CHL membranes demonstrated similar stiffness at different CHL concentrations, whereas FL membranes became stiffer as CHL concentration increases (Table 5). From our calculation, HMMM-CHL membranes demonstrate a 10–15% increase in the area per lipid (APL) for both CHL and PC lipids (Table 5). This increase in APL has been found to lead to expedited lipid lateral diffusion.^54,56 Indeed, the lipid lateral diffusion in HMMM-CHL exhibited one to two orders of magnitude enhancement when compared to FL membranes (Table 5), a signature feature of HMMM simulations.^54,56,58 We note that the lipid lateral diffusion coefficients computed here are finite self-diffusion coefficients, which do not account for the finite-size effects imposed by the periodic cells being used with a limited box dimension.¹¹⁰ Nevertheless, we believe the comparison of the computed values from MD simulations would still be legitimate here. As a result, both a constant ratio and a constant area with a 10% increase to the corresponding equilibrated FL membrane systems are suitable choices to provide enhanced lipid mixing/diffusion when running HMMM-CHL simulations in practice.

Table 5:

Comparison of membrane properties between HMMM-CHL and FL membrane simulations^a

	${\mathit{\text{K}}}_{\text{A}}(\text{mN}/\text{m})$		APL (Å2)		$D_{\text{L}}\left({\AA }^2/\text{ns}\right)$
	HMMM-CHL	FL	HMMM-CHL	FL	HMMM-CHL	FL
5% CHL	553	244	34.08 ± 4.19	29.70 ± 3.54	8.56 ± 0.54	0.58 ± 0.13
95% PC			69.70 ± 1.22	62.53 ± 1.11	5.64 ± 0.15	0.41 ± 0.03
20% CHL	550	282	32.94 ± 2.03	28.65 ± 1.67	6.46 ± 0.45	0.29 ± 0.02
80% PC			66.38 ± 1.26	57.48 ± 1.07	4.97 ± 0.25	0.27 ± 0.01
50% CHL	556	1368	33.09 ± 1.07	29.76 ± 0.91	3.98 ± 0.34	0.09 ± 0.01
50% PC			62.63 ± 1.55	54.26 ± 1.12	3.39 ± 0.14	0.09 ± 0.01

^aArea compressibility modulus $\left(K_{\mathrm{A}}\right)$, area per lipid (APL), and lipid lateral diffusion coefficient $\left(D_{\mathrm{L}}\right)$.

Characterizing protein-CHL interactions with HMMM-CHL

To test the utility of the HMMM-CHL model in characterizing protein-CHL interactions, we applied the model to two membrane proteins with distinct folds, an $\alpha$-helical receptor protein, ${\beta }_2$ adrenergic receptor (${\beta }_2\text{AR}$), and a $\beta$-barrel channel, voltage-dependent anion carrier-1 (VDAC-1). Harmonic restraints were employed on the proteins’ $\mathrm{C}\alpha$ atoms to prevent large conformational changes from the experimental structures during the sampling of CHL binding by HMMM-CHL. We evaluated the effect of harmonic restraints on the protein structures by removing them after 300 ns (Fig. 4). For ${\beta }_2\text{AR}$, the backbone structure remained stable even without the restraints, while for VDAC-1, a significant increase in the backbone root-mean-square deviation (RMSD) from the crystal structure was observed (Fig. 4) due to asymmetrical narrowing of the $\beta$-barrel pore. Our new solvent, SCSE2, used in the HMMM-CHL model did not impair the stability of the $\alpha$-helical protein but affected the stability of the $\beta$-barrel protein. Based on these observations, we believe that it is advisable to apply and maintain $\mathrm{C}\alpha$ restraints when running HMMM-CHL simulations especially for $\beta$-barrel proteins.

Figure 4:

Backbone RMSD of ${\beta }_2\text{AR}$ and VDAC-1 in HMMM-CHL simulations. Harmonic restraints on protein $\mathrm{C}\alpha$ atoms were applied during the first 300 ns but removed in the last 200 ns (gray).

${\beta }_2$ Adrenergic Receptor

The human ${\beta }_2\text{AR}$ consists of seven transmembrane helices, H1 to H7, and a short juxtamembrane helix, H8 (Fig. 5A). As evidenced by thermal stability analysis and single-molecule force spectroscopy, cholesteryl hemisuccinate (CHS), a CHL analog, enhances the stability of ${\beta }_2\text{AR}$.^13,85 In the crystal structure of ${\beta }_2\text{AR}$, two CHL molecules were found at a structurally conserved site formed by H1, H2, H3, and H4.¹³ To systematically explore potential CHL binding sites on the ${\beta }_2\text{AR}$, we carried out three independent, 300-ns HMMM-CHL simulation replicas: one including the two co-crystallized CHL molecules (termed CHL-bound) and two without (termed CHL-unbound). From HMMM-CHL simulations, we identified several CHL high-occupancy sites in both leaflets (Fig. 5A). We labeled these sites as either extracellular (EC) or intracellular (IC) followed by an index related to helices forming them: IC1234, IC435, IC56, IC67, IC18, EC12, EC45, and EC67. Notably, the site with the highest occupancy (Fig. 5B), IC1234, has been proposed as a CHL consensus motif conserved among class A GPCRs¹³ and also identified as a major CHL interaction site in $\mu$s-long atomistic^31,33 and in coarse-grained⁴⁴ simulations. Three other high-occupancy sites, IC56, EC12, and EC67, were also captured in prior $\mu$s-long atomistic simulations,^31,33 whereas the site IC435 was observed with relatively weak CHL occupancy.³³ The site IC18 has been identified as a putative CHL binding site for regulating receptor dimerization based on crystal packing¹¹¹ and simulation results.³¹ The other two sites in our simulations, IC67 and EC45, were identified with the lowest CHL occupancies and might indicate transient CHL binding. Overall, HMMM-CHL simulations predicted potential CHL binding sites in good agreement with previous studies.

Figure 5:

(A) CHL high-occupancy sites on ${\beta }_2\text{AR}$ identified by HMMM-CHL simulations. High-occupancy sites were identified using an average mass-weighted density larger than 0.5 from both CHL-bound (pink mesh) and two replicas of initially CHL-unbound simulations (white and yellow solid surfaces). (B) Superposition of the two CHL molecules, CHL1 and CHL2, that bind to the site IC1234 in CHL-unbound simulations in blue and green from two replicas and the two resolved CHL in the ${\beta }_2\text{AR}$ crystal structure (PDB: 3D4S) in red.

In addition, both replicas of CHL-unbound simulations captured spontaneous CHL binding at the CCM site and reproduced the CHL binding configurations as resolved in the crystal structure¹³ (Fig. 5B). In replica 1, the two CHL molecules, CHL1 and CHL2, reached a minimum heavy atom RMSD of 0.56 Å and 0.69 Å, respectively, when compared to the crystallized configurations (Fig. 6A,B).

Figure 6:

CHL RMSD and the ${\beta }_2\text{AR}$-CHL center of mass (COM) distance between CHL from simulations and the binding site of CHL1 (A) and CHL2 (B) in the first replica of CHL-unbound simulations. (A) CHL1 adopted two configurations with either its $\alpha$- or its $\beta$-face (shaded grey) facing H4. (B) CHL2 left the site IC18 and hopped to IC1234 in the end. (C) CHL1/CHL2 RMSD in the second replica of CHL-unbound simulations. CHL1 configuration switching and CHL2 site hopping were also observed. (D) CHL1/CHL2 RMSD in the CHL-bound simulation. CHL exchange was observed at the CHL2 binding sites.

In replica 2, CHL1 and CHL2 reached a minimum heavy atom RMSD of 0.57 Å and 1.32 Å, respectively (Fig. 6C). Particularly, we observed two configurations of CHL1 in both replicas at the binding site with either its rough $\beta$-face or its smooth $\alpha$-face interacting with H4 (Fig. 6A,C). Besides, site-hopping of CHL2 between IC18 and IC1234 was observed in both replicas (Fig. 6B,C). In the CHL-bound simulation, CHL1 retained its rough side towards H4, whereas an exchange of two interacting CHL molecules occurred at the CHL2 binding site (Fig. 6D). The spontaneous CHL association, CHL site hopping and CHL exchange events observed in our simulations suggest that HMMM-CHL simulations can provide enhanced sampling of CHL dynamics, especially those usually occurring on a $\mu$s timescale.^40,112 In addition to capturing CHL high-occupancy sites, our HMMM-CHL simulations also facilitate CHL binding and unbinding processes owing to the expedited lipid diffusion.

VDAC-1

VDAC-1 is a $\beta$-barrel ion channel in the outer mitochondrial membrane. Its voltage-dependent gating and oligomerization are regulated by CHL as well as by anionic lipids.^88,89,113 Experimental evidence from NMR and photolabeling has suggested several CHL binding sites on the protein.^84,87

We probed CHL high-occupancy sites on VDAC-1 using three independent HMMM-CHL simulation replicas (Fig. 7). The site with the highest CHL occupancy was found near E73, a residue critical for gating and dimerization of VDAC-1,^88,107,114 regulation of N-terminal dynamics,¹⁰⁶ Ca²⁺ binding,¹⁰⁵ and CHL binding.⁸⁷ Interestingly, in our HMMM-CHL simulations, a few water molecules along with a Na⁺ were observed to diffuse along the outer surface of VDAC-1 into the membrane and interact with the charged E73, an event accompanied by CHL translocation (Fig. 8). As shown in Fig. 8A, the dynamics of the E73 side chain was reduced upon binding to the Na⁺ and CHL molecules. Water coordination around E73 in this study was not similar to the water poration reported in prior HMMM simulations using the original SCSE solvent,⁵⁸ in which water formed a pore in the membrane when no lipid restraints were used, likely because of excessive SCSE self-interaction in those simulations. This defect (water poration) was not even observed in the HMMM-CHL simulations with no lipid restraints (data not shown), likely due to the improved interaction terms for SCSE2.

Figure 7:

Mapping of CHL high-occupancy sites on VDAC-1 in HMMM-CHL simulations. High-occupancy sites were identified as sites with an average mass-weighted density larger than 0.15 from the three simulation replicas (blue, red, and orange meshes, respectively). Potential CHL interacting residues suggested from NMR⁸⁴ and photolabeling⁸⁷ experiments are shown in green and magenta, respectively. Three additional CHL binding sites, a-c, were observed in more than two simulation replicas.

Figure 8:

(A) HMMM-CHL simulations captured stabilization of the E73 side chain by Na⁺ (yellow sphere) and CHL. (B) The Na⁺ was coordinated with the E73 carboxy group, water, and CHL.

Altogether, we believe the coordination of the E73 side chain by the Na⁺ ion, water, and CHL acts as intermediate stages to stabilize deprotonated E73 in the membrane. This stabilization effect by cations and CHL may shed light on the function of Ca²⁺ binding and CHL binding at E73 observed in photolabeling experiments.^87,105 However, we have yet to understand its implication in the mechanism of VDAC-1 dimerization and channel gating.

Among the other high-occupancy sites in VDAC-1, several are located close to the CHL binding residues, F169 and S260, which were suggested in an NMR study⁸⁴ (Fig. 7, S7A–C). In our simulations, CHL was observed to have a direct interaction with the side chain of F169 (Fig. S7A) and residues adjacent to S260, i.e., L259 and A261 (Fig. S7B,C). These interactions might explain the CHL-induced chemical shift changes of F169 and S260 in NMR experiment.⁸⁴ We did not observe strong CHL interactions with the other residues suggested by NMR, which were also captured in an earlier docking study.³² We believe that this result could be due to the tilt angle restraints imposed on CHL molecules in our study, as a much tilted configuration of CHL was observed in the previous docking study.³² Apart from the high-occupancy sites mentioned above, our HMMM-CHL simulations captured additional CHL binding sites that were reproducible in two or the three replicas (Fig. 7, S7D–F). In summary, even with some limitations originating from the CHL tilt angle restraints, our HMMM-CHL simulations captures potential CHL interaction sites providing additional insights into CHL modulation of the protein.

Conclusions

In this study, we aimed to develop an improved version of an in silico solvent for HMMM simulations, which is compatible with the force-based LJ switching scheme and allows for use of the non-phospholipid membrane component, CHL. With the parameterization of the new solvent, termed SCSE2, the updated HMMM-CHL model produced structural properties in great agreement with conventional FL membrane simulations, while CHL/lipid lateral diffusion was expedited by one to two orders of magnitude. To test whether the new model is capable of capturing protein-CHL interactions with efficiency and accuracy, we applied it to two transmembrane proteins with distinct topologies and structures, ${\beta }_2\text{AR}$ and VDAC-1. Comparing the results with experimental data and other simulation studies, HMMM-CHL simulations were able to predict potential CHL binding sites, capture CHL dynamics observed in prior $\mu$s-timescale simulations, and even provide insights into some of the regulatory effects of CHL on certain protein structures. Admittedly, the additional restraints used on CHL and phospholipid tails in HMMM-CHL simulations caused slightly altered CHL tilting and phospholipid fluctuations. We believe that the protocols used in this study can be applied to the majority of transmembrane protein systems for characterizing protein-CHL interactions, while the side effects of restraints could be removed or at least ameliorated by customized modifications in a system-dependent manner.

HMMM-CHL simulations are not a substitute for conventional FL membrane simulations, as lipid saturation and lipid tail interactions are completely omitted in the model. Due to this design principle, one major limitation of our model is that the effect of lipid tails on CHL-protein interactions could not be examined. However, as a large part of phospholipids’ binding selectivity originates from the interactions of their head groups with transmembrane proteins, the atomistic description of protein interactions with phospholipid head groups and a part of their tail, as well as with CHL, in HMMM-CHL simulations can still partially capture the competition between CHL and phospholipid binding. In practice, multiple replicas of HMMM-CHL simulations could be performed at an acceptable cost for collecting good statistics on putative CHL binding sites. Additionally, HMMM-CHL membranes could be converted into FL membranes for a more complete evaluation of CHL-protein interactions and for the further investigation of CHL modulation.

Data and Software Availability

Scripts for converting full-length membranes to HMMM membranes with SCSE2, scripts to apply constraint in HMMM simulations, as well as all the input files needed for reproducing the membrane simulations are deposited at Zenodo: https://zenodo.org/records/10963119.