Gramicidin A Channel Formation Induces Local Lipid Redistribution I: Experiment and Simulation

Abstract

Integral membrane protein function can be modulated by the host bilayer. Because biological membranes are diverse and nonuniform, we explore the consequences of lipid diversity using gramicidin A channels embedded in phosphatidylcholine (PC) bilayers composed of equimolar mixtures of di-oleoyl-PC and di-erucoyl-PC (dC_18:1+dC_22:1, respectively), di-palmitoleoyl-PC and di-nervonoyl-PC (dC_16:1+dC_24:1, respectively), and di-eicosenoyl-PC (pure dC_20:1), all of which have the same average bilayer chain length. Single-channel lifetime experiments, molecular dynamics simulations, and a simple lipid compression model are used in tandem to gain insight into lipid redistribution around the channel, which partially alleviates the bilayer deformation energy associated with channel formation. The average single-channel lifetimes in the two-component bilayers (95 ± 10 ms for dC_18:1+dC_22:1 and 195 ± 20 ms for dC_16:1+dC_24:1) were increased relative to the single-component dC_20:1 control bilayer (65 ± 10 ms), implying lipid redistribution. Using a theoretical treatment of thickness-dependent changes in channel lifetimes, the effective local enrichment of lipids around the channel was estimated to be 58 ± 4% dC_18:1 and 66 ± 2% dC_16:1 in the dC_18:1+dC_22:1 and dC_16:1+dC_24:1 bilayers, respectively. 3.5-μs molecular dynamics simulations show 66 ± 2% dC_16:1 in the first lipid shell around the channel in the dC_16:1+dC_24:1 bilayer, but no significant redistribution (50 ± 4% dC_18:1) in the dC_18:1+dC_22:1 bilayer; these simulated values are within the 95% confidence intervals of the experimental averages. The strong preference for the better matching lipid (dC_16:1) near the channel in the dC_16:1+dC_24:1 mixture and lesser redistribution in the dC_18:1+dC_22:1 mixture can be explained by the energetic cost associated with compressing the lipids to match the channel’s hydrophobic length.

Introduction

Cell membrane lipid composition is diverse and tightly regulated (1, 2), with the cellular lipidome containing 1000+ unique species (3). Each of these species has distinct physical properties that contribute to the organization of the bilayer and the energetics of membrane protein-bilayer interactions. Studies using single-component bilayers have demonstrated how changes in a given lipid characteristic, such as acyl chain length, may alter protein function (4, 5, 6, 7, 8, 9, 10) and highlighted the importance of the hydrophobic coupling between a protein and its host lipid bilayer (11). Mismatch between a protein’s hydrophobic domain and the bilayer’s hydrophobic core is highly unfavorable, as exposing hydrophobic residues to water incurs a 25–75 cal/(mol·Å²) energetic penalty (11, 12). Deforming the bilayer to match the protein’s hydrophobic domain also has an associated energetic cost, which includes compression and bending energy contributions (13, 14, 15, 16, 17). These bilayer contributions to the change in free energy are known to affect the conformational preference of many diverse membrane proteins (see Andersen and Koeppe (11) for a review).

In a multicomponent bilayer, these energetic penalties may be reduced if a particular lipid species redistributes laterally to be preferentially enriched near a given protein. This lipid sorting has been studied experimentally with sarco/endoplasmic reticulum Ca²⁺-ATPase (4, 18, 19) and bacteriorhodopsin (BR) (20), which showed limited lipid preference in liquid-crystalline bilayers. Both sarco/endoplasmic reticulum Ca²⁺-ATPase and BR, however, aggregate when embedded in bilayers that are either very thin or thick (21, 22), such that the protein/bilayer boundary can vary as the bilayer thickness is varied, which may obscure any lipid sorting. KcsA (K⁺ channel) (23), however, exhibited clear selectivity among lipids with different chain lengths (a threefold change in the preference for the protein/bilayer interface between dC_10:1 and dC_22:1).

Less is known about single membrane-spanning α-helices, but the available evidence shows little, if any, acyl chain-length-dependent preference among phospholipids (24). This could reflect the imperfect hydrophobic matching between single bilayer-spanning α-helices and their host bilayers (25) or the perfect matching by helix tilting (26). In the case of gramicidin channels (showing only relatively small tilting), Fahsel et al. (27) found a preference for the thinner di-myristoyl-phosphatidylcholine (dC_14:0, DMPC) in studies on dC_14:0-dC_18:0 mixtures in both fluid-gel and gel-gel coexistence.

The lateral distribution of lipids also has been explored in simulation studies. Dumas et al. (20) and Sperotto and Mouritsen (28) used lattice Monte Carlo lipid models and a smooth cylindrical membrane protein to show that lateral lipid sorting should be feasible, although there was little evidence for such sorting in the experiments on BR (20). Later Monte Carlo-molecular dynamics simulations on gramicidin channels or the OmpA protein embedded in dC_14:0-dC_18:0 mixtures in the liquid-crystalline state similarly found little enrichment of either lipid adjacent to the channel or membrane protein (29, 30). Coarse-grain simulations, however, have more convincingly demonstrated lipid redistribution as a function of hydrophobic mismatch (30, 31, 32).

This study explores the redistribution of liquid-crystalline lipid species with different acyl-chain lengths adjacent to a bilayer-spanning channel, [Val¹]gramicidin (gA), which has been extensively characterized by electrophysiology (7, 33, 34, 35), spectroscopy (36, 37, 38, 39, 40), and molecular dynamics (MD) simulations (9, 41, 42, 43). Gramicidin channels are small and cylindrical (allowing for lipid radial properties to be easily calculated) with ample evidence for hydrophobic matching between the channel and the host bilayer (44), and can be studied at single-molecular resolution (where there is no lateral aggregation). Hence, gA is an excellent tool for probing the physics underlying lipid redistribution.

gA channels have only one major conformational transition, which is their formation by transmembrane dimerization of two nearly cylindrical monomers residing in opposite leaflets with their axes aligned to form a channel across the bilayer (Fig. 1). That gA has only a single major conformational change is important, in that it mainly adjusts to its environment through changes in the monomer↔dimer equilibrium, with minimal changes in other properties, such as the helical pitch (45) and single-channel conductance (46). Additionally, the single-leaflet monomer most likely produces minimal bilayer deformations (9). Thus, the bilayer must deform to accommodate the dimer (and the dimer-to-monomer transition state), meaning that any local enrichment of a preferred lipid in the vicinity of a gramicidin dimer must be reflected in the channel lifetime.

Figure 1.

(A) Space-filling model of [Val¹]gramicidin; the two β-helical subunits are indicated by yellow and green coloring of the carbon atoms. (B) Gramicidin channels form by the transmembrane dimerization of two nonconducting subunits. Channel formation and dimer dissociation are visible as rectangular current transitions. Channel formation is associated with a local decrease in bilayer thickness, with an associated energetic cost, which gives rise to a disjoining force that the bilayer imposes on the channel. Thus, the average channel lifetimes depend on the channel-bilayer hydrophobic mismatch. To see this figure in color, go online.

This article first presents the results of single-channel experiments. These demonstrated that gA single-channel lifetimes are increased (relative to a single component reference bilayer) in bilayers formed from lipid mixtures, where the lipids can redistribute to minimize the total bilayer deformation energy. The tentative conclusion from the electrophysiological experiments, that lipid redistribution occurs, was then substantiated using long-timescale MD simulations to determine the lipid redistribution as a function of time and distance from the channel. The relevant timescales and concentrations are discussed, and a comparison between experimental and MD results with a discussion of redistribution energetics follows. Because the lipid environment can modulate any embedded protein’s function (11, 47), results and conclusions here should be applicable to a wide range of membrane-embedded proteins.

It is important to note that although redistribution is an important feature by itself, the magnitude of redistribution is related to channel-bilayer hydrophobic mismatch, and so it can confirm model energetics that in turn affect protein function. When considered with the results of the second part of this work (the accompanying article, henceforth referred to as Article II, which develops and analyzes a continuum model of hydrophobic mismatch), a cross-validated base is built for interpreting the effect of protein-lipid coupling on function and compositional heterogeneity. The connections among experiment, simulation, and theory are briefly summarized at the conclusion of this article to emphasize how our results provide, to our knowledge, new insight into the physics of lipid redistribution.

Materials and Methods

Experimental methods

Materials

Di-palmitoleoyl-phosphocholine (16:1cΔ⁹)₂PC (dC_16:1), di-oleoyl-phosphocholine (18:1cΔ⁹)₂PC (dC_18:1), di-eicosenoyl-phosphocholine (20:1cΔ¹¹)₂PC (dC_20:1), di-erucoyl-phosphocholine (22:1cΔ¹³)₂PC (dC_22:1), and di-nervonoyl-phosphocholine (24:1cΔ¹⁵)₂PC (dC_24:1), were from Avanti Polar Lipids (Alabaster, AL). n-Decane (99.9% pure) was from Wiley Organics (Columbus, OH). gA was a gift from Drs. Roger E. Koeppe II and Denise V. Greathouse (Department of Chemistry and Biochemistry, University of Arkansas). gA was dissolved in ethanol (200 proof) or DMSO (Sigma-Aldrich, St. Louis, MO). NaCl was Purissimum grade from Sigma-Aldrich (St. Louis, MO). Electrolyte solutions were prepared daily using deionized Milli-Q water (Millipore, Bedford, MA).

Planar lipid bilayers were painted with a solution of lipid/n-decane across a 0.8–1.2 mm diameter hole in a Teflon partition separating two Teflon chambers each containing 5 mL of solution (unbuffered 1.0 M NaCl). Single channel experiments were done using the bilayer punch (33). All experiments were done at 25 ± 1°C, with a membrane potential of ±200 mV. The current signal was amplified using an AxoPatch 1B (Axon Instruments, Foster City, CA). The signal was filtered at 500–1000 Hz, digitized, and sampled by a PC/AT compatible computer. Single-channel average lifetimes (τ) were determined by fitting single exponential distributions to the lifetime distributions, $N\left(t\right)/N\left(0\right)=\text{exp}\left(-t/\tau \right)$, where $N\left(t\right)$ is the number of channels with a duration longer than t. All experiments were done at very low gA/lipid molar ratios (∼1/10⁵) to minimize any uncertainties associated with lateral interactions among gA channels.

Simulation methods

System setup

The simulation systems were built using the Membrane Builder module (48, 49) in CHARMM-GUI (www.charmm-gui.org) (50). A single gA dimer (PDB: 1JNO) (39) was inserted into three different bilayers (dC_16:1+dC_24:1, dC_18:1+dC_22:1, and dC_20:1) (Fig. S1). Each bilayer has 90 lipids per leaflet, which has been shown to have at least three lipid shells around the protein and extend into the effective bulk in previous gA simulations (9). 0.15 M KCl was used for all simulations. Including water and ions, each of the three systems contains ∼63,000 atoms (see Table S1 in the Supporting Material for system information).

Each system was initially minimized and equilibrated using CHARMM (51). After this short procedure, a further 60-ns equilibration was performed using NAMD (52) in the isothermal-isobaric (NPT) ensemble at 303.15 K and 1.0 atm. Langevin dynamics were used to maintain constant temperature with a Langevin coupling coefficient of 1 ps^–1. A Nosé-Hoover Langevin piston (53, 54) maintained constant pressure with a piston period of 50 fs and a piston decay of 25 fs. All simulations were run using P1 periodic boundary conditions. The CHARMM all-atom C22 protein force field (55) including dCMAP (56, 57) was used together with the C36 lipid force field (58) and a TIP3P water model (59). A 2-fs time-step was used along with the SHAKE algorithm (60). Electrostatic interactions were calculated using the particle-mesh Ewald method (61) (mesh size ∼1 Å, κ = 0.34 Å^–1, and sixth-order B-spline interpolation), and van der Waals interactions were smoothly switched off between 10–12 Å by a force-switching function (62).

The coordinates from the end of the NAMD simulations were used to initiate 3.5-μs simulations on Anton, a special-purpose supercomputer designed for long timescale MD simulations (63), using the same force fields and water model as above. The NPT ensemble was employed in these Anton simulations with the pressure and temperature held constant at 1 bar and 303.15 K using Berendsen’s coupling scheme (64). The lengths of all bonds involving hydrogen atoms were constrained using M-SHAKE (65), and the cutoff distance of the van der Waals and short-range electrostatic interactions was set to 10.05 Å. Long-range electrostatic interactions were evaluated with the k-space Gaussian split Ewald method (66) using a 64 × 64 × 64 mesh. The r-RESPA integration method (67) was employed with a time-step of 2 fs, and the long-range electrostatic interactions were evaluated every 6 fs. Due to the length of the simulation, atomic coordinates were saved every 0.24 ns.

In addition to the gA-bilayer systems, single- and two-component bilayer-only simulations were performed to gather equilibrium bilayer properties (thickness, area compressibility, and per lipid area) to better quantify how lipids adapt to the channel and each other in the mixed bilayers, as well as to use the computed bilayer properties for continuum model calculations. Single-component bilayers (dC_16:1, dC_18:1, dC_20:1, dC_22:1, and dC_24:1) were built with 50 lipids per leaflet. Two-component bilayers (dC_18:1+dC_22:1 and dC_16:1+dC_24:1) were built with 90 lipids per leaflet (see Table S1 for system information). Each bilayer was simulated for at least 100 ns with the same simulation parameters and protocols described above for the gA-bilayer NAMD simulations.

Lipid shell definition

Lipids that are approximately within the same radial distance from a protein define a lipid shell around the protein, and lipids in the same lipid shell generally have similar bilayer properties (e.g., thickness, area per lipid, and compressibility). Recent studies using estimations of shell locations based on one-dimensional (1D) radial and two-dimensional (2D) density distribution functions have yielded some success (9, 68, 69). However, lipid radial or density distribution functions often do not allow for high-resolution data of the location, population, and bilayer properties of lipid shells beyond the first shell.

In this study, an alternative approach was developed to define high-resolution lipid shells, based on marking lipid locations by a 2D Voronoi tessellation, in which the gA Cα atoms were used to represent the gA structure and the lipid locations were defined by the center of mass of each lipid projected onto the Z = 0 plane (i.e., the membrane plane). 2D Voronoi tessellations are particularly useful in this context as they divide the bilayer into regions associated with individual lipids on the bilayer plane. These regions are divided by tessellation borders, which represent the spatial boundaries between individual lipid areas. After defining the 2D areas for each lipid, it is possible to determine the neighbors (adjacent areas belonging to either a lipid or the channel) of a specific lipid site. Because tessellation borders between lipids rapidly fluctuate (and may be quite small) due to the nature of stochastic lipid diffusion and conformational change, a threshold (empirically defined as 4 Å) can be used to determine whether lipids that share a border with another lipid or the channel are true neighbors. Thus, a target site and a neighbor are only considered to be true neighbors if the tessellation border between them is above the threshold. In Fig. 2 A, lipid site 1 is in the first shell because it shares at least a 4 Å tessellation border with the channel (in orange). Lipid site 2 is in the second shell because it shares a border with a lipid in the first shell (i.e., lipid site 1) and does not share a border with the channel. A lipid in the third shell would therefore neighbor lipids in shell 2, etc.

Figure 2.

(A) Lipids shown with associated Voronoi area. The first four lipid shells surrounding the gA channel (orange) are defined (yellow, blue, green, and purple), respectively, with all lipids past these shells (gray). (B) Individual lipids around gA based on the same shell definition in (A). To see this figure in color, go online.

To determine instantaneous shell identities for all lipids throughout the trajectory, a 2D Voronoi tessellation was obtained for the first snapshot of the MD trajectory. Using this tessellation, lipids were examined iteratively to determine the first shell lipids. Then, other lipids in contact with these first shell lipids were assigned to the second shell. In other words, the lipids were continuously assigned, first defining and filling the first shell, then defining and filling the second shell, etc. The assignment stopped when all shell identities were unchanged from the previous iteration. For each following snapshot of the trajectory, nearly the same procedure was applied for assigning neighbor relationships.

The fast border fluctuations mean that a lipid’s shell assignment could change nearly instantaneously (every snapshot, or 0.24 ns). For example, a border could fluctuate between 3.8 and 4.2 Å throughout the simulation (i.e., crossing the threshold that defines a true lipid neighbor). To reduce these rapid, unphysical transitions, an additional step was added to the algorithm for all snapshots after the first. Once a border between two lipids reached the 4 Å threshold, the algorithm backtracked through time to the point of initial contact between the target lipid and the neighbor to mark the border as “effective”. Thus, two lipids were considered to be neighbors from the point of first contact until the border between them went to 0 Å (complete separation). By using this scheme of reaching a defined threshold; backtracking; and then relaxing the threshold, the strong dependence of lipid shell identity on the threshold can be removed. Ultimately, the lipid shells can be defined with high resolution throughout the simulation trajectory. Once a lipid’s shell is determined, any of its characteristics (e.g., hydrophobic thickness, which is the average position of the C22 and C32 atoms (i.e., the carbon atom next to the carbonyl carbon in each acyl chain) along the membrane normal (i.e., the z axis) can be calculated. Subsequently, any characteristic can be averaged for all lipids in a particular shell.

First shell lipid residence time determination

The average amount of time that a single lipid spends in the first shell before moving to the second is called the “expected residence time” in this study. Characterizing the residence time is important to properly judge equilibration of the system (i.e., the simulation must be run many times longer than the residence time), and to build a model of how quickly the lipid environment around a channel relaxes (this model is discussed in Article II). Reliable characterization of the residence time from a simulation trajectory is a challenging task, however, due to the coexistence of different lipid motions in and out of the first shell. Despite the shell definition using 2D Voronoi tessellations, fast lipid motions near the boundary of the first and second shells can occur due to difficulties in first-shell assignments, and the relaxation of such fast and physically meaningless events is unrelated to lipid diffusion for the residence time. Likewise, it is possible that lipids under strong interactions (e.g., hydrogen bonding) with the channel have much longer residence times. In this study, we used statistical modeling of the observed residence times and its technical procedure is described at the beginning of the Supporting Material. Briefly, two timescales are observed, the longer of which, typically ∼50–100 ns, corresponds to a residence time that is consistent with lipid diffusion (Table S2).

Results and Discussion

Experimental results

Single-channel lifetime measurements support lipid redistribution

The transmembrane association of gA subunits to form the conducting channel is described by:

$$2\text{M}\underset{k_{\text{dis}}}{\overset{k_{\text{assn}}}{\rightleftarrows }}\text{D}\text{and}\left[\text{D}\right]=\frac{k_{\text{assn}}}{k_{\text{dis}}}{\left[\text{M}\right]}^2,$$ (1)

where $k_{\text{assn}}$ and $k_{\text{dis}}$ are the rate constants for association and dissociation, respectively. The dissociation rate constant can be modeled as an activated process along a reaction coordinate that separates the subunits normal to the bilayer. Assuming that the free monomer subunit imposes no deformation of the membrane, only a dimerized gA has a contribution to the deformation energy. Thus, $k_{\text{dis}}$ is increased and the channel lifetimes decrease as the deformation energy increases. gA dimerization in a lipid environment X (with a hydrophobic thickness that differs from the channel’s hydrophobic length) causes a generic bilayer deformation with an associated energetic cost (14, 17). Because the intrinsic curvature of phosphatidylcholines is close to zero (70), we can approximate the deformation energy as

$$E_{\text{def},\text{dimer}}=H{\left(h_{\text{X}}-l\right)}^2,$$ (2)

where H is a phenomenological spring constant, $h_{\text{X}}$ is the unperturbed hydrophobic bilayer thickness of lipid environment X, and l is the channel length. The magnitude of H is determined by the shape of the protein and the physical properties of the bilayer, such as the bulk area compressibility and bending moduli and the channel-bilayer boundary condition (17). At the transition state (where the channel subunits have moved apart, breaking some intersubunit hydrogen bonds), the channel length is increased by δ:

$$E_{\text{def},\text{t}.\text{s}.}=H{\left(h_{\text{X}}-\left(l+\delta \right)\right)}^2,$$ (3)

and the bilayer contribution to the activation energy (dissociation barrier) becomes $\Delta E_{\text{A},\text{X}}=E_{\text{def,t}.\text{s}.}-E_{\text{def},\text{dimer}}$. For such a process, with uncorrelated events occurring at an average rate, the distribution of channel lifetimes will be determined by a parameter $\tau$, the average lifetime, as

$$N\left(t\right)/N\left(0\right)=\text{exp}\left\{-t/\tau \right\},$$ (4)

where $N\left(t\right)$ is the number of events occurring after some time t. The difference in activation energy between lipid environments X and Y that differ in thickness ($h_{\text{X}}$ and $h_{\text{Y}}$, respectively), but have the same H, thus becomes (71):

$$\Delta E_{\text{A},\text{X}-\text{Y}}=\Delta E_{\text{A},\text{X}}-\Delta E_{\text{A},\text{Y}}=2H\delta \left(h_{\text{Y}}-h_{\text{X}}\right),$$ (5)

and the logarithm of the ratio of τ in two different lipid environments becomes:

$$\text{ln}\left({\tau }_{\text{X}}\right)-\text{ln}\left({\tau }_{\text{Y}}\right)=\frac{2H\delta \left(h_{\text{Y}}-h_{\text{X}}\right)}{RT}.$$ (6)

That is, the logarithm of the lifetime varies as a linear function of bilayer thickness with a slope of $2H\delta {\left(RT\right)}^{-1}$.

In the experiments reported here, τ was measured for three single-component bilayers (dC_16:1, dC_18:1, and dC_20:1, which form stable, though decane-containing bilayers) to obtain the phenomenological product, $2H\delta {\left(RT\right)}^{-1}$, for this lipid chemistry (phosphoglycerol lipids, two acyl chains with one double bond each). Table 1 and Fig. 3 A show results obtained in planar lipid bilayers formed by dC_16:1, dC_18:1, and dC_20:1 (there was an ∼10-fold change in τ when the phospholipid acyl chains were shortened or extended by two methylene groups).

Table 1.

Experimental gA Dissociation Timescales and $\Delta h_0^{\text{eff}}$ and $n_s^{\text{eff}}$ for the Mixtures

Bilayer	τa (ms)	$\Delta h_0^{\text{eff}}$b (Å)	$n_{\text{s}}^{\text{eff}}$c
dC16:1	6820 ± 510
dC18:1	530 ± 22
dC20:1	64 ± 10
dC18:1+dC22:1	95 ± 10	–0.72 ± 0.3	0.58 ± 0.04
dC16:1+dC24:1	195 ± 20	–2.9 ± 0.3	0.66 ± 0.02

^aData for dC_20:1 and the mixtures are shown in Fig. 3.

^bComputed from Eq. 7.

^cComputed from Eq. 9.

Figure 3.

(A) The natural log of the average gA single-channel lifetimes as a function of the difference in bilayer thickness for dC_16:1, dC_18:1, and dC_20:1, relative to dC_20:1. The points show the averages with associated uncertainty. (Black line) Linear fit to the data, with a slope of 0.622 ± 0.021 Å^–1. (B) Single-channel lifetime distributions in dC_20:1, dC_18:1+dC_22:1, and dC_16:1+dC_24:1 membranes. The distributions (thinner line) were fit with single exponential distributions (thicker line) and the average lifetimes are listed in Table 1. To see this figure in color, go online.

A key issue is what to use as an appropriate bilayer thickness. The single-channel experiments were done in hydrocarbon-containing membranes, which are thicker than the hydrocarbon-free membranes used in the simulations. The hydrophobic thickness of dC_18:1 membranes formed using decane is ∼40 Å (72), whereas the thickness of a hydrocarbon-free dC_18:1 bilayers is ∼27 Å (Lewis and Engelman (21), Kučerka et al. (73), and Table S4). Although the hydrocarbon-containing and hydrocarbon-free thicknesses are different, Helfrich and Jakobsson (74) noted that the membrane thinning associated with channel formation is likely to first involve the expulsion of the hydrocarbon solvent in the bilayer adjacent to the channel followed by the compression of the bilayer leaflets. The key variable of interest, however, is the difference in thickness when the acyl chain length is varied, which is similar in the two systems, varying ∼1.6 Å per CH₂ residue (dC_18:1 to dC_24:1) in solvent membranes (21) versus ∼1.1 Å per CH₂ residue (dC_16:1 to dC_24:1) in hydrocarbon-containing planar bilayers (75). For this analysis, we therefore chose to use the bilayer thickness from MD simulations (see below and Table S4), which agrees well with the thickness determined by hydrocarbon-free experiments (21, 73). If the thicknesses of hydrocarbon-containing bilayers had been used instead, the slope of the ln(τ)-h relation would have been steeper, and we would have deduced a larger enrichment of the shorter lipid in the vicinity of the channel.

We thus find that the slope of the ln(τ)-h relation in single-component bilayers, Eq. 6, is 0.622 ± 0.021 Å^–1 (fit using uncertainties found in Tables 1 and S4). It is not necessary to individually specify the values of H and δ because it is their product that is important in the calibration of timescale and bilayer thickness. Nevertheless, δ can be reasonably assumed to be on the Å length scale necessary to break the hydrogen bonds between gA subunits. A δ-value of 1.6 Å is justified in the literature (72, 76, 77, 78), which yields H = 0.117 ± 0.004 kcal/(mol·Å²) (49.0 ± 1.6 kJ/(mol·nm²)) from the data in this work, in reasonable agreement with estimates obtained using different gA analogs (72). This value is in acceptable agreement with the estimate computed independently in Article II, i.e., H = 0.0853 kcal/(mol·Å²) (35.7 kJ/(mol·nm²)).

Using the H estimate from gA dimer lifetime measurements in single-component bilayers, we can define an effective bilayer thickness around the channel (i.e., the thickness that the channel experiences) to interpret the lifetime measurements in two-component bilayers, as follows:

$$h_0^{\text{eff}}=h_{{\text{dC}}_{20:1}}-\frac{RT}{2\delta H}\text{ln}\left(\frac{{\tau }_{\text{mix}}}{{\tau }_{{\text{dC}}_{20:1}}}\right)=h_{\text{l}}+n_{\text{s}}^{\text{eff}}\left(h_{\text{s}}-h_{\text{l}}\right),$$ (7)

which can be written in terms of the change in effective thickness, as:

$$\Delta h_0^{\text{eff}}=h_0^{\text{eff}}-\frac{1}{2}\left(h_{\text{s}}+h_{\text{l}}\right),$$ (8)

where $h_{{\text{dC}}_{20:1}}$ is the unperturbed thickness of the reference dC_20:1 bilayer, ${\tau }_{\text{mix}}$ is the gA single-channel lifetime in a mixed bilayer, ${\tau }_{{\text{dC}}_{20:1}}$ is the gA lifetime in dC_20:1 lipid (channel lifetime results are listed in Table 1 and shown in Fig. 3 B), and $n_{\text{s}}^{\text{eff}}$ is the fraction of short lipids in direct contact with gA (first lipid shell). Here, the subscript s refers to the short and the subscript l refers to the long lipids in the mixture. Assuming that the thickness of a lipid mixture is the weighted average of the thicknesses of its constituents, i.e., $h_0^{\text{eff}}=n_{\text{s}}^{\text{eff}}{h}_{\text{s}}+n_{\text{l}}^{\text{eff}}{h}_{\text{l}}$ (where $n_{\text{l}}^{\text{eff}}=1-n_{\text{s}}^{\text{eff}}$), the effective fraction of short-chained lipids in the vicinity of the channel, $n_{\text{s}}^{\text{eff}}$, is then determined by:

$$n_{\text{s}}^{\text{eff}}=\frac{1}{2}+\frac{\Delta h_0^{\text{eff}}}{\left(h_{\text{s}}-h_{\text{l}}\right)}.$$ (9)

If $\Delta h_0^{\text{eff}}$ is zero, the lipids are randomly mixed in the vicinity of the channel $\left(n_{\text{s}}^{\text{eff}}=1/2\right)$. Article II shows that the major contribution to the deformation energy comes from the lipids in the first shell, justifying the interpretation of $n_{\text{s}}^{\text{eff}}$ as the first shell lipid enrichment. Estimates of $n_{\text{s}}^{\text{eff}}$ are shown in Table 1. The measured lifetimes thus correspond to bilayers composed of a mole-fraction 0.58 ± 0.04 dC_18:1 in the dC_18:1+dC_22:1 bilayer and 0.66 ± 0.02 dC_16:1 in the dC_16:1+dC_24:1 bilayer. The single-channel experiments thus provide strong evidence for lipid redistribution in the vicinity of the channel for dC_16:1+dC_24:1.

Simulation results

Microsecond simulations show ∼100-ns first shell lipid residence times

In the case of semi-cylindrical integral membrane proteins such as gA, it is convenient to define lipid shells and other bilayer properties as a function of radial distance from the protein. In this context, the lipid shell locations from gA, defined using the 2D Voronoi tessellation described in the Materials and Methods, correspond to the center of each shell. By averaging shell locations, a typical shell boundary can be approximated (Table S3), e.g., the first lipid shell boundary is the average of the first and second shell locations. The shell locations (black vertical lines, in Fig. 4) coincide well with the first peak in the 1D lipid radial distribution function (RDF) in gA+dC_16:1+dC_24:1; the results for gA+dC_18:1+dC_22:1 and gA+dC_20:1 are similar and not shown. Slight discrepancies arise because the lipid shell location represents an average location within each shell, which is not necessarily the most populated location in the 1D-RDF peaks. When the shell boundaries (dashed red vertical lines) are considered, this shell method clearly provides much finer resolution of each lipid shell, compared to the 1D-RDF. In fact, it is difficult to define even the second lipid shell based solely on the 1D-RDF. The Voronoi tessellation, however, provides an unambiguous lipid shell definition that allows for a high-quality definition of the first shell residence time and other shell-dependent bilayer properties.

Figure 4.

1D lipid radial distribution function in gA+dC_16:1+dC_24:1. (Vertical black lines) Calculated locations of the radial lipid shells by the 2D Voronoi tessellation; (red dashed lines) each shell boundary. To see this figure in color, go online.

Using the lipid shells, as well as a fitting procedure that properly weights the transition time series in the longer time regime (see Materials and Methods and Fig. S2), the first shell residence times were calculated; the results are summarized in Table S2. Not unexpected, the fit for the residence time requires a double exponential distribution. Rabinowitch (79) in the 1930s showed that in a condensed phase, a particle must wait some amount of time (proportional to the density) to find a new (unoccupied) lattice hole. During the wait, the particle rattles in an effective cage created by its neighbors. That is, with respect to lipid hops, a lipid molecule has a short timescale motion that is associated with being confined (this short timescale is not related to the timescale associated with the Voronoi glitches; see Materials and Methods) and a long timescale motion that is associated with the full hop into a hole in the lattice.

In gA+dC_16:1+dC_24:1 and gA+dC_20:1, the mean first shell residence times are ∼70–75 ns; gA+dC_18:1+dC_22:1 has longer residence times (∼90–110 ns). A simple estimate using the Einstein-Smoluchowski equation suggests that the time required for a lipid to diffuse 7 Å (the approximate distance between lipid shells) in one dimension with a diffusion coefficient of ∼5 × 10⁻⁸ cm²/s is ∼50 ns, in agreement with the above values. The longer mean residence time in gA+dC_18:1+dC_22:1 is due mainly to a few very long lipid residence times; six lipid residence times are longer than 500 ns, the longest being ∼760 ns. In comparison, there is only one lipid residence time longer than 500 ns in gA+dC_16:1+dC_24:1. These very long lipid residence times (and their fitting) cause the difference in mean values between gA+dC_18:1+dC_22:1 and the other two systems. Our analysis demonstrates that: first, measuring lipid redistribution near a membrane protein using all-atom MD simulations remains a difficult task due to the long timescales involved; and second, a simulation time of 3.5 μs in each system is sufficient to allow for ∼3 μs sampling at equilibrium (assuming that the system is in equilibrium after ∼5 residence times). Additionally, the relaxation time for lipid redistribution around the gA is ∼500 ns, which is less than 1/100,000 of the lifetime of gA in dC_20:1 (64 ± 10 ms). So, relative to gA dimer average lifetimes, lipid redistribution is nearly instantaneous, and the measured experimental lifetimes can truly be considered a result of the channels residing in an enriched environment.

Whereas the observed residence times are much shorter than the total duration of the simulation, the decorrelation time of the first shell enrichment of a lipid requires multiple lipid hops. In Article II, the timescale is modeled by using this simulation-extracted timescale (75 ns) as well as the membrane energetic model to probe the expected enrichment and standard deviation in the simulation results. This model predicts first shell enrichments in good agreement with both experiment and MD; the ratios of short lipids predicted in Article II are 0.59 ± 0.03 dC_18:1 in dC_18:1+dC_22:1 and 0.65 ± 0.03 dC_16:1 in dC_16:1+dC_24:1.

Simulated lipid distributions agree qualitatively with experiment

Assuming a 500-ns equilibration (deduced from the residence time analysis), the average first shell dC_18:1 mole-fraction in gA+dC_18:1+dC_22:1 is 0.50 ± 0.04, and the average first shell dC_16:1 mole-fraction in gA+dC_16:1+dC_24:1 is 0.66 ± 0.02. Standard errors were calculated by dividing the last 3 μs into six consecutive 500-ns blocks. Table 2 summarizes the mole-fractions of dC_18:1 and dC_16:1 in the first three lipid shells. The mole-fraction of short lipid per shell in the two leaflets is similar, indicating satisfactory convergence. The 95% confidence interval (CI) shows that redistribution is statistically significant for dC_16:1+dC_24:1, but not for dC_18:1+dC_22:1; i.e., the fluctuations in the latter obscure the results. Hence, the simulation results for both bilayers agree with experiment (Table 1), but the CIs suggest that 3 μs is still a short timescale for this type of biophysical problem.

Table 2.

Summary of dC_18:1 and dC_16:1 Shell Mole-fractions in their Respective Bilayers

Shell	gA+dC18:1+dC22:1			gA+dC16:1+dC24:1
	Top	Bottom	Average	Top	Bottom	Average
1	0.52 ± 0.07	0.48 ± 0.02	0.50 ± 0.04 (0.10)	0.64 ± 0.04	0.69 ± 0.03	0.66 ± 0.02 (0.06)
2	0.53 ± 0.03	0.48 ± 0.02	0.51 ± 0.02 (0.05)	0.53 ± 0.02	0.57 ± 0.01	0.55 ± 0.01 (0.04)
3	0.51 ± 0.01	0.52 ± 0.01	0.52 ± 0.01 (0.02)	0.49 ± 0.01	0.49 ± 0.01	0.49 ± 0.01 (0.02)

Means and standard errors are reported for the individual leaflets, and the average of both leaflets. The 95% CI for the shell averages are the means ± the values in parentheses.

The first shell mole-fractions of dC_18:1 and dC_16:1 are plotted as functions of time in Fig. 5. Both systems are dynamic, and the evolution of the mole-fractions show lateral lipid redistribution in the first and second shells in gA+dC_16:1+dC_24:1, with the second shell’s enrichment being lesser in magnitude (Table 2). Although the simulations should have been long enough to ensure equilibration, the first shell concentrations were still changing rapidly up to the end of the 3.5 μs. Moreover, there were, on average, only seven lipids in the first shell per leaflet (Table S3), so it is difficult to assign an equilibrium concentration because the fluctuation of a single lipid can drastically alter the instantaneous value.

Figure 5.

First shell mole-fractions of (A) dC_18:1 in gA+dC_18:1+dC_22:1 and (B) dC_16:1 in gA+dC_16:1+dC_24:1. In both plots, the red curves are the top and bottom leaflet concentration and the thick black curve is the average of the leaflets at each time after leaving off the first 500 ns. The plotted mole-fractions denote 100-ns block averages of the trajectory. To see this figure in color, go online.

The disjoining force that a bilayer exerts on the channel is mostly due to the strain on the first shell lipids (Nielsen et al. (17) and Article II), which allows for comparison of the first shell lipid enrichment in the experiments (Table 1) and simulations (Table 2). These results are in qualitative agreement. There is less first-shell enrichment in the gA+dC_18:1+dC_22:1 simulation than in the experiment, but, given the sampling difficulties, we attach the greater significance to the gA+dC_16:1+dC_24:1.

Lipids redistribute to better match the channel and each other

Individual lipids adjust to the channel as well as to the other lipids in the bilayer. Even in the case of a bilayer with large disparity in the constituent chain lengths (e.g., ∼9 Å difference in preferred monolayer height in dC_16:1+dC_24:1, Table S4), the lipids are observed to adopt configurations that lead to a nearly smooth surface (Fig. 6) and the thickness of the mixed bilayer is near the average of the two constituents’ thicknesses (Table 3).

Figure 6.

Number density plots of lipid headgroups, defined as the phosphocholine groups: (A) dC_20:1; (B) dC_18:1 (red), dC_22:1 (blue), and dC_18:1+dC_22:1 (black); and (C) dC_16:1 (red), dC_24:1 (blue), and dC_16:1+dC_24:1 (black). The decomposition of headgroup locations in (B) and (C) show that headgroups match very closely in an equimolar mixed lipid bilayer. To see this figure in color, go online.

Table 3.

Lipid Hydrophobic Thickness in Å by Shell with Standard Errors^a

Shell	gA+dC18:1+dC22:1			gA+dC16:1+dC24:1			gA+dC20:1
	dC18:1	dC22:1	dC18:1+dC22:1	dC16:1	dC24:1	dC16:1+dC24:1	dC20:1
1	25.94 ± 0.12	26.24 ± 0.13	26.05 ± 0.07	25.28 ± 0.11	25.86 ± 0.15	25.46 ± 0.08	26.11 ± 0.04
2	29.88 ± 0.09	30.25 ± 0.06	30.05 ± 0.06	29.44 ± 0.10	30.22 ± 0.09	29.79 ± 0.08	30.30 ± 0.02
3	31.81 ± 0.05	32.04 ± 0.05	31.91 ± 0.04	31.55 ± 0.05	32.48 ± 0.06	32.01 ± 0.06	32.04 ± 0.02
4	32.41 ± 0.03	32.66 ± 0.03	32.54 ± 0.02	33.47 ± 0.08	33.50 ± 0.04	33.10 ± 0.03	32.57 ± 0.02

^aStandard errors were calculated by dividing the trajectory into 350-ns blocks.

The adjustment of the acyl chains is most visible in gA+dC_16:1+dC_24:1, where the dC_16:1 acyl chains do not strongly interdigitate across the bilayer center (z = 0), whereas the dC_24:1 acyl chains are highly interdigitated in all lipid shells (Fig. S3). The same acyl chain changes also were observed, though to a lesser amount, for gA+dC_18:1+dC_22:1 (data not shown). The lipid head matching thus occurs at the cost of deforming the chains.

The overall changes in lipid order due to lipid-lipid and lipid-channel hydrophobic matching can be further illustrated using acyl-chain lipid order parameters (S_CD) calculated for the neat bilayers, as well as for each lipid type as a function of shell in gA-containing systems:

$$S_{\text{CD}}=\left|\frac{1}{2}\langle 3{\text{cos}}^2{\theta }_{\text{CH}}-1\rangle \right|,$$ (10)

where ${\theta }_{\text{CH}}$ is the angle between the CH bond vector and the bilayer normal. Changes in these lipid order parameters represent how much an acyl chain has deformed relative to its bulk state. For dC_16:1 in gA+dC_16:1+dC_24:1, as shown in Fig. S4, chain order increases as the radial distance from the protein increases (i.e., shell number increases), indicating that dC_16:1 in the bulk becomes more ordered. The dC_16:1 lipid order in the first shell, in contrast, is similar to that of the single-component dC_16:1 system, indicating a good match to the channel. As expected, dC_24:1 shows a drastically different order parameter profile when comparing the first shell and the dC_24:1-only bilayer. To match the length of the channel, the dC_24:1 acyl chains must adjust their configurations (bend or compress), which decreases the chain order. Consequently, the dC_24:1 acyl chain order increases as the shell number increases, but it does not become as ordered as in the single-component dC_24:1 system because it is still neighbored by some dC_16:1. These profiles suggest that: 1) dC_16:1 is a good match to the channel; 2) dC_16:1 stretches to accommodate headgroup matching in the bulk of gA+dC_16:1+dC_24:1 and in dC_16:1+dC_24:1; 3) dC_24:1 deforms near the channel; and 4), dC_24:1 has more order in the bulk (and binary lipid-only systems), but must compress to match the shorter lipid. Although dC_24:1 is near its melting temperature (26.7°C; Lewis et al. (80)), the order parameters indicate that the acyl chains are in the fluid phase in each shell, including the effective bulk. Therefore, the simulations show that lateral lipid redistribution occurs in completely fluid two-component lipid systems.

The dC_18:1 and dC_22:1 order parameters also explain why there is less lateral lipid redistribution in gA+dC_18:1+dC_22:1. Fig. S5 shows that both dC_18:1 and dC_22:1 adjust their conformations to be near the channel, and the order parameters of the two lipid types in the fourth lipid shell are not drastically different from those of their respective pure bilayers. That is, there is no strong penalty for having them mixed in the bilayer (i.e., they need not stretch or compress dramatically to coexist).

A simple continuum elastic model can explain lipid redistribution

Lipid redistribution around a membrane protein will be affected by general and specific mechanisms. General mechanisms refer to redistribution that depends on the material properties of the membrane, e.g., thickness, spontaneous curvature, compressibility, and bending modulus, whereas specific mechanisms refer to occupancies that cannot be simply correlated to material properties (and are likely to involve residence times typical of a strongly bound lipid, e.g., much longer than 100 ns). Therefore, this study pertains to the general mechanism, and the discussion below refers only to this case.

The thicknesses of the dC_18:1+dC_22:1, dC_16:1+dC_24:1, and dC_20:1 systems are similar, and importantly, all three have nearly the same thickness profiles when perturbed by gA (Fig. 7). They all show local thinning near the channel, which has been demonstrated for model and biological systems (see Kim et al. (9) and Mitra et al. (81)). The small differences between the profiles are explained by the redistribution discussed above; for dC_16:1+dC_24:1, the thickness is less in the first shell that is enriched in the short lipid, which results in an enrichment of the long lipid in the outer shells.

Figure 7.

Radial hydrophobic thickness profiles around gA in gA+dC_20:1, gA+dC_18:1+dC_22:1, and gA+dC_16:1+dC_24:1. Hydrophobic thickness is the average z distance between the C22/C32 atoms (i.e., the first carbon atoms after the carbonyl of each fatty acid tail) in each leaflet. To see this figure in color, go online.

The total bilayer deformation energy includes compression and curvature penalties. Assessing the simulated curvature in the first shell is difficult because curvature is highly sensitive to the definition of the complex hydrophobic surface (Fig. 7). Also, the calculation is dependent on first (tangential curvature) and second (radial curvature) derivatives with respect to the hydrophobic surface profile (see Article II). Lipid compression, in contrast, can be simply estimated from the radial (per shell) thicknesses from simulation. Additionally, it is shown in Article II that the compression energy is the major component governing redistribution (only ∼25% of the deformation energy is from curvature, similar to the ∼35% for model bilayers examined by Nielsen et al. (17)). Therefore, the analysis in this article uses a simple compression-only model (neglecting curvature contributions that are difficult to obtain by simulation and are shown to be smaller than the compression contributions) that is based on the simulation results. Nonetheless, the compression-only model provides insight into the redistribution and highlights the importance of curvature in reducing the predicted lipid redistribution.

Compression penalties are incurred when the lipid length is perturbed from its equilibrium length $\left(h_0\right)$ along the membrane normal. Assuming that a lipid can be compressed like a spring with constant density (i.e., a change in height is directly correlated to a change in lateral area, $V_{\text{lipid}}=Ah=A_0{h}_0$), the amount of energy required to stretch/compress a lipid is given by:

$$\begin{array}{c}{E}_{\text{area}}=\frac{1}{2}{K}_{\text{A},\text{m}}{A}_0{\left(\frac{A}{A_0}-1\right)}^2=\frac{1}{2}{K}_{\text{A},\text{m}}{A}_0{\left(\frac{h_0}{h}-1\right)}^2\\ =\frac{1}{2}{K}_{\text{A},\text{m}}{A}_0{\left(\frac{h}{h_0}-1\right)}^2+\mathcal{O}\left[{\left(h-h_0\right)}^3\right],\end{array}$$ (11)

where $K_{\text{A},\text{m}}$ is the monolayer lipid area compressibility ($K_{\text{A},\text{m}}$ is assumed to be one-half of the bilayer $K_{\text{A}}$ and has units of energy per area), $A_0$ is the unperturbed area per lipid, and A and h are the perturbed area and height, respectively. Equation 11 is a simple quadratic expansion of the energy about the compression energy minimum (i.e., when the lipid is unperturbed).

Using simulation values, the compression energy is estimated by subtracting the energy necessary to compress an unperturbed long lipid ($h_{\text{pure}}$, the lipid thickness in a single-component bilayer) to the thickness of the bulk mixture $\left(h_{\text{mixed}}\right)$ from the energy necessary to compress an unperturbed lipid to the thickness of the channel (l):

$$\Delta E=\frac{1}{2}{K}_{\text{A},\text{m}}{A}_0\left[{\left(\frac{l}{h_{\text{pure}}}-1\right)}^2-{\left(\frac{h_{\text{mixed}}}{h_{\text{pure}}}-1\right)}^2\right].$$ (12)

The resulting $\Delta E$ is the energy difference between a lipid residing in the mixed bulk and a lipid residing in the first lipid shell proximal to the channel. Values for $K_{\text{A},\text{m}}$ and $h_0$ (Table S4) are taken to be the two-component values (naturally with the exception of dC_20:1). The situation is clear for long lipids—they must compress to be in the mixed bilayer, and must compress to be near the channel. Short lipids must stretch to be in the mixed bulk membrane and little energy will be required for them to be near the channel. For simplicity, we assume their energy to be in the mixed bulk also to be zero because the conformational space accessible to the lipid is assumedly unhindered by having excess space in the opposing leaflet. This is justified by considering the terminal methyl density in Fig. S3 A, which is shifted in z, rather than stretched to fit the full leaflet profile. Order parameters in Fig. S4 A agree qualitatively, where the order is unchanged for the first 10 carbons as the lipid is placed in the outer shells. These compression-only $\Delta E$ values can be compared to those calculated by the three-dimensional (3D) continuum elastic model (3D-CEM) in Article II (Table 4).

Table 4.

First Shell Compression Energy for each Lipid Type, kcal/mol, Dependent on the Assumed Length of the Channel

	h = l = 22 Å (kcal/mol)	h = l = 26 Å (kcal/mol)	3D-CEM (kcal/mol)
dC16:1	—	—	—
dC18:1	0.20	—	—
dC20:1	0.69	0.24	0.07
dC22:1	1.1	0.48	0.27
dC24:1	1.4	0.69	0.43

3D-CEM values are from Article II and assume l = 26 Å. Dashes indicate situations that are presumed to have negligible compression penalty.

The canonical hydrophobic length of gA is 22 Å, as deduced from both experiment and theory (13, 44, 82), but some lipids are still able to protrude above the channel, i.e., matching is nonideal, and so the definition of the hydrophobic length is ambiguous even given the molecular detail of a simulation. In Fig. 7, the minima of the hydrophobic thickness profiles only reach ∼26 Å due to lipid protrusions (e.g., Kim et al. (9)). Therefore, for the analysis in Table 4, we decided to use channel lengths of both 22 and 26 Å for illustrative purposes (Tables 3 and 4 of Article II use l = 26).

This simple compression-only calculation serves as a starting point for understanding redistribution around the channel. As described in detail in Article II, these first shell compression penalties are reduced at the expense of curvature penalties in a way that is sensitive to the protein-lipid boundary. The high estimate of the compression energy from the simple compression-only model is typical of the majority of previous estimates (e.g., Huang (13)), which have concluded that the lipid meets the channel with nearly zero slope, a conclusion that is inconsistent with simulation thickness profiles (Fig. 7 and (9, 14)). The 3D-CEM in Article II naturally incorporates curvature (i.e., nonzero slope boundary condition), which reduces the compression energies, which then reduces the expected redistribution compared to the compression-only model.

From the density distributions of the terminal carbons (Fig. S3) and order parameters (Fig. S4), we find that dC_18:1 and dC_16:1 configurations are not as strongly perturbed as their longer counterparts in the first shell, meaning that the short lipids do not contribute much to the compression energy when they are near the channel. We also find that lipids can extend over the top of the channel and interdigitate into the opposite leaflet. These forms of lipid compression relaxation (protrusion, interdigitation, and curvature, which is discussed above) allow for more long lipids to reside in the first lipid shell than would be expected from simple compression-only modeling.

Conclusions

It has been hypothesized that integral membrane proteins can introduce local order and nanoscale heterogeneity in the distribution of lipids adjacent to the protein. Theoretical models have predicted that lipids with better hydrophobic match to a protein would be preferentially enriched around the protein, but there has been little experimental evidence supporting this conjecture.

This work intertwines experiment, long timescale all-atom MD, and simple compression theory to describe lipid redistribution driven by hydrophobic mismatch. Single-channel lifetime experiments provided insight into the energetics within a bilayer: the larger the disjoining force, the lower the lifetime. By using two-component bilayers, where one lipid species provided a better hydrophobic match to the channel, the mean channel lifetime was increased relative to a control bilayer, which led to the calculation of an effective bilayer concentration based on the estimated composition of the bilayer in the first shell surrounding the channel. We thus predicted the mole-fractions of dC_18:1 and dC_16:1 to be 0.58 ± 0.04 and 0.66 ± 0.02 in the channel’s vicinity in gA+dC_18:1+dC_22:1 and gA+dC_16:1+dC_24:1, respectively.

All-atom MD was then used to explore the timescales and details of lipid redistribution. A lipid shell definition was built using a 2D Voronoi tessellation that allowed for a well-defined and high-resolution method for tracking and calculating bilayer properties around the channel. Using the shell definition, the timescale for lipid redistribution in the first shell could be calculated, and was observed to be ∼100 ns, demonstrating that long timescale simulations are required for a multicomponent bilayer to reach an equilibrium state around an embedded protein. After 500-ns simulation, which allowed for first shell equilibration, concentrations were 0.50 ± 0.04 for dC_18:1 and 0.66 ± 0.02 for dC_16:1 in the gA+dC_18:1+dC_22:1 and gA+dC_16:1+dC_24:1, respectively. These values are in agreement with the concentrations inferred from experiment (0.58 ± 0.04 and 0.66 ± 0.02, respectively) and theory in Article II (0.59 ± 0.03 and 0.65 ± 0.03, respectively). The large uncertainty in the dC_18:1+dC_22:1 bilayer indicates that longer timescale simulations are necessary to compute equilibrium distributions of lipids around an embedded channel. Nevertheless, the modeling in Article II is consistent with the all-atom model, and thus predicts that given longer simulations, enrichment of dC_22:1 would emerge. Testing this will require longer simulations to reduce stochastic uncertainty. Finally, lipid configurations as a function of shell were determined with atomic resolution. It was found that well-matched short lipids exist in near-native conformations, while long lipids must strongly compress to match the hydrophobic length of the channel.

Supported by the configuration analysis, a simple compression-only model was used to demonstrate that the lipid redistribution in this study could be mainly attributed to reducing the bilayer deformation energy (i.e., decreasing the disjoining force that the bilayer imposes on the channel) by general interactions between lipids and the channel. It is now well established that stresses within the bilayer influence conformation and dynamics of embedded proteins. One of the contributors to bilayer stress is compression, which can be alleviated by a protein conformational change, protein diffusion into a better-matched lipid patch, or lipid redistribution, so that better-matched lipids are near the protein. This study focused on the latter option, where experiment and simulation both predicted lateral lipid redistribution. The bridges in this work between experiment, all-atom MD, and theory allow for cross validation of all methods and deeper understanding from the atomistic to the continuum levels.

Author Contributions

A.H.B., A.M.M., O.S.A., and W.I. designed the research; A.H.B., A.M.M., A.J.S., and H.R. performed the research; A.H.B., A.M.M., and A.J.S. analyzed the data; and A.H.B., A.J.S., R.W.P., O.S.A., and W.I. wrote the article.

Editor: Scott Feller.