Aggregation of Model Membrane Proteins, Modulated by Hydrophobic Mismatch, Membrane Curvature, and Protein Class

Abstract

Aggregation of transmembrane proteins is important for many biological processes, such as protein sorting and cell signaling, and also for in vitro processes such as two-dimensional crystallization. We have used large-scale simulations to study the lateral organization and dynamics of lipid bilayers containing multiple inserted proteins. Using coarse-grained molecular dynamics simulations, we have studied model membranes comprising ∼7000 lipids and 16 identical copies of model cylindrical proteins of either α-helical or β-barrel types. Through variation of the lipid tail length and hence the degree of hydrophobic mismatch, our simulations display levels of protein aggregation ranging from negligible to extensive. The nature and extent of aggregation are shown to be influenced by membrane curvature and the shape or orientation of the protein. Interestingly, a model β-barrel protein aggregates to form one-dimensional strings within the bilayer plane, whereas a model α-helical bundle forms two-dimensional clusters. Overall, it is clear that the nature and extent of membrane protein aggregation is dependent on several aspects of the proteins and lipids, including hydrophobic mismatch, protein class and shape, and membrane curvature.

Introduction

Membrane proteins play significant roles in the biology of the cell (1). Their interactions with the surrounding lipid environment (2) can play important roles in their stability and function (3–5). Consequently, the biophysics of membrane/protein interactions have been the focus of intensive investigation for a number of years (6,7).

A key concept in the understanding of such interactions is that of hydrophobic mismatch (3,7–11), which refers to the difference between the length of the hydrophobic region of a membrane protein and the thickness of the hydrophobic core of the lipid bilayer in which it is embedded. Hydrophobic mismatch can induce a number of possible responses in a membrane, including: 1), local bilayer stretching if the hydrophobic length of the protein is longer than the hydrophobic thickness of the lipid bilayer (i.e., positive mismatch); 2), local bilayer compression in the case of negative mismatch (i.e., when the hydrophobic length of the protein is shorter than the hydrophobic thickness of the bilayer) (12); 3), tilting of α-helical TM regions of proteins, which will distinguish between α-helical and β-barrel proteins (13); 4), TM protein deformation (14); and 5), TM protein aggregation (15).

Computer simulations at the molecular level, using either molecular dynamics (MD), Monte Carlo, or dissipative particle dynamics (DPD), play an important role in understanding complex membrane systems (16–19). In particular, they can provide insights into the adjustment of protein/membrane systems to mismatch. Such simulations may be performed at atomistic resolution (see, e.g., (20)), in which case they provide a detailed picture of local adjustments for relatively simple peptide/bilayer systems. For larger systems and/or longer simulation times involving multiple interacting proteins, coarse-grained molecular dynamics (CG-MD) (see, e.g., (21–36)) or DPD (37–39) simulations may be employed, in which groups of atoms are treated as single particles.

In this study, we employ a CG-MD force field derived from MARTINI (25,26,28) and modified for membrane peptides and proteins (33–35). As in a previous study (40), we explore simple models of α-helix bundle and β-barrel membrane pore proteins to explore how hydrophobic mismatch can drive protein aggregation. Thus, we study protein pore-lipid bilayer systems with 16 identical copies of a protein pore embedded in a ∼7000 lipid bilayer to probe protein aggregation and lipid demixing over a range of system parameters, such as protein class (α-helical or β-barrel), lipid bilayer hydrophobic thickness, and membrane curvature (by comparing planar bilayer systems to vesicle systems). Our focus is on α-helical protein pores as the majority of TM proteins are of this class (41), but we extend to β-barrel TM protein (42) pores to explore the robustness of our findings. Protein aggregation driven by hydrophobic mismatch has been reported in a number of previous studies (e.g., (15,43)). Other studies have been extended to explore protein-induced lipid sorting (44,45) and lipid-induced protein sorting (46).

Methods

Protein pore models

In this study, we focus on two protein pore models (Fig. 1). These are simplified models derived from: 1), an NMR-based model of the nicotinic acetylcholine receptor M2δ peptide helical bundle (M2; PDB ID: 1EQ8) (47), a simple α-helical protein pore; and 2), the TM domain of Staphylococcal α-hemolysin (HL; PDB ID: 7AHL), a well-studied β-barrel protein pore (48).

Figure 1.

(A) Sequences of the Gα and Gβ models, with the hydrophobic leucines (black), the polar serines (green), and the amphipathic aromatic tryptophans (red). (B) CG structures of the Gα and Gβ pores with the protein backbone (orange) and the side chains in the same color scheme (with leucines in gray rather than black). The structures are snapshots from (separate) simulations with CG2/CG3 bilayers; the phosphate groups of the surrounding lipids are shown (blue).

The structures of these proteins, which represent the two main classes of membrane protein, were simplified to yield the two model protein pore structures: Gα (generalized α) and Gβ (generalized β). Each of the model proteins has a hydrophobic outer surface (leucine residues), a hydrophilic inner pore surface (serine residues), and rings of membrane-anchoring tryptophan residues (49,50) at each end of the protein. We note that Gα resembles the sequence of Lear et al.'s (51) de novo designed pore-forming peptide LS3. The hydrophobic lengths of the protein pores are 2.7 nm (Gα) and 2.8 (Gβ).

Preparation of the protein pore-lipid bilayer systems

In the CG model, each phospholipid is represented by a positively charged particle (choline), a negatively charged particle (phosphate), two polar particles (glycerol), and a variable number of hydrophobic particles to represent acyl chains of different lengths (25). Our nomenclature is that CGn indicates a lipid with two chains of (equal) length n hydrophobic CG particles, of which each particle corresponds approximately to four -CH₂- groups. Thus, e.g., CG4 is approximately equivalent to dipalmitoyl (i.e., (C16:0)₂) phosphatidylcholine. A range of bilayer hydrophobic thicknesses (from 3.1 nm to 4.4 nm) was studied by using lipid bilayer compositions ranging from 1:1 CG2/CG3 to CG4/CG5 (see Fig. S1 in the Supporting Material).

Systems similar to CG3, CG4, and CG5 have been used in a previous study of membrane proteins by Periole et al. (27). The corresponding lipid bilayer systems, each comprising 512 lipids, were formed via 200-ns self-assembly simulations. Single copies of each model protein were inserted into the bilayer centers, with a small number of lipids removed from the site of protein insertion. After a subsequent energy minimization step, the systems were solvated with CG water particles. These systems were energy-minimized and then simulated for 200 ns. To make the larger systems with 16 proteins, the final frame of each of these single protein systems was replicated onto a 4 × 4 grid in the bilayer plane. The final systems thus comprised 16 identical copies of one protein pore species and ∼7000 lipids. These were used in production simulations of duration 5 μs (see the Supporting Material for details of the simulation protocol).

Preparation of the vesicle systems

The CG2/CG3 and CG4/CG5 mixtures were also used to form unilamellar vesicles of ∼7000 lipids and diameter ∼32 nm. To do this, a hollow inner shell (8.2 nm diameter) of purely hydrophilic particles (repulsive to all CG particles other than water) was placed in the center of the simulation box. By adding CG lipids randomly oriented in a surrounding shell, the inner shell thus acts as a mold around which the lipids can form a vesicle, preventing artifacts such as hemifusion. A ∼7 nm-thick shell of water was placed between the lipids and inner shell. A rhombic dodecahedron simulation box was used; 100 ns simulations were then used to form vesicles. We note that this method is similar in spirit to an earlier study of lipid vesicles (52), which used mean-field boundary potentials instead of a shell.

After vesicle formation, the central restrained shell was removed and replaced by waters, and 16 Gα proteins were inserted with equal spacing around the membrane. Lipids were removed from the vesicle membrane to accommodate the proteins. Their positions within the bilayer were matched to a snapshot from a flat bilayer simulation, and their orientations were matched to the local bilayer-normal so that the C-terminal end of each helix was facing outwards from the center of the vesicle. The resulting structures were energy-minimized using 500 steps of the steepest descents method, then briefly equilibrated for 1000 MD steps with a timestep of 10 fs. Subsequent simulations were performed without the central restrained shell, and significant deviations in vesicle shape were not observed (data not shown).

Results

Simulations of multiple TM proteins in planar bilayers

Two simplified models of membrane proteins were studied (Fig. 1), as described earlier (40). One model was a generalized α-helix bundle (Gα) and the other was a generalized β-barrel (Gβ). Each model was homo-oligomeric: homo-pentameric in the case of Gα, and homo-heptameric for Gβ. (Note this corresponds to a 14-stranded β-barrel for Gβ, as each monomer consists of a two-stranded β-hairpin.) For both Gα and Gβ, the amino-acid sequences were such as to reproduce key aspects of biological pores: 1), a central pore lined by polar (serine) side chains; 2), a hydrophobic exterior formed by leucine side chains; and 3), a band of tryptophan side chains defining the preferred region of interaction of the protein surface with lipid headgroups.

To explore possible aggregation as a result of protein/bilayer mismatch, we prepared large (∼50 × 50 nm²) bilayers containing 16 copies of the protein in a bilayer at a protein/lipid ratio ∼1:450. The progression of the Gα CG2/CG3 simulation (in which there was a positive hydrophobic mismatch, i.e., the hydrophobic region of the protein is longer than the bilayer thickness) is illustrated in Fig. 2 A. Initially the 16 identical copies of the Gα TM protein were spaced equally (∼12 nm apart). Over the course of the 5 μs simulation, the proteins sampled the whole of the lipid bilayer plane. After ∼0.5 μs initial protein/protein contacts had been formed, and by 5 μs three aggregates (of 3, 5, and 8 proteins) had been formed. This behavior may be contrasted with that of the corresponding hydrophobically matched system (Gα CG4/CG5; Fig. 2 D) where although random transient encounters between pairs of proteins occurred over the course of the simulation, they subsequently rapidly dissociated and did not form aggregates.

Figure 2.

Simulations of multiple 16 TM proteins in planar lipid bilayers. In each case, the protein (yellow) and the bilayer surface (blue) are shown. (A) For the hydrophobically mismatched Gα CG2/CG3 system, snapshots at the start (0 μs), early on during (0.5 μs), and at the end (5 μs) of the simulation are shown, indicating the progress of the aggregation process. (Yellow ring) Cluster shown in more detail in panel B. (D) For the other three systems (Gα CG4/CG5, Gβ CG2/CG3 and Gβ CG3/CG4), a snapshot at the end of each 5 μs simulation is shown. (Yellow ring) Gβ CG2/CG3 cluster shown in more detail in panel C.

A comparable behavior was seen for the β-barrel systems, where the more markedly mismatched system (Gβ CG2/CG3) formed a small number of substantial clusters whereas the better-matched system (Gβ CG3/CG4) did not do so to such an extent. Interestingly, both visual inspection of the clusters formed by the end of the simulations (Fig. 2, B and C) and measurement of the number of neighboring proteins versus time (Fig. 3) suggests a difference whereby the Gα TM proteins form two-dimensional clusters whereas the Gβ proteins form elongated (linear) aggregates. This is of interest in the context of recent comparable simulation studies on clustering of rhodopsin (27), suggesting that the pattern of interacting surfaces on the protein may modulate the nature of the cluster induced by hydrophobic mismatch.

Figure 3.

Aggregation analysis of the multiple TM protein planar bilayer simulations. For a given simulation, each row represents the number of neighboring proteins (defined using a cutoff of 2.4 nm between the center-of-mass of two proteins) on a scale from 0 = dark blue to 8 = dark red for each of the 16 proteins in the system over the duration of the simulation.

It is also of interest to examine the dynamic aspects of clustering, i.e., the formation and dissolution of contacts of each protein (Fig. 3 and Table 1). This shows another difference between the Gα and the Gβ CG2/CG3 system—dissolution events are more frequent for the Gα CG2/CG3 system. The analysis also confirms the occurrence of transient encounters in the bilayer matched systems (Gα CG4/CG5 and Gβ CG3/CG4) which, however, do not lead to significant cluster formation.

Table 1.

Protein clusters

System	Mean cluster residency time (ns)	Number of cluster residencies per protein per 1000 ns
Gα bilayer
CG2/CG3	540 ± 750	1.8
CG4/CG5	54 ± 38	1.8
Gα vesicle
CG2/3	270 ± 320	2.0
Inv CG2/CG3	2800 ± 660	0.35
CG4/CG5	62 ± 61	1.5
Gβ bilayer
CG2/CG3	620 ± 970	1.2
CG4/CG5	290 ± 690	2.1

Cluster residency analysis, estimated over the final 3 μs of each simulation. A cluster is defined as having at least two proteins within 6 nm of each other. The mean cluster residency time is the amount of time that a protein is resident in a particular cluster, averaged for each residency over the course of the simulation, and for each protein. Residency times of 16 ns or less are discounted from the analysis. The number of cluster residencies per 1000 ns indicates the frequency with which proteins join and leave clusters.

Simulations of multiple TM proteins in vesicles

We extended our simulations to multiple TM proteins in a closed membrane vesicle, to explore a model of biological membranes (e.g., those of virions or organelles) which may have a pronounced curvature. To this end the Gα CG2/CG3 and CG4/CG5 simulations were repeated in vesicles of diameter ∼32 nm containing 16 approximately equally spaced proteins, again at a protein/lipid ratio of ∼1:450 (Fig. 4). As with the planar bilayer simulations, a clear difference in aggregation was observed between the mismatched and matched systems. However, the rate and extent of protein aggregation during the vesicle Gα CG2/CG3 simulation appeared to be reduced compared to the equivalent planar bilayer simulation. The change in rate follows with a general reduction in diffusion rates in curved membranes, especially of lipids in the inner leaflet (see Discussion below). The reduction in the extent of aggregation is confirmed by analysis of the numbers of contacting proteins (Fig. 5), which suggests the formation of smaller clusters with more frequent dissolution events than for the equivalent planar bilayer simulation. This can also be seen by comparing the mean cluster lifetime over the last 3 μs of simulation for the Gα CG2/CG3 planar bilayer (mean 0.54 ± 0.75 μs) with that for the vesicle system (mean 0.27 ± 0.32 μs) (Table 1).

Figure 4.

Simulations of 16 Gα TM proteins in vesicle membranes. Proteins (yellow), inner leaflet lipid phosphates (solid blue), and outer leaflet lipid phosphates (transparent blue). (Top-left picture) Starting configuration (t = 0 μs) for the Gα CG2/CG3 simulation; the proteins start as far apart from each other as possible, and this same configuration is used for the Gα CG4/CG5 and Gα-inv CG2/CG3 simulations. (Other pictures) Simulations at t = 5 μs. In the Gα-inv CG2/CG3 system, the proteins are embedded in the membrane in the opposite orientation. The shape of the protein is thus a good match for the curvature of the membrane, leading to greatly increased aggregation.

Figure 5.

Aggregation analysis of the multiple TM protein vesicle membrane simulations. See Fig. 3 caption for details. The same scale of 0–8 is used for ease of comparison.

A key aspect of the behavior of the Gα protein models in the vesicles is that the protein is shaped approximately like a truncated cone (Fig. 1 B). Thus packing together of Gα proteins is likely to be influenced by the orientation of insertion of the proteins relative to the curvature of the membrane in the vesicle. In the Gα CG2/CG3 simulations the protein was inserted with the narrower, C-terminal end of the truncated cone directed outwards, which would be anticipated to disfavor aggregation. Another 5-μs Gα vesicle simulation (Gα-inv CG2/CG3) was therefore performed, with the protein orientation inverted (i.e., with the narrower, C-terminal end directed inwards), which would be anticipated to favor aggregation. Gα-inv CG2/CG3 shows greatly increased aggregation (Figs. 4 and 5), with two main clusters remaining tightly bound for the last 2 μs. It therefore seems that there is a complex interplay among protein/bilayer mismatch, protein shape, and membrane curvature which governs the stability of an aggregate. In contrast, the mean cluster duration for the hydrophobically matched Gα CG4/CG5 system (for which the clusters correspond to brief encounters) is unchanged between the planar (mean 0.05 ± 0.04 μs) and vesicle (mean 0.06 ± 0.06 μs) systems.

Lateral diffusion of lipids and proteins

We examined the lateral diffusion coefficients of the proteins and lipids (Table 2), which is of interest given recent studies of protein diffusion in extended atomistic simulations of membrane proteins (53). The trends which emerge are consistent, with slower diffusion of both protein and lipid in the longer chain lipid simulations, as has been seen in recent studies (e.g., (54)). The Gα proteins also diffuse more quickly than the larger-diameter Gβ proteins. The values obtained are comparable with those reported in CG simulations of rhodopsin (27), once one notes that we have not corrected our CG timescale by a factor of 4. We note that such a correction, if applied, would bring the diffusion rate for the lipids in the CG4/CG5 systems down to ∼3 × 10⁻⁷ cm² s⁻¹, which is comparable to, e.g., the experimental estimate for POPC (2 × 10⁻⁷ cm² s⁻¹) (55).

Table 2.

Protein and lipid diffusion coefficients

System	D (10−7 cm2/s)
	Protein	Shorter lipid	Longer lipid
Gα bilayer
CG2/CG3	5.1	28	24
CG4/CG5	3.6	12	11
Gα vesicle
CG2/CG3	5.6	25	21
Inv CG2/CG3	3.9	25	22
CG4/CG5	3.1	11	11
Gβ bilayer
CG2/CG3	2.7	25	23
CG3/CG4	2.6	14	13

Lateral diffusion coefficients, determined for the period 1–5 μs of each simulation. They are not corrected by a factor of 4 to adjust for the CG force field.

In the vesicle simulations, the Gα proteins diffuse at a similar rate to the equivalent bilayer simulations when oriented with their narrower C-terminal ends outwards. In the inverted orientation, however, diffusion is slowed considerably by extensive aggregation of the proteins. The correlation between aggregation and decreased diffusion rate can also be observed, for example, in the Gα CG2/CG3 bilayer simulation, in which the protein diffusion rate coefficient decreases from 6.5 ± 1.2 × 10⁻⁷ cm² s⁻¹ over the period 1–2 μs (when the system forms mostly small clusters of 2–4 proteins) to 2.8 ± 0.3 × 10⁻⁷ cm² s⁻¹ at 4–5 μs (2–3 large clusters).

Another feature observed was that the diffusion of lipids was slower when in close proximity to proteins. In the Gα CG4/CG5 vesicle simulation, diffusion coefficients reduced from 11.3 ± 0.4 × 10⁻⁷ cm² s⁻¹ for bulk lipids (>3 nm from the center of mass of a protein; either CG4 or CG5 type) to 7.8 ± 0.3 × 10⁻⁷ cm² s⁻¹ for annular lipids (<3 nm from the center of mass of a protein). We note that the annular lipids are not bound strongly to the proteins, and are freely exchanged for other lipids. The simulation results are in keeping with electron spin-resonance measurements which found similar reductions in the rates of diffusion of annular phospholipids around a number of membrane proteins (56,57) and also agree with simulation studies suggesting that proteins diffuse concertedly with lipids as dynamic protein-lipid complexes (53).

Lipid distribution around the proteins

A substantive degree of hydrophobic mismatch between a lipid bilayer and integral membrane proteins may result in a lipid sorting mechanism in mixed lipid bilayers (see, e.g., (58–60)). Thus, with positive protein/bilayer mismatch (i.e., the hydrophobic length of the protein is greater than the hydrophobic thickness of the lipid bilayer), the longer tail lipids would be expected to accumulate in close proximity to the protein pore. Analysis of the nature of the lipids adjacent to the protein in our simulations (Fig. 6) shows that where one lipid matches the hydrophobic topology of a protein more closely than the other (i.e., Gα CG4/CG5, Gα-ves CG4/CG5, both Gβ simulations), it will demix from others to increase its own concentration proximal to the protein. We also note cases where no demixing is evident (e.g., the Gα CG2/CG3 simulations), which appears to be due to both lipids being poor hydrophobic matches for the protein. In general, the degree of lipid demixing appears to be independent of the extent of protein aggregation. The effect is also relatively small—lipids do not completely demix, so that proteins are surrounded by only one type of lipid—which is in agreement with experiment (5).

Figure 6.

Lipids adjacent to the proteins. For each system the average (over 16 protein pores) numbers of each lipid species around the protein is shown as a function of time, using a cutoff distance determined from protein-lipid radial distribution functions. (Gray lines) Raw data. (Red/blue lines) Calculated using a moving average over 20 ns. The results of this analysis for both the planar bilayer (A) and vesicle (B) systems are shown.

Discussion

Our simulations demonstrate how the extent and nature of aggregation of proteins within a lipid bilayer are sensitive to the degree of hydrophobic mismatch, the class of membrane protein (α-helix versus β-barrel), and the curvature of the lipid bilayer. We have examined relatively large systems, with a protein/lipid ratio of ∼1:450. We note that in many biological membranes with a protein/lipid mass ratio of ∼1:1 this corresponds to a protein/lipid molar ratio of ∼100, and for an average membrane protein the number of annular lipids is ∼30 (61). We also note that the protein models used attempted to reproduce the canonical outer surface of a membrane protein, with hydrophobic (leucine) side chains in the TM region and amphipathic (tryptophan) side chains in the lipid/water interfacial region. Both the Gα and the Gβ proteins were approximately circularly symmetrical in cross section, and so this study is in many ways complementary to, e.g., that of Periole et al. (27), who explored mismatch-driven aggregation of rhodopsin and demonstrated that there were preferred interaction regions on the surface of this more asymmetrical protein. We have also focused on mismatch-driven aggregation in the absence of lateral phase separation of the lipids, to aid the dissection out of the complex effects likely to take place in real biological membranes.

The binding strength of protein clusters was modulated primarily by the degree of hydrophobic mismatch and the membrane curvature, ranging from very strong (Gα-inv CG2/CG3 vesicle simulation) to essentially nonexistent (Gα CG4/CG5 simulations). Intermediate binding strengths were also observed; in the Gα CG2/CG3 vesicle simulation, for example, clusters would form, break up, and reform multiple times (see cluster residency times in Table 1; Fig. S2 and Movie S1 in the Supporting Material show an example of a cluster dissociating and then reassociating).

A number of other subtle effects were observed, depending on the exact nature of the protein and of the bilayer. Thus, the β-barrel protein seemed to prefer to form linear aggregates (i.e., strings) within the bilayer plane, in contrast to the α-helical protein which formed extended two-dimensional clusters. This difference will merit further investigation with a wider range of membrane proteins—both simplified models (as here) and real membrane proteins. A further subtlety revealed by the vesicle simulations was that the shape and orientation of the protein relative to the vesicle bilayer could have profound influence on its aggregation properties. The relative importance of hydrophobic mismatch and curvature deformation have been discussed in the context of experimental studies of aggregation of, e.g., rhodopsin in membranes (43).

A range of other features observed can be compared with recent simulation studies. For example, aggregates were seen to diffuse more slowly than individual peptides, and annular lipids were slowed in comparison to bulk lipids. These findings are in keeping with the picture of concerted movement of protein-lipid complexes, as recently highlighted by an atomistic simulation study (53). Local bilayer deformation was also observed in all cases where hydrophobic mismatch was present, as has been commented on in a number of previous studies (e.g., (27,37,63,64)). In mixed bilayers where one lipid species matches a protein for hydrophobic length much better than another, a degree of lipid demixing about the protein has been observed. This is in contrast with some recent simulations of a single α-helical peptide (65). The difference between the two studies may be the larger size of the inserted protein in this study, such that it will have a larger annulus of lipids.

There have also been a number of recent computational studies which have followed a similar overall theme of investigating mismatch-induced aggregation and related behaviors of membrane proteins. Several studies have used DPD simulations combined with more radically simplified models of membrane proteins. Thus, de Meyer et al. (66) have conclusively demonstrated that protein aggregation can be simply a consequence of mismatch in simulations with no attractive potential between proteins and that such clustering may be modulated by the presence of cholesterol in the membrane (38). Again using DPD and a simple cylindrical model of membrane proteins, Schmidt and co-workers (46,58) have explored mismatch-induced aggregation in the context of membrane protein sorting (58) and have suggested that protein acylation may modulate such aggregation (67).

As mentioned above, Periole et al. (27) have used CG-MD simulations in a detailed study of mismatch-induced rhodopsin clustering and its possible relationship to the importance of GPCR dimers in signaling. CG-MD has also recently been used to study hydrophobic (WALP) α-helices in a complex mixed lipid system (diC16:0-PC/diC18:2-PC/cholesterol), revealing that the peptides prefer to cluster in the liquid-disordered phase rather than enter the liquid-ordered phase (60). Single WALP helices have also been studied in atomistic simulations in terms of the effect of hydrophobic mismatch and helix tilt (68).

It is important to consider the possible limitations of these studies:

One major limitation is the use of a CG force field which inevitably approximates the nature of the protein-lipid and protein-protein interactions. However, we note that comparisons with available experimental data suggest that this force field accurately reproduces protein-lipid interactions for a number of membrane proteins (36). Recent studies on the free energies of interactions of transmembrane α-helices using the Martini CG force field (69,70) have resulted in potentials of mean force for helix/helix interactions comparable to those obtained by earlier all-atom simulations (71). In the context of the CG force field, we note that there has also been discussion (72,73) of time steps in CG-MD simulations. We therefore ran test simulations on a Gα CG4/CG5 system (see Supporting Material for details) with time steps of 5, 10, 20, and (as in the main study) 40 fs. We evaluated a number of structural and dynamic properties of the system and did not see any statistically significant differences in behavior for the different time steps. We are therefore persuaded that our results are robust to the exact choice of time step.

The second major limitation is that our studies have been restricted to relatively simple systems, in terms of the protein and lipid species, and to relatively small systems, in terms of vesicle dimensions, compared to genuine biological complexity. The proteins we have simulated are canonical models of the most common types of TM protein. Although experimental work has reported mismatch-induced aggregation of simple TM peptides (15) and more complex membrane proteins (43), other studies have hinted that membrane proteins are not always affected by bilayer thickness (57,74). In terms of lipid complexity, it is reassuring that comparable simulations have now been performed for ternary mixtures of lipids (60), but there remains much to be done in bridging the gap between in silico and in vivo studies of protein aggregation within biological membranes. Regarding the size of vesicles in our simulations, these are comparable to, e.g., synaptic vesicles (diameter 30–80 nm) (75) while a little smaller than, e.g., the influenza virion (diameter ∼120 nm) (76). Based on our comparison with planar membranes, we predict that the modulation of protein aggregation by membrane curvature would reduce with increasing vesicle size. A more detailed investigation via simulation of a wider range of vesicle sizes would be of some interest.

We also performed a number of test simulations of small vesicles (see the Supporting Material for details) to evaluate whether the self-assembly procedure enabled correct equilibration of the number of lipids between the inner and outer leaflets. For 15-nm diameter vesicles, the mean (over 10 simulations) fraction of inner leaflet lipids was 0.275, with a standard deviation of 0.004. The latter represents ∼3–4 lipids per vesicle. This suggests that although the self-assembly of lipid vesicles may result in small deviations from the ideal lipid composition, such deviations are not sufficient to alter the results presented.

Reflecting on the likely biological relevance of our studies and related efforts from a number of other groups and approaches (see summary above), they confirm the complex, coupled interplay of protein/protein, protein/lipid, and lipid/lipid interactions in membranes which may lead to membrane protein aggregation. Such effects are likely to be of importance both for experimental studies of simpler systems consisting of single species of membrane proteins reconstituted in vitro (e.g., (43)) and for more complex, biological membranes containing multiple lipid and protein species. In particular, simulations of protein aggregation in simple systems might be usefully extended to explore aspects of the likely mechanisms of two-dimensional crystallization of membrane proteins (77). Indeed, our simulations with simple models have suggested different cluster geometries for different proteins, which is of possible interest in this context. However, a detailed understanding of the nature of clusters formed will require a more systematic examination of a wider range of proteins than in this study.

In terms of in vivo relevance, our results have bearing on our understanding of lateral complexities in membrane structures such as rafts, etc. (78,79), and are also of possible relevance to membrane protein sorting (58,59). In future studies it will be important to use simulations to explore the behavior of such complex systems which exhibit considerable lipid and protein heterogeneity.