Article pubs.acs.org/Langmuir
Stability of Bicelles: A Simulation Study Robert Vácha*,† and Daan Frenkel‡ †
National Centre for Biomolecular Research, Faculty of Science and CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno-Bohunice, Czech Republic ‡ Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom S Supporting Information *
ABSTRACT: Aqueous mixtures of long-tailed lipids (e.g., dimyristoylphosphatidylcholine - DMPC) and detergents can sometimes form membrane disks called bicelles. Bicelles have found applications as an embedding medium for membrane proteins in the context of NMR studies and protein crystallization. However, the parameters that determine the thermodynamic stability of bicelles are not well understood. Here we report a coarse-grained simulation study of the relationship between lipid-aggregate morphology and the composition and temperature of the surfactant mixture. In agreement with experiments, we find that bicellar mixtures are destabilized at higher temperatures and detergents are present at membrane edges as well as in flat membranes with a strong preference for the edges. In addition, our results suggest that the free-energy difference between bicelles and the perforated lamellar phase is typically very small for molecules without intrinsic curvature and charge. Cone shaped surfactant molecules tend to favor the formation of bicelles; however, none of the systems that we have studied provide unambiguous evidence for the existence of thermodynamically stable bicelles in mixtures of uncharged lipids with long and short tails. We speculate that small changes in the properties of the system (charge, dopants) may make bicelles thermodynamically stable.
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INTRODUCTION Mixtures of phospholipids with surfactants can self-assemble into a variety of structures. One particularly interesting structure is the bicelle, a flat bilayer disk composed mostly of phospholipids in the flat part with surfactant molecules or short-tailed lipids concentrated on the rim of the disk.1−3 Bicelles thus represent a morphology between the lamellar phase and spherical micelles. A number of studies have shown that trans-membrane proteins can be embedded in bicelles and that the resulting system is potentially useful for the structure determination of the embedded proteins.4 Importantly, bicelles can be crystallized or possibly oriented in a magnetic field, something that is rather challenging with multilamellar phases and vesicles.5−7 The advantage of bicelles for membrane protein structure determination is that the embedded proteins are in their natural environment. Under these conditions, we are less likely to observe the structural artifacts that may be induced by detergents that are commonly used in the structure determination of transmembrane proteins.8−10 In addition, bicelles have found a variety of other applications, such as delivery vehicles to oocyte membranes,11 additives in electrokinetic chromatography,12,13 and templates for the synthesis of platinum nanowheels.14,15 To exploit the full potential of bicelles, it is important to know under what conditions they are stable and how their size can be controlled. Size control can be crucial for crystallization, where it is important that the disk is large enough to host a © 2014 American Chemical Society
transmembrane protein yet at the same time is small enough not to disturb the crystal packing. Experiments have shown that the bicelle phase diagram can be quite complex.1,16−19 For instance, in some studies, bicelles were found only in a narrow temperature range,20,21 whereas in others bicelles occur only below a certain temperature threshold.1,17,22,23 The bicellar phase has been found to be rather viscous and has been studied by a number of techniques.16−18,22,24−26 When the bicellar phase ribbons are heated, wormlike micelles or a lamellar phase can form. Smallangle neutron scattering experiments have shown that the magnetically oriented phase has the properties of a chiral nematic phase.16,17,22 Moreover, NMR experiments cannot distinguish easily between perforated lamellar phases and solutions of oriented bicelles.27 In fact, it is not even obvious that solutions of isolated bicelles or ribbons represent a thermodynamically stable phase as, in some experiments, vesicles were observed after a prolonged period of incubation of the bicellar system at low temperatures.28 An experimental system that has been shown to form bicelles is a mixture of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipid and 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC).4,16,29 Other molecules that have been shown to form bicelles are saturated and unsaturated lipids,30 ether-linked,31,32 Received: December 17, 2013 Revised: March 24, 2014 Published: March 26, 2014 4229
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ester lipids,20,33 cholesterol,30 other lipids,21,34 acids,35 and surfactants.36,37 The fact that a wide variety of molecules can form stable, or at least metastable, bicelles suggests that a generic model of amphiphilic lipidlike molecules should be able to capture the process of bicelle formation. In the present study, we consider such a coarse-grained model. We have used molecular dynamics simulations of a coarsegrained model to elucidate the phase behavior and stability of bicellar mixtures. The model was designed to mimic DMPC and DHPC lipids; however, the model is sufficiently coarsegrained to account for a whole class of amphiphilic molecules with similar behavior.
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Figure 1. Representative snapshot of a simulations box, where a membrane composed of long lipids (LLs) is surrounded by short lipids (SLs). Some of the SLs are adsorbed onto the LL membrane. For the sake of clarity, only SLs in the vicinity of LLs are displayed. On the right-hand side of the plot, graphical representations of the coarsegrained model for LLs and SLs are shown.
METHODS
We performed Langevin Dynamics simulations using the ESPResSo38 program package. Each simulated system contained about 5000 molecules consisting of a mixture of long and short lipids. The size of our simulation box was chosen such that the lipid particles occupy 12% of the total volume. Unless stated otherwise, the initial configuration was a random mixture. We used a coarse-grained, implicit solvent model for the phospholipids. This model was introduced by Cooke and Deserno39 and is known to reproduce the experimental properties of membranes such as the compressibility and bending moduli.40 Moreover, the model can account for the gel−fluid phase transition of the lipid bilayer. In the model of ref 39, phospholipids are represented by a chain of beads with a purely repulsive hydrophilic headgroup as its first bead. The following beads (one bead in the case of DHPC, two for DMPC) represent hydrophobic tails with relatively long-ranged attraction (2.8σ) with a minimum depth of 1.0kT. The Langevin MD simulations were performed at constant NV and T. In all cases, periodic boundary conditions were employed. In what follows, lengths are expressed in units of a tail bead diameter (1σ), which can be roughly equated to 1 nm by a comparison of the simulated membrane thickness (i.e., 5 σ) to its experimental value (i.e., 5 nm). The interaction energy was measured in units of ε, which is the depth of the attractive potential between lipid tail beads. The units of time can be estimated by comparing the emulated and experimental diffusion coefficients of the lipids. This comparison suggests that τ ≈ 10 ns. As the solvent is treated implicitly, hydrodynamics effects are not included, which may influence the rate of self-assembly but does not change the final outcome of the aggregation process.41 The simulation time step was 0.01τ, and the total time of each simulation was at least 70 000τ. The free energy of pore formation was calculated using the Wang− Landau method42 with the reaction coordinate of the largest pore. The pore was defined as an area without any hydrophobic beads (with a bin size of 0.09 nm2), which was shown to be a good choice for the collective variable for the free energy of pore formation.43 The freeenergy profiles for small (up to 2 nm2) pore sizes were obtained from the Boltzmann inversion of the spontaneous pore size distribution.
Figure 2. Illustrative diagram of observed phases at different temperatures and mixture compositions at the end of simulation 75 000τ. At high q values, only the lamellar (L) phase is formed, but at low q values (q < 0.1), only micelles (M) are formed. For 0.1 < q < 1.0, wormlike (W) micelles were found and they were in a coexistence with the lamellar fraction at higher temperatures. For q ≈ 1.0, we find bicelles (B) at low temperatures.
3.0, where the SL concentration is so small that it does not disrupt the LL bilayer. This is in agreement with our simulations, where the starting configuration was an equilibrated lipid bilayer of LL, where the intact membrane was stable for q > 3.0. This suggest that the lamellar phase is perforated for q ≤ 3.0. We found that in some systems (e.g., q = 6.69 and T = 1.05) the bilayer closed on itself to form a spherical vesicle. In other systems (e.g., q = 11.5 and T = 1.0), a planar membrane was formed that extended through the periodic boundaries. At low q values (below 0.1), where SLs are dominant, only SL micelles are formed with the occasional inclusion of LL molecules. In range of q values from 0.1 to 1.0, we have observed wormlike micelles with the partial formation of the lamellar phase at higher temperatures, where the structure can best be described as pieces of a bilayer interconnected by wormlike micelles. In systems with q values from 1.0 to 3.0, lipid disks and perforated bilayers formed at low and high temperatures, respectively. Note that the lipid gel/fluid transition is around T = 0.95 in the employed model.39
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RESULTS AND DISCUSSION We first investigated the effect of DHPC (short lipids = SLs) as a detergent on membranes of DMPC (long lipids = LLs), in particular, its ability to disrupt the lipid bilayer above the concentration threshold. A representative starting snapshot of a simulation box consisting of an LL membrane in contact with SL is depicted in Figure 1. Below q = 3.0, a parameter that denotes the ratio of the number of long and short lipids, q = LL/SL, the membrane was found to disintegrate over the entire temperature ranges studied (Supporting Information). We investigated the behavior of the lipid mixtures for a range of temperatures and system compositions. Figure 2 shows the illustrative diagram of observed phases in simulations that started from a random configuration that mimics the state of the solution after sonication. A lamellar phase formed for q > 4230
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The observed phases are shown separately in Figure 3, and trajectories and final snapshots can be found in the Supporting
Figure 4 shows the formation of a bilayer vesicle. The simulation started from random initial conditions at T = 0.95
Figure 3. Detailed snapshots of the observed phases illustrate the different aggregate structures that we observe in our simulations.
Figure 4. Time sequence from a simulation trajectory that shows the formation of an LL vesicle. The simulation started from a random configuration. Initially, only small disks of membrane were formed, which subsequently fused together. When the membrane size exceeds a fairly sharply defined threshold, the membrane closes on itself to form a vesicle. The simulation shown was performed on a pure LL system (q = inf) at T = 0.95.
Information or online.44 For the sake of clarity, we show only those short lipids that are in contact with the longer ones; we do not show short lipids in solution because these would obscure the view of the aggregate. The observed phase diagram is consistent with the experimentally determined phase diagrams, where a lamellar phase was reported for these systems at higher temperatures and intermediate and high q values. For intermediate q values (between 2.0 and 7.0) and temperatures below the lipid gel/ fluid phase transition, the presence of bicelles was deduced from polarized optical microscopy and small-angle neutron scattering experiments.1,16,17 However, the experiments also found bicelles at much higher temperatures for q = 2.0. In contrast, we see no bicelles17 at q = 1.63 or q = 3.0. In general, the LL phase contains fewer SL molecules and becomes more rigid at lower temperatures and higher q values, which agrees with recent NMR measurements.45 In our simulations we observed wormlike micelles in the region of the phase diagram between the micellar and lamellar phases. In experiments, a chiral nematic phase was observed between the bicellar and lamellar phases.17,19,22 This chiral nematic phase is supposed to consist of wormlike micelles or ribbons. Superficially, these structures are similar to those found in the simulations. However, we find no evidence for a (chiral) nematic phase. This may be because the simulation box is too small to observe the formation of larger ordered structures. In experiments, a chiral nematic phase was found to exist at temperatures between the range of stability of bicelles and the lamellar phase.17 The chiral nematic phase consists of elongated aggregates that were interpreted as wormlike micelles or ribbons.18,19,22 Interestingly, we find wormlike micelles for low q values and high temperature existing between the range of stability of micelles and of the lamellar phase. However, the comparison is not straightforward because the wormlike micelles in our simulations are thin (about the thickness of the LL bilayer) in two dimensions occasionally interconnected by the larger part of the bilayer. However, in experiments the wormlike micelles or ribbons were suggested to be elongated chunks of the bilayer.22
and a pure LL composition. Because of the effective attraction between the hydrophobic tails, a very fast condensation is observed. This leads to the formation of small disks (pieces of a bilayer) at time t = 3000τ. Subsequently, small disklike fragments diffuse in the system and fuse upon contact. At t = 5500τ, a large membrane has formed. Once the piece of membrane is large enough, it is favorable to eliminate the edges by forming a vesicle (Figure 4) at t = 13 500τ. Alternatively, pieces of membrane can connect via periodic boundary conditions to form a lamellar phase. This path is consistent with previous simulations.41 Importantly, although lipid disks are observed in these simulations, they represent a transient species. We argue that the observation of the disks at the lower temperatures and lower q values can be due to the finite length of the simulations. We find that there is a difference between the disks that form in pure LL systems and those that occur in mixtures with SL. The main difference is the composition of the membrane edge at the rim of the disk. In general, the presence of the membrane edge is thermodynamically unfavorable, which can be quantified in terms of a positive line tension. When the SL molecules are introduced into the system, they adsorb on the rim of the LL bilayer, thereby decreasing its line tension and thus stabilizing the disks. Note that SL molecules are also present within the membrane plane but in much smaller amounts. The latter observation is in agreement with experiment.1,2 A decrease in temperature below the gel/fluid phase transition (around T = 0.95)39 might result in the breakage of small vesicles into disks as the bending modulus of the membrane increases. However, such small disks need not represent the thermodynamically stable state because disks can fuse to reform larger vesicles that could be thermodynamically stable. In simulations, we are of course limited by the size of the simulation box, which dictates the maximum size of the disk that we can obtain. To evaluate the thermodynamic stability of the disks present at q = 1.0 and T = 0.80, we heated the system to T = 1.00 and subsequently cooled it back to T = 0.80. When the temperature 4231
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was increased, the disks transformed (fused) into a perforated lamellar phase. However, when we cooled the system back to T = 0.80 the membrane stayed intact and did not split into disks within the time scale of our simulation. One possible interpretation of these findings is that the disk phase is only metastable at T = 0.80. We investigated the free energy associated with membranepore formation in systems over a range of temperature and compositions (Figure 5). Unsurprisingly, there is a large free-
Figure 6. Chemical potential difference between LL and SL in systems with varying composition and temperatures of T = 0.95 and 0.75. The chemical potential difference for an ideal mixture is displayed for the sake of comparison.
composition suggests that there can be large compositional fluctuations in the system at fixed Δμ. This would suggest that, in this temperature regime, the free-energy cost of pore formation is small. The suggestion that pores can form quite easily is also supported by the occasional observation of a large disk with a small pore in the middle (Figure 7). This structure
Figure 5. Free energy of pore formation for systems with varying temperature T and q. Whereas the free energy is increasing with pore size in systems with pure bilayer or a small number of SLs (q = 3.0), pores spontaneously opened in systems with larger numbers of SLs and LLs (q = 1.0).
energy cost (several kT) associated with the opening of pores in pure LL membranes. The free energy values that we computed are in agreement with those found in previous studies.43,46 The presence of a small number of SL molecules lowers the freeenergy cost of pore formation, but a pore-free lamellar phase is still the most stable phase for q = 3.0. In contrast, the membrane pores form spontaneously in a 50:50 mixture of SL/ LL molecules. Hence, for this composition a perforated lamellar phase has a lower free energy than a defect-free lamellar phase. Interestingly, there is a free-energy minimum for pore size of around 10 nm2, which is a small area compared to the size of the bilayer. This observation suggests that the perforated lamellar phase is at least locally stable. The slow increase in free energy with pore size for larger pores suggests that the freeenergy difference between the perforated lamellar phase and bicelles can be small. Interestingly, there is not much difference between the free energy profiles at different temperatures. However, the free energy profiles at lower temperature (T = 0.90) are subject to a relatively large error as in that temperature regime the simulations converge slowly. Similar results were obtained when we used semigrand canonical Monte Carlo (SGC-MC) simulations to study the phase behavior of the membranes. In the SGC-MC simulations, we include trial moves that attempt to transform SL into LL molecules or vice versa. The chemical potential difference between the SL and LL molecules at temperatures of T = 0.95 and 0.75 are displayed in Figure 6. The data in the figure provide no evidence for a first-order phase transition as the membrane composition is changed. If such a transition would occur, one would expect to see a van der Waals loop in the Δμ − q curve. Rather, the fact that Δμ is independent of
Figure 7. Snapshot of a bicelle with a small pore in the middle. All edges of the LL membrane are covered with SLs, and some of the SL molecules can also be found to be adsorbed in the membrane. The snapshot was taken from the system with q = 1.0 and T = 0.75.
has not yet been reported in experiments. In view of the experimental observation of the existence of a wide region in the phase diagram (at slightly higher temperatures then in simulations) where bicelles and ribbons or multilamellar vesicles coexist,17,19,22 it is hardly surprising that we find only a small free-energy difference between bicelles and the perforated lamellar phase. In fact, Sanders and Prosser had even suggested the existence of perforated lamellae as an alternative explanation for their experimental data.47 Because the short lipids tend to accumulate on bicelle rims, it seems plausible that the stronger tendency of detergent molecules to accumulate in regions of high curvature would favor bicelle formation. To test this hypothesis, we constructed an LL/SL model where the SL molecules had been made conical. (The tail bead was given a radius that was 40% smaller than in regular SL molecules). The illustrative diagram of 4232
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observed phases at different temperatures and q starting from a random configuration are shown in Figure 8. The final
particular, the most stabilized structures were bicelles and a perforated lamellar phase in mixtures of DMPC/DMPG/ CHAPSO.19 Our main conclusion is that whereas bicelles appear easily as transient species in our simulations they may not survive unless another stabilizing factor is present. These could be charged lipids or detergents, transmembrane proteins, membrane-edge-active proteins/peptides (APO-A1, antimicrobial peptides, etc.), or possibly also lower lipid dilution that can entropically stabilize the bicelles. We have seen that detergent molecules with a more conical shape lead to the formation of bicelles over a larger range of q values, which suggests that molecules of the right shape could also lead to thermodynamically stable bicelles.
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CONCLUSIONS We have presented coarse-grained molecular dynamics simulations of lipid mixtures. By varying the system temperature and composition of long and short lipidlike molecules, we have obtained a wide variety of long-lived and transient morphologies including spherical micelles, wormlike micelles, bicelles, perforated lamellae, and lamellae/vesicles. Our findings suggest that the free-energy difference between bicelles and the perforated lamellar phase is very small for molecules with cylindrical or conical shapes and that the coexistence can result in interesting structures of perforated bicelles. With our model, we cannot reproduce the formation of thermodynamically stable bicelles at lipid concentration of 12 vol %, but we speculate that a small change in the properties of the constituent molecules (e.g., the addition of charged species or other host molecules) could move bicelles from the transient to the stable regime.
Figure 8. Illustrative diagram of observed phases at different temperatures and mixture compositions of LL an SLc at the end of simulation 115 000τ. At high q values, only lamellar (L) phases are formed, and at low q values, (below 0.1) only micelles (M) are found. In systems with q between 0.1 and 3.0, we observed disks and perforated lamella.
snapshots trajectories are in the Supporting Information or online.48 In the simulations of mixtures containing conical SLc, almost no wormlike micelles were observed, and bicelle disks were observed over a wider range of temperatures and concentrations than for the cylindrical SLc. However, simulations at temperatures above the LL fluid/gel transition resulted either in a perforated lamellar phase or (for low SL concentrations) the formation of a single large disk. Both structures survived cooling below the fluid/gel transition. Hence, again, we have no evidence for the formation of stable bicelles within the time scale of our simulations. On the basis of our findings, we conclude that a simple model for mixed phospholipid bilayers can capture the formation of transient bicelles but does not reproduce the formation of thermodynamically stable bicelles at the simulated lipid concentration (12% of the total volume). A possible weakness of our model is the relative ease with which lipid molecules can escape into the bulk of the solution (high critical micelle concentration). In addition, to keep our model computationally tractable, we have made rather strong simplifying assumptions that may have affected the stability of bicelles. Earlier computer simulations either have studied the details of preformed bicelles or found that the occurrence of bicelles depended on the initial configuration of the system, a typical behavior of insufficiently equilibrated systems.49−51 The thermodynamic stability of bicelles was not explicitly addressed in previous simulations.51,52 In experiments, reproducible bicelle formation has recently been reported for mixtures containing charged lipids.23 It is conceivable that such charged lipids would provide additional stabilization for bicelle formation. Indeed, the addition of a small amount of negatively charged phospholipid DMPG was found to result in dramatic changes in the structural phase diagram and the stabilization of some structures.19,53 In
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ASSOCIATED CONTENT
S Supporting Information *
Short lipids as a detergent. Simulation snapshots. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected],
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS R.V.’s research has been supported by the European Regional Development Fund (CZ.1.05/1.1.00/02.0068 − project CEITEC) and by the EU Seventh Framework Program (contract no. 286154 − SYLICA project). R.V. acknowledges the use of computing facilities at the University of Cambridge and MetaCentrum provided under the program “Projects of Large Infrastructure for Research, Development, and Innovations” (LM2010005). D.F. acknowledges ERC support (advanced grant agreement 227758), EPSRC Programme Grant EP/I001352/1, and support from a grant of the Royal Society of London (Wolfson Merit Award).
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