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-to-Inverted Phase Transition Using Coarse-Grain Molecular Dynamics
* Center for Molecular Modeling and Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania; Department of Chemistry and Biochemistry, University of the Sciences in Philadelphia, Philadelphia, Pennsylvania; and Schrödinger Inc., Portland, Oregon
Correspondence: Address reprint requests to S. O. Nielsen, E-mail: snielsen{at}cmm.upenn.edu.
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ABSTRACT |
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) phase. The transmembrane peptide is constructed of hydrophobic sites with hydrophilic caps. The hydrophobic length of the peptide is smaller than the hydrophobic thickness of a bilayer consisting of an equal mixture of long and short alkanoyl tail lipids. When incorporated into the membrane, a meniscus forms in the vicinity of the peptide and the surrounding area is enriched in the short lipid. The meniscus region draws water into it. In the regions that are depleted of water, the bilayers can fuse. The lipid headgroups then rearrange to solvate the newly formed water pores, resulting in an inverted phase. This mechanism appears to be a viable pathway for the experimentally observed L-to-inverse hexagonal (HII) peptide-induced phase transition. |
INTRODUCTION |
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). Theoretically, the main approaches to study membranes are through statistical thermodynamics as exemplified by Safran (1994), wherein Ginzburg-Landau expansions of the free energy are considered, or through classical all-atom molecular dynamics (MD) simulations (Scott, 2002). Due to the traditionally fast timescales accessible to MD simulations, the study of lipid miscibility has been largely ignored. Through the use of new methodologies we present a study of a model miscible lipid system.
It has been shown that various lipid molecule types present on a membrane can result in subdomain formation within the lipid membrane. Bilayer microdomains have been observed under different conditions such as in cholesterol mixtures (in which case they are called rafts) or a transmembrane peptide. Subdomains may also form under surface-pressure modifications in a Langmuir monolayer (LM) (Gopal and Lee, 2001). Incidentally, domain formation between different phases of the same lipid species can be observed in LMs (Schief et al., 2000). Most of these systems are too complicated and cannot be studied using current computational techniques with atomistic detail.
To gain some insights about the interactions between different lipids in a bilayer and their interactions with constructs that perturb the bilayer environment, we explore two different, yet complementary, effects that a short cylindrical peptide can induce in a mixed-lipid system. We limit our study to effects arising solely from hydrophobic mismatch. The first process we study is domain formation in an otherwise mixed-lipid bilayer. The second is the transition from the lamellar L phase to an inverted phase. In both cases the driving force for the reorganization of the system is the extent of hydrophobic mismatch between the lipid bilayer and the peptide.
It has been proposed that lipid domains of different hydrophobic thickness are used to sort membrane proteins based on the length of their transmembrane domains (Sprong et al., 2001), but this picture is misleading because it is known that proteins themselves passively induce lipid domain formation (Dumas et al., 1999). The hydrophobic matching principle states that in the immediate vicinity of the peptide there is an accumulation of the lipid that is hydrophobically best matched (Dumas et al., 1997). Typically one pictures the bilayer-spanning part of a transmembrane peptide as a hydrophobic alpha-helix with caps that preferentially associate with the interfacial lipid headgroup-water region. Lipid bilayers are more easily deformed than transmembrane proteins (de Planque et al, 2001), and the assumption is made that the bilayer deforms to match the hydrophobic length of the protein (Harroun et al., 1999a), leaving the protein virtually unchanged. Theoretical considerations point to a range of effects that contribute to the free energy in the presence of such a peptide inclusion. These consist of elastic acyl chain stretching/compression, surface tension terms accounting for the average interfacial area per molecule, curvature contributions from the formation of a meniscus around the inclusion, and tilt modulus of the acyl chains (Fattal and Ben-Shaul, 1993; Sens and Safran, 2000; May and Ben-Shaul, 1999; Gil et al., 1998; Wahab et al., 2001; Nielsen et al., 1998; Duque et al., 2002).
At high concentration, transmembrane peptides can have more dramatic effects on the membrane structure. Short peptides, namely peptides whose hydrophobic length is shorter than the bilayer thickness, have been shown to induce phase transitions from the lamellar to an inverted phase (Killian et al., 1996). Long peptides do not have this effect—they tilt instead, and the lipid remains in the lamellar phase (Li, 2000; Killian et al., 1996). If the peptide hydrophobic length is grossly mismatched from the membrane thickness, the peptide may fail to insert (de Planque et al, 2001; van der Wel et al., 2000). More generally, inverted phases can be induced in phospholipid membranes by dehydration (Yang and Huang, 2002), heating (Rappolt et al., 2003), the addition of divalent cations (Ortiz et al., 1999), the addition of lipids of negative intrinsic curvature (Zimmerberg and Chernomordik, 1999; Li and Schick, 2000; Marrink and Mark, 2003), or the addition of synthetic peptide (Killian et al., 1996).
For the tryptophan-capped synthetic peptides used experimentally (Killian et al., 1996), the two dominant effects of the peptide are thought to come from its hydrophobic length and from the tryptophan anchoring residues (Petrache et al., 2002). The bulky multiple tryptophan groups at each end of the peptide are thought to play a dual role in anchoring the peptide ends in the headgroup region of the bilayer, and in preventing peptide aggregation. Since there should be a lipid-mediated peptide-peptide attractive force present in the system, aggregation is otherwise a strong possibility (Harroun et al., 1999a,b; Gil et al., 1998; Kralchevsky and Nagayama, 2000; Sharpe et al., 2002; Weikl, 2001; Lagüe et al., 1998, 2001; Dan et al., 1993). We avoid the possibility of aggregation in this work by considering only a single peptide assembly per unit cell. This, together with the orthorhombic cell geometry, does not permit the experimentally observed inverse hexagonal (HII) phase (Killian et al., 1996) to form; rather we observe the formation of an inverted phase with a different symmetry.
Neither the existing experimental nor theoretical studies shed light on the mechanism that could drive such a phase transition (Killian et al., 1996; May and Ben-Shaul, 1999). Rather, the stability of the resulting HII phase is justified a posteriori. In this study, which uses coarse-grain MD, we propose a mechanism wherein the transbilayer peptide induces the formation of a meniscus, causing the accretion of interbilayer water into the meniscus region. This movement depletes the water layer far from the peptide, allowing the bilayers in these regions to fuse. This fusion event pinches off the water sheets, trapping the water in cylindrical pores, which are the hallmark of inverted phases. The headgroups then rearrange to solvate these water pores.
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METHODS |
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; Shelley et al., 2001a,b; Shelley, 2003).
A series of 1,2-di-n-alkanoyl-sn-glycero-3-phosphocholine lipids (DCnPC) are used; namely DC11PC (referred to as the short lipid), DC14PC (commonly known as DMPC), DC17PC, and DC29PC (referred to as the long lipid). Coarse-grain DC14PC and water parameters have been developed and characterized (Shelley et al., 2001a,b; Shelley, 2003; Lopez et al., 2002a,b). The remaining lipids are generated from DC14PC simply by adding or removing tail units (see Fig. 1) (Shelley et al., 2001b).
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,b; Whitehead et al., 2001). The simulation times given in this article are simply the number of time steps used multiplied by the time step size. However, lateral diffusion in the membrane plane occurs two orders of magnitude faster than this, so that a simulation time of 1 ns corresponds roughly to 100 ns of an all-atom simulation.
Peptide
The cylindrical assembly is aimed to mimic a small bundle of peptides or a macromolecular construct. The assembly is built as follows. Four rings of twenty hydrophobic sites are flanked by two rings of twenty hydrophilic sites to form the body of the cylinder. To cap the cylinder so that it is impenetrable and to increase the hydrophilicity of the cylinder ends, a 10-hydrophilic site middle ring and a 5-hydrophilic site inner ring are added to each end (see Fig. 1). In total there are 150 sites with 420 bond and 1950 bend potentials between them. Bonds are placed between all neighboring sites as shown in Fig. 1. There is a bend potential involving every triplet of atoms that are connected by bonds. All bonds and bends are harmonic with a force constant of 10,000 K. The equilibrium length and angle vary, however. All bonds have req = 4.65 Å except for the inner hydrophilic ring intraring bonds, which have req = 6.50 Å. All bends have 
eq = 135° with the following exceptions: eq = 90° is used between a hydrophobic, an outer-ring hydrophilic, and a middle-ring hydrophilic site to hold the cylindrical cap in place; in addition, the inner hydrophilic ring intraring bends are chosen to be one of eq = 108°, eq = 72°, or eq = 36°, depending on which is appropriate from the geometry. The assembly is 
15 Å in radius and 20 Å long. By way of comparison, the mechanosensitive channel MscL consists of five -helices surrounding a pore that is 30 Å in diameter (Betanzos et al., 2002). The hydrophobic and hydrophilic sites have intermolecular potentials identical to the lipid alkanoyl tail sites and the water sites, respectively. All the peptide sites have a mass of 160 atomic units and are uncharged.
Small systems
Seven different systems, each consisting of 160 lipids and 1500 water sites (which represent three water molecules each), were employed. Each system is run in the NPT ensemble at 1 atm and 313.15 K. The lipid composition of the seven systems consists of four single-lipid and three mixed-lipid systems. The four single-lipid systems are DC11PC (short lipid, S1), DC14PC (S2), DC17PC (S3), and DC29PC (long lipid, S4). The three mixed-lipid systems are composed of DC11PC and DC29PC in differing proportions and have a short/long lipid ratio of 1:1 (S5), 1:3 (S6), and 3:1 (S7), respectively.
The initial condition is prepared as follows. A pair of lipids of the same type is generated such that their tails just meet. The x-y plane is then tiled uniformly with this pair using a 9 x 9 grid of side length 75 Å. One pair is deleted from the grid to obtain 80 lipids per leaflet. The 1:1 mixed system is constructed by placing the long and short lipids on alternating sites of the lattice. The 1:3 and 3:1 mixed systems are generated by populating three out of every four consecutive lattice sites with one lipid species, with the remaining sites being reserved for the other species. The mixed systems thus generated have a width mismatch—this mismatch heals quickly after which the headgroups all align in the same z range in each leaflet. These systems were each simulated for 1 ns; we remind the reader that this corresponds to roughly 100 ns for the equivalent all-atom simulation.
The width of the resultant bilayers is determined as follows. Each headgroup density peak in Fig. 2 A is fitted with a three-parameter Gaussian in a very localized region around the maximum. Then the centers of the pair of Gaussians for a single curve are subtracted to give the width.
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The starting configuration of the previous system (L2, with peptide) was taken and the water/lipid ratio was reduced to 25:1 (3450 waters, keeping in mind that one coarse grain site represents three water molecules) from 75:1 by removing water sites that were farthest from the lipids. The box length Lz was then reduced accordingly. This system was run for 10 ns (L3). Similarly, by reducing the x-y box size, two smaller peptide/water/lipid systems were generated and run for 10 ns. These consisted of 73 short lipids in each of the two leaflets, 74 long lipids in each of the two leaflets, and 2721 waters (L4); and 48 short lipids in each of the two leaflets, 50 long lipids in each of the two leaflets, and 1949 waters (L5).
Lastly, to demonstrate that the inverted phase transition also occurs in membranes composed of a single-lipid species, simulations were performed with the lipid DC20PC. In this case, at a water/lipid ratio of 25:1, the threshold lipid/peptide ratio required for the phase transition is 155:1.
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RESULTS |
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The mixed-lipid densities are broken down into the contributions from their constituent lipids in the three panels of Fig. 3. There are two features of note. The first is that the headgroups all occupy the same z plane – that is, the same plane parallel to the plane of the bilayer. The second is the hydrocarbon tail density. The determining factor for the bilayer width is the lipid-tail packing. The total tail density, irrespective of lipid identity, is similar in all cases, including the single-lipid systems (see Fig. 2 A). For the widest mixed-lipid bilayer (S6), the short lipids in either leaflet are completely separated from one another, as seen by the zero lipid density in Fig. 3 A. The long lipids bridge this depletion region with alkanoyl tail density, bringing the net density back up to its bulk value. For the intermediate mixed-lipid bilayer (S5), in which the two lipids are equally mixed (Fig. 3 B), the headgroup regions are seen to align perfectly, whereas the tail density for the short lipids is depleted in the middle of the bilayer. The long lipids once again fill the hydrocarbon region up to its bulk density value. For the shortest-width mixed-lipid bilayer (S7), the short lipid tails touch across leaflets, but their density is still depressed in the middle of the bilayer (see Fig. 3 C). The long lipid tails are severely constrained in their extension normal to the bilayer plane and hence splay parallel to this plane, packing the middle of the bilayer up to its full tail density.
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Lipid mixing in bilayer
For a two-component bilayer, consisting of otherwise identical lipids of differing tail length, the miscibility of the lipids depends upon the temperature. Domain formation in mixed bilayers is usually attributed to islands of the gel phase of the longer tail species in the gel-liquid region of the phase diagram (Gliss et al., 1998). We wish to study the effect of a membrane inclusion on an otherwise well-mixed system (Sens and Safran, 2000; Fattal and Ben-Shaul, 1993). Hence we first demonstrate that we are in the liquid-liquid region of the phase diagram where domain formation, in the absence of transmembrane peptides, is not observed (Dumas et al., 1997). It should be pointed out that all the lipids mentioned in the manuscript are in the fluid phase under the simulation conditions used. This is not in accordance with experiments and is due to the nature of the coarse-grained (CG) force field. See Nielsen et al. (2003) for a detailed discussion of alkane chain length.
A system consisting of 208 short lipids, 208 long lipids, and 10,400 water sites was prepared in a patchwork fashion (L1; see Fig. 4 and Large systems). This patchwork melts and the two lipids mix. The extent of miscibility is quantified by calculating the three headgroup-headgroup center-of-mass two-dimensional radial distribution functions in the plane of the bilayer (see Fig. 5). From Peptides, above, we know that the headgroups align in the same z plane, so that we need only quantify miscibility in the x-y plane. It is seen in Fig. 5 that the lipids are completely miscible.
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). The meniscus then drives the lipids to segregate on the basis of hydrophobic mismatch. The concentration of lipids around the peptide is initially slightly enriched in the long species as shown in Fig. 6 A. This is done deliberately so as not to bias the domain formation, since we eventually expect the short lipid to collect around the peptide. A meniscus forms in the vicinity of the peptide as depicted in Fig. 7. The lipids residing next to the peptide, at a distance of roughly 15 Å from its center (see Fig. 7), are maximally perturbed from their equilibrium position. The mismatch is roughly 7.5 Å for each of the two bilayer leaflets. The lipids closer to the peptide are farther away from the bilayer center because they reside with their headgroups immediately above (for the upper leaflet) the hydrophilic peptide cap, with their alkanoyl tails bent to flank the length of the hydrophobic core of the peptide. After 10 ns of simulation, domain formation is clearly seen. The lipid species are distributed around the peptide as shown in Fig. 6 B. The region within 30 Å of the peptide center is enriched in the short-lipid species.
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water/lipid ratio of around 25:1, the role of the short peptide is more complicated. In the 400:1 lipid/peptide system (L3, see Large systems for the construction of the 400:1, 300:1, and 200:1 systems) a meniscus forms around each end of the peptide similar to that seen in Fig. 7. Water, which before the meniscus formed was distributed in a uniformly thick layer between the bilayers, accumulates in the meniscus region and is depleted from the regions far from the peptide (and its periodic images). In the 300:1 system (L4) this depletion is significant enough for the bilayers to come into contact midway between the peptides, pinching off most of the water into cylindrical pores. The system remains trapped in a defective state where water, lipid headgroups, and lipid tails mingle together as shown in Fig. 8. In the 200:1 system (L5) these defects heal as the lipid headgroups rearrange to solvate the water pores, and the remaining water migrates into the pore region. The process is shown in Fig. 9, A–C, and the final phase is shown from a different perspective in Fig. 9 D to show a perspective view of the cylindrical water pores. These results are consistent with experiment in the sense that the transition to an inverted phase is only observed at high peptide/lipid ratios. The peptide concentration controls the phase transition through the extent of interbilayer water depletion caused by the meniscus regions. If we think of the water farthest from the peptide as a reservoir (e.g., the corner regions in the unit cell in Fig. 9 A) from which the meniscus region is filled, the depletion of the reservoir is negligible if the peptide concentration is extremely small. However, at higher and higher concentration, the reservoir region becomes smaller and smaller, until it does not contain enough water to fill the meniscus. The three concentrations we chose to study are representative of the different possible scenarios. We would like to stress that the L phase is stable in the absence of peptide.
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155. This shift is due in part to the domain segregation in the mixed-lipid case. The regions of the bilayer that are depleted of water gradually become enriched in the long lipid by the domain formation process. This facilitates the membrane fusion event since the long tail lipids tend to increase the bilayer width, which tends to push water out of the interbilayer region. Before the bilayers come into contact, the water subphase extends in the x and y directions (the directions parallel to the membrane plane) in an infinite two-dimensional sheet. The initial contact is localized, with the bilayers only connected by a thin stalk. The water at this point is not segregated into the tubular domains shown in Fig. 9 D but rather forms a cross-hatched pattern in which the tubes are connected to one another. This is shown in the top panels of Fig. 10 immediately after membrane contact. Over time, however, a spontaneous symmetry breaking occurs, as shown in the bottom panels of Fig. 10, resulting in the final phase shown in Fig. 9 D.
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). It has been argued that the short peptides occupy the shortest distance between water pores, relieving the longer alkanoyl lipid tails from having to pack into this geometry, and allowing them to occupy the more spacious "corner" regions where their tails can stretch out more (May and Ben-Shaul, 1999; Killian et al., 1996). |
CONCLUSIONS |
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The domain formation induces a nonhomogeneous lipid concentration field around the peptide. In a lattice Monte Carlo simulation (Wahab et al., 2001) it was found that if two such regions with nonhomogeneous concentration fields overlap, an attractive force between the peptides results (Gil et al., 1998). The pair potential for this indirect force can be obtained from the free energy of the system, which depends on the distance between the peptides. We are currently investigating lipid-mediated peptide-peptide forces by placing more than one peptide assembly in the simulation cell. This would also allow for the possibility of forming an inverse hexagonal phase.
This study illustrates the use of the coarse-grain methodology as a testing ground for exploring the effect of individual physically motivated concepts in isolation from the full complexity of the problem. In conclusion, the mechanism we observe causes local water depletion to instigate membrane contact. Dehydration has the same effect—the likelihood of contact is increased. Heating increases the amplitude of the membrane undulations and bending fluctuations, again making contact likely (Goetz et al., 1999). In membrane protein crystallization the addition of salt, in the route reviewed by Caffrey, causes dehydration (Caffrey, 2000). The addition of cations can also be rationalized in terms of water depletion. The presence of lipids of negative intrinsic curvature lowers the barrier for the initial stalk formation because, for example in this case, the curvature due to the peptide-induced meniscus is positive and is hence highly unfavorable. We have demonstrated that with a deep meniscus and a high peptide/lipid ratio, we can induce an inverted phase transition even with phosphocholine lipids. We propose that the observed mechanism is largely responsible for the experimentally observed synthetic peptide-induced phosphocholine lipid lamellar-to-inverse hexagonal phase transition.
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ACKNOWLEDGEMENTS |
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This work was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada and the National Institutes of Health.
Submitted on January 19, 2004; accepted for publication June 14, 2004.
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  L. Thogersen, B. Schiott, T. Vosegaard, N. Chr. Nielsen, and E. Tajkhorshid Peptide Aggregation and Pore Formation in a Lipid Bilayer: A Combined Coarse-Grained and All Atom Molecular Dynamics Study Biophys. J., November 1, 2008; 95(9): 4337 - 4347. [Abstract] [Full Text] [PDF]
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P. J. Bond, D. L. Parton, J. F. Clark, and M. S. P. Sansom Coarse-Grained Simulations of the Membrane-Active Antimicrobial Peptide Maculatin 1.1 Biophys. J., October 15, 2008; 95(8): 3802 - 3815. [Abstract] [Full Text] [PDF]
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C. L. Wee, K. Balali-Mood, D. Gavaghan, and M. S. P. Sansom The Interaction of Phospholipase A2 with a Phospholipid Bilayer: Coarse-Grained Molecular Dynamics Simulations Biophys. J., August 15, 2008; 95(4): 1649 - 1657. [Abstract] [Full Text] [PDF]
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C. F. Lopez, S. O. Nielsen, B. Ensing, P. B. Moore, and M. L. Klein Structure and Dynamics of Model Pore Insertion into a Membrane Biophys. J., May 1, 2005; 88(5): 3083 - 3094. [Abstract] [Full Text] [PDF]
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r, where r = 0 corresponds to the center of the peptide assembly. The short lipid is denoted by solid line and the long lipid by dotted line. The two leaflets appear as positive and negative height values.
