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Chemistry and Physics of Lipids 163 (2010) 530–537

Contents lists available at ScienceDirect

Chemistry and Physics of Lipids

journa l homepage: www.e lsev ier .com/ locate /chemphys l ip

oarse-grained molecular dynamics of tetrameric transmembrane peptideundles within a lipid bilayer

huy Hien T. Nguyena, Niny Z. Raob, William M. Schroedera, Preston B. Moorea,∗

Department of Chemistry & Biochemistry and the West Center for Computational Chemistry and Drug Design, University of the Sciences in Philadelphia,00 South 43rd Street, Philadelphia, PA 19104-4495, United StatesPhiladelphia University, Henry Avenue and School House Lane, Philadelphia, PA 19144, United States

r t i c l e i n f o

rticle history:eceived 24 November 2009eceived in revised form 5 March 2010ccepted 19 April 2010vailable online 28 April 2010

eywords:on-channelS2 peptide

a b s t r a c t

The conformations of model transmembrane peptides are studied to understand the structural anddynamical aspects of tetrameric bundles using a series of coarse grain (CG) molecular dynamics (MD)simulations since membrane proteins play a crucial role in cell function. In this work, two differentamphipathic models have been constructed using similar hydrophobic/hydrophilic characteristics withtwo structurally distinct morphologies to evaluate the effect of roughness and hydrophilic topology onthe structure of tetrameric bundles, one class that forms an ion-channel and one class that does not.Free energy calculations of typical amphipathic peptide topologies show that using a relatively smoothsurface morphology allows for a stable conformation of the tetramer bundle in a diamond formation.

ll-atometramer bundleALP peptide

MPC bilayer

However, the model with side chains attached to the core in order to roughen the surface has a stablesquare tetramer bundle which is consistent with experimental data and all-atom (AA) MD simulations.Comparisons of the CG simulations with AA MD simulations are in reasonable agreement with the for-mation of tetrameric homo-oligomers, partitioning within the lipid bilayer and tilt angle with respect tothe bilayer normal. We concluded that a square or diamond shape tetrameric homo-oligomers could bestabilized by rational design of the peptide morphology and topology of the surface, thus allowing us to

the bu

tune the permeability of

. Introduction

Membranes and their embedded proteins play a crucial role inumerous cell processes such as signaling, energy conversion, and

on conductance (Estes et al., 2008). In particular, ion-channels reg-late the ionic concentration by selectively allowing certain speciesf ion, such as Na+, Ca2+, and K+, to be transported across the mem-rane (Nichols and Flagg, 2009). They are ubiquitous in processes

nvolving basic cell function as well as intercellular communi-ations. In many cases, ion-channels are homo-oligomeric withhydrophilic lumen, which assemble from separate monomers

Torres et al., 2001; Yang et al., 2001). A common motif found inonomers forming these ion-channels is the amphipathic nature

f the �-helices in the transmembrane domain (Lopez et al., 2005).he polar residues of the peptide are lined up to form a hydrophilic

egion or patch, which form the lumen, leaving the rest of the helixydrophobic with non-polar residues that interact with the bilayerydrophobic layer. Various experimental techniques such as NMRpectroscopy and X-ray crystallography have been used to deter-

∗ Corresponding author. Tel.: +1 215 596 7537; fax: +1 215 596 8543.E-mail address: p.moore@usp.edu (P.B. Moore).

009-3084/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved.oi:10.1016/j.chemphyslip.2010.04.007

ndle or channel.© 2010 Elsevier Ireland Ltd. All rights reserved.

mine the structures of various ion-channels with this motif (Jianget al., 2002; Marassi and Opella, 1998; Oiki et al., 1988a,b; Stevens,2000; Unger, 2001). Properties such as gating, conductivity, andion selectivity of some simple ion-channels including the influenzaM2 channels (Duff and Ashley, 1992; Husslein et al., 1998; Sugrueand Hay, 1991; Yin et al., 2007; Zhong et al., 1998b), synthetic LS2(Howard et al., 2002; Lear et al., 1988, 2001; Slovic et al., 2004),LS3 channels (Zhong et al., 1998a,d), WALP (peptide bundle) (Bondet al., 2007; de Planque et al., 2003; Killian, 2003), and HIV1 VPU(Lopez et al., 2002a; Moore et al., 1998) have been extensively stud-ied both experimentally (Bond and Sansom, 2004; Li et al., 2003;Wang et al., 1994) and theoretically (de Vries et al., 2004; Newnset al., 2000; Sansom et al., 2000; Tieleman et al., 2001). Here in thisstudy, we investigated model ion-channels (LS2) and WALP liketransmembrane peptides. WALP peptides form similar transmem-brane oligomers as ion-channels but they do not conduct ions.

Molecular dynamics (MD) simulations have been used exten-sively to study a variety of dynamical events ranging from

self-assembly of a lipid bilayer to insertion of helical peptides intoa membrane (Newns et al., 2000; Zhong et al., 1998a,b,d). How-ever, conventional all-atom (AA) MD simulations can only accesssmall temporal (<100 ns) and spatial scales (<10 nm) (Ross andMohanty, 2008) which is too short to see homo-oligomerization.

d Physics of Lipids 163 (2010) 530–537 531

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Fig. 1. Hydrophilic residues shown in red and hydrophobic residues shown in green:(A) LS2 synthetic peptide; (B, type Ia) a smooth surface peptide model of the LS2

synthetic peptide; (C, type IIa) a rough surface peptide model of the LS2 syntheticpeptide. The cylindrical hydrophilic core (pink) serves as the backbone of the helicalpeptide and hydrophobic and hydrophilic beads are attached onto the surface, whichact as “side chains”; (D) the WALP peptide; (E, type Ib) a smooth surface peptide

T.H.T. Nguyen et al. / Chemistry an

n complex systems such as the formation of ion-channels in lipidilayers, coarse grain (CG) techniques can be employed resulting

n the removal of certain structural details (Thogersen et al., 2008)hich allows for simulations in spatial and temporal ranges beyondA MD simulations into the microsecond and micrometer range.

Due to the reduction in the number degrees of freedom, CGodeling usually incorporates some of the entropy of fine detail

nto the potentials of the enthalpy term which allows for the cor-ect free energy by compensating the entropy loss with enthalphy,hus describing the �G more accurately. Recent CG models devel-ped by Klein et al. (Lopez et al., 2002a, 2004; Shelley et al., 2001),oth et al. (Chang et al., 2005), Marrink et al. (de Vries et al., 2004;arrink and Mark, 2003), and Scheraga et al. (Makowski et al.,

007; Nanias et al., 2006) retain specific chemical identities andpecific interactions. The model-building scheme had been showno properly describe specific biological materials in amphipathicystems (Chang et al., 2005; Shelley et al., 2001). By using the CGodel developed by Klein et al. (Lopez et al., 2004, 2002c; Shelley

t al., 2001), pore insertion into a lipid bilayer has been observedLopez et al., 2004, 2005). The same model has also been used totudy lipid bilayer perturbation by a transmembrane nanotubesodel (Nielsen et al., 2004).It has been shown by Hummer et al. (2001) that nanotubes archi-

ecture may be used to represent homo-oligormeric peptides thatssemble to form an ion-channel for water and protons. Previousorks done by Fernandez-Lopez et al. (2001) involves forming syn-

hetic structures from naturally occurring units in the assemblyf tubular peptides. Motivated by Hummer and Fernadez-Lopezesearches, we constructed two nanotube models where one modelan assemble into a tetrameric bundle that can form an ion-channelith a pore large enough to allow water to pass through, while the

ther model does not.The initial representation of the nanotube peptide model while

implistic captures some of the essential features of peptides form-ng an ion-channel; it is however overly schematic compared toealistic homo-oligomeric ion-channels. The structural criteria nec-ssary for helices to assemble into a tetramer bundle have beentudied for many years, at least since the de novo designed of LS2ynthetic peptides (Degrado et al., 1989). The LS2 peptide has a sim-le sequence of (LSLLLSL)3 and is known to form a square tetrameric

on-channel (Degrado et al., 1989). The small polar serine residuesre designed to line the lumen of the channel in order to facilitateon transport. The hydrophobic leucine residues are chosen to allowartition of the peptide into the membrane, and are able to sus-ain a vertical transmembrane orientation (Degrado et al., 1989).n addition to the amphipathic nature of the peptide, the lengthf the peptide is designed to be comparable to the thickness of theydrocarbon portions of the lipid bilayer minimizing the hydropho-ic mismatch (Horia et al., 2002). The topology of LS2 can be seen

n Fig. 1A. For comparison purposes, the model peptides that hadample hydrophobic–hydrophilic topology as the WALP peptidesere also used (Bond et al., 2007; de Planque et al., 2003; Killian,

003) (see Fig. 1D). Although the WALP peptides do not form anon-channel, it does form a similar ion bundle but without any iononductance. The simplicity of the LS2 and WALP peptides has beensed in AA MD to further understand the structural and functionalroperties of channel forming peptides (Newns et al., 2000; Zhongt al., 1998c).

Our overall goal is to identify the salient structural and dynam-cs features of homo-oligomeric tetrameric bundles as well as theirssembly that can provide us further insights into designing future

on-channel and transmembrane helical packing. Specifically, we

anted to quantify the packing arrangements of peptides thatssemble into ion-channels or peptide bundles. By understandinghe packing of proteins into these homo-oligomers within a lipidilayer, we could control the properties and the function of the

model of the WALP peptide; (F, type IIb) a modified rough surface peptide model.Other than the two hydrophilic caps, there is no hydrophilic patch on the peptidesimilar to the WALP peptide. (For interpretation of the references to color in thisfigure legend, the reader is referred to the web version of the article.)

channel. If the peptides assemble into a close-packed geometry, itwould prevent water or ions to travel through the channel. How-ever, if the peptides form an open geometry, it would allow thebundle to be “open” so water or ions can travel through the bundle.Therefore, if we could understand the dynamics features as wellas the structural features in the geometry packing of the peptidesassembling to form tetrameric homo-oligomers, we would havethe ability to tune the permeability of ion-channels or the packingarrangement and control the properties of the bundle.

In addition to MD simulations, we also ran metadynamics sim-ulations in order to explore the free energy of the assembledhomo-oligomers, specifically one class that can form an ion-channel and another class that can assemble into a WALP likebundle. Metadynamics are capable of exploring free-energies inthe space defined by a manifold of collective coordinates thatcharacterizes the reaction process. As has been shown elsewhere,meaningful results can be obtained in a relatively short simulationtime, if the coordinates can discriminate between the initial andfinal state and includes all the relevant reaction coordinate motions.This method has already been successfully applied to the study ofthe mechanism of oxidation of DNA (Ensing and Baerends, 2002)and to clarify the translocation of antibiotic molecules througha porin (Ensing et al., 2006), as well as the peptide backbone(Takahashi et al., 2002). With our metadynamics simulations, we

quantify the differences between the packing of the peptide modelsforming tetrameric bundles in a lipid bilayer, which has not beenshown before to our knowledge.

For this study, we constructed CG LS2 and WALP tetramer bun-dles, where each �-helix is modeled using the CG model developed

5 d Physics of Lipids 163 (2010) 530–537

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32 T.H.T. Nguyen et al. / Chemistry an

y Klein and Shinoda (2008). This construction scheme is appro-riate for a homo-oligomeric tetramer bundle. In addition, weodified the smooth nanotube model to capture a rough topology

f the monomers which are found in ion-channels. By designingifferent topologies (rough surface and smooth surface), we wouldave the ability to control the properties of the tetramer bundlehich would allow us to tune the permeability of ion-channels andeptide bundles.

. Methodology

.1. Construction of the CG model

CG models of the phospholipid dimyristoylphosphatidylcholineDMPC) and water developed by Klein et al. were used in this studyLopez et al., 2002a,b; Nielsen et al., 2003; Shelley et al., 2001). TheseG models have been tested extensively in previous computationaltudies of lipid bilayers (Lopez et al., 2002a,b, 2005; Nielsen et al.,003, 2004, 2005; Shelley et al., 2001) and were able to reproducexperimental bulk densities as well as surface tension (Lopez et al.,002b). In this study, four tubes are used for each system to modelfour-helical bundle of transmembrane peptides. We constructed

wo types of models, a smooth tube (Fig. 1B and E), which we labeledype I, and a rough tube that more closely resembles an �-helicaleptide (Fig. 1C and F), which we labeled type II. In addition, two dif-erent subtypes of each type were also modeled, subtype a (Fig. 1Bnd C) has the same hydrophilic/hydrophobic topology as LS2 andubtype b (Fig. 1E and F) has the same hydrophobic/hydrophilicopologies as the WALP peptides (Bond et al., 2007). All types haveydrophilic caps that act as anchors at the ends, which are sol-ated by water and keep the model in a transmembrane orientationLopez et al., 2005). Subtype a also contained a vertical hydrophilicatch to model the amphipathic nature of LS2 peptide, whereas sub-ype b is entirely hydrophobic between the caps (see Fig. 1) which

odels the peptide bundles.

.1.1. Type I model (smooth, Fig. 1B and E)Type I model was first used by Lopez et al. (Lopez et al., 2005;

ielsen et al., 2005), in which the helical protein was modeled ascylindrical object similar to a nanotube with eight 8-bead rings

64 beads total) that were stacked vertically and linked with bondsnd bends between neighboring beads. The equilibrium bond dis-ance was 4.65 Å for all bonds. The intramolecular morphology ofype I CG peptide model (Fig. 1B and E) was constructed as fol-ows: each individual ring was a perfect octahedral that had 8 bondsnd 8 bends of 45◦ angle in the plane of the ring. Eight individualings were stacked on top of each other, with every adjacent ringffset from by a 22.5◦ rotation, which was then connected by 16onds for a total of 112 bonds in the TM peptide model. There are aotal of 176 bonds and 752 bends per tube model. For the subtypeCG model, two out of the eight beads are hydrophilic (Fig. 1B),hich is very similar to the LS2 peptides. As for the subtype b CGodel, there are only hydrophilic caps and the ends of the tube,

eaving the rest of the tube hydrophobic (Fig. 1E). This model isery similar to the WALP peptides (Killian, 2003). The harmoniconds and bends were included in the model with force constantsf 10,000 K/rad2 (19.86 kcal/Å2) and 10,000 K/rad2 (19.86 kcal/Å2),espectively, which keeps the structure fairly rigid.

.1.2. Type II models (rough, Fig. 1C and F)

For the second model (type II), two subtypes were constructed.

he differences between the two subtypes are in the hydrophilicatches. In subtype a there is a vertical patch of hydrophilic beadso line the lumen of the ion-channel (Fig. 1C). This mimics the LS2eptide topology (Fig. 1A). In subtype b there is no hydrophilic patch

Fig. 2. The smooth surface peptide model cannot support a void with the bundle.The initial square arrangement of peptides (left) collapsed into a diamond shape(right).

(Fig. 1F), which is similar to the WALP peptides (Fig. 1D). The diam-eter of both type I and II models are ∼14.00 Å which is consistentwith the peptide interactions distances.

The type II models were constructed similar to the type I models,however the eight levels of CG atoms were rotated by 45◦ ratherthan 22.5◦. Each level consisted of 4 beads in a perfect square, whereeach core bead has a CG group (side-residue) attached to it extend-ing away from the center of the core. This construction mimics thehydrophilic core of a peptide (the peptide backbone) with the corebeads, and amino acids side chains with the residues attached to thecore. There are 4 bonds (32 total) and 4 bends (32 total) in the planeof the ring for each ring. All bonds have an equilibrium distance of5.00 Å or 2.5 Å for rough and intermediate cases. 56 bonds and 168bends connected the adjacent rings together with an equilibriumangle of 60◦. There are 112 bends involved in the adjacent rings. Theharmonic force constants used for bonds and bends are 8000 K/rad2

(15.89 kcal/Å2) and 8000 K/rad2 (15.89 kcal/Å2), respectively. Bothends of the tube are capped with one hydrophilic ring. The cylin-drical center core of the tube is hydrophilic in order to mimic thepolar backbone of a peptide.

For the type II CG tube models, the length of the “side chains” was5.00 Å, which is longer than the side chain length of leucine and ser-ine residues. Since the purpose of this research is to understand thephysical properties of TM peptides that lead to ion-channel stabil-ity, structure and dynamics, we extended the existing type I CG tubemodels with a rough topology; but without the difference in sidechain length and our type I tubes are shorter in length, and the tubeopening is less flexible compared to the model presented by Smei-jers et al. Our type II tubes have similar features as the scramblasesmodel presented by Smeijers et al. (2006). However, the diameterof the core tubes in our type II models had been reduced so that theoverall diameter of the type II tubes remains the same as the typeI tubes.

2.2. Simulation details

We investigated four different systems in this study, with fourproteins embedded within the bilayer of each type and subtype.In each system, four tubes were placed 15 Å apart (the approxi-mate van der Waals radius for nanotube–nanotube interactions) ina square arrangement (Fig. 2). A cavity large enough to accommo-date the homo-oligomeric bundle was then created by removinglipids from the center of a pre-equilibrated hydrated lipid bilayer.Each system consists of four peptides, 190 lipids, and 4640 waterbeads. A constant temperature (300 K) and pressure (bilayer plane

in which 85 × 85 box sides are constrained to change in the sameproportion, and bilayer normal (z) pressure was separately set to1 atm) ensemble was used with Nose-Hoover chains of length 3(Evans and Holian, 1985). The systems were allowed to equilibrateuntil the volume of the system and each component of energy

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T.H.T. Nguyen et al. / Chemistry an

erm fluctuate around equilibrium values. The average box size waspproximately 83 Å × 83 Å × 97 Å. After equilibration, 15 ns trajec-ories for each system were collected at 1 ps intervals and were usedor analysis. Longer trajectories were not needed for each systemince the pressure, volume, and potential energy of the systemsuctuated around a constant value. This can be observed by theistance measurements shown in Fig. 5, where drifting or irregularovements were not observed. All simulations were carried out

sing the Code for Molecular Modeling and Molecular DynamicsCM3D) designed by Moore (2005).

.3. Free energy methods

Initial simulations indicated that there are two stable conforma-ions, a diamond (close packed) and a square arrangement (openacked). Both structures are observed to be stable for type II modelsor the duration of the simulations with no conversion between thewo structures. We thus employed “metadynamics” (Ensing et al.,006; Laio and Parrinello, 2002) in order to explore the free energyrofile of conversion between these two arrangements. Metady-amics is a validated method that aims to enhance the explorationf free energy surface (Ensing et al., 2006; Laio and Parrinello, 2002).sing metadynamics, the free energy of conversion from diamondrrangement to square arrangement, and back to diamond arrange-ent was explored for both type I and type II CG tetramer systems.

he collective variable is defined as the diagonal distance of theetramer bundle, measured from the centers of mass (COM) of twoubes at opposite corners, ranging from 14 Å to 30 Å. There were nother potentials employed in the systems, thus the peptide modelsere free to rotate or shift with respect to the bilayer. Only two col-

ective variables were placed between the two different corneredeptides center of mass which leaves the other two peptides toove according to Newton’s equations. The width of each Gaus-

ian was at 0.5 Å, and the hill depth was 100 K (0.1986 kcal/mol). Forach system, a diamond arrangement of tetramer bundle was con-tructed and equilibrated. The equilibrated structure was then useds an initial conformation for 15 ns of metadynamics simulations,hich is long enough to explore the conformations of space.

. Results and discussions

We hypothesized that a rough surface topology model of the LS2eptide would prefer the ion-channel to have a stable conforma-ion in a diamond and a square orientation, and a smooth surfaceopology would prefer the ion-channel to be in a diamond orien-ation. This information is critical because a diamond orientationould be close-packed which would not allow water or ions to

ravel through the ion-channel whereas a square or rectangularrientation would allow the ion-channel to be “open” so water orons can travel through the channel. By having the ability to controlhe properties of the ion-channel, one can also control the functionf the channel as well. For example, when using the rough surfaceopology model, the square or diamond orientation can be made toe stable which means that the pore size and dynamics of the chan-el can be influenced. The opening and closing of the ion-channelill be slowed in the square conformation due to peptide–lipid andeptide–peptide interactions, which will allow larger ions to trans-erse through the channel. Thus, using different topology modelsould allow one to control the overall properties and functions of

he ion-channel.

.1. Simulation of type Ia CG tube tetramer

Four type Ia CG tubes were initially placed in the center of anquilibrated CG DMPC bilayer and water in a square arrangement.

sics of Lipids 163 (2010) 530–537 533

The coordinates of the tubes were initially fixed in place, allow-ing lipids and water to equilibrate around the tetramer for 1 ns.The tubes were then allowed to move and the system was equi-librated for another 0.5 ns. Within 100 ps of simulation, the tubesrearranged to form a diamond shaped tetramer (Fig. 2), insteadof the initial square configuration as previously reported in bothexperimental (Degrado et al., 1989; Howard et al., 2002; Lear et al.,2001) and computational studies (Newns et al., 2000; Zhong et al.,1998c). The observed diamond configuration was allowed to fur-ther evolve for 15 ns. During which no change of configuration wasobserved. To test the hypothesis that the hydrophilic interactionswere the primary driving force between tubes, the width of the ver-tical patch was widened to 4 beads per ring instead of 2 beads perring allowing for more interaction of the pore residues. Again, dia-mond arrangements of the tetramer were observed within the first100 ps during the equilibration, thus indicating that it was not thehydrophilic interactions, but more likely the smooth morphologyof the peptide model. In all cases, the diamond arrangement wasstable throughout the production run following the equilibrationprocess.

Topologically, the diamond orientation is of a close contact con-figuration; therefore it is preferred over the square configurationon packing considerations. However, experimentally, LS2 peptidesare observed to form a tetramer bundle in a slightly distortedsquare configuration (Degrado et al., 1989; Howard et al., 2002;Lear et al., 2001). Further examination of the structure suggestedthat the smoothness of the tube surface and the rigidity of the typeIa CG tube model may not be able to withhold the lateral pres-sure exerted by the surrounding lipid, thus collapsing to a diamondconfiguration (Fig. 2). The side chains of leucine and serine in theAA model are able to interact with the surrounding lipid throughsteric interactions, therefore sustaining the square tetramer bun-dle structure. Experimental crystallographic data have shown thatrigid transmembrane �-helices, such as those in rhodopsin, forms aclose-packed heptamer bundle suggesting that the stiffness of thehelices play an important role in determining if the square or dia-mond arrangement is preferred (Krzysztof Palczewski et al., 2000).Therefore, we modified the type Ia model to be able to simulatea square conformation as observed in the AA simulations and inexperiments by allowing for roughness and flexible side chains.

3.2. Simulation of type Ib CG model

Research done by Lopez et al. (2005) using the type Ib modelwas compared with our type Ia model. From this research, it wasdetermined that the type Ib model in a tetramer bundle was morestable in a diamond conformation. We initially thought that thetype Ib tetramer model would be stable in a diamond conforma-tion based on this research, and that the type Ia tetramer modelwould be slightly more stable in a square conformation due to theincrease in polarity between the peptides. However, based on thesimulations of the type Ia that was conducted, it was determinedthat both type I models are more stable in a diamond conformation.We conclude that the smooth model topology will lead the tetramerpeptide bundle to be more stable in a diamond conformation thana square conformation (Fig. 2).

3.3. Simulation of type IIa CG model

Type IIa model (Fig. 1C) was constructed based on the origi-nal concept of type Ia CG (Fig. 1B) tube model, a cylindrical shape

with a hydrophilic patch running the length of the peptide. Thecore tube consists of only hydrophilic beads to resemble the back-bones of LS2 peptide. For each bead on the core tube, a “side chain”bead was attached to resemble side chains in the atomistic model.In addition, the harmonic force constant for all bonds and bends

534 T.H.T. Nguyen et al. / Chemistry and Phy

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ig. 3. The type IIa model was able to support either a void within the bundle or aundle filled with water. The initial square tetramer arrangement (left) was retainedhrough out the simulation (right).

as reduced from 10,000 K/rad2 to 8000 K/rad2 in order to intro-uce more flexibility to the model. For each ring on the tube, onlyne side chain bead was designated hydrophilic. Since the ringsre stacked in a zigzag fashion, the resulting hydrophilic arrange-ent resembles the original design of the LS2 peptide (Degrado et

l., 1989), in which the idealized packing diagram shows a squareype interaction among the serine residues at the same level, ands also staggered from the adjacent levels. The length of the sidehain was 5.00 Å, which is the equilibrium distance between twoG beads and is longer than the AA model.

The CG MD simulation of type IIa CG tube tetramer was similaro that of type Ia CG tube tetramer, in which four tubes are placedn the center of a CG lipid bilayer in a square formation. Follow-ng similar simulation protocols, the tube coordinates were initiallyxed to allow lipid and water to equilibrate around the tetramer

or 1 ns. The constraints on the tubes were removed and the systemas allowed to further equilibrate for another 0.5 ns again. Within

00 ps, the monomers congregate together in a square arrange-ent. The observed square arrangement of tetramer remained

table during the 15 ns production run. We conclude that the rough-ess in the model allows for interactions that stabilize the squareonformation over the diamond conformation (Fig. 3).

.4. All-atom comparison

Comparing our CG models with AA models from previousesearch, we found that our CG model gives similar results to theA models (Bond and Sansom, 2006; Lopez et al., 2005). The dimen-ion of the atomistic model is comparable with the CG models byesign. The length of the AA LS2 model is 32.85 Å in length mea-ured from cap to cap. Both type I and II CG models are 32 Å inength that also included the hydrophilic caps on both end (Lopezt al., 2005). Since both types of CG models are capped with oneing of hydrophilic beads on each end of the tube, the hydropho-ic tube body length is actually 24.20 Å, which is similar to the

ipid hydrophobic layer. These two hydrophilic caps are neces-ary to anchor the models into the bilayer in a transmembranerientation (Lopez et al., 2004). This has been seen in early sim-lation of tube insertion into a lipid bilayer indicates that withoutydrophilic caps, the CG tube model would not stay embedded inhe bilayer (Lopez et al., 2004). Previous CG simulation of DMPCipid bilayer indicates that the average height of lipid head grouprom the center of the bilayer is around 15.5 Å (Lopez et al., 2005),

aking the average thickness between top and bottom layer lipidead groups to be around 31 Å. The length of the CG tubes cho-

en here ensured that the hydrophilic caps anchor the tube so thathe hydrophobic portions of the tube and lipid bilayer match. Theidths of the hydrophilic vertical patch on both type I and type II CGodels were around 9 Å. The hydrophilic patch width is chosen to

nsure hydrophilic interactions between CG tubes resembling that

sics of Lipids 163 (2010) 530–537

of all-atom simulations (Newns et al., 2000; Zhong et al., 1998c)(Fig. 1).

The structural details of the square tetramer bundle were ana-lyzed using data collected during the production run. The distancesbetween COM of two tubes are plotted in Fig. 4. The figure indi-cated that the formation is slightly rectangular rather than a perfectsquare where the average distances of the four sides are 13.7 Å,14.2 Å, 13.6 Å, and 14.2 Å (instead of all at 14 Å). The rectangu-lar shape results from the preferential bonding of the hydrophilicbeads. These residues interlace with each other forming a pair,these pairs then form a rectangular tetrameric bundle. PreviousAA MD simulation reported that the pair-wise distances betweentwo helixes are around 8.8 Å and 10.0 Å, a dimerization of thetetramer bundle (Lopez et al., 2005). Dimerization of the tetramerwas observed in the present CG simulations; however, the pair dis-tance in the CG model is significantly larger than that of the AAmodel. Such difference is due to the force field that was employedin this study. Former AA MD simulations have reported the averagepore radius size for a LS2 tetramer bundle to be around 2 Å, whichallows for a single water molecule to pass through the channel(Lopez et al., 2005).

The square tetramer bundle of type IIa CG tubes was observed totilt collectively with respect to the bilayer normal. The average tiltangle is around 10.4 ± 3.4◦. In addition, the average “helix crossingangle”, defined by the angle between two tubes, is measured to beless than 2◦ over the course of the simulation, indicating that thereis no twisting of the tube in contrast to previous AA simulations(Newns et al., 2000; Zhong et al., 1998c). The lack of twisting indi-cates that the present model is most likely too stiff compared to theAA. In order to more closely match the AA results, further parame-terization of the CG beads used as side chains would be required andis beyond the scope of this research, and we believe a more flexiblemodel would not change the structural results reported herein.

Upon further examination of the trajectory, the side chains areobserved to “interlace”, meaning that the side chains from neigh-boring tubes are stacked one on top of each other (Fig. 5). The typeIIa CG model is constructed by stacking rings on top of each otherand 45◦ out of phase from the nearest neighbor. As a result, the dis-tance between the two closest in phase rings on a type II CG tube isabout 8.5 Å, which provides ample room for nearby hydrophilic sidechain beads to interact with the polar CG core. The interlaced sidechain beads are positioned at equal distances from the hydrophiliccore beads and the nearby side chain beads to maximize the inter-action. Energetically, these “interlacing” hydrophilic interactionsstabilize the tetramer bundle into a square formation, and resemblethe strong serine–serine–water and serine–water–backbone inter-actions observed in AA simulations.

3.5. Simulation of type IIb CG model

To investigate the hydrophilic interactions between the type IIaCG tubes, a simulations of type IIa CG tubes with no hydrophilicpatches (type IIb) ware carried out. Similar to the WALP peptidesthese models will not have the strong intermolecular interactionsof type IIa model from the capping residues. During the equilibra-tion stage, a square arrangement of the tetramer bundle was againobserved. The square arrangement again remained stable through-out the 15 ns simulation. The structural property of the tetramerwas analyzed in a similar fashion as the type IIa CG tubes withhydrophilic patch. The distances between two neighboring tubesare 14.13 Å, 14.11 Å, 14.12 Å, and 14.15 Å (Fig. 4), which is very

close to a perfect square conformation. Unlike type IIa CG tubes,no dimerization was observed. This is expected as the type b mod-els are cylindrically symmetric and have no directional preference.This is in contrast to the type a models, which have a hydrophilicpatch running the length of the model, which allows for dimer-

T.H.T. Nguyen et al. / Chemistry and Physics of Lipids 163 (2010) 530–537 535

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ig. 4. Distance between COM of two CG tubes in the tetramer. (left) Type IIa. Twohe tetramer is more rectangular in shape instead of square. On the other hand, the dn the diagonal distances results from type IIb tetramer in a diamond shaped config

zation. Therefore, by tuning the strength of the interaction, onehould be able to control how square the conformation is. Suchnvestigations are beyond the scope of the present paper but arengoing.

Similar to type IIa CG simulation, the “helix crossing angle” devi-tes very little from zero, indicating that here is no twisting of theubes (coil–coil). However, although the tubes were collectivelyilted with respect to the bilayer norm, the average tilt angle of7.5 ± 3.2◦ is much larger than the observed value in type IIa sys-em. Compared to previous research done by Bond et al. (2007), ourype IIb model is representative of the WALP peptide, whose aver-ge tilt angle was reported as 14.0 ± 8.0◦. Since the bonds and bendsorce constants of the model does not allow twisting of the tube,ydrophobic interactions between the tubes and lipid bilayer tailan only be achieved by tilting the tubes with respect to the bilayer

ormal orientation, resulting in large tilt angles as observed dur-

ng the simulation. Similar to type IIa tetramer, “interlacing” effects also observed in type IIb tetramer. This interlacing is similar tohe interactions that can occur between protein hydrophobic side

ig. 5. The final square arrangement of the type IIa CG tetramer has an interlac-ng effect. The side chain beads stack themselves one on top another to maximizeydrophilic interactions. A similar effect was observed in type IIb CG tetramer.

(right) type IIb. A slight dimerization is observed for type IIa CG tetramer in whiche of four sides in the type IIb tetramer are nearly identical. The significant differencen.

chains within the interior of proteins or between proteins in lipidbilayers.

3.6. Metadynamics simulation

Using metadynamics (Ensing et al., 2006; Laio and Parrinello,2002), the free energy of conversion from diamond arrangementto square arrangement, and back to diamond arrangement wasexplored for both type I and type II CG tetramer systems. For eachsystem, a diamond arrangement was constructed and equilibrated.The collective variable was defined as the distance between theCOM of two tubes diagonally located in the tetramer. This choice ofcollective variable restricts the distance between two of the pep-tides but makes no constraints on the orientation, tilt, height, orother structures of the peptides. Further, there is no constraintsplace on the other peptides or the lipids. Thus as the distancevaries between the peptides many conformations can result. Forexample, a T-shape or dissociation of the bundle as well as lipid

penetration into the interior of the ion-channel did results whenwe allowed distance between the peptides to increase beyond 30 Å,which corresponds to dissociation of the bundle. The metadynam-ics simulation for each system was carried out for 15 ns. The energyprofiles are plotted in Fig. 6. In all three cases, at least two energy

Fig. 6. Free energy profiles of converting from a diamond tetramer bundle to asquare tetramer bundle from metadynamics simulations. The collective variableis defined as the distance between the COM of two diagonally located CG tubes.We have zeroed the energy minimum to put the free energy surface on the samescale and averaged the two diamond configurations. Type II short has a shortenedside chain bond, and as expected can be used to tune the square conformationstabilization.

5 d Physics of Lipids 163 (2010) 530–537

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Table 1Summary of all CG systems and their preferred orientationbased on the MD simulations.

Coarse grain models Orientation

Smooth (type I)LS2 DiamondWALP Diamond

Rough (type II)LS2 SquareWALP SquareModified LS2 Square

36 T.H.T. Nguyen et al. / Chemistry an

inima were located, corresponding to the two diamond arrange-ents, i.e. close packed.Energy minimum corresponding to the square arrangements

ere located in type II simulations and not in type I. A slight asym-etric nature of the free energy profile was observed which is most

ikely due to the incomplete description of the reaction coordinatey the collective variables (Ensing et al., 2006) and sampling issues.ince the reaction coordinate is symmetric, we accepted the twoiamond shape free energies to have the same free energy. Higherrder metadynamics simulations could be used to fully explorehe free energy profiles but were not preformed due to limitedomputational resources. There are a lot of variables within theeaction coordinate that would be needed to be included withinhe simulations, such as the interlacing, rotation, height, pack-ng, and solvation of the helices for a complete description of thenergetics of the bundle which would require enormous compu-ational resources to explore. However, both the symmetric andlight asymmetric profiles gave the same calculations and barriereights. Therefore, the free energy profiles support the conclusionhat type II models forms both diamond and square formations.nterlacing and sliding of the models relative each other, are partf the transition between stable minimum.

In type Ia or type Ib CG tubes, there is no energy minimum cor-esponding to the square arrangement, meaning that type Ia CGodel will only formed a diamond arrangement. The energy bar-

ier between one diamond configuration and the symmetric otheriamond configuration is greater then 30 kcal/mol, which wouldot be crossed in typical MD simulations. Although it would be

nteresting to see the transformation of a diamond arrangement tosquare arrangement, the probability of finding the configurationn top of the emergy barrier is to low (1.39 × 10−22). Hence, theubes will be constrained to that region of space. It is possible toesign a peptide model that would have a smaller energy barrierhich would enable us to use observe a transition between the dia-ond and square geometry, but that is out of scope of this paper

nd a topic of ongoing research.In the free energy profile of type II peptides, there are three

nergy minimums, which correspond to the structural arrange-ent of diamond, square, and then diamond again. It is observed

hat significant energy, e.g. greater than 20 kcal/mol is requiredo convert a diamond tetramer to the square tetramer. Researchone by Lopez et al. (2005) has shown a similar free energy pro-le for the type Ib model, where the diamond orientation is moretable for the tetramer. For the type IIa CG tubes, the relative freenergy difference between the square arrangement and the dia-ond arrangement is ∼9 kcal/mol, whereas the difference in type

Ib is less than ∼3 kcal/mol. The differences in energy between theype IIa and b model can be attributed to the hydrophilic patch in theype IIa CG model. This patch favors hydrophilic-hydrophilic inter-ctions, in turn, creating a more stable structure. Hence, it wouldower the energy of the square or rectangular conformation thusy tuning the hydrophilic interactions within the peptide, the rel-tive stabilities of the square and diamond configuration can beodified.Although the free energy profiles support the observation of a

table square tetramer for type II CG tubes, it also suggested thathe diamond tetramer for type II is stable, but was not observedn our initial simulations. To confirm this finding, 15 ns of CG MDimulations were carried out using the initial diamond tetramersf both type IIa and type IIb CG models. During the simulations,ach tetramer remained in the diamond formation as expected.

lthough type IIa and type IIb have identical geometries (a roughurface), their energy profiles have different energy barriers andnergy minimums. This means that not only does geometry haveignificance on the peptides packing arrangement, but the peptidesolecular interactions sequence also contribute to their packing

A diamond orientation represents a close-packed tetramerichelical bundle, and a square orientation represents an open-packed tetrameric helical bundle.

arrangements.Finally to test the hypothesis that the stabilization can be tuned

via the topology of the peptide, we constructed a type IIa modelwith a short bonding to the hydrophilic backbone core. We setthe bond length at 2.5 Å, which is 1/2 of the original bond length.This result in a roughness between the smooth type Ia model andthe rough type IIa models discusses above. As expected the squareconfiguration was destabilized, but was still at a local minimum.

4. Conclusion

We performed a series of CG MD and metadynamics simulationsof four LS2 and WALP peptide bundle using two different typesof CG model transmembrane peptides. A summary of the varioustubes simulated and their preferred orientation can be found inTable 1. Hydrophilic and hydrophobic characteristics of the LS2 andWALP peptides were taken into consideration when constructingthe models. The main difference between the two models is that theLS2 model can form an ion-channel while the WALP model cannot.In all of our simulations, we found reasonable agreement betweenthe CG and AA results. Our free energy metadynamics calculationsshow that using a smooth surface nanotube type model (type I)will lead a diamond formation for the tetramer bundle instead ofa square formation. Our simulations indicated that by attachingside chains to the tube surface (type II) in order to make the modelrougher, a square formation is observed. This is due mostly to theincrease roughness of the model peptides and not the hydrophilicinteractions.

The free energy calculations support the observation from theMD simulations, in which diamond tetramer is the most stableformation for type I CG tubes, whereas both diamond and squaretetramers are stable for type II CG tubes. Energy barriers of fur-ther than 30 kcal/mol to convert a diamond formation into a squareformation were observed indicating stable structure for these mod-els. These simulations suggest that particular topologies (square ofdiamond shaped) are designable with appropriate interactions. Weverified this by changing the roughness of the peptide and destabi-lizing the square conformation. In particular, the relative energiesand barrier heights between the square and diamond shape can betuned by the strength of the hydrophilic interactions. It is possi-ble that different ion-channel and peptide bundle similar to our CGmodels or peptide topologies can be constructed with particulartetrameric topologies.

Acknowledgements

The authors acknowledge that this research was supported inpart by a gift from the H.O. West Foundation, a grant from theUniversity of the Sciences in Philadelphia (USP), a grant from theNational Institute of Health (R15GM075990), and grants from theNational Science Foundation (CHE-0420556 and CCF-0622162).

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he authors are thankful for many useful discussions with Dr. Zhi-ei Liu, Dr. Bernd Ensing, and Dr. Steve Nielsen.

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