Article
ThermodynamicsofMicelleFormation
AntimicrobialLipopeptideActivity
Medica
fungi.
case,
or
vulnerabletoevolvedresistancethantraditionalantibiotics.
andthusmusthaveasignificantnumberofhydrophobic
requiredtomakethepeptidesselectiveforanionicbacte-
ria-likemembranes.TheresultisthatmostnaturalAMPs
bialmembranesarebelievedtobethemajortargetsof
phenomenon.Onecouldattempttoexaminetheimpactof
propensitytoformoligomers,butthisapproachwould
alsoalterthestructureoftheindividualmolecules,and
manufacturing;moreover,thechoiceoflinkagewould
Correspondence:alan_grossfield@urmc.rochester.edu
750BiophysicalJournalVolume109August2015750–759
Editor:MarkusDeserno.
C2112015bytheBiophysicalSociety
likelythemembraneinteractionaswell.Alternatively,one
couldcovalentlylinkthemonomerstogether(14),butthis
approachwouldsignificantlyincreasethecostofAMP
SubmittedApril16,2015,andacceptedforpublicationJuly1,2015.
sidechainstoovercomethepolarityofthepeptide
backbone.Additionalresidues,oftencationic,areusually
AMPoligomerizationonmembranebindingbysimply
introducingmorehydrophobicaminoacidstoincreasethe
Moreover,AMPs’membranebindingmechanismshields
themfromseveralresistancestrategies,suchasmultidrug
effluxtransporters(3,4).
However,therearealsodisadvantagesthatlimitAMPs’
clinicalapplication.Oneofthemajorhurdlesisthatthey
areexpensivetomanufacture,process,andstorebecause
theyaremuchlargerandchemicallycomplexthantypical
drugmolecules(5,6).Thisisinpartbecausethereappears
tobealowerlimittothesizeoftraditionalAMPs;they
mustbehydrophobicenoughtobindmembranesstably,
AMPs,onecannotruleoutthepossibilitythatothercellsur-
facestructurescouldaffectthemembraneactivityofAMPs.
Infact,itwassurmisedthatthepreassembledAMPsmight
beretainedbymacromoleculesoncellsurfacesandkept
frominteractingwithmembranessimplybecauseoftheir
increasedsizescomparedtomonomers(11,14).Unfortu-
nately,thelimitedresolutionfromexperimentsandthe
lackofmolecularinsightsmakeithardtoexplainwhy
thiskindofblockagewouldonlyoccurforcertainmicrobial
specieswithspecificAMPs,asopposedtobeingauniversal
antimicrobialdrugs.Membranecompositionisrelatively
conservedduringevolution,whichmakesAMPsless
orexclusionfromdegradingenzymes’activesites,the
reasonforthelatterremainsamystery.Althoughthemicro-
DejunLin
1
andAlanGrossfield
1,
1
DepartmentofBiochemistryandBiophysics,UniversityofRochester
ABSTRACTAntimicrobiallipopeptides(AMLPs)areantimicrobial
branes.OneclassofAMLPs,composedofcationictetrapeptides
tionsinthemicromolarrangeagainstarangeofbacteriaand
simulationsandfreeenergymethodstostudythethermodynamics
Here,weextendedthestudytothebiologicallyrelevantmicellar
basedonhydrophobiccontacts.Usingumbrellasamplingalong
stateswhenmicellesinsertintomembranes.Theresultsindicate
thermodynamicallyfavorable,butincontrasttothemonomeric
thesefreeenergybarriersdependsonthemembranecomposition,
bacterialmembranesmaybeasmuchkineticasthermodynamic.
omericstateinsolutionascriterionwhenoptimizingpeptides
INTRODUCTION
Thepressingneedfornovelantibioticsagainstresistant
strainsofbacteriaandfungihasbecomeaglobalmedical
concern.Anemergingclassofantimicrobialdrugcandi-
dates,antimicrobialpeptides(AMPs),hasbeenthefocus
ofsignificantresearchonantiresistanceantibiotics(1).
Unliketraditionalantibioticsthattargetspecificgrowthor
functionprocessesofthemicrobes,manyAMPswerefound
todisruptthestructureandfunctionoftheirmembranes(2).
AMPs’lipophilicityendowsthemwithafewadvantagesas
0006-3495/15/08/0750/10
andMembraneFusionModulate
lCenter,Rochester,NewYork
drugcandidatesthatpreferentiallytargetmicrobialmem-
attachedtoanacylchain,haveminimalinhibitoryconcentra-
Previously,weusedcoarse-grainedmoleculardynamics
oftheirinteractionwithmembranesintheirmonomericstate.
state,using,toourknowledge,anovelreactioncoordinate
thisreactioncoordinate,weidentifiedthecriticaltransition
thatthebindingoftheseAMLPmicellestomembranesis
therearesignificantfreeenergybarriers.Theheightof
suggestingthattheAMLPs’abilitytoselectivelytarget
Thismechanismhighlightstheimportanceofconsideringolig-
lipopeptidesasantibioticleads.
are12–40aminoacidslong,farlargerthanmostdruglike
molecules.
AnothermajorobstacletoAMPs’applicationisthelack
ofunderstandingtherelationbetweentheiroligomerization
insolutionandtheirbiologicalactivity.SomeAMPoligo-
mersareassociatedwithimprovedpeptidaseresistance
(7,8)andenhancedcellselectivity(7,9–14)comparedto
theirmonomers.Whiletheformercanbeunderstoodas
theconsequenceofstructuralchangesuponoligomerization
http://dx.doi.org/10.1016/j.bpj.2015.07.011
almostcertainlyaffectthenatureofthemembrane-bounditisprohibitivelyexpensivetoquantitativelymeasurethe
LipopeptideMicelleThermodynamics751
state.
Alltheaforementionedcomplexitiescomplicatethe
effortstooptimizetheirperformance.Forexample,in
typicalvirtualscreeningstudieswhereAMPs’activityis
modeledbasedontheirprimarysequences,thelargeamount
oftrainingdatarequiredtobuildanaccuratemodelisprac-
ticallyimpossibletoobtainforlargepeptidesduetothe
limitingeneratinghigh-throughputscreeningarrays,where
thenumberofarrayelementsscalesexponentiallywiththe
peptidelength(15).Also,peptidestendtobeflexible,witha
broadrangeofaccessibleconformations;thiscansignifi-
cantlycomplicatetheinterpretationofmutagenesisdata,
asevenseeminglysimplesubstitutionscansignificantly
alterthepeptides’conformationandposerelativetothe
membrane.ThisflexibilityalsomakesAMPschallenging
targetsforcomputersimulation;theirstructuralplasticity
combinedwiththeslowrelaxationtimesforlipid-peptide
interactionsmakeitveryhardtoacquireadequatestatistical
sampling,evenusingstate-of-the-artenhancedsampling
methods(16,17).Forthesereasons,aswellastheirsuscep-
tibilitytoproteasedegradationinvivoandtheirpotential
toxicitytohumancells(5),therehasbeenonlylimitedsuc-
cessinmakingAMPsintointernalantibiotics(15).
InanattempttobypassthespecificissuesofAMPs,
AvrahamiandShai(18,19)devisedanalternativeapproach
toutilizeAMPs’membraneactivitybyconjugatingfatty
acidstoshortcationicpeptides.Thesesmallsyntheticmol-
ecules,calledantimicrobiallipopeptides(AMLPs),mimic
AMPs’amphipathicityandcationicnature,andhavebeen
showntobepotentantimicrobialswithminimalinhibitory
concentrationsinthemicromolarrange.Basedonamore
recentdesignofAMLPscaffold,C16-KXXK,where
‘‘C16-’’denotesthepalmitoylchainattachedtotheN-termi-
nusofthetetrapeptideKXXKcontainingtwolysinesand
twoguestresiduesX,Makovitzkietal.(20)foundseveral
potentantimicrobialsthathadinsignificanthemolysis.Later
workfurthershowedthatsimilarAMLPswereabletoclear
infectionsinvivo(21).Mostnotably,C16-KGGK(thebold
letterdenotestheD-enantiomer,includedtoconferresis-
tancetopeptidasedegradation(22)),themostpotentamong
theseAMLPs,hasamicromolarMICagainstseveral
pathogenicmicrobes,includingbothbacteriaandfungi.
Theattachmentoftheacylchainstopeptidesalsopromoted
theiraggregation(23),makingtheselipopeptidesexcellent
modelsforstudyingoligomerization.
MostoftheexperimentalworkontheseAMLPstodate
focusedontheirefficacyonamacro-ormesoscopicscale,
sorelativelylittleisknownabouttheirmechanismsatthe
levelofindividualmolecules.TobetterunderstandAMLPs’
modeofaction,ourlabhasbeenusingacombinationof
all-atomandcoarse-grained(CG)moleculardynamics
(MD)simulationstoexaminetheselipopeptides’membrane
activity.Whileall-atomsimulationsprovideatomicdetails
aboutthemembraneperturbationcausedbyAMLPs(24),
thermodynamicsofmembranebinding.Wethususeda
CGmodeltoexamineslowprocessessuchasAMLPs’bind-
ingtomembranes(25,26).TheCGmodelweused,the
MARTINIforcefield,isdesignedsuchthateachCGparticle
representsfourheavyatoms;itgenerallyrunsatleasttwo
ordersofmagnitudefasterthananequivalentall-atom
model(27,28)andisabletoreproduceexperimentalresults
inmanycases(29–34).
OurprevioussimulationsusingtheMARTINImodel
quantifiedthebindingthermodynamicsofmonomeric
C16-KGGKtomembranes(26).Ourresultsindicatedthat
theacylchainoftheseAMLPsdominatestheirbinding
affinitytomembranes,whilethepeptideportionconfers
selectivityforanionicmembranes(26).However,bothex-
periments(23)andsimulations(24,25)suggestedthatthese
AMLPstendtoaggregateintonanostructuresatmoderate
concentrations;suchaggregatesarethoughttoenhance
AMLPs’solubilityandantimicrobialactivityandcould
contributetotheirresistancetodegradation.Thus,thefocus
ofthisworkistostudytheinteractionsbetweenlarger
aggregates(micelles)ofAMLPsandmembranes.
However,therearetechnicaldifficultiesregardingthe
simulationofamphiphileaggregation.Aggregatesofeven
moderatesizetendtobeatleastmetastable,soobtaining
awell-equilibratedsizedistributionisverychallenging,
requiringeitherverylongsimulationsorefficientenhanced
samplingalgorithms.Forexample,ananalogousprocess,
vesiclefusion,takesplaceinmillisecondstohundredsof
microseconds,whichisextremelychallengingtosimulate
usingbrute-forcemethods(35),evenwithaCGforcefield.
ToexploretheprocessofAMLPsbindingtomembranesby
brute-forcemeans,wewouldneedtoconsiderthetransferof
anyAMLPfromoneaggregatetoanotheraswellasfroman
aggregatetomembrane.Thesetransitionsareveryslow,
becausetheyrequirepartialexposureofthehydrophobic
tailstowater(26).
Inthisstudy,weintroduce,toourknowledge,anovel
reactioncoordinate,thehydrophobiccontactnumber,that
characterizestheaggregationofamphiphilesandtheirbind-
ingtomembranes.Usingumbrellasamplingalongthis
reactioncoordinate,wecalculatedthefreeenergyofthe
formationofaC16-KGGKmicelleinwaterandthebinding
ofthismicelletomembranes.Ourresultsshowthatthis
micellehasmuchhigheraffinitytotheanionicbacterial-
likemembranethantheneutralmammalian-likemembrane,
consistentwithourpreviousresultsonthemonomericC16-
KGGK(26).Mostsurprisingly,thesecalculationsrevealed
asignificantfreeenergybarriertomicellemembraneentry,
whichwasabsentinthemonomericC16-KGGKcase.This
barrierismuchhigherinthecaseofthezwitterionic
mammalian-likemembranethantheanionicbacterial-like
membrane,whichmeansthebindingtothelatterismore
favorablenotjustthermodynamicallybutkineticallyas
well.Ouranalysisrevealsthatthemechanismsofmicelle
BiophysicalJournal109(4)750–759
membraneentrydependonthemembranecompositions,
leaflet),andcarewastakentoensurebothleafletshadthesamecom-
position.HydrationwasmodeledusingthepolarizableMARTINIwater
C0C1
1
XX
therangeofRCsinTableS1,andthereferencepositions(C
AB
inEq.3)
ofalltheumbrellasamplingwindowsareplottedinFig.S1.Thisrange
valueswereasclosetothecentersofthewindowaspossible.
752LinandGrossfield
S
ij
r
ij
?
1t
C0
r
ij
C14
r
0
C1
n
(1)
wherer
0
isthedistanceatwhichthecontactisexactly0.5andncontrols
thesteepnessofthefunction.Thetotalnumberofcontactsbetweentwo
groupsofparticlesAandBisthesumofS
ij
overalltheuniquepairs
betweenAandB:
model(36).
TheC16-KGGKmoleculewasconstructedbymergingtheMARTINI
palmitoylwiththeMARTINIKGGKpeptide.TheMARTINImodeldoes
nothavesufficientresolutiontorepresentchirality,butthisisnotaserious
limitation:afour-residuepeptideistooshorttoformsecondarystructure,
andinanyevent,experimentsshowthatvaryingthebackbonechirality
hasnosignificanteffectonthelipopeptide’sproperties(38).Forthepur-
posesoftheMARTINImodel,wetreatedthesepeptidesasrandomcoil,
anddidnotapplyanysecondarystructurerestraints.Aboxofwaterwith
randomlyscatteredC16-KGGKswasequilibratedforseveralhundred
nanosecondsuntiltheC16-KGGKsaggregatedintomicelles.Weextracted
thelargestofthesemicellesandremovedseverallipopeptidestoproduce
a48-mer;bindingasingle48-lipopeptidemicelletoeithermembrane
compositionproducesa10:1lipid/peptide.
Foreachbilayercomposition,weplacedtheC16-KGGKmicelle~60A
?
fromthebilayercenterofmass.Thesystemwasthensolvatedwithwater,
andsodiumandchlorideionswereaddedtoreachaconcentrationof
~100mM.Extracounterionswereaddedtoneutralizethechargesonlipids
andlipopeptides.Themembranebindingsimulationscontainedatotalof
51,300CGparticles,whilethesimulationsofmicelleformationinwater
contained12,730particles.
Umbrellasampling
Thepotentialsofmeanforce(PMF)tobindaC16-KGGKmicelletoalipid
bilayerwerecalculatedusingumbrellasamplingandtheweightedhisto-
gramanalysismethod(WHAM)(39).Thereactioncoordinates(RCs)we
usedwerebasedonthenumberofhydrophobiccontactswithinthemicelle
andbetweenthemicelleandthemembrane;thereasonsusingtheseRCs
(inplaceofmorecommonchoices,suchasthedistancefromthemembrane
center)arediscussedinSectionS1.1intheSupportingMaterial.
Specifically,thenumberofcontactsbetweenapairofmoleculesiandjis
definedasasmoothfunctionofthedistancebetweentheircenters-of-mass
distancer
ij
,
cellesandtheirmembraneselectivityandprovidebiophys-
icalinsightintoantimicrobialdrugoptimizationbasedon
AMLPs.
MATERIALSANDMETHODS
Systemconstruction
AllsystemsweremodeledusingtheMARTINIcoarse-grainedforcefield,
Vers.2.2P(36,37).Weusedtwolipidbilayercompositions:a2:1mixture
ofPOPE(1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine)and
POPG(1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol),representing
aGram-negativebacteria-likemembrane,andpurePOPC(1-palmitoyl-
2-oleoyl-sn-glycero-3-phosphocholine),representingamammal-like
membrane.Constructionofthemembranebilayerswasdescribedprevi-
ouslyinHornetal.(25).Eachsystemcontained480lipids(240per
whichexplainsthevariationinthebarrier.Theresults
suggestalinkbetweenthestabilityofthelipopeptidemi-
BiophysicalJournal109(4)750–759
Theweightedhistogramanalysismethod(WHAM)(39)wasusedto
calculatethePMFsfromtheumbrellasamplingdata.Thedynamicrange
ofthePMFsineachsystemweweredealingwithinthisstudywas
usually~200–300kcal/molandthenumberofumbrellasamplingwindows
was~600–800.PerformingWHAMonsuchadatasetturnedouttobequite
challenging,andcommonimplementationsofWHAM(41)failedtocom-
pletethecalculationduetonumericalinstability.Moreover,insomecases
theterminationconditionofWHAMiterationproducedunconverged
solutionseveninthecaseofarelativelysmalltolerance(10
C06
).Thisis
dueintrinsicallytotheslowerconvergenceofWHAMiteration,which
hasbeendiscussedbeforeinZhuandHummer(42).Totackletheseissues,
weimplementedanoptimizedversionofWHAMinCttbasedontheidea
proposedbyZhuandHummer(42),wheretheWHAMequationswere
solvedbymaximizingthetargetlikelihoodfunctionviathePolak-Ribiere
conjugategradientmethodwithBrent’slinesearch(43).Amultiplepreci-
sionlibrary(44)wasusedinthisimplementationtoachievenumerical
stabilityinWHAM.
Hamiltonianreplicaexchange
Forthemicelleformationsimulations,Hamiltonianreplicaexchange
(HREX)wasusedtofacilitatetheconvergenceoftheumbrellasampling.
TheumbrellasamplingwindowswereexchangedusingaGibbssampling
algorithmdescribedinChoderaandShirts(40).TheHREXwasattempted
every500steps.Inprinciple,wecouldhaveusedHREXforthemicelle-
membranebindingsimulationsaswell,buttheverylargenumberofsimu-
lationwindowsusedinthesecalculations(z800)madetheprocedure
unfeasiblewithourcomputationalresources.
Weightedhistogramanalysismethod
ofRCscoversthetransformationfromthemicellebeingfarawayfrom
themembranestoalllipopeptidesinthemicelleinsertedandspreadout
intheupperleaflet.
Thestructuresusedtoseedtheumbrellasamplingwindowsweregener-
atedbysteeredMD(SMD)simulations,wheretheequilibriumpositionsof
theharmonicpotentialinEq.3weremovedfromastartingpositiontoan
endingpositionatconstantvelocity.MultipleSMDsimulationswith
differentstartingandendingpositionswereusedsothatthedesiredrange
ofthereactioncoordinatewascovered.SnapshotsfromtheSMDsimula-
tionswereusedtoseedtheumbrellasamplingssuchthatthestartingRC
C
AB
?
i?Aj?B
S
ij
:(2)
NotethatinthecaseofA?B,weconstrainedthesumsothatisjandany
pairofiandjappearsonlyonceinthesum.
Tofacilitatethecomputation,weusedaneighborlistwithacutoff
distanceR
cut
tokeeptrackofthepairsinvolvedinEq.2.WechoseR
cut
sothatbothS
ij
(R
cut
)anddS
ij
=dr
ij
eR
cut
Tweresufficientlysmall(see
TableS1).Inallcases,theneighborlistwasupdatedeveryfivestepsin
allthesimulations.
Therestraintpotentialsinumbrellasamplingareoftheform
U?
k
2
C0
C
AB
C0C
0
AB
C1
2
;(3)
withC
0
AB
beingthereferencepositionofeachwindow.
ThedetailsofRCdefinition,theparametersinEqs.1–3,andthenumber
ofsamplingwindowsaresummarizedinTableS1.Notethatinthemem-
branebindingsimulations,wepurposelychosetoonlysampleasubsetof
0
UsingthisimplementationofWHAM(45),thePMFsformicelle
formationwerecalculatedusing472binsandaconvergencethreshold
of10
C010
ThePMFsofmicelle-membranebindingwerecalculatedusing
a300C2300gridandaconvergencethresholdof10
C010
.
Minimumfreeenergypaths
Fromeachofthetwo-dimensionalmembranebindingPMFs,weusedthe
stringmethod(46)tocalculatetheminimalfreeenergypaths(MFEPs)in
thetwo-dimensionalcontactspace.Inallcases,thestringwasinitiallycon-
structedby200imagesornodeslinearlyinterpolatedbetweenthetwo
terminalnodesattheminimacorrespondingtotherespectivesurface-bound
andinsertedstates.Wereferthereaderto‘‘PMFsforMembraneBuilding’’
andFig.2laterinthearticleforthedefinitionofthesestates.Theforward
Eulermethodwasusedtopropagatetheimageswithastepsizeof0.1in
bothdimensions.Bicubicinterpolationwasusedtoevaluatethenumerical
gradientsattheimagesateachstep.Weterminatedthecalculationifthe
meanCartesiandistanceoftheimagesbetweentwoconsecutivesteps
was<0.001.Insomecases,thestringfluctuatedaroundanequilibrium
withafluctuationof0.01andwesimplyterminatedthecalculationand
tookthefinalstringasourresult.Suchfluctuationisduetotherelatively
coarsegridonwhichthePMFswerecalculatedwherenotallthestationary
pointsofunderlyingcontinuousPMFswereresolved.Also,theinterpolated
numericalgradientsinevitablyintroducedsomeerrors.However,wedonot
thinkthiswouldaffectanyoftheconclusionsinthisstudybecausesuch
errorsareminuscule.
Eachofthemicelleformationumbrellasamplingsimulationswasrun
for~500nswherethefirst100nswereconsideredequilibrationphase,
andwereexcludedfromWHAMandanyanalysis.Thistotalsto348ms
(500ns/windowC2696windows)simulationtime.Thedurationoftheequil-
ibrationphasewasdeterminedbygraduallyexcludingNsamplesfromthe
beginningofthesimulationswhenweranWHAM,whereNincreased
withastepsizeof50ns.WecalledthefirstNsamplestheequilibrationphase
whenincreasingNdoesnotchangethecorrespondingPMFssignificantly.
ThePMFscorrespondingtoNintherangebetween50and250areplotted
inFig.S11.Mostofthemembranebindingsimulationswererunfor
~1.3msandthewindowsnearthetransitionstates(wherethereisthemost
structuraldiversity)wereextendedto~3.7ms,wherethefirst350nswere
consideredequilibrationphaseandexcludedfromWHAMandanyanalysis.
Thetotalsimulationtimeis1626.4msand1434.4ms,intherespectivecases
ofPOPE:POPGandPOPCmembrane.ThedynamicsintheMARTINIforce
fieldisusuallyfasterthananequivalentall-atomforcefieldbecausethe
coarse-grainingresultsinasmootherpotentialenergysurface;othergroups
havesuggestedthatsimulationtimesshouldbemultipliedbyafactorof4to
compensate(30),butbecausethefocusofthisworkisthermodynamics
ratherthankinetics,webelieveitisclearernottodoso.
RESULTS
PMFsofmicelleformation
Thepotentialofmeanforce(PMF)for48C16-KGGKmol-
LipopeptideMicelleThermodynamics753
A
B
Simulationprotocol
AllsimulationswereperformedusingGROMACS,Ver.4.6.3(47–49)with
themodificationdescribedinUmbrellaSampling.ForthegeneralMD
simulationparameters,weuseda20-fstimestep,andupdatedtheneighbor
listeveryfivesteps.Simulationswereperformedinisothermo-isobaric
(NPT)ensemblewithNose′-Hoovertemperaturecoupling(50,51)andthe
Parrinello-Rahmanbarostat(52),setto300Kand1bar,respectively.Elec-
trostaticswereaccountedforusingtheshiftfunctionwithaCoulombcutoff
of12A
?
.AshiftwasusedforvanderWaalsaswell,withaswitchdistance
of9A
?
andacutoffof12A
?
.
FIGURE1(A)PMFinkcal/mol(yaxis)asa
functionofthetotalnumberofC16-C16contacts
(xaxis,thesameasB)betweenalluniquepairs
of48C16-KGGKs.(B)Thejointprobabilityin
log
10
scale(colorbox)asafunctionofthenumber
ofC16-C16contacts(xaxis)andthesizeof
lipopeptideclusters(yaxis).(Twodashedlines)
Referencestoa32-anda16-mer,respectively.
Toseethisfigureincolor,goonline.
eculestoaggregateintoonemicelleisshowninFig.1A.
ThePMFhasthreedistinctminima,eachcorrespondingto
adistinctoligomerizationstateofthelipopeptides.Thefirst
(xz270)andsecondminima(xz345)representa
mixtureofdifferentsizesofoligomersrangingfrom10to
30lipopeptides;thethirdminimum(xz450)corresponds
toamicelleof48lipopeptides.Themaximumatsmallest
RCvalues(xz28)correspondstodispersedlipopeptides
inwater.Interestingly,theglobalminimumisnotthe
48-merbutmostlikelythecoexistenceofa17-anda
BiophysicalJournal109(4)750–759
31-mer(Fig.1B)andthefreeenergybarriertocombining
betweenthePOPGphosphatesandthelysinesidechainsin
opeptidemicellegetsflattened,withtheC16tailsstretching
outfrominsidethemicelletothePOPE:POPGmembrane;
thisdistortioniscompensatedbystrongelectrostaticinter-
actionsbetweenthelipidphosphates(particularlyforPG
lipids)andthelysinesidechains.Bycontrast,themicelle
doesnottendtostablyinteractwiththesurfaceofthe
POPCmembrane;instead,thelipopeptidesaretransferred
intothePOPCmembraneoneatatime,whilethemicelle
bouncesoffthesurface.Theone-at-a-timemechanismis
visibleintheseriesoflocalminimaaroundthelabeled
transitionstateinFig.2B,witheachlocalminimumrepre-
sentingadifferentfractionoflipopeptidestransferredfrom
themicelletothePOPCmembrane.Wewilldiscussthe
implicationsforthemechanismin‘‘MolecularBasisfor
AMLPs’CooperativeBindingtoBacterialMembranes’’.
MFEPsofmembranebinding
TheMFEPsoftheC16-KGGKmicellebindingtomem-
branesandthePMFvaluesalongthepathsareshownin
Figs.2,AandB,and3,respectively.TheMFEPtobind
105090130170210
C16?C16contacts
105090130170210
C16?C16contacts
A2B2
FIGURE2ThePMFsinkcal/mol(color-scale)ofbindingaC16-KGGK
micelletoeitheraPOPE:POPG(A)orPOPC(B)lipidmembraneasafunc-
tionofthenumberofC16-C16(xaxis)andC16-lipidtail(yaxis)contacts
(bottompanel).TheMFEPwasplotted(blackline)ontherespectivePMF.
(A1–A3andB1–B3)Statesalongtheminimumfreeenergypath;1refersto
thesurface-associatedstate,2tothetransitionstate,and3tothefullyin-
sertedstate.(Labelsandlines)LocationsofthesestatesonthePMF(bottom
panel).POPClipids(cyan),POPE(pink),POPG(blue),C16(red),and
KGGK(green).Toseethisfigureincolor,goonline.
754LinandGrossfield
thelipopeptides.Incontrast,theequivalentstateinthe
POPCcase(Fig.2B1)isnotmetastable(Fig.2B);itap-
pearsthatlysine-phosphateinteractionsarenotstrong
enoughtostabilizesurfacebindingintheabsenceofanionic
headgroups.However,westillreferthisstatetothesurface-
boundstateforthesakeofcomparison.Theinsertedstates
inbothlipidsarestructurallysimilar,withtheC16tailsof
lipopeptidesembeddedinthemembranehydrophobic
core,leavingtheKGGKpeptidesinthemembrane-solvent
interface.
Asidefromthedifferenceinshape,thetwoPMFsarealso
distinctfromeachotherintheirscales,asshownbytheup-
perlimitsofthecolor-barsinFig.2,AandB.Thisisshown
moreclearlyinthePMFsalongtheMFEPsinFig.3,mak-
ingitevidentthatbindingtotheanionicPOPE:POPGmem-
braneisfarmorefavorablethanbindingtoPOPC.
Moreover,thebindingmechanismandtransitionstates
differsignificantlydependingonthemembranecomposi-
tion.WhenbindingtothePOPE:POPGmembrane,thelip-
the17-and31-merintothe48-meris~22kcal/mol;the
48-merismetastableby~9.0kcal/mol.Atleastsomeof
thisfreeenergydifferenceisduetothefinitesizeofthe
simulationcell;eachadditionallipopeptideaddedtothe
micelleremovesalipopeptidefromthesurroundingbath,
artificiallyincreasingtheentropicpenaltytoaddthenext
one(see‘‘C16-KGGKOligomerizationIsLikelyToBe
Polydisperse’’formoredetails).
Fig.1Bshowsthejointprobabilityofobservingaspecific
lipopeptidemicelle/clustersizeandthenumberofhydro-
phobiccontactsformedamongthelipopeptides.Itisclear
thatamixtureoflipopeptidemicelles/clustersofdifferent
sizesdominatetheglobalPMFminima(xz345),indi-
catingthattheC16-KGGKsolutionispolydisperse(see
C16-KGGKOligomerizationIsLikelyToBePolydisperse
formorediscussion).Itisworthnotingthatatraceamount
ofmonomerscoexistswithbiggeroligomersneartheglobal
minimumaswellasthetransitiontothethirdminimum
(rightmostwellinFig.1A).
PMFsformembranebinding
ThePMFsfora48-C16-KGGKmicellebindingtoamem-
branecontactsareshowninFig.2,AandB.ThesePMFsare
characterizedbyasurface-bound(Fig.2,A1andB1)state
andaninsertedstate(Fig.2,A3andB3).Thesetwostates
arebridgedbyvarioustransitionstates(Fig.2,A2andB2)
residingalongasetofsaddlepointsonthePMFs.Forrefer-
ence,wecalledthecasewherethemicelleisfarawayfrom
themembrane,correspondingtotheupper-rightcornerof
Fig.2,AandB,thefreestate.
WhenthemicellebindstothePOPE:POPGmembrane,
thesurface-boundstate(Fig.2A1)isalocalminimumof
thePMF(Fig.2A),stabilizedbythefavorableinteractions
BiophysicalJournal109(4)750–759
0
200
400
600
800
1000
C16?lipidcontacts
0
20
40
60
80
100
120
140
160
180
200
220
240
PMF(kcal/mol)
0
200
400
600
800
1000
C16?lipidcontacts
0
10
20
30
40
50
60
70
80
90
100
110
120
PMF(kcal/mol)
A3
AB
A1
A3
A2
B2
B3
B1
B3
A1B1
whichcausesthecalculationtounderestimatethestability
weareonlyabletoconcludethatbothminimaarelikely
40
statevarieswithmembranecomposition(seeFig.S4).Toseethisfigure
LipopeptideMicelleThermodynamics755
tothePOPE:POPGmembranegoesfromthesurface-bound
statetotheinsertedstatewitharelativelysmalltransition
barrierof1.3kcal/mol.Incontrast,theMFEPtobindto
thePOPCmembraneencompassesthesurface-boundand
insertedstate,theformerofwhichispartofthetransition
ensemble.Thebarriertomakingthetransitionisboth
veryhighandbroadandpeaksat~79kcal/mol.Theloca-
incolor,goonline.
0
20
MFEP
FIGURE3PMFsinkcal/mol(yaxis)alongtheMFEP(xaxis)as
showninFig.2,AandB,ofbindingaC16-KGGKmicelletoeitherthe
POPE:POPG(solidline)orPOPC(dashedline)lipidmembrane.(Inset,
thePOPE:POPGcurve)Transitionfreeenergybarrieris~1.3kcal/mol.
ThebarrierinthePOPCcaseis~79kcal/mol(labeledbyarrows).Note
thatthepathparameters(xaxis)ofbindingtothetwodifferentmembranes
arenotcomparable,becausethenumberofcontactsformedinthebound
60
80
100
120
140
160
180
200
220
240
PMF(kcal/mol)
79.0kcal/mol
POPE:POPG
POPC
206
207
tionsofthetwoMFEPsinthetwo-dimensionalcontact
spaceareputtogetherinFig.S4forcomparison.
DISCUSSION
Usingfreeenergycalculationsandcoarse-grainedmole-
culardynamicssimulations,wearetryingtoaddressthe
followingquestionsregardingtheoligomerizationofC16-
KGGKandtheoligomers’interactionwithmembranes:
1)whatistheequilibriumdistributionofdifferentC16-
KGGKoligomers,and2)doesoligomerizationalterthe
bindingaffinityofC16-KGGKtomembranes?
C16-KGGKoligomerizationislikelytobe
polydisperse
AsshowninFig.1,themostlikelyoligomerizationstatefor
48C16-KGGKmoleculesistheformationofa17-anda
31-mer,withmonomerspresentonlyoccasionally.This
configurationismorefavorablethanthe48-mermicelle
(secondminimum)byz9.0kcal/mol.However,thisresult
isalteredbythefinitesizeofthesimulationcell;asthe
micelleforms,theconcentrationoffreelipopeptidesdrops,
thermodynamicallyaccessible.Moreover,thesesimulations
aretoosmalltocompletelyrepresentmesoscopicstructures
suchasfibrilsthatwereobservedexperimentallyinthe
caseofasimilarAMLP(23).Althoughthepreciserelative
stabilitiesofdifferent-sizedaggregatesmaybealteredby
thefinitesizeofthecalculation,theumbrellasampling
resultsclearlysuggestthattheC16-KGGKismostlikely
polydisperseinsolution.
Totesttheeffectsofsystemsizeonthedistributionof
oligomers,wealsoranthreeindependentsimulationsof
480C16-KGGKmoleculesatthesameconcentrationas
intheumbrellasamplingones.Thesimulationswerestarted
fromeitherdispersedmonomericlipopeptides,48-mers,or
amixof17-and31-mers;seeSectionS4intheSupporting
Materialformoredetails.Thesizedistributionfunctionsof
theC16-KGGKoligomersfromthesesimulations,shownin
Fig.S6,showthatthetwosystemsstartingfromthetwo
oligomericstatesstayedaroundtheirrespectiveminima
throughoutthesimulations,whiletheonestartingfrom
monomersresultedinamixtureofoligomerswithsizes
rangingfrom10to38lipopeptides.Thisdemonstratesthat
thefreeenergyminimacalculatedfromtheumbrellasam-
pling(Fig.1)areatleastmetastable,regardlessofsystem
size.Thepopulationoflargeraggregatesremainslow
eveninthebiggersimulations,andevenwhentheyoccur,
theyarenotstable.Rather,inthesetrajectoriesthelarge
aggregatesreallyjusttheresultoftwosmalleraggregates
momentarilycolliding,withoutactuallyfusing.Thiscould
beakineticartifact:medium-sizedaggregatesdoareason-
ablejobofhidingtheacylchainsfromsolvent,sofusing
themrequiresthesamekindsofconcertedopeningevents
requiredformembraneinsertion,withsignificantbarriers.
Thus,weconcludethat1)themedium-sizedaggregates
areatleastmetastableattheconcentrationstudied,2)larger
aggregatesareeitherlessfavorablethermodynamically
orformonmuchlongertimescales,and3)asolutionof
C16-KGGKislikelytofeatureabroadrangeofaggregate
sizes.
Micellesgreatlyenhancemembraneselectivity
Giventhebroaddistributionofoligomersizes(Figs.1and
S6),itisnotimmediatelyobviouswhicholigomericstate
ismostrelevanttothemembraneactivityseenexperimen-
tally.Inthisstudy,wechosethe48-merC16-KGGKmicelle
andalipopeptide/lipidof1:10asourmodelsystem
oflargeraggregates.Weproposeasimpleanalyticalcorrec-
tionforthisissue,discussedinSectionS3intheSupporting
Material.Whenreasonablevaluesforthevolumesof
thesystemandindividualmoleculesarepluggedin,the
correctionlowersthefreeenergyofthelargeraggregate
byz24kcal/molrelativetothe17-mer/31-mermix.How-
ever,giventhesignificantuncertaintiesinthecorrection,
BiophysicalJournal109(4)750–759
becausetheexpectedpeptide/lipidinthemembrane-bound
bindingbacterialmammalian
246.7–19.3)z227.4kcal/mol(Fig.2).Indeed,onaper-
ToquantifytostructuralchangesduringC16-KGGK’s
756LinandGrossfield
lipopeptidebasis,bindingtothemodelmammalian
membraneisz0.40kcal/mol,lessthek
B
T,while
bindingtothemodelbacterialmembraneisfavorable
byz5.14kcal/molpermolecule.Thisvalueismuchsmaller
thantheonewehadmeasuredpreviously(26)fortheisolated
lipopeptidesusingthesamemodel,wherebindingtothe
anionicmembranewasfavorablebyC014.5kcal/mol;thedif-
ferencereflectsthestabilityofthemicellerelativetothe
monomerinsolution.
However,theeffectofmicellizationonbindingkinetics
isevenmorestriking.WhereindividualC16-KGGKmole-
culesbindwithoutbarriertobothPCandPE:PGmembranes
(26),micellesexperiencedistinctbarriersthatdependon
themembranecomposition.Thebarriertoenteringa
POPE:POPGbilayerisrelativelysmall(1.3kcal/mol),
particularlyincontrasttothebarriertoenterazwitterionic
POPCbilayer(79kcal/mol).Thedifferenceinbarrierheight
is77.7kcal/mol,suggestingadifferenceinbindingrates
of10
56
.
Thisresulthelpsexplainthefunctionofsimilarlipo-
peptidesinvivo,wherehostmembraneswillgenerally
bemoreabundantthanbacterialones.Barrierlessbinding
suggeststhatisolatedlipopeptideswilltendtobind
strongly(DG
theyencounterfirst,makingithardtounderstandhow
thelipopeptideseverreachedtheirbacterialtargets.
Theseresultssuggestanovelmechanismforselectivity:
bindingtohostmammalianmembraneswillbeslow
andinefficientaslongasthelipopeptidesaremicellized
insolution,whilebindingtothebacterialsurfacewill
stillbeefficient.Toourknowledge,thisfavorableaspect
ofAMLPoligomerizationhasnotbeendiscussedprevi-
ouslyineithertheexperimentalorcomputational
literature.
MolecularbasisforAMLPs’cooperativebinding
tobacterialmembranes
ThecooperativebindingofC16-KGGKmicellestothe
membraneisimportantforitskineticselectivity.Because
thismechanismhasnotbeenexploredpreviously,itisworth
examiningthemolecular-leveldetailsoftheprocess,in
hopesthatwecanusetheinsightstoguiderationaloligo-
merization-basedoptimization.
stateofmanyantimicrobialpeptideswithmicromolarmin-
imalinhibitoryconcentrations(53)isroughlyaroundthis
value.
Theumbrellasamplingresultsforthe48-merC16-KGGK
micellebindingtomembranesshowthatthemicellarstate
hasstrongthermodynamicselectivityforanionicmem-
branes;thethermodynamicbindingaffinityforthemodel
bacterialmembraneismuchhigherthanthatforthemamma-
lianone,yieldingaDDG(DGC0DG?
BiophysicalJournal109(4)750–759
membranebinding,wemeasuredtheorientationofthe
lipopeptide’acylchains,thesizeofthelipopeptide
micelle/aggregation,thehydrationofthelipopeptides,and
thelateralradialdistributionfunctionsofdifferentlipids
indifferentstagesofthisprocess.Thedetailsofthisanalysis
andtheresultsarepresentedinSectionsS5.2,S5.3,S5.4,
andS5.5intheSupportingMaterial.Asdescribedin
SectionsS5.2andS5.5intheSupportingMaterial,the
C16-KGGKmicelleinitiallyboundtothebacterialmem-
braneviaasurface-boundstatestabilizedbyelectrostatic
interactionsbetweenthepeptidesidechainsandthemem-
brane.Theseelectrostaticinteractionswerealsoevidentin
previousbrute-forcesimulationsdonebyourgroup(25),
aswellastheumbrellasamplingsimulationsofmonomers
bindingtomembranes(26);theseinteractionsreducethe
freeenergybarriertobindingbacterialmembranesrelative
tozwitterionicones.Thiscanbeunderstoodfromtwoper-
spectives,asfollows.
First,thelong-rangeelectrostaticsdrawthemicelle
towardthemembrane,effectivelylettingitfalldownhill
towardtheboundstate;thereisnoequivalentinteraction
withzwitterionicmembranes.Itisworthnotingthatthese
calculationswereperformedwith100mMsalt,andthat
thiseffectwouldbestrongerstillinpurewater.Moreinter-
estingly,themicellealteredthelateralstructureofthemem-
brane,concentratingthePOPGlipidsevenwhenthemicelle
isrelativelyfarawayfromthemembrane(Fig.S10A1).
Thissuggeststhatlipopeptides’directcontactwithmem-
branesisnotanecessaryconditiontoinducelipiddemixing.
Thissuggeststhatlipopeptidemicellescouldpossiblyalter
bilayerstructureinawaydeleterioustocellhealthevenif
othercomponentsofthemicrobe’scellsurface,suchas
thelipopolysaccharides,preventedfullbindingand
insertion.
Second,whenthemicelleassociatedwiththemembrane
surface,itrecruitedPOPGlipidstostabilizethesurface-
boundstate.Thesecondstepisparticularlyimportantin
ordertolowerthetransitionbarriertoinsertion,because
thefavorableinteractionscompensatefortheunfavorable
exposureoflipopeptideacylchainstowaterrequiredfor
insertion(Fig.2A2).Thisdemixingofanioniclipidshas
beenproposedasaseparate,pore-independentmechanism
forAMPfunction(54–56).
Withthemammalianmembrane,therewerenofavorable
long-rangeinteractionstodrawthemicelletothemembrane
surface,sothelipopeptideswereinsteadtransferredindivid-
uallyfromthemicelleintothemembranewhilethemicelle
remainedmoreorlessundistortedinsolution;thissituation
continueduntilthemicellebecametoosmalltoeffectively
hidetheremainingacylchains,atwhichpointtheremaining
AMLPsweretransferredsimultaneouslyintothemem-
brane.Thisistheoriginofthelargebarriertoinsertion
seeninFig.2B2.Thiscanalsobeseenfromtheprogression
ofsizedistributionoflipopeptideclusterswherethe
diminishingoligomerslingeredmuchlongerinthebacterial
statebutmuchlesssignificantlysocomparedtothe
membranerapidlyandwithhighaffinity(26),thiswork
S0006-3495(15)00717-1.
2.Jenssen,H.,P.Hamill,andR.E.W.Hancock.2006.Peptideantimicro-
bialagents.Clin.Microbiol.Rev.19:491–511.
LipopeptideMicelleThermodynamics757
mammaliancase(seeSectionS5.2intheSupportingMate-
rial).Thispartialinsertionisduetothemetastabilityofthe
whole48-mermicelleasdiscussedinSectionS4.1inthe
SupportingMaterialaswellasthepresenceoftheanionic
membrane,whichabsorbedtheinsertedmonomersandsta-
bilizedthedegradedmicelleviafavorableelectrostatic
interactions.
Asmentionedabove,therewasaturningpointinthe
mammalianmembranecasewherethemicellebecame
smallenoughsuchthatitsinsertionintothemembrane
becamecooperative(compareFig.S7,B1andB2).The
systemarrivedatacriticalpointwherethebarriertotrans-
ferringonemorelipopeptideintothemembranebalanced-
outthatofpushingtheentireoligomerintothemembrane;
atthispoint,therestofthelipopeptideswentintothemem-
branetogether.Thesizeofthisintermediatemicellewas
somewherebetweena20-anda30-mer,whichwasaround
theequilibriumsizesexpectedinsolution(seeFigs.1and
S6andSectionS4.1intheSupportingMaterial).Thisraises
averyimportantquestionregardingthemembraneselec-
tivityofAMLPs:ifsuchintermediatemicellesarewell
populatedascomparedtolargerones,theAMLP’sbinding
tothemammalianmembraneviatheseintermediatemi-
cellescouldbecomecomparablyfastastothebacterial
membrane.Ifso,onecouldimaginerationallyoptimizing
theoligomerizationstateinordertoimproveselectivity
andreducesideeffectsfromdamaginghostmembranes.
However,doingsowouldrequireustoconsiderthesurface
structuresofdifferentcelltypesastheymightinteractwith
micellesofaspecificrangeofsizes.
CONCLUSIONS
Inthisstudy,weusedcoarse-grainedMDsimulationsofan
antimicrobiallipopeptidetoquantifyitsfreeenergyof
oligomerizationinsolution,aswellasthefreeenergyofa
typicaloligomer’sbindingtotwolipidbilayercom-
positions,chosentomimicbacterialandmammalian
membranes.Ourresultsindicatedthatthislipopeptide,
C16-KGGK,ispolydisperseinsolution,withanequilib-
riumofoligomersofvarioussizes.Whileaprevioussimu-
lationstudyshowedthatthemonomerbindstoany
membranecasethanthemammalianmembranecase,asis
evidentbythehigh-endorangecurvesshowninFig.S8
A2comparedtothoseinFig.S8B2.What’smore,because
theintermediate-sizemicellesaremetastableinwateras
discussedinSectionS4.1intheSupportingMaterial,the
gradualinsertionintothemammalianmembranecase
gaverisetoamoreruggedfreeenergylandscape,especially
aroundthetransitionpeaks(Figs.2Band3).Itisworth
mentioningherethatevenincaseofthebacterialmem-
brane,thelipopeptidescouldbetransferredindividually
fromthemicelleintothemembraneduringthetransition
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ACKNOWLEDGMENTS
WethanktheCenterforIntegratedResearchComputingattheUniversityof
Rochesterforprovidingcomputationalresourcesinourresearch.
ThisworkwassupportedbygrantNo.GM095496fromtheNationalInsti-
tutesofHealth,Bethesda,MD.
AUTHORCONTRIBUTIONS
D.L.andA.G.designedtheresearch;D.L.performedtheresearch;D.L.
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