Evaluation of Reduced Point Charge Models of Proteins through Molecular Dynamics Simulations: Application to the Vps27 UIM-1 – Ubiquitin Complex

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Evaluation of Reduced Point Charge Models of Proteins through Molecular Dynamics

Simulations: Application to the Vps27 UIM-1 – Ubiquitin Complex

Leherte, Laurence; Vercauteren, Daniel

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Journal of Molecular Graphics and Modelling

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2014

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Leherte, L & Vercauteren, D 2014, 'Evaluation of Reduced Point Charge Models of Proteins through Molecular

Dynamics Simulations: Application to the Vps27 UIM-1 – Ubiquitin Complex', Journal of Molecular Graphics and

Modelling, vol. 47, pp. 44-61.

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JournalofMolecularGraphicsandModellingxxx(2013)xxx–xxx

ContentslistsavailableatScienceDirect

Journal

of

Molecular

Graphics

and

Modelling

jo u r n al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / J M G M

Graphical

Abstract

JournalofMolecularGraphicsandModellingxxx (2013)xxx–xxx

Evaluationofreducedpointchargemodelsofproteinsthrough MolecularDynamicssimulations:ApplicationtotheVps27 UIM-1–Ubiquitincomplex

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Journal

of

Molecular

Graphics

and

Modelling

jo u r n al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / J M G M

Highlights

JournalofMolecularGraphicsandModellingxxx (2013)xxx–xxx

Evaluationofreducedpointchargemodelsofproteinsthrough

MolecularDynamicssimulations:ApplicationtotheVps27UIM-1–Ubiquitincomplex

LaurenceLeherte∗_,_Daniel_P._Vercauteren

•ReducedpointchargemodelsprovidestableMolecularDynamicstrajectoriesoftheproteincomplex.

•H-bondnetworksareprogressivelymodiﬁedasthereductiondegreeincreases.

•Themodelsallowtoprobelocalpotentialhyper-surfaceminimathataresimilartoall-atomones.

•Themodelsallowtosampleproteinconformationsmorerapidlythantheall-atomcaseduetoaloweringofenergybarriers.

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JournalofMolecularGraphicsandModellingxxx(2013)xxx–xxx

Journal

of

Molecular

Graphics

and

Modelling

jo u r n al hom epa g e :w w w . e l s e v i e r . c o m / l o c a t e / J M G M

Evaluation

of

reduced

point

charge

models

of

proteins

through

Molecular

Dynamics

simulations:

Application

to

the

Vps27

UIM-1–Ubiquitin

complex

1

2

3

Laurence

Leherte

∗

,

Daniel

P. Vercauteren

Q1 4

UnitédeChimiePhysiqueThéoriqueetStructurale,UniversityofNamur,RuedeBruxelles61,B-5000Namur,Belgium

5 6

a

r

t

i

c

l

e

i

n

f

o

7 8 Articlehistory: 9 Accepted31October2013 10 Availableonlinexxx 11 12 Keywords: 13

Molecularelectrostaticpotential

14

Electrondensity

15

Smoothingofmolecularﬁelds

16

Criticalpoints

17

Pointchargemodel

18 Protein 19 Ubiquitincomplex 20

a

b

s

t

r

a

c

t

Reducedpointchargemodelsofaminoacidsaredesigned,(i)fromlocalextremapositionsincharge densitydistributionfunctionsbuiltfromthePoissonequationappliedtosmoothedmolecular electro-staticpotential(MEP)functions,and(ii)fromlocalmaximapositionsinpromolecularelectrondensity distributionfunctions.Correspondingchargevaluesareﬁttedversusall-atomAmber99MEPs.Toeasily generatereducedpointchargemodelsforproteinstructures,librariesofaminoacidtemplatesarebuilt. TheprogramGROMACSisusedtogeneratestableMolecular Dynamics trajectoriesofanUbiquitin-ligand complex(PDB:1Q0W),undervariousimplementationschemes,solvation,andtemperatureconditions. Pointchargesthatarenotlocatedonatomsareconsideredasvirtualsiteswithanulmassandradius. Theresultsillustratehowtheintra-andinter-molecularH-bondinteractionsareaffectedbythedegree ofreductionofthepointchargemodelsandgivedirectionsfortheirimplementation;aspecialattention totheatomsselectedtolocatethevirtualsitesandtotheCoulomb-14interactionsisneeded.Results obtainedatvarioustemperaturessuggestthattheuseofreducedpointchargemodelsallowstoprobe localpotentialhyper-surfaceminimathataresimilartotheall-atomones,butarecharacterizedbylower energybarriers.Itenablesallowstogeneratevariousconformationsoftheproteincomplexmorerapidly thantheall-atompointchargerepresentation.

21

1. Introduction

22

Numerous modelshave already been proposedin literature 23

regarding the coarse-graining of biomolecules and their corre-24

spondinginteractionpotentials.Severalreferenceswerealready 25

givenin[1].Reviews[2–6]aswellassoftware[7,8]areregularly

26

publishedonthesubject.

27

Inrecentpublications,wedescribedreducedpointcharge

mod-28

els [9,10] built from critical point (CP) analyses of smoothed

29

molecularproperties,andtheirapplicationstoMolecularDynamics

30

(MD)simulationsofproteins[1].Thesesimulationswereachieved

31

invacuumusingtheprogrampackageTINKER[11]whereinpoint

32

chargeswereconsideredasmassesattachedtotheprotein

struc-33

turethroughharmonicbonds.Themassthatwasassociatedwith

34

thechargeswassettoavalueofm=2inordertolimitthemass

35

increaseoftheproteinstructureandtoallowatimestepvalueof

36

1fs,alowervalueofmimplyingtoostrongadecreaseofthetime

37

steptogetstableMDtrajectories.Allothertermsoftheselected

38

∗ Correspondingauthor.Tel.:+3281724560;fax:+3281725466.

E-mail address:laurence.leherte@unamur.be(L.Leherte).

forceﬁeld(FF),Amber99[12],werecalculatedattheall-atomlevel, 39

i.e.,asintheoriginalFFversion. 40

Inthepresentwork,thedesignofreducedpointchargemodels 41

isnotintendedtoleadtoacoarse-grainedmodelperse.Itispart 42

ofamoreglobalprojectregardingtheanalysisoflowresolution 43

molecularpropertiessuchaselectrondensity(ED)andmolecular 44

electrostaticpotential(MEP).FromtheveryﬁrstMDapplicationsof 45

areducedpointchargemodeltoproteinstructures[1],itwasfound 46

thatthesecondarystructureoftheproteinswasonlypartlylost 47

duringthesimulationswhiletheoverallthree-dimensional(3D) 48

foldremainedstable.Additionally,adecreaseofaboutafactor2of 49

thecalculationtimewasobservedforthesimulationsinvacuum. 50

Asa perspectivetotheworkreportedin[1],itwasexpectedto 51

adoptotherimplementationapproachestogetridofthenon-zero 52

massassignedtothecharges.Thisperspectiveledtothepresent 53

paper. 54

Inthepresentwork,twomolecularpropertiesleadingtodif- 55

ferent reduced point charge models areconsidered. First, asin 56

[1,10],alimitednumberofpointchargesisobtainedthroughthe 57

searchforthemaximaandminimaofasmoothedversionofthe 58

chargedensity(CD)generatedbytheatomicchargesdeﬁnedin 59

Amber99(orAmber99SB)FF[12].Second,thepointchargesare 60

obtainedthroughasearchofthemaximaofthefullpromolecular 61

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EDofthemolecularstructureand,asintheﬁrstapproach,charge

62

valuesareassignedtothosemaximausingaleast-squarecharge

63

ﬁttingprocedure.Thislastmolecularpropertyiseasilycalculated

64

usingtheso-calledPromolecularAtomShellApproximation(PASA)

65

formalismthatwasdevelopedbyAmatandCarbó-Dorca[13,14].

66

Thosetwoapproachesledtovariousimplementationswhichare

67

discussedin thepresentpaper. Theprogram GROMACS[15,16]

68

wasselectedduetoitsimplementationtowardsshortercalculation

69

timesandthepossibilitytodeﬁnevirtualsites,i.e.,particleswith

70

nulmassandradiusthatarecoupledtothemolecularstructure

71

throughgeometricalrules.

72

Theaimofthepaperistogodeeperinthemodellingof

pro-73

teinstructuresanddynamicsusingreducedpointchargemodels,

74

withanapplicationtoaparticularproteincomplex.Suchasystem

75

wasselectedtoprovideinformationontheusefulnessofthe

mod-76

elstosimulateshortpeptidesandproteinsaswellastheirmutual

77

interactions.Theeffectofthepointchargedistributionsonboth

78

theintra-andinter-molecularinteractionsinvarioussimulation

79

conditions,suchastemperatureandsolvation,isalsoinvestigated.

80

Atthisstageofourresearchwork,onlytheelectrostaticpartof

81

theFFismodiﬁed.Energetic,structural,anddynamicalproperties

82

arecalculatedandcomparedtotheall-atomones,whichiseasily

83

achievedasnoconversionstageisrequiredbetweenthereduced

84

andall-atommodels.However,keepingasigniﬁcantnumberof

all-85

atomcontributionstotheFFlimits,forthemoment,thepossible

86

gainincalculationtime.

87

Inthenextsection,wedetailhowthemodelsandtheir

imple-88

mentationwere designed. Then, MDsimulation resultsfor the

89

proteincomplexinvolvingtheUbiquitinInteractingMotifUIM-1

90

ofproteinVps27andUbiquitin(PDBaccesscode1Q0W)with

vari-91

ouspointchargemodels,andunderdifferentsimulationconditions

92

(temperature,solvationstate),areanalysedanddiscussed.

93

2. Backgroundtheory 94

Inthissection,wepresentthemathematicalformalismthatwas

95

usedtodesignamolecularreducedpointchargerepresentationand

96

itscorrespondingchargevalues.Asalltheseaspectswerealready

97

detailed before[9,10], we only providea short overview. First,

98

thesmoothingalgorithmisbrieﬂydescribed.Then,theapproach

99

appliedtolocatethepointchargesispresented,aswellasthe

pro-100

ceduretoassignchargevalues.Finally,theautomationprocedure

101

thatisimplementedtorapidlydeterminethepointchargelocations

102

foranyproteinstructureisexplained.

103

2.1. Smoothingofamolecularproperty

104

Inthepresentapproachtogeneratesmoothed3Dfunctions,a

105

smoothedCDorEDmapisalowerresolutionversionthatisdirectly

106

expressedasthesolutionofthediffusionequationaccordingtothe

107

formalismpresentedbyKostrowickietal.[17].Fromtheformalism

108

givenin[1],thesmoothedanalyticalCDdistributionfunctiona,s(r)

109

thatisobtainedfromanatomicchargeqaandthePoissonequation

110 isexpressedas: 111 a,s(r)= qa (4s)3/2e−r 2_/₄_s (1) 112

wherea,s,andr,standfortheatomindex,thesmoothingfactor

113

(inBohr2_,₁_Bohr₌_0.52918_×₁₀−10_m)_,_and_the_distance_versus_the 114

atomposition,respectively.ThefullpromolecularEDiscalculated

115 as: 116 a,s(r)= 3

i=1

a,i where a,i=˛a,ie−ˇa,ir 2 (2) 117 with 118 ˛a,i=Zawa,i

2ςa,i

3

_⁄

₂ 1 (1+8ςa,is)3/2 and ˇa,i= 2ςa,i (1+8ςa,is) 119 (3) 120

where Za, wa,i and a,i, are theatomic number of atoma, and 121

thetwoﬁttedparameters,respectively.Unsmoothedfunctionsare 122

obtainedbyimposings=0Bohr2_. ₁₂₃

2.2. Searchforcriticalpoints 124

AnalgorithminitiallydescribedbyLeungetal.[18]wasimple- 125

mented tofollow the trajectories of CPs,more speciﬁcally,the 126

maximaand/orminimainaCDorEDfunction,asafunctionofthe 127

degreeofsmoothing.Asalreadyreportedbefore[9],weadapted 128

theirideato3Dmolecularpropertyfunctions,f,suchas: 129

r_f(s)=rf(s−s)+

∇

f_f(s)₍_s)· (4) 130

whererstandsforthelocationvectorofapointina3Dfunction, 131

suchasamolecularscalarﬁeld,and/f(s)isthesteplength. 132

Thevariousstepsoftheresultingmerging/clusteringalgorithm 133

areasfollows.First,atscales=0,eachatomofamolecularstructure 134

isconsideredeitherasalocalmaximum(peak)orminimum(pit) 135

ofthescalarﬁeldf.Allatomsareconsequentlytakenasthestarting 136

pointsofthemergingprocedure.Second,assincreasesfrom0toa 137

givenmaximalvaluesmax,eachpointmovescontinuouslyalonga 138

gradientpathtoreachalocationinthe3Dspacewheref(s)=0.On 139

apracticalpointofview,thisconsistsinfollowingthetrajectoryof 140

thepeaksandpitsonthemolecularpropertysurfacecalculated 141

atsaccordingtoEq.(4).Thetrajectorysearch isstoppedwhen 142 |f(s)|islowerorequaltoalimitvalue,gradlim.Onceallpeak/pit 143

locationsarefound,closepointsaremergediftheirinter-distance 144

islowerthantheinitialvalueof1/2_._The_procedure_is_repeated ₁₄₅

foreachselectedvalueofs.Iftheinitialvalueistoosmallto 146

allowconvergencetowardsalocalmaximumorminimumwithin 147

thegivennumberofiterations,itsvalueisdoubled(ascalingfactor 148

thatisarbitrarilyselected)andtheprocedureisrepeateduntilﬁnal 149

convergence. 150

2.3. Chargecalculation 151

TostayconsistentwiththeanalyticalexpressionoftheAmber99 152

FF,onlypoint charge values areassigned toeach ofthe CPsof 153

a3Dmolecularpropertyﬁeld.Inrecentliterature,onealsoﬁnds 154

coarse-grainedelectrostaticenergytermswhichalsoinvolvedipo- 155

lar terms, such asin thework of Spiga et al. [19]. The charge 156

ﬁttingprogramQFIT[20]wasusedasdetailedin[9].AllMEPgrids 157

werebuiltusing theAmber99[12] atomiccharges whichwere 158

assignedusingthesoftwarePDB2PQR[21,22],withagridstepof 159

0.5 ˚A.FittingswereachievedbyconsideringMEPgridpointslocated 160

between1.4and2.0timesthevanderWaals(vdW)radiusofthe 161

atoms.Thesetwolimitingdistancevalueswereselectedafterthe 162

so-calledMerz-Singh-Kollmanscheme[23].Sidechainsandmain 163

chainsoftheaminoacids(AA)weretreatedseparately,asdiscussed 164

in[9]. 165

Inallﬁttings, thetotal electricchargeand themagnitudeof 166

themoleculardipolemomentwereconstrainedtobeequaltothe 167

correspondingall-atomAmber99values.Alldipolemomentcom- 168

ponentswerecalculatedwiththeoriginoftheatomcoordinates 169

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L.Leherte,D.P.Vercauteren/JournalofMolecularGraphicsandModellingxxx(2013)xxx–xxx 3 3. Designofaminoacidreducedpointchargemodels

171

ReducedpointchargerepresentationsofeachofthetwentyAAs

172

wereobtainedbyconsideringtheAAsinspeciﬁcconformational

173

states.ExceptforGlyandAla,mostrecurrentrotamerswere

gen-174

eratedbyconsideringtheangularconstraintsgiveninTable2of[9].

175

AllAAswereconsideredaselectricallyneutralexceptforArg+,His+,

176

Lys+,Asp−,andGlu−.Histidinewasalsomodelledinitsneutral

177

protonatedstatesHis_␦andHis_␧.

178

3.1. CD-basedtemplates

179

FromextendedpentadecapeptidechainsGly7-AA-Gly7

gener-180

atedusing SMMP05[24,25] onlythecentral AAwas keptwith

181

mainchainatoms(C␣ C O)AA(N H)AA+1.Then,thedesignofthe 182

AA point charge templateswas achievedin four stages, as

fol-183

lows.First,isolatedAAstructureswereassigned Amber99atom

184

chargesusingPDB2PQR[21,22].Sidechainextremawerelocated

185

usingourmerging/clusteringalgorithmappliedtotheCD

distri-186

butionfunctionssmoothedats= 1.7Bohr2_,_with

init=10−4Bohr2

187

andgradlim=10−6e−Bohr−2.Thiswascarriedoutseparatelyforthe

188

positivelyandnegativelychargedatoms.Second,thecharge

val-189

uesoftheresultingpeaksandpitstogetherwereﬁttedversusthe

190

all-atomMEPgeneratedfromthesidechain atomsonly.In this

191

procedure,severalrotamerdescriptionswereconsidered

accord-192

ingtotheiroccurrenceprobability(seeTable2of[9]).Third,the

193

mainchainpointchargeswerelocatedinaccordancewiththemotif

194

foundforGly8inanextendedGly15strand[9]and,fourth,asecond

195

chargeﬁttingprocedure,nowcarriedoutversustheMEPcalculated

196

usingalltheAAatoms,wasachievedtodeterminethecharge

val-197

uesofthetwomainchainpointchargeswhilepreservingtheside

198

chainpointchargevaluesﬁrstobtained.

199

Allmainchainpointcharges,observedtobelocatedveryclose

200

totheCandOatoms,weresetexactlyonthoseatoms[1]

(Supple-201

mentaryInformationSI1).AllAAbearsidechainchargesexcept

202

Ala,Gly,Ile,Leu,andVal.AAmodelsaregiveninSI2andwere

203

discussedwithdetailsin[1].Inthepresentwork,anextra

proto-204

nationstateforHiswasgenerated,i.e.,His+.Itischaracterizedby

205

thehighestnumberofpointcharges,i.e.,6,versustheother

histi-206

dineresidues,i.e.,4and5.AsmostofthesepointchargesofHis+

207

areclosetoHatoms,theyweresettobelocatedexactlyonthese

208

atomstofacilitatetheimplementationofthepointchargemodel.

209

Fortheendresidues,achargeof+0.9288or−0.9288e−isseton

210

theNandOXTatoms,respectively[9,10].Inthefurtherpartsof

211

thispaper,themodelwillbereferredtoasmodelmCD.

212

Asecondpointchargedescriptionwasderivedfromthemodel

213

describedabove.Inthissecondmodel,tofullyfacilitatethe

imple-214

mentationoftheAAmodelsinGROMACS,mostofthepointcharges

215

weresetexactlyonatomsoftheresidues,andachargeﬁtting

algo-216

rithmwasagainapplied.ResultsarepresentedinSI3.Thisimplies

217

thatonlythreeAAresidues,His+,Phe,andTrp,haveapointcharge

218

thatisnotlocatedonanatomoftheirstructure.Inthatmodel,one

219

obtainsendchargevaluesof+0.7705and−0.7705fortheendN

220

andOXTatoms.Inthefurtherpartsofthispaper,thesecondmodel

221

willbereferredtoasmodelmCDa.

222

AlastmodelbasedonthepointchargedistributionmCDwas

223

consideredsimilarlytotheapproachadoptedin[1]withthe

pro-224

grampackageTINKER[11].Amassm=2wasassignedtoeachpoint

225

chargeandharmonicconstraintswereappliedtobondsandangles

226

presentedinSI2.ThemodelwillbereferredtoasmodelmCDh.

227

3.2. PASA-basedtemplates

228

CPsearchesofthePASA EDdistributionfunctionswere

car-229

riedouttogeneratestillcoarserchargedescriptionsfortheAAs.

230

Indeed,withtheCD distributionfunctionsdepictedabove,it is

231

not possible toobtain less than two main chain point charges 232

perresidue,i.e.,onenegativeandonepositivechargeassociated 233

withtheOand Catoms, respectively.Withintheframeworkof 234

thePASA,theEDdepends onlyontheatomic numberZa ofthe 235

atoms,notontheircharge(Eqs.(2)and(3)).Theuseofthemerg- 236

ing/clustering algorithm wascarried out withinit=10−4Bohr2 237

andgradlim=10−5e−Bohr−2.Thislimit isanorderofmagnitude 238

greaterthanintheCDcaseastooﬁneagradlimthresholdincreases 239

thepossibilitytomisstherecognitionofduplicateCPsduringthe 240

search. A smoothing degreeof s=1.4Bohr2 _was_considered. _An ₂₄₁ exceptionoccursforTrp forwhichoneobservestwosidechain 242

CPsatsbeloworequalto1.05Bohr2_._We_selected_that_value_to ₂₄₃ betterdifferentiatethatresiduefromtheotheraromaticresidues 244

characterizedbyonlyoneCP.AseachAAmainchaininvolvesonly 245

oneCP,itschargevaluewasdirectlysetasthesumoverthecor- 246

respondingatomiccharges.Then,forAAsinvolvingmorethanone 247

sidechainCP,achargeﬁttingprocedurewasappliedasfortheCD- 248

basedmodels.Forendresidues,oneobservednomainchainCPon 249

theterminalNH3+group.ThechargeofthemainchainCPofthe 250

N-terminalresidueisthusincrementedby+1,whilethemainchain 251

chargeoftheC-terminalresidueisincrementedby−1.Individual 252

AApointchargerepresentationsaregiveninFig.1.Regardingthe 253

sidechains,mostoftheresiduesarecharacterisedbyonlyoneCP. 254

Theirlocationismostlydeterminedbytheatomswiththehighest 255

atomicnumber,i.e.,S,O,N,andC.TheHatomsdonotsigniﬁcantly 256

affecttheEDdistributionfunctionsandthismakesallHisresidues 257

lookingalike.Inthefurtherpartsofthispaper,themodelwillbe 258

referredtoasmodelmPASA.Itsimplementationwithintheprogram 259

GROMACSisdetailedinSI4. 260

3.3. Automatedpointchargegenerationprocedure 261

Thefourpointchargetemplatesdescribedaboveareestablished 262

forisolatedAAstructures.Theirpropertiesarethusindependenton 263

theneighbourhoodoccurringinaparticularproteinofacomplex 264

structure.Thispresentsagreatadvantagewhenthoseproperties 265

are transferable.In a previous work[9], one indeedsuggested, 266

throughagoodapproximationofMEPproﬁlesofionchannelsand 267

numerousfreeenergycalculations,thattransferabilityoccursfor 268

rigidproteinstructures.Additionally,intheirpaperregardingthe 269

optimalnumberofcoarse-grainedsitesinbiomolecularcomplexes, 270

Sinitskiyetal.concludedthatthetransferabilityofindividualpro- 271

teinpropertiesbetweenunboundandboundstatesissupported 272

bythepossibilitytocoarse-graincomplexpartnersindependently 273

onefromeachother[27]. 274

To study large protein structures, an automation stage was 275

developedtorapidlylocatepointchargesonthestructure.Itisfully 276

basedontheapplicationofasuperimpositionalgorithmofCPtem- 277

platesofeachAAontotheircorrespondingall-atomstructureof 278

theproteinunderstudy.WeusedtheprogramQUATFIT[28,29] 279

to,ﬁrst,superimposealimitedsetofatomsfromthetemplateon 280

thestudiedstructure,andthenusetheresultingtransformation 281

matrixtogeneratethecorrespondingpointchargecoordinates.The 282

templatesobtainedfromCDdistributionfunctionswerealready 283

madeavailableinTable3of[9].TheHis+templatenewlystudied 284

inthepresentworkisprovidedinSI5.Additionally,thetemplates 285

obtainedfromtheanalysisofthePASAEDdistributionfunctions 286

arereportedinSI6.TheGROMACStopologyﬁle,whereinpoint 287

chargesaredeﬁnedasvirtualsites,isfurthergeneratedthroughan 288

in-houseprogramthatoutputsgeometricalparametersasreported 289

inSI1,3,and4,forthemCD,mCDa,andmPASAmodels,respectively. 290

WhenaGROMACSvirtualsiteisgenerated,anumberofatoms, 291

twoorthree,areselectedtodetermineitslocationinspace.The 292

choiceofthereferenceatomsforeachpointchargeisnotunique. 293

Wehavemostofthetimeconsideredtheclosestatomsbyexcluding 294

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Fig.1.Pointchargemodelforthe20AAresiduesasestablishedats=1.4Bohr2_from_the_hierarchical_{merging/clustering}_algorithm_applied_to_the_all-atom_PASA_ED_function.

PointchargesarenumberedasinSupportingInformationSI4.FiguresweregeneratedusingOpenDX[26].

rotationsaroundtheC Obond.Othermodelsmightobviouslybe

296

tested,forexampleforneutralHisresidues,thatarenotusedin

297

thepresentstudies,especiallytodeterminetheirinﬂuenceon

H-298

bondinteractions.DuringaMDsimulation,theforcesactingonthe

299

virtualsitesareredistributedamongtheirreferenceatoms.Force

300

redistributionwaspartlylimitedinmodelmCDabylocatingmost

301

ofthepointchargesonatoms.

302

Asalreadymentioned,pointchargesareconsideredasvirtual

303

sitesthat actonly throughCoulombinteractions. Anadditional

304

implementationstrategywasconsideredwherepointchargesare

305

seen as masses interactingwith the protein structure through

306

restrainedharmonicbonds.Theadvantageofsuchanapproachlies 307

inthefactthattheelectrostaticforcesactingonthechargesarenot 308

redistributedamongtheatoms,butthemodelisbiasedbyartiﬁcial 309

massesaddedtothesystem. 310

4. ApplicationtotheMDoftheVps27UIM-1–Ubiquitin 311

complex 312

Vps27UIM-1,ashort_␣-helicalstructuremadeof24AAresidues 313

(numbered255–278in thePDB),isknowntointeractwiththe 314

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L.Leherte,D.P.Vercauteren/JournalofMolecularGraphicsandModellingxxx(2013)xxx–xxx 5

Table1

DescriptionofthepointchargemodelsusedfortheAmber99SB-basedMDsimulationsoftheVps27UMI-1–Ubiquitincomplex.

No.ofwater molecules

Totalno.ofpointcharges associatedwithbothcomplex partners(Vps27UIM-1/Ubiquitin)

No.ofnon-atomic pointcharges

Boxsize(nm)(from ﬁnalsnapshot) All-atom 10,553 394/1227 0 6.915 All-atom-2 13,269 394/1227 0 7.442 mCD 10,542 96/286 112 6.909 mCDa 10,551 96/286 3 6.899 mCDh 10,542 96/286 112 6.916 mPASA 10,551 36/102 136 6.919

hydrophilicresidues,encompassingahydrophobicmotifthat con-316

tainsresiduesLeu262,Ile263,Ala266,Ile267,Leu269,andLeu271, 317

thatinteractwithresiduesLeu8,Ile44,Val70,andAla56ofUbiquitin 318

[30,32].AccordingtoSwansonetal.[30],electrostaticinteractions

319

areexpectedtooccurbetweennegativelychargedGlu−residues

320

ofVps27UMI-1(Glu−257,Glu−259,Glu−260,andGlu−261)and

321

Arg+residuesofUbiquitin(Arg+42,Arg+72,andArg+74),aswell

322

as between Glu₋₂₇₃ and His+68, while H-bonds are observed

323

betweenAla266andHis+68,Ser270andAla46andGly47,aswell

324

asbetweenGly47andHis+68[33].

325

The study of such a protein-protein system using MD

326

approachesisnotnew[33–35]andtheapplicationspresentedin

327

thispaperareintended totest andassess,versustheirall-atom

328

counterpart,thepoint chargereducedmodelsdevelopedabove.

329

Ourreferenceworksarethusthedataavailableinliteratureaswell

330

asourownall-atomMDsimulationresults.

331

Molecularsimulationconditionswerekeptascloseaspossible

332

ofthoseproposedbyShowalterand Brüschweilerintheirwork

333

abouttheAmber99SBFF[36].MDtrajectoriesofthesystemwere

334

runusingtheGROMACS4.5.5programpackage[15,16]withthe

335

Amber99SBFF[37]underparticlemeshEwaldperiodicboundary

336

conditions.Long-rangedispersioncorrectionstoenergyand

pres-337

surewereapplied.Theinitialconﬁgurationswereretrievedfrom

338

theProteinDataBase(PDB:1Q0W)andsolvated,ifrequired,using

339

TIP4P-Ewwatermolecules[38]soasproteinatomslieatleastat

340

1.2nmfromthecubicboxwalls.TheVps27UMI-1andUbiquitin

341

partnersinvolveeach394and1227atoms,respectively.To

can-342

celthenetchargeofstructure1Q0W,twoNa+_ions_were_added

343

tothesystemusingtheiongeneratortoolofGromacs.As

speci-344

ﬁedin[30],theHisresidueofUbiquitinisfullyprotonated(His+

345

state).Thesystemswereﬁrstoptimizedandthenheatedto50K

346

througha10pscanonical(NVT)MD,withatimestepof2fsand

347

LINCSconstraintsactingonbondsinvolvingHatoms.The

trajec-348

torywasfollowedbytwosuccessive20psheatingstages,at150

349

and300K,underthesameconditions.Next,eachsystemwas

equi-350

libratedduring 50ps in theNPT ensembleto relaxthesolvent

351

molecules.Finally,a20nsMDsimulationwasperformedintheNPT

352

ensemble,forsolvatedsystems.Invacuum,onlytheNVTensemble

353

wasused.The‘V-Rescale’and‘Parrinello-Rahman’algorithmswere

354

selectedtoperformNVTandNPTsimulations,respectively.Incase

355

ofobviouslackofequilibration,anextraproductionrunof20ns

356

wasperformed.WhenconsideringmodelmCDh, theconstraints

357

actingonthebondsinvolvingHatomshadtoberemovedandthe

358

timestepwassetequalto1fs,thusleadingtotwicethenumber

359

ofMDiterationsasintheall-atom,mCD,andmCDasimulations.

360

Snapshotsweresavedevery2ps,i.e.,twicethevalueconsidered

361

byShowalterandBrüschweiler[36];thatchoicedidnot

signiﬁ-362

cantlyaltertheresults.Adescriptionofthesystemsunderstudyis

363

presentedinTable1.Thetotalnumberofpointchargestobe

con-364

sideredfortheproteincomplexisreducedbyafactorof4.2and11.7

365

fortheCD-andPASA-basedmodels,respectively.Dependingupon

366

theimplementation,thenumberofnon-atomicchargesislargely

367

variable.Forinstance,thereareonlythreeofsuchpointcharges

368

inmodelmCDa,whichoriginatefromtheHis+andPheresidues

369

ofUbiquitin.Thereare,ineachsimulation,approximately10,500 370

watermoleculesthatarenotcoarse-grained.Alargersolvationbox 371

wasusedforthesystemnamedAll-atom-2whichcorrespondstoa 372

highlydifferentstructureofthecomplex.Thisparticularcasewill 373

bedescribedlaterinthepaper,inSection4.4. 374

It is clear that a real gain in simulation time will be pos- 375

sibleif coarse-graining occursat thesolvent level. Areview of 376

coarse-grainedwatermodelscan,forexample,befoundin[39,40]. 377

Workingwithanimplicitsolventrepresentationisanotherefﬁ- 378

cientwaytolargelyreducethecalculationtimeasdiscussedin 379

[41,42].Asarecentexample,letusmentiontheapproachadopted 380

inthecoarse-grainedFFPRIMObyKaretal.[43].Atthepresent 381

stageofourwork,noinformationisavailableregardingtheradius 382

valuetobeassignedtothenon-atomicpointcharges.Theapproach 383

weemployedearliertocalculatefreeenergyofsolvationusingthe 384

programAPBS[44],i.e.,toassignanulradiustothepointcharges 385

[10],appearednottobeeffectivewithGROMACS.Thus,interfacing 386

ourreducedpointchargemodelswithcoarse-grainedorimplicit 387

solventrepresentationsis a perspectivetobring tothepresent 388

work. 389

4.1. Molecularelectrostatic maps 390

MEPmapsaredisplayedinFig.2forthefouroptimizedcom- 391

plexes,i.e.,thestartingpointsoftheMDsimulations,described 392

using the all-atom, mCD, mCDa, and mPASA models. Solvent 393

molecules and ions werenot included in thecalculations. It is 394

noticedthatthecontoursdisplayedatFig.2,i.e.,anegativeMEP 395

contourforVps27UIM-1(−0.2e−Bohr−1)andapositiveMEPcon- 396

tourforUbiquitin(+0.1e−Bohr−1),showsimilar3Dshapesforeach 397

ofthefourmodels.Similarbehaviourswerealreadyputforwardin 398

thestudyofrigidsystemssuchasionchannels[9].Atshortrange, 399

e.g.,in thecaseof intramolecularinteractions, thepoint charge 400

models are expected toaffect thedynamical behaviour of the 401

moleculesasdetailedfurtherinthepaper.Topreliminaryillustrate 402

thatassumption,MEPmapsaredisplayedfortwoindividualAAs, 403

Glu−andHis+(Fig.3).Inthecaseofglutamate,oneobserveshigher 404

MEPvaluesatthetwonegativesidechainchargesformodelmCD 405

and,obviously,theabsenceofsuchaseparationformodelmPASA 406

whichinvolvesonlyonesidechainnegativecharge.Theall-atom 407

representationofthemainchainistheonlyonetoletappeartwo 408

negativelychargedsites.Onemaythusexpectstructuralchanges, 409

especiallyinsecondarystructureelements.Forprotonatedhisti- 410

dine,thepositiveMEPareaslooksimilar,exceptforthemainchain 411

andthemPASAmodel.Onethusassumesthatachangeinthepoint 412

chargemodelwillaffect,atleast,theformationofH-bondsduringa 413

MDsimulation.AsseenlaterduringtheanalysisoftheMDtrajecto- 414

ries,changesinthesecondarystructureelementswillbeobserved, 415

aswellasinthefoldofthecomplexinsomecases.Asatentative 416

toeliminatetheeffectofUbiquitinstructuralchangesonVps27 417

UIM-1,separateMDsimulationswerecarriedoutbyrestraining 418

Ubiquitintoitscrystalstructure.SuchtrialsdidnotpreventVps27 419

UIM-1toalter its shape and theseMDsimulations willnot be 420

(10)

Fig.2.MEPcontoursofUbiquitin(red:+0.1e−_B_ohr−1₎_and_Vps27_UIM-1_(blue:_−0.2_e−_Bohr−1₎_in_their_initial_optimized_{conﬁguration,}_as_obtained_using_the_All-atom,

mCD,mCDa,andmPASAmodels.Ubiquitinanditsligandaredisplayedusinglightblueandblackspheres,respectively.FiguresweregeneratedusingOpenDX[26].(Foran

interpretationofthereferencestocolourintheartwork,thereaderisreferredtothewebversionofthearticle).

Q2

Fig.3. MEPcontoursof(top)Glu−273(−0.4to−0.1e−_Bohr−1₎_a_nd_(bottom)_His₊₆₈_(0.1_to_0.5_e−_Bohr−1₎_a_s_obtained_using_the_All-atom,_mCD,_mCDa,_and_mPASA_models.

(11)

Fig.4.SecondarystructureofthecomplexVps27UIM-1–Ubiquitinobservedduringthelast20nsAmber99SB-basedMDtrajectoriesinwater(left)andinvacuum(right) at300K,asobtainedusingtheAll-atom,All-atom-2,mCD,mCDa,mCDh,andmPASAmodels.Vps27UIM-1andUbiquitininvolvetheﬁrst24andlast76aminoacidresidues, respectively.Secondarystructureelementsarecolour-codedasfollows:Coil(white),␣-helix(blue),␲-helix(purple),310helix(grey),␤-sheet(red),␤-bridge(black),bend

(green),turn(yellow),chainseparation(lightgrey).

ﬂexiblesystems,exceptforconstraintsappliedtobondsinvolving

422

Hatomsasmentionedabove.

423

4.2. All-atomMDtrajectories

424

AﬁrstanalysisoftheMDtrajectoriesobtainedforthemodel

425

namedAll-atomdealtwiththesecondarystructureofthewhole

426

complexandshowedthatitisslightlymoreconservedinwater

427

(Fig.4left)thaninvacuum(Fig.4right),duetothestabilizing

con-428

tributionofwaterontheproteinstructure.Invacuum,allsecondary

429

structureelementslike␣-helicesand␤-strands,except␤-strands

430

2–7and12–16ofUbiquitin,areshorter.Inbothcases,thehelical 431

structureoftheUIM-1unitisloosen,toalargerextendinvacuum 432

(Figs.4and5). 433

Astudyof the3D foldoftheproteincomplex wasachieved 434

toespeciallydeterminethebindingofVps27UIM-1toUbiquitin. 435

Distancemapsbetweentheatomsofthetwopartnerswerebuilt 436

byconsideringtheminimaldistancesbetweentheAAatomsof 437

thetwopartnersand arereportedin Fig.6.Thedistances were 438

calculatedoverthelast10nsoftheMDtrajectoriestominimize 439

theeffectofa slowsecondary structure relaxationprocessthat 440

(12)

Fig.5.FinalsnapshotsoftheproteincomplexVp27UIM-1(red)–Ubiquitin(blue)obtainedfromthelast20nsAmber99SB-basedMDtrajectoriesinwater(left)andin vacuum(right)at300K,asgeneratedusingtheAll-atom,All-atom-2,mCD,mCDa,mCDh,andmPASAmodels.Structuralelementsarecolour-codedasfollows:␤-strandsof UbiquitininteractingcloselywithVps27UIM-1(yellow),Arg+72 and Arg+74 (green), Glu−257andGlu−259toGlu−261(white),H-bondsbetweenthetwopartners(purple spheres).FiguresweregeneratedusingVMD[45].(Foraninterpretationofthereferencestocolourintheartwork,thereaderisreferredtothewebversionofthearticle).

mCD,mCDa,and mCDh.Inthemapgeneratedbytheanalysisof

442

thesolvatedAll-atomMDtrajectory,oneclearlydistinguishesthree

443

regionsextendedalongtheVps27UIM-1chain.Thisextensionis

444

duetothespatialalignmentofVps27UIM-1withanumberof

␤-445

strandsofUbiquitin.Theﬁrstregioncorrespondstothecontacts

446

occurringbetweensegment259to272ofVps27UIM-1and

␤-447

strand4–10ofUbiquitin,whilethesecondandthirdregionsaredue

448

tocontactswith␤-strands40–45and48–49and␤-strand66–72, 449

respectively.Theshortestdistances,below0.3nm,appearinthese

450

twolastareas.Thereisalastregionofinterest,generatedbythe

451

contactsbetweenGlu−257andGlu−259ofVps27UIM-1andArg+

452

residueslocatedattheC-terminalsegmentofUbiquitin.Invacuum,

453

thesefourregionsareenhancedduetothecloserlocationofVps27

454

UIM-1versusUbiquitin.Theyarelargerastheynowinvolvethe

455

C-terminalresiduesofVps27UIM-1withemphasizedelectrostatic

456

“contacts”betweentheN-terminalGlu−residues(257,259–261)

457

ofUIM-1andN-terminalArg+residues(72and74)ofUbiquitin.

458

Theanalysisof selectedenergytermsaveragedover thelast

459

10nsoftheMDtrajectoriesprovidedtheresultsreportedinTable2.

460

Theabsolutevalueoftheinteractionenergybetweenthetwo

part-461

nersofthecomplex,|E12|, occurswitha ratioof4.6 and 13.6% 462

versusthetotalsolutepotentialenergy(E1+E2),inwaterandin 463

vacuum,respectively.WhenCoulombinteractionsareconcerned,

464

thecorresponding ratio in water, 2.2%, also increases toreach

465

a value of 7.8% in vacuum. The higher relative contribution of

466

|E12|and|Cb12|supportsthehighercompactnessofthecomplex 467

asjustdiscussed fromdistancemaps.Intra-moleculartotal and

468

Coulombpotential energies of Vps27 UIM-1,i.e., |E1| and |Cb1|

469

terms,areratherconstant.Theycontributeto25.9and24.7%,and

470

26.2and23.6%,respectivelyinwaterandinvacuum(Table2).The 471

vacuum-inducedcompactnessinvolvesadecreaseinthemobil- 472

ityoftheUIMatomsversusUbiquitin asillustratedbytheRoot 473

MeanSquareFluctuations(RMSF)oftheVps27UIM-1atomswith 474

Table2

EnergyratioscalculatedfromvaluesobtainedfromAmber99SB-basedMD trajec-tories(reportedinSI7)fortheVps27UIM-1Ubiquitinsystem.Indices‘1’and ‘2’,standforVps27UIM-1andUbiquitin,respectively.EandCbstandfortotal (Coulomb+Lennard–Jones)andCoulombpotentialenergy,respectively.

E12 E1+E2 Cb1+Cb2Cb12 E1+E2E1 Cb1+Cb2Cb1 Solvated All-atom −4.6 −2.2 25.9 24.7 All-atom-2 −2.1 −0.6 26.8 25.1 mCD −2.2 −1.0 21.1 20.5 mCDa −3.7 −2.0 24.2 22.8 mCDh 0.001 −363.6 18.5 53.4 mPASA 34.6 34.8 12.9 29.9 mCD(277K) −2.3 −1.4 22.4 21.2 mCD(250K) −2.1 −1.0 22.6 21.3 mCD(150K) −2.4 −0.9 21.5 20.9 Vacuum All-atom −13.6 −7.8 26.2 23.6 All-atom-2 −11.4 −6.6 24.7 22.7 mCD −9.6 −5.9 19.3 18.0 mCDa −11.4 −7.0 24.2 22.1 mCDh −5.8 −620.4 18.1 −3.0 mPASA 24.0 23.3 21.3 27.9 mCD(277K) −6.4 −3.4 18.5 17.2 mCD(250K) −8.4 −4.8 19.5 18.3 mCD(150K) −7.2 −4.0 18.5 17.2

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Fig.6.DistancemapsoftheproteincomplexVps27p–Ubiquitinestablishedduringthelast10nsoftheAmber99SB-basedMDtrajectoriesinwater(left)andinvacuum (right)at300K,asobtainedusingtheAll-atom,All-atom-2,mCD,mCDa,mCDh,andmPASAmodels.Scaleiscolouredusingadistanceincrementof0.1nm.(Foraninterpretation ofthereferencestocolourintheartwork,thereaderisreferredtothewebversionofthearticle).

All

-a

tom

All

-atom

-2

mCD

mCDa

mCDh

mPASA

0.0 0.4 0.8 1.2 0 200 400 600 800 1000 1200 1400 1600 RMSF (nm) Atom number 0.0 0.4 0.8 1.2 0 200 400 600 800 1000 1200 1400 1600 RMSF (nm) Atom number 0.0 0.4 0.8 1.2 0 200 400 600 800 1000 1200 1400 1600 RMSF (nm) Atom number 0.0 0.4 0.8 1.2 0 200 400 600 800 1000 1200 1400 1600 RMSF (nm) Atom number 0.0 0.4 0.8 1.2 0 200 400 600 800 1000 1200 1400 1600 RMSF (nm) Atom number 0.0 0.4 0.8 1.2 0 200 400 600 800 1000 1200 1400 1600 RMSF (nm) Atom number

Fig.7. RMSFoftheVps27UIM-1andUbiquitinatoms(atoms1–394and395–1621,respectively)inwater(black)andinvacuum(red)calculatedfromthelast10nsofthe Amber99SB-basedMDtrajectoriesat300K,asobtainedusingtheAll-atom,All-atom-2,mCD,mCDa,mCDh,andmPASAmodels.(Foraninterpretationofthereferencesto colourintheartwork,thereaderisreferredtothewebversionofthearticle).

(14)

Table3

AveragenumbersofH-bondsoccurringbetweenvariouscomponentsoftheVps27UIM-1–Ubiquitinsystem,asobtainedfromtheanalysisofthelast10nsofthe Amber99SB-basedMDtrajectoriesat300K.

UIM–Ubiquitin Complex–water UIM–water

Solvated Vacuum Total Mainchain Sidechains N H C O

All-atom 3.6±1.7 14.0±1.4 287.8±8.3 105.2±5.0 182.5±7.3 20.9±2.9 69.1±3.7 84.5±4.6 All-atom-2 0.9±1.0 10.4±1.1 300.1±8.9 119.6±5.1 180.5±7.4 9.3±1.6 95.2±1.3 97.4±4.9 mCD 1.6±1.0 7.7±1.5 330.2±9.5 197.0±6.0 133.2±7.1 23.8±3.9 158.2±4.2 90.0±5.0 mCDa 0.6±0.8 5.7±1.7 333.2±11.4 175.1±7.8 157.9±6.8 23.2±3.8 138.7±5.9 101.6±4.8 mCDh 2.0±1.2 4.7±1.4 300.4±9.3 176.2±6.7 124.2±7.2 20.8±3.7 140.1±6.0 89.6±5.0 mPASA 2.3±1.4 3.2±1.4 116.3±8.2 21.7±4.1 94.6±6.7 6.5±2.6 6.2±2.3 42.2±4.8 mCD(277K) 1.2±0.9 1.0±0.9 328.4±9.2 188.3±5.3 140.1±7.4 24.1±3.6 148.6±3.6 104.8±6.3 mCD(250K) 0.6±0.7 5.5±1.2 308.5±8.5 161.7±8.1 146.8±7.2 18.0±3.3 128.4±6.0 101.6±4.9 mCD(150K) 3.1±0.4 3.2±0.7 264.2±5.4 118.0±2.3 146.2±4.8 9.3±1.6 95.2±1.3 81.1±2.8

time(Fig.7).Oneclearlydistinguishesadrasticdecreaseinthe

475

RMSFvalues associatedwiththeatomsoftheend segmentsof

476

thepeptideUIM-1,i.e., aroundatoms1–100and 300–394.This

477

decreaseinmobilityiscorrelatedtoahigheraveragenumberof

H-478

bondsoccurringbetweenthetwopartnersofthesystem,14.0±1.4,

479

aboutfourtimesthenumberofH-bondsinwater,i.e.,3.6±1.7,as

480

reportedinTable3.H-bondsaredeterminedbasedoncut-off

val-481

uesof30◦ and0.35nmfortheangleHydrogen–Donor–Acceptor

482

andthedistanceDonor–Acceptor,respectively.Inwater,verylow

483

numbersofH-bondscanbeobservedbetweenthetwopartners.

484

Forinstance,thesolvatedcomplexletsappearonlytwoH-bonds

485

att=20ns,which areformedbyN H(Gly47)···OG(Ser270)and

486

NE2-HE2(His+68)···OE2(Glu−273)atoms.ThesetwoH-bondsare

487

characterizedbyapercentageofoccurrenceabove80%duringthe

488

simulationtimeandarethusthemostpersistentonesas

empha-489

sizedinSI8wheretheoccupancyoftheH-bondsformedbetween

490

thetwoproteinpartnersisreported.H-bondoccupancyalongMD

491

trajectorieswascalculatedusingVMD1.9.1[45]withthreshold

dis-492

tanceandanglevaluesof3.5 ˚Aand30◦,respectively.Contrarily,

493

invacuum,upto15 H-bondsappear att=20ns(Fig.5), which

494

mostlyinvolvetheendsegmentsofUIMwithGlu−residuesthat

495

foldtowardstheArg+residuesofUbiquitin.Invacuum,alarger

496

numberofH-bondsappearasasubstitutetotheprotein-solvent

497

H-bondnetworkobservedinthesolvatedstate.

498

ProteinhydrationcanbestudiedthroughtheanalysisofRadial

499

DistributionFunctions(RDF)asplottedinFig.8.Asexplainedinthe

500

paperbyVirtanenetal.[46],aﬁrsthydrationshelloccursbetween

501

0.1and0.2nmfromtheproteinatoms,andisfollowedbya

sec-502

ondsharplymarkedshelljustbelow0.3nm(Fig.3of[46]).Inthe

503

presentwork,RDFbetweenoxygenatomsofwaterandtheprotein

504 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RDF (O w -p ro te in) r (nm) All-atom All-atom-2 Uncharged protein atoms mCD

mCDa mCDh

mPASA

Fig.8.RDFofwateroxygen–proteinatompairsofthesolvatedsystemVps27UIM

-1–Ubiquitincalculatedfromthelast10nsoftheAmber99SB-basedMDtrajectories at300K,asobtainedusingtheAll-atom,All-atom-2,mCD,mCDa,mCDh,mPASA,and neutralproteinatommodels.(Foraninterpretationofthereferencestocolourin

theartwork,thereaderisreferredtothewebversionofthearticle).

atomsshowaslightﬁrsthydrationshellatadistanceof0.192nm 505

withacontactdistanceof0.154nm.Thisshellinvolvesaverylim- 506

itednumberofwatermolecules;integrationundertheﬁrstpeak 507

oftheRDFfunctionleadstoavalueof84H2Omolecules.Asecond 508

shellappearsatabout0.280nm,adistancethatwasactuallyiden- 509

tiﬁedastheﬁrsthydrationshellofcrystallineproteinsbyChen 510

etal.[47].ThesecondshellidentiﬁedbyChenetal.,correspond- 511

ingtowaterinteractionswithproteinnon-polaratomsis,inour 512

simulatedproteinsystem,locatedat0.372nm. 513

BesidesadifferenceintheUIMshapebetweenthesolvatedand 514

vacuumstates(Fig.5),oneadditionallynoticesthatthegyration 515

radiusrGofUbiquitinisaffectedbytheenvironment.Indeed,mean 516

valuesof1.20±0.01and1.15±0.01nmareobtainedinwaterand 517

invacuum,asreportedinTable4whereinaverageswerecalcu- 518

latedoverthelast10nsof theﬁnal MDtrajectoriesasdriftsin 519

rGwerestillappearingduringtheﬁrst10ns.Theslightstructure 520

contractionobservedinvacuumisduetothelackofinteractions 521

withsurroundingwatermoleculesandcomeswithreducedatom 522

ﬂuctuations(Fig.7). 523

Regardingthesolventitself,acalculationofthemeansquare 524

displacement as a function of time, carried out for molecules 525

locatedwithin0.35nm, andbetween0.35 and 1.2nmfromthe 526

proteinstructure,showsthatallsetsofwatermoleculesbehave 527

asaBrownianﬂuidwithasimilarself-diffusioncoefﬁcientDof 528

(2.38±0.01)×10−5and(2.40±0.02)×10−5cm2_s−1_,_respectively 529

(Table4).TheveryslightdecreaseinDforwatermoleculesinter- 530

actingcloselywiththesolutedoesnotappeartobesigniﬁcant;all 531

Dvaluesstayclosetotheself-diffusioncoefﬁcientofwatercalcu- 532

latedwiththeTIP4P-Ewpotential,i.e.,(2.4±0.06)×10−5cm2_s−1 533

[38]. 534

4.3. mCDMDtrajectories 535

AsexplainedlaterwhendiscussingtheshapeoftheUbiquitin 536

partner,asecond20nsMDproductionstagewascarriedoutforthe 537

solvatedcomplexwhenusingthemCDmodel.Allresultsdiscussed 538

belowwereobtainedfromtheanalysisofthatadditionalrun. 539

Thestudyofthesecondarystructureofthecomplexinwaterand 540

invacuumdirectlyshowsanenhancedlossofthesecondarystruc- 541

tureelementsofthesystemversustheAll-atomsimulationresults 542

(Fig.4).Partofthe␤-strandsdisappearsandhelicesarethemotifs 543

thatarethemostperturbedduringthesimulations.However,in 544

vacuum,regularmotifs,especiallythehelixoftheUbiquitinstruc- 545

ture,appeartobeslightlymorepreserved.Indeed,inwater,the 546

electrostaticinteractionoftheproteinwiththesolventmolecules 547

isparticularlymodiﬁedasillustratedbythenumberofH-bonds 548

occurringbetweenthemainchainandthesidechainsofthesolute 549

andwater(Table3).Surprisingly,alargeraveragenumberofmain 550

chainH-bonds,197.0_±6.0versus105.2_±5.0,isobtainedformCD 551

despitetheabsenceofchargesonNandHatoms.Itappearstobe 552

(15)

Table4

MeangyrationradiusrGofUbiquitinandself-diffusioncoefﬁcientDofwatermoleculessolvatingtheVps27UIM-1–Ubiquitinsystemasobtainedfromtheanalysisofthe

last10nsoftheAmber99SB-basedMDtrajectoriesat300K.

rG(nm) D(×10−5cm2s−1)

Solvated Vacuum Within0.35nmof thesolute Between0.35and 1.20nmfromthe solute All-atom 1.20±0.01 1.15±0.01 2.38±0.01 2.40±0.02 All-atom-2 1.19±0.01 1.12±0.00 2.46±0.08 2.39±0.04 mCD 1.36±0.02 1.15±0.00 2.35±0.05 2.31±0.02 mCDa 1.30±0.01 1.12±0.00 2.20±0.02 2.33±0.02 mCDh 1.28±0.01 1.13±0.00 2.37±0.03 2.36±0.05 mPASA 1.17±0.01 1.14±0.01 2.46±0.08 2.47±0.05 mCD(277K) 1.25±0.01 1.13±0.00 1.21±0.01 1.26±0.04 mCD(250K) 1.20±0.01 1.12±0.00 0.38±0.00 0.43±0.00 mCD(150K) 1.20±0.00 1.12±0.00 ∼10−5 _∼10−5 versustheAll-atomcase,affectstheformationofsuchatypeof

inter-554

action.EvenintheabsenceofchargesontheNandHatomsofthe 555

AAmainchains,theaveragenumberofH-bondsisnotdrastically 556

modiﬁed,with23.8±3.9versus20.9±2.9bondsobservedforthe 557

mCDandAll-atommodels,respectively.Contrarily,thenumberof 558

H-bondsinvolvingthesidechainatomsisreducedtoanaverage 559

valueof133.2_±7.1versus182.5_±7.3formCDandAll-atom mod-560

els.TheconsequenceofthosechangesinthenumberofH-bonds 561

formedwiththesolventisillustratedinFig.8,whereitisclearly

562

seenthattheveryﬁrsthydrationshellisreducedtoaweak

shoul-563

derintheRDFcurvewithmodelmCD.Nevertheless,astudyofthe

564

distanceandanglevaluesadoptedbytheH-bondsshowsthatthe

565

distributionsformodelmCDaresimilartothosethatarevalidfor

566

theAll-atommodel,i.e.,centredaround0.27nmand10.5◦ (Fig.9

567

top).Itishowevernoticedthat,regardingintra-proteinH-bonds

568

(Fig.9bottom),ifthedistancedistributionisrathersimilartothe

569

all-atomone,thereisasigniﬁcantdisplacementofthemaximum

570

oftheangledistributiontowardshigheranglevalues,i.e.,about25◦ 571

versus15◦fortheAll-atommodel.Theselasttrendsareobservedfor 572

boththesolvatedandisolatedsystems. 573

Asvisualizedin Fig.5,both ends ofthe solvatedUIM-1get 574

separatedfromUbiquitinwhilethecentralhydrophobicsegment 575

(Ile263toLeu271)staysattheproximityofthetwostable␤-strands 576

ofUbiquitin,i.e.,segments39–44and67–70.Theconsequenceof 577

suchaconﬁgurationchangeisillustratedbythedistancemapsdis- 578

playedinFig.6whereacontactareainvolvingtheﬁrstresidues 579

ofUbiquitinfadesawayduetothelossofthetwoﬁrst␤-strand 580

elementsoccurringalongtheUbiquitinchain,i.e.,segments2–7 581

and12–16.Onthecontrary,␤-strands40–45and48–49,aswell 582

as strand 66–72 are strongly preserved but the H-bonds they 583

formarecharacterizedbyoccurrencepercentagevalueslowerthan 584

20%.Nevertheless,theloweraveragenumberofH-bondsformed 585

betweenthetwopartnersadoptasimilarbehaviouraswiththe 586

All-atommodel,inthesensethatitisverylimitedinwaterwhile 587

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 0.1 0.2 0.3 0.4 0.5 Dis tance dis tribuon funcon

Hydrogen -Acceptor distance (nm)

All-atom

Uncharged protein atoms mCD mCDa mCDh mPASA 0.00 0.01 0.02 0.03 0.04 0.0 10.0 20.0 30.0 40.0 50.0 Angle dis tribuon funcon

Donor -Hydrogen - Acceptor angle (°)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 0.1 0.2 0.3 0.4 0.5 Dis tance dis tribuon funcon

Hydrogen -Acceptor distance (nm)

0.00 0.01 0.02 0.03 0.04 0.0 10.0 20.0 30.0 40.0 50.0 Angle dis tribuon funcon

Donor -Hydrogen - Acceptor angle (°)

Fig.9.(Left)Distanceand(right)angledistributionfunctionsofthesolvatedsystemVps27UIM-1–Ubiquitincalculatedfromthelast10nsoftheAmber99SB-basedMD trajectoriesat300K,asobtainedusingtheAll-atom,mCD,mCDa,mCDh,mPASA,andneutralproteinatommodels.(Top)Protein-waterH-bonds,(bottom)intra-molecular H-bonds.(Foraninterpretationofthereferencestocolourinthe artwork,thereaderisreferredtothewebversionofthearticle).

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Table5

Totalandinter-proteinenergyvalues(kJmol−1₎_of_the_optimized_{conﬁgurations}_of_system_Vps27_{UIM-1–Ubiquitin}_in_vacuum_used_as_starting_points_for_{Amber99SB-based}

MDsimulations.Subscripts‘1’and‘2’standforVps27UIM-1andUbiquitin,respectively.‘14’denotesinteractionsbetweenatomsseparatedby3chemicalbonds.

All-atom mCD mCDa mCDh mPASA Stretching 334.9 287.4 153.2 193.6 150.9 Bending 619.8 593.2 741.0 557.1 663.5 Torsion 3780.0 3774.0 3845.5 3773.7 3777.6 Improper 43.2 45.1 55.5 47.5 23.9 LJ-14 1823.4 1824.8 1574.0 1785.6 1471.7 Cb-14 17,025.5 20,693.4 16,909.2 20,670.8 – LJ −1651.8 −1631.1 −2473.6 −1774.7 −2773.3 Cb −26,887.7 −28,909.8 −26,792.9 −32,096.4 −2687.9 Cb12 −996.9 −1038.2 −1239.5 −1285.7 −932.7 LJ12 13.1 15.8 −130.0 −3.6 −155.4

itincreasesinvacuum(Table3).Asanexample,thereareno

H-588

bondsoccurringatt=20nsin thesolvatedsystem(Fig.5).The

589

apparentseparationofVps27UIM-1fromUbiquitindoeshowever

590

notcomewithadrasticchangeofthenumberofH-bondsformed

591

betweentheUIMandthesolvent(Table3).Ontheaverage,there

592

isanincreaseofonly5.5H-bonds,from84.5±4.6to90.0±5.0.

593

Indeed,theexpectedlargerincreaseofthenumberofH-bondsdue

594

totheconﬁgurationchangeiscompensatedbythedecreaseinthe

595

possibilitytoformH-bondsduetothereducedpointchargemodel.

596

Energyvaluesobtainedwiththedifferentpointchargemodels

597

arehardlycomparableonetoeachother.Wethereforechoseto

598

considerenergyratiossuchas|E12|/(E1+E2)and|Cb12|/(Cb1+Cb2)

599

to evaluate the proportion of the protein–protein interaction

600

energyversusintra-molecularenergyvalues(Table2).In water,

601

thecorrespondingenergyratios,2.2and1.0%respectively,indicate

602

alowerrelativeimportanceofthemCDinter-molecularpotential

603

energyversustheAll-atommodel,i.e.,4.6and2.2%,respectively,

604

with, however, a similar ratio [E12/(E1+E2)]/[Cb12/(Cb1+Cb2)].

605

Similartrendsareobserved invacuum.Toallowmore detailed

606

comparisonsbetweenenergycontributionsfromthevariouspoint

607

charge models, a detailed decomposition of the total potential

608

energywas achievedfor theoptimized initialstructures ofthe

609

complexinvacuumtoavoidanysolventcontribution(Table5).

610

Allenergytermsoftheseconformationallyclose3Dstructuresare

611

ofthesameordersofmagnitude,butthebondenergy islower

612

versustheall-atomcontribution,287.4versus334.9kJmol−1,and

613

theCoulombterminvolvingatomsseparatedbythreebonds,

Cb-614

14,ishigheranddestabilizing,20,693.4versus17,025.5kJmol−1.

615

Similarly to the All-atom model, the RMSF function clearly

616

emphasizesthegreatermobilityoftheVps27UMI-1endsversus

617

Ubiquitininwater(Fig.7).Ubiquitinitselfisalsoaffectedbythe

618

changeinthepointchargerepresentation.Thiscanbeshown,for

619

example,byananalysisofitsgyrationradiusrGwhich

progres-620

sivelyincreasesduringtheﬁrst20nsproductionstage.Asalready

621

mentioned,anadditional20nssimulationwasperformedand

con-622

ﬁrmeda highervalueof thegyrationradiusrG forUbiquitin in

623

waterthaninvacuum,with1.36±0.02and1.15nm,respectively

624

(Table4).Asactuallyseenfurtherinthepaper,allrGvaluesobtained

625

inwaterarehigherthanthoseinvacuum,regardlessofthepoint

626

chargemodelused.ModelmCDleadstoanincreaseofrGbyabout

627

12%(from1.20to1.36nm),whilethechangeinvacuumis

imper-628

ceptible(1.15nmin bothcases)even ifthesecondary structure

629

elementsareaffected.Itindicatesthatthesolventmayserveasan

630

intermediateinthemodiﬁcationoftheproteinstructure.

631

Havingobservedthatthestructuralstabilityofthesystemis

632

modiﬁedwithmodelmCDversustheAll-atomrepresentation,

addi-633

tionalMDsimulationswereachievedatthreelowertemperatures,

634

i.e.,277, 250, and150K.The twolast temperaturevalues were

635

notselectedtoreﬂect aphysical stateforwater (theyare both

636

belowthefreezingpointofthesolvent)butwerechosentolocally

637

probethepotentialenergyhyper-surfaceofthesystem.The

anal-638

ysesofthe150Ktrajectoryclearlyshowstableproteinstructures,

639

as illustratedby the time evolution of the secondary structure 640

(Fig.10).Athighertemperaturevalues, a deconstructionofthe 641

secondarystructureelements,particularlythehelices,isobserved, 642

withaslowdownasthetemperaturedecreases.Simultaneously, 643

theRMSFoftheatomsofbothpartnersalsodecreasesand,at150K, 644

donotshowanymaximaatproteinends. 645

At the lowest temperatures, i.e., 250 and 150K, the time- 646

dependencyofrGforUbiquitinshowslittleﬂuctuationswithboth 647

anaveragevalueof1.20nm(Table4).Suchavalueisstrictlycom- 648

parabletothemeanAll-atomvalue,i.e.,1.20nm,obtainedat300K. 649

Contrarily,a contractionof Ubiquitin invacuum isobserved at 650

temperatureslowerthan300K.Indeed,meanvaluesof1.15and 651

1.12nmareobtainedat300and250K,respectively.Asthesec- 652

ondarystructureispreservedatlowtemperatures,oneassumes 653

thatthepotentialminimumoccurringattheall-atomlevelalso 654

existsforthemCDpointchargemodel.Thiscanalsobededuced 655

fromvacuumsimulationscarriedoutattemperaturesbelow300K. 656

Theanalysisofthesecondarystructureelementsinsuchconditions 657

showsaverystablestructure(Fig.10)withpreservedhelicesand␤- 658

strands,thatarehoweverslightlyshorterthaninthecorresponding 659

All-atomsimulation. 660

TheevolutionofthenumberofH-bondsformedbetweenVps27 661

UIM-1andUbiquitinisdescribedinTable3.Inwateraswellas 662

invacuum,thetrendisnotmonotonic,i.e.,thelowestnumberof 663

H-bonds,i.e.,0.6±0.7and1.0±0.9,isnotobservedatthelowest 664

temperaturebutat250and277K,respectively.Belowandbeyond 665

thosevalues,thenumbersincreaseextremelyfastinvacuumbut 666

smoothlyinwater.Itmightbedue,atlowertemperatures,toa 667

freezingofthestructurefavouringapersistenceoftheH-bonds 668

and,athighertemperatures,toanincreasedprobabilitytoform 669

polarcontactswithdiverseresiduesduetotheincreasedmobility 670

oftheatoms.OneclearlydistinguishesalossinpersistentH-bonds 671

when using modelmCD in water versusthecorresponding All- 672

atomcase. AllH-bondsarenow characterizedbyanoccurrence 673

degreebelow20%.Suchvaluesareincreasedonlywhenworking 674

invacuumand/orbyreducingthetemperature.Indeed,inwater 675

atT=150K,oneﬁndthreetypesofH-bonds,i.e.,Leu73···Glu−259, 676

Gly47···Ser270,His+68···Glu−273.Thetwolastareidenticaltothe 677

All-atomH-bonds(SI8). 678

Studying thebehaviour of model mCDat low temperatures 679

allows tore-evaluate the H-bondratioscalculated from values 680

reportedinTable3.LetusﬁrstconsiderthatthemCDsystematthe 681

lowtemperatureof150Kprobessimilarconformationsthanthe 682

All-atomsystem.TheproportionofmainchainH-bondsrepresents 683

44.7%ofthetotalnumberofH-bonds.Thatvaluestayshigherthan 684

thecorrespondingAll-atomone,i.e.,36.6%.Thus,oneconcludesthat 685

thechangeinthepointchargemodelindeedleadstoanincreaseof 686

themainchainH-bonds,regardlessofachangeintheconformation. 687

Aspeciﬁcstudyoftheintra-molecularH-bondsoccurringinsol- 688

vatedUbiquitinshows thatatemperaturedecrease tendstoan 689

increaseinthenumberofsuchH-bonds,goingfromaveragesof 690

(17)

Fig.10.SecondarystructureofthecomplexVps27UIM-1–Ubiquitinobservedduringthelast20nsmCDAmber99SB-basedMDtrajectoriesinwater(top)andinvacuum (bottom)atvarioustemperatures.Vps27UIM-1andUbiquitininvolvetheﬁrst24andlast76aminoacidresidues,respectively.Secondarystructureelementsare colour-codedasfollows:coil(white),␣-helix(blue),␲helix(purple),310helix(grey),␤-sheet(red),␤-bridge(black),bend(green),turn(yellow),chainseparation(lightgrey).(For

aninterpretationofthereferencestocolourinthe artwork,thereaderisreferredtothewebversionofthearticle).

and150K,respectively(Table6),i.e.,onecomescloserandcloserto

692

thevalueof48.0±3.2obtainedfortheAll-atommodel.Thetrend

693

isslightlydifferentforVps27UIM-1withaminimumnumberof

694

H-bonds,1.9±1.3,observedat277K.Asinterpretedearlierinthe

695

Table6

Averagenumbersofintra-molecularH-bondsoccurringinVps27UIM-1andin Ubiq-uitinasobtainedfromtheanalysisofthelast10nsoftheAmber99SB-basedMD trajectoriesat300K.

Vps27UIM-1 Ubiquitin

Solvated Vacuum Solvated Vacuum All-atom 16.2±2.8 28.4±2.1 48.0±3.2 81.8±3.7 All-atom-2 12.0±2.4 26.7±2.2 50.1±3.4 81.7±3.8 mCD 4.6±1.5 13.9±2.4 11.5±2.7 31.3±3.5 mCDa 2.5±1.3 13.7±2.2 14.3±3.3 42.6±3.7 mCDh 6.0±2.1 12.0±2.0 16.5±3.1 30.5±3.7 mPASA 3.8±2.0 5.3±1.7 14.5±3.6 19.7±3.3 mCD(277K) 1.9±1.3 13.0±2.3 16.0±2.8 34.9±3.7 mCD(250K) 5.6±1.6 11.8±2.2 23.3±3.1 41.5±3.6 mCD(150K) 11.5±1.4 14.2±1.9 32.9±2.7 39.4±3.2

paper,highernumbersofH-bondsobservedatlowertemperatures 696 mightbeduetoanincreasedpersistenceoftheH-bondswhile,at 697 highertemperatures,toanincreasedmobilityoftheatoms. 698 AstheproteinstructuresmodelledwithmCDreorganizeatroom 699 temperature,bothinwaterandinvacuum,oneconcludesthatthe 700 potentialhyper-surfacecorrespondingtothereducedpointcharge 701 modelis,atleastlocally,characterizedbylowerenergybarriers 702

thanwiththeall-atommodel[6]. 703

Inconclusion,themCDmodelallowstoobtainstableMDtra- 704

jectorieswithoutanyseparationofthecomplexpartners.Ithasa 705

contractingeffectinvacuumthatdoesnotoccurinwater,leading, 706

inthatlastcase,toamoremobilepeptidethanintheall-atomcase. 707

Theoverall3Dfoldingofthecomplexispreservedespeciallyforthe 708

largestandglobularpartner(thismaybepartlyduetothepresence 709

ofall-atomvdWcontributionstotheFF)whilethesecondarystruc- 710

tureissigniﬁcantlydismantledforthehelix-shapedVps27UIM-1 711

peptide.Thiseffectiscancelledatlowertemperatures,i.e.,atabout 712

250K,whichimpliesthatthechangeinthepointchargerepresen- 713

tationdoesnotaffectthelocationoftheenergyminimumonthe 714