CONTENTS2Contents1Coarse-graininganatomicstructure81.1Coarse-grainingo - PDF document

CONTENTS2Contents1Coarse-graininganatomicstructure81.1Coarse-grainingofaBARdomainmonomer............91.2Mappingthecoarse-grainedmonomerstructureontoadierentcopyofthemonomer.........................132ParameterizingSBCGforceeld162.1Non-bondedinteractionparameters.................162.2Obtaininginitialguessforbondedinteractionparametersfromall-atomsimulations..........................192.3Iterativerenementofbondedinteractionparameters.......213Buildingashape-basedcoarse-grainedmembrane273.1Generateapatchofcoarse-grainedmembrane...........283.2Addchargedlipidstothemembranepatch.............294Combiningproteinsandmembraneforasimulation305Runningacoarse-grainedsimulation325.1Preparingacongurationle.....................325.2Simulationoutputs..........................34 CONTENTS5RequiredProgramsThefollowingprogramsarerequiredforthistutorial:VMD:ThetutorialassumesthatyoualreadyhaveaworkingknowledgeofVMD,whichisavailableathttp://www.ks.uiuc.edu/Research/vmd/(forallplatforms).TheVMDtutorialisavailableathttp://www.ks.uiuc.edu/Training/Tutorials/vmd/tutorial-html/NAMD:InordertoperformsimulationswiththeCGmodelinthistu-torial,NAMDshouldbecorrectlyinstalledonyourcomputer.Forinstal-lationinstructions,pleaserefertotheNAMDUsers'Guide.TheNAMDtutorialisavailableinbothUnix/MacOSXandWindowsversions:http://www.ks.uiuc.edu/Training/Tutorials/namd/namd-tutorial-unix-html/http://www.ks.uiuc.edu/Training/Tutorials/namd/namd-tutorial-win-html/PlottingProgram:UnderUnix/MacOSX,onecanuseprogramxm-grace,availableathttp://plasma-gate.weizmann.ac.il/Grace/(Freedown-load),orgnuplot,http://www.gnuplot.info/(Freedownload).UnderWin-dows,onecanuseMicrosoftExcel,availableathttp://oce.microsoft.com/en-us/FX010858001033.aspx(Purchaserequired),orscilab,availableathttp://www.scilab.org/(Freedownload).Otherusefulgraphingprograms,withversionsavailableforbothUnix/MacOSXandWindows,areMathematica,http://www.wolfram.com/(Purchasere-quired)andMatlab,http://www.mathworks.com/(Purchaserequired).MostoftheexercisesinthetutorialareperformedusingShape-BasedCoarse-Graining(SBCG)ToolsinVMD.TheToolsareimplementedasasetofpluginsavailablewiththeirGraphicalUserInterfaces(GUIs)throughVMDmenu:Extensions!Modeling!CGBuilder CONTENTS6 Figure2:MainGraphicalUserInterfacefortheCGBuilderToolsinVMD.AvailableareseveraltoolsfortwoCGmodels,oneofwhichistheSBCGmodeladdressedinthistutorial. CONTENTS7GettingStartedIfyouareperformingthistutorialataComputationalBiophysicsWorkshopoeredbytheTheoreticalandComputationalBiophysicsGroup,acopyofthelesneededforthistutorialhavebeensetupforyou.Theycanbefoundinyourhomedirectory,underthepath/Workshop/sbcg-tutorial/files/.Unix/MacOSXUsers:InaTerminalwindowtype:cdpathtothedirectorysbcg-tutorial/files/&#x]TJ/;༧ ; .96; Tf;&#x 20.;ड ;� Td;&#x[000;Youcanlistthecontentofthisdirectorybyusingthecommandls.WindowsUsers:Navigatetothesbcg-tutorial!filesdirectoryusingWindowsExplorer.Ifyoudownloadedthetutorialfromthewebyouwillalsoneedtodownloadtheappropriateles,unzipthem,andplacetheminadirectoryofyourchoosing.Youshouldthennavigatetothatdirectoryinasimilarmannerasdescribeddirectlyabove.Thelesforthistutorialareavailableathttp://www.ks.uiuc.edu/Training/Tutorials/Inthegurebelow,youcanseethestructureofthedirectorycontaininglesforeachofthetutorialexercises. Figure3:DirectoryStructurefortutorialexercises.Sampleoutputforeachexerciseisprovidedinan\example-output"subdirectorywithineachfolder.Whenpossible,exemplaryoutputlesfromoneexerciseareusedasexemplaryinputlesforthenextexercise;theycanbefoundin\example-input"subdirectories. 1COARSE-GRAININGANATOMICSTRUCTURE81Coarse-graininganatomicstructureWewillworkwiththeamphiphysinBARdomaindimerfromDrosophila(Peteretal.,Science,303:495,2004).Itisahomodimer,i.e.,itconsistsoftwoidenticalmonomers.ItisnaturaltoemployexactlythesameSBCGmodelforeachmonomer,whichcanbedonebycoarse-grainingonemonomerrst,andthencopyingtheresultingSBCGmodelandaligningitwiththeorientationandpositionofthesecondmonomer.Inthissection,wewilllearnhowtouseSBCGVMDpluginsforbothsteps. Figure4:BARdomainhomodimer.Thetwomonomersareshowningreenandpurple.Theall-atomstructureisshownontheleft,andanexampleofaSBCGstructureisshownontheright.Bothall-atomandSBCGstructuresareshownfromthetopandfromtheside.MappinganSBCGstructurecreatedforoneproteinontoothercopiesofthatproteinisacommontaskincoarse-grainingoflargemacromolecularassemblies,whichoftencontainmultiplecopiesofoneprotein.Agoodexampleareviralcapsids,theproteinshellsenclosinggeneticmaterialofviruses.Mostknownviralcapsidsarehighlysymmetric(e.g.,icosahedral)structures,composedofmultiplecopiesofafewproteins(see,e.g.,Arkhipovetal.,Structure,14:1767,2006).Navigatetothedirectory1 build cg model/.YoucanexaminethewholedimerinVMD(lesdimer.pdbanddimer.psfin1 build cg model/).OnemonomerisdesignatedassegnameP1,andtheotherassegnameP2.YoucansaveeachmonomerfromVMDtoseparatePDBlesusingthewritepdbcom-mandforatomselectionssegnameP1orsegnameP2,andaPSFusingthewritepsfcommand(onePSFlewillworkforeithermonomer,sincetheyareidenticalexceptfortheatoms'positions).SuchPDBandPSFarealreadycreated:seemonomer.psf,monomer.pdbandmonomer-2.pdbinthedirectory1 build cg model/.Notethatbothdimer.psfandmonomer.psfcontainin- 1COARSE-GRAININGANATOMICSTRUCTURE10 Figure5:SBCGBuilderGUI. 1COARSE-GRAININGANATOMICSTRUCTURE11 LearningparametersintheSBCGBuilder.InSBCGmodels,CGbeadsaredistributedinspaceoccupiedbytheall-atomproteinusingaself-organizingneuralnetwork.Afewparameters,suchas\eps"and\Lambda"areusedbythenetworktogothroughiterationsofthelearningalgorithm(seeArkhipovetal.,Structure,14:1767,2006).TheSBCGBuilderwilladjustvaluesofthoseparametersautomaticallyforoptimalconvergence,dependingonthenumberofCGbeadsrequestedbytheuser,buttheusercanalsomodifythem,ifdesired.Thelearningalgorithmisstochastic,i.e.,eachtimeitisusedtocreateaCGmodelofthesameall-atomstructure,theresultwillbeslightlydierent.However,theoverallshapeoftheproteinismaintainedeachtime. 7.OnceCGbeadpositionsareassigned,thealgorithmconnectssomeofthembybonds.Bydefault,abondbetweentwobeadsisestablishedifthepartsoftheproteinrepresentedbyeachbeadaredirectlyconnectedbytheproteinbackbone(\DetermineBondsFromAllAtom").Toggletheotherswitchon,ProvideBondCutoff,andsetthecutovalueto18.Now,abondbetweentwobeadswillbeestablishedifthebeadsarewithin18Aofoneanother.Whichofthetwooptionstochoosedependsontheapplication.Choosingconnectivityaccordingtotheproteinbackboneismorerealistic,butfortheexercisewithBARdomainsthischoicedoesnotmattermuchfortheendresult.8.Changethe\CGResidueName"to\BAR",and\CGNamePrefix"to\A".NamesoftheCGbeadswillbe\A1",\A2",\A3",andsoon,upto\A25".9.Hitthe\BuildCoarseGrainModel"button.CompletionoftheSBCGalgorithmwilltakeafewmoments.10.Themainresultofrunningthealgorithmistheproductionofoutputlesthatarewrittenontheharddrive,namelytheSBCGtopology,parameter,andPDBles,andanall-atomreferencePDBle.Ifyouwanttohavespecicnamesforthoseles,theycanbechangedintheSBCGBuilderGUIbeforehitting\BuildCoarseGrainModel"button.TheoutputPDBlecontainingthenewlyconstructedSBCGmodelisautomaticallyloadedinVMDasanewmolecule,overlappedwiththeoriginalall-atommodel. 2PARAMETERIZINGSBCGFORCEFIELD17unlesstheyareboundtootherparticles;ijfortwocompletelyhydrophobicbeadsismax,whichshouldbetunedtorepresenthydrophobicaggregationrealistically.For150atomsperCGbead,anappropriatevalueisapproximatelymax=10kcal/mol.Theformulaandparametervaluesusedhere(suchasmax=10kcal/mol)werefoundtobeoptimalforcertainSBCGapplications(Arkhipovetal.,Bio-phys.J.,95:2806,2008).ForSBCGapplicationstosignicantlydierentsys-tems,onemayneedtomodifytheformulaorparameters,orboth,whichcanbedonebyeditingthepluginscriptsthataredeliveredtogetherwithVMD. Figure7:GUIforassigningparametersfornon-bonded(LJ)interactionsfortheSBCGmodel.AssigningtheseparametersiseasilydonewithanotherGUIintheVMDCGtools.1.StartVMDifyouhaveclosedit,andloadthereferenceall-atommonomerPDBaa ref monomer.pdb.2.StarttheSBCGLJGUIinVMD:Extensions!Modeling!CGBuilder!AssignLennard-JonesParamsForCGModelFromAll-Atom.3.Intheeld\OriginalCGParamFile",providethepathtotheCGpa-rameterle,cg monomer.par,thatwascreatedwhenyouranSBCGBuilder.Theeasiestwayistocopythisledirectlyinthefolderyouareworkingin,2 parameters/.Then,youcanjusttype\cg monomer.par"inthecorrespond-ingeldintheGUI(makesurethatVMD'sworkingdirectoryis2 parameters/-youcancheckitbyusingthecommand\pwd"intheVMD'sTkConsole,andifnecessarynavigatetotherightdirectoryusingcommand\cd").Otherwise, 2PARAMETERIZINGSBCGFORCEFIELD18providethefullpathintheGUI'seld.4.For\AllAtomStructure",choosethemoleculeaa ref monomer.pdb.5.\MaxenergyforLJwelldepth"istheaforementionedmax;setitto10kcal/mol.6.TheLJradiusijfortheinteractionbetweenbeadsiandjisobtainedinNAMDbydefaultasij=(i+j)=2,whereiandjareradiiassociatedwitheachatom.InSBCGmodel,eachiisobtainedasaradiusofgyrationofthegroupsofatomsrepresentedbytheCGbead,increasedbyaconstantvalue
,whichaccountsforthefactthateachatomhasaradius(typically,1-2A).ThisvalueischosenbytheuserintheGUIeld\AdditiontoLJradius".Set
=1A.7.ChoosetheOutputParameterfilename"tobecg monomer updated LJ.parandhitthe\AssignParameters"button.8.Compareentriesfornon-bondedinteractionsintheoriginallyproducedpa-rameterlecg monomer.parwiththoseinthenewle,cg monomer updated LJ.par.TheLJradiiiareverysimilarbetweenthetwoles,becausetheoriginalSBCGBuilderalgorithmusesalmostthesameprocedureaswejustemployedtoassignthesevalues(
=1Ainbothcases).However,LJenergiesincg monomer.pararesetuniformlyto4kcal/molbytheSBCGBuilder,andnowtheyarechangedsignicantlyintheupdatedle,accountingforthechoicemax=10kcal/molandforthespecicityofeachCGbead. AssigningLJParametersinthetextmode.Thesyntaxforthiscommandis�::cgtools::sasa LJ networkingstatusProcpar CGpdbrefIDf outELJRLJFortheexamplethatwehavejustconsidered,wewouldneedtorunthiscommandusingthefollowingvalues:�::cgtools::sasa LJ networking0cg monomer.par0cg monomer updated LJ.par10.01.0MakesurethatyouareusingthecorrectVMDmoleculeIDfortheall-atomreferencele! 2PARAMETERIZINGSBCGFORCEFIELD192.2Obtaininginitialguessforbondedinteractionparam-etersfromall-atomsimulations.ThetermsforbondedinteractionsintheSBCGmethodaredescribedbypo-tentialsVbond(r)=Kb(L�L0)2andVa()=Ka(�0)2forbondlengthLandangle,whereKb;L0;Ka,and0aretheforce-eldparameters.Theprocedureforextractingthevaluesfortheseparametersfromanall-atomsimulationisbasedontheconceptoftheso-calledBoltzmanninversion:foreachvariablex(suchasi-thbondlengthLi),oneobtainsthedistribution(x)fromtheall-atomsimulation,andusestheBoltzmannrelation(x)=0exp[�V(x)=kBT]toobtainV(x).Thisprocedurecanbeillustratedbythesimpleexampleofaone-dimensionalharmonicoscillator,withaparticlemovingalongthexcoor-dinateinthepotentialV(x)=f(x�x0)2(notethatthereisno1=2factor,accordingtotheCHARMMforce-eldnotation).Withthesysteminequilib-riumattemperatureT,theaveragepositionhxiisequaltox0,andtherootmeansquaredeviationofx(RMSD)isgivenbyhx2i�hxi2=kBT=(2f)(kBistheBoltzmannconstant).UsinganMDsimulation,onecancomputehxiandtheRMSD,thusobtainingx0andf;notethatinthiscaseitisnotnecessarytocomputecomplete(x).TheseformulasareusedintheSBCGmethodtoobtainaninitialguessforKb;L0;Ka,and0. Figure8:ExtractingbondsandanglesfortheCGmodelfromanall-atomsimulation.TheGUIisshownontheleft.AnexampleofanalyzingaCGbondisshownontheright.Listhedistancebetweenthecentersofmassofall-atomdomains(blueandred)thatcorrespondtothetwoCGbeadsbeinganalyzed(green).Theprocedureconsistsofcomputingpositionsofcentersofmassforeachall-atomdomainthatisrepresentedbyoneCGbead,ateachtimeframefromtheall-atomtrajectory.Then,foreachpairofbeadsthatformsabond,ortripleofbeadsthatformanangle,thedistanceLoranglebetweentherespectivecentersofmassiscomputedandaveragedoveralltimeframes;RMSDsarealsocalculated. 2PARAMETERIZINGSBCGFORCEFIELD224.WewillnowusetheSBCGBondsGUItoanalyzetheSBCGsimulationtrajectoryandobtainRMSDsofbondsandangles,justthesamewayaswedidbeforeforanall-atomtrajectory.TheSBCGBondsGUIrequiresareferencePDBle(seeabove),wherethebeta-valuesofatomsareassignedaccordingtothenumberofCGbeadthattheatomcorrespondsto.Here,thestructurewean-alyzeisthesameastheSBCGmodel.Thus,thebeta-valuesforeachCGbeadinthereferencePDBleshouldbethesameasthenumberofthatbead.Notethatthisnumberstartsfrom1,i.e.,itisosetbyonefromthebeadindexinVMD,whichstartsfrom0.YoucancopyyourCGPDBlecg monomer-psfgen.pdbtocreatethereferencePDB,cg monomer-beta.pdb;llthebetaeldsintheleusingatexteditor(seetheexampleinthefolderexample-input/).Alter-natively,youcanusethesimplescript,example-input/beta.tcl,todothisautomatically.5.EmploytheSBCGBondsGUIasyoudidbeforeforanall-atomsimulation.Usecg monomer-psfgen.psfandcg monomer-psfgen.pdbforCGPSFandPDBles.Forthetrajectorytoanalyze(\AADCDFile"),usetheCGtrajec-torythatyoujustobtainedfromthesimulation:iteration1/output/iteration1.dcd.Forthereferencele,typethenameofthejustcreatedCGreferencePDB,cg monomer-beta.pdb.SetSimulationTemperatureto310K.SetOutputParameterFilename,andlenamesforthebondandangledatales,toiteration1/from-iter1.par,iteration1/from-iter1-bonds.dat,anditeration1/from-iter1-angles.dat.HittheExtractParametersbutton.6.Theextractedparametersareinthefolderiteration1.Wecanignorethelefrom-iter1.par.Letuslookatthelesfrom-iter1-bonds.datandfrom-iter1-angles.dat,whichcontaincolumnsofdataobtainedfromtheCGsimulation,inthefollowingorder.Forthelefrom-iter1-bonds.dat:nameofbead1,nameofbead2,averagedistancebetweenthetwobeads,itsRMSD,andthebondspringconstantobtainedfromtheRMSDusingBoltzmanninver-sion(seeabove).Forthelefrom-iter1-angles.dat:nameofbead1,nameofbead2,nameofbead3,averageanglebetweenthethreebeads,itsRMSD,andtheanglespringconstantsimilarlyobtainedfromtheRMSD.7.Wecannowcomparethesedatawiththoseobtainedfromtheall-atomsimu-lationusingaplottingprogram(e.g.,compareiteration1/from-iter1-bonds.datwithfrom-aa-bonds.dat).Onecanseethataveragebondlengthsandangles,whichforCGsimulationaremainlydenedbyL0and0intheCGparameterle,areessentiallythesameintheall-atomandCGsimulations.Thus,theoriginalassignmentofL0and0isappropriate,andwedonotneedtotunethemfurther.8.WecanfurthercomparetheRMSDsofbondsandangles,whichdemonstratethestructure exibility.However,practicallyitismoreconvenienttocompareinverseRMSDs,which,inBoltzmanninversionprocedure,areproportionaltoKbandKa.Thus,wecancomparethelastcolumnsofthe*datlesforbonds 2PARAMETERIZINGSBCGFORCEFIELD23andanglesobtainedfromtheCGsimulationwiththosefromtheall-atomsimu-lation.Noteagainthedierence:whatwecompareisnottheparametervaluesusedinthetwosimulations,butstinessesofbondsandanglesobservedinthosesimulations. Figure9:Comparisonofbondandanglestrengths,KbandKa,obtainedusingBoltzmanninversionfromsimulationswithsuccessivelyscaledparameterleentries.SincetheBoltz-mannprocedureisused,thevaluesofKbandKaareinverselyproportionaltotheRMSDsofcorrespondingbondlengthsandangles,asobservedinsimulations.Thus,essentially,herewecomparestinessesofthestructureinsimulationswithdierentparameters.ComparingRMSDsdirectlyisnotasinformativeascomparingtheirinverses,orKbandKa.Left:bonds;right:angles.Blackcircles:fromall-atomsimulation.Redsquares:fromSBCG,iteration1.Greendiamonds:fromSBCG,iteration2.Bluetriangles:fromSBCG,iteration3.Theiter-ationnumberscorrespondtothelesprovidedinthefolder2 parameters/example-output/.9.YouwillseethattheproteinstructureismuchstierintheSBCGsimulationthanitwasintheall-atomsimulation(i.e.,bondandangleRMSDsaresmaller,or,inverseRMSDsarehigher).Thisisduetothestronginterconnectionbe-tweenbeadsintheSBCGmodel,whichmakesthedirectBoltzmanninversionprocedurenotquiteadequate,asmentionedabove.Toovercomethis,weneedtodecreaseKbandKainourparameterle.Onecanchangetheseparametersone-by-one,andrunmanyCGsimulationstondthesetofvaluesthatgivestherightstinessforeverybondandangle;thisis,however,verytedious,and,forsuchcoarsemodelasours,isprobablyunnecessary.Below,wefollowasimplerapproach,whereKbandKaarescaleduniformlyoverallbondsandangles,tomatchthestructurestinessroughly.10.ToscaleKbandKa,wewillusetheScalingGUIintheSBCGtoolset(en-titled\ScaleBond/AngleSpringConstants").NotethatthisGUIcanbeusedforanyCHARMM-styleparameterle,notnecessarilyforCGonly.Remem-ber,theparameterlewewanttoscaleistheoneweusedforthesimulationiniteration1,i.e.,thelefrom-aa.par.Donotmakeamistakeofscalingtheleiteration1/from-iter1.par;parametersinthislere ectthepropertiesoftheCGmodeliniteration1,whileweareinterestedinreproducingtheprop- 2PARAMETERIZINGSBCGFORCEFIELD24ertiesoftheall-atomsimulation. Figure10:GUIforscalingbondsandanglesinaparameterle.11.SettheInputParameterFileintheGUItofrom-aa.par.Setscalingcon-stants,forexample,to0.3forbothBondSpringConstantScalingandAngleSpringConstantScaling.12.TheproblemwiththedirectBoltzmanninversionisthatitusuallymakestheCGstructuretoosti,i.e.,bondandanglespringconstantsaretoolarge.However,wecanseethatforsomeofthespringconstantsthathaverelativelysmallvalues,theresultsoftheall-atomsimulationandoftheCGoneinitera-tion1agreequitewell.Itis,therefore,counterproductivetoscaleKbandKaforsuchweakbondsandangles,sincethatwouldmakethemmuchweakerthanwewant.Thus,wedonotwanttoapplyscalingtothebondsandanglesforwhichKbandKaarebelowcertainthreshold.ThiscanbeachievedbysettingthecutolevelforscalingintheGUI,forexample,settingtheBondSpringConstantCutoffto3.5kcal/(molA2)andAngleSpringConstantCutoffto170kcal/(molrad2).YoushouldchoosetheactualvaluesforscalingandcutosaccordingtotheagreementbetweenyourCGandall-atomsimulations.13.Makeanewfolder,iteration2,forthenewCGsimulation.Addthesamelesandsubfoldersintothisfolderasyoudidforiteration1.Theonlydierenceisthatwewillneedtoreplacetheparameterlefrom-aa.parinfolderiteration2/inputbytheonewithscaledKbandKa.IntheGUI,setOutputParameterFiletoiteration2/input/scaled1.par,andhittheScaleValuesbutton. 2PARAMETERIZINGSBCGFORCEFIELD25(YoumustagaincopytheLJparametersintothenewle.)14.WecannowrunthenewCGsimulationinthefolderiteration2.Afteritisdone,analyzetheCGtrajectoryusingtheSBCGBondsGUI,asinthestep5above(youcanreusetheSBCGreferencePDBlethatyoucreatedear-lier).Thisprocedurewillgiveyouthefollowinglesinthefolderiteration2:from-iter2.par,from-iter2-bonds.dat,andfrom-iter2-angles.dat.Plotthedatafromtheselesandcomparethemwiththedatafromtheall-atomsimulationandfromiteration1.Thebondandanglesstinessininteraction2shouldbeclosertothoseobservedintheall-atomsimulationthanthestinessfromiteration1.15.Thescalingstepsshouldberepeatedseveraltimes,possibly,separatelyforbondsandangles.Usually,forthenextiterationitisconvenienttoscalethevaluesfromthepreviousiteration,e.g.,scalevaluesfromthelefrom-aa.partoobtainscaled1.par,thenscalevaluesfromscaled1.partoobtainscaled2.par,andsoon.16.ThenalstinessofCGbondsandanglesdoesnothavetobeexactlythesameasthatfromtheall-atomsimulation.Iftheaveragedeviationis25%,thisalreadycanbeconsideredareasonableagreementforsuchacoarsemodel.Intheexample-output,weperformedthreeiterations.Initeration1,theoriginallefrom-aa.par,withparametersobtaineddirectlyfromtheall-atomsimulation,wasused.Foriteration2,thevaluesinfrom-aa.parwerescaledasdescribedinsteps11-12,toyieldscaled1.par.Foriteration3,theBondSpringConstantScalingwassetto1.0,BondSpringConstantCutoffto100.0kcal/(molA2),AngleSpringConstantScalingto0.7,andAngleSpringConstantCutoffto300kcal/(molrad2),i.e.,bondswerenotscaled.17.NowtheSBCGproteinstructureisestablishedandtheproteinforce-eldisfullyparameterized.WecanrunproductionSBCGsimulations!Notethat,dependingonthestinessofthebondsandanglesintheresultingmodel,thetimestepforsimulationscanbelargerorsmaller.Thetimestepof100fs,whichweusedduringtheparameterizationrun,canbepotentiallyincreased,resultinginfastersimulations. 2PARAMETERIZINGSBCGFORCEFIELD26 ScalingBondandAngleSpringConstantsinthetextmode.Toscalebondsandangles,runthefollowingcommandintheTkconsole:�::cgnetworking::scaleParameterConstantsstatusProcbondScaleFactorbondCutoffangleScaleFactorangleCutoffoutParFilenameFortheexampleofscalingconsideredabove,namely,thescalingafteriteration1,thisbecomes�::cgnetworking::scaleParameterConstantsputscg monomer.par0.33.50.3170.0scaled1.par 3BUILDINGASHAPE-BASEDCOARSE-GRAINEDMEMBRANE273Buildingashape-basedcoarse-grainedmem-braneAbuildingblockoftheSBCGlipidmodelconsistsoftwobeads-a\head"beadanda\tail"bead-connectedbyaharmonicbond.Thisisthesimplestrepresentationthatpreservestheelongatedshapeofareallipidmoleculeaswellastheseparationofhydrophobicandhydrophilicparts.Evenso,ifweweretorepresentasingleall-atomlipid,whichcontainslessthan150atoms,inthisway,theresultingbeadswouldbetoolighttoaccommodatethelongtimestepsdesiredinaSBCGsimulation.WethereforehavetoviewSBCGlipid\molecules"inamoreabstractsense,allowingthatoneSBCG\molecule"representsasmallpatchofall-atomlipids,ratherthanonerealall-atomlipidmolecule.Atthislevelofcoarse-graining,thedierencesbetweenlipidsofdierenttypes(e.g.POPEvs.POPCorDOPC)becomealmostnegligible.However,SBCGlipidscanbematchedtoall-atomsimulationsbyconsideringqualitiessuchasthebilayerthicknessandareaperlipid.Sincethelipidbilayerthicknessisapproximatedtobe50A,eachbeadthereforehasadiameterof12.5A.OneSBCGlipidoccupiesthenacross-sectionalareaofapproximately156A2.Inthistutorial,wewillbeworkingmainlywithDOPC,whichoccupies72.5A2perlipid.OneSBCGDOPClipidmustthenrepresentapproximately2.2all-atomDOPClipids.Themassofthe2.2lipidsisdividedequallyamongthe\head"andthe\tail"beads,meaningthatthe\head"beadactuallyrepresentsboththeheadgroupsofthelipidsandsomeportionofthetails,andthe\tail"beadrepresentstheremainderofthelipidtails.SinceoneDOPClipidcontains138atoms,2.2lipidscorrespondsto300atoms,or150atomsperSBCGbead,consistentwiththelevelofcoarsegrainingusedfortheBARdomainproteins.Inmanycircumstances,onewillwanttoincludechargedaswellasneutrallipids.WethereforewillalsodenenegativelychargedSBCGlipidstorepresentDOPStouseinamixedDOPC/DOPSmembrane.SinceDOPCisthemainlipid,andwehavealreadydeterminedthatoneSBCGlipidrepresents2.2all-atomlipids,thisconventioniskeptforDOPS.SinceDOPSisslightlyheavier,theextramassisaddedtotheDOPS\head"beadsothatthe\tail"beadsofthetwolipidscanremainidentical.TheDOPS\head"beadisgivenachargeof-2.2toaccountforthefactthatitincorporates2.2all-atomDOPSlipids.Allthesecharacteristicsarere ectedintheprovidedtopologyleforSBCGlipids,3 cg membrane/lipid-ion.top.ThebondparametersandnonbondedparametersfortheSBCGlipidswerechosentoconsistentlyreproducethebilayerthicknessandareaperlipidvaluesinall-atomsimulations,asdescribedindetailinArkhipovetal.,Biophys.J.,95:2806,2008.Sincewedonotrunsimulationsinthissection,aparameterleisnotnecessaryatthispoint.Wewillneedtheparameterlelater,whenwerunaCGsimulationofacombinedlipid-proteinsystem. 3BUILDINGASHAPE-BASEDCOARSE-GRAINEDMEMBRANE29andsplitchainsusingcurrentselections".InStep3,click\CreateChains"tocreatethepsfle.4.LoadtheresultingpdbandpsflesintoVMD.Youshouldseea379arrayofSBCGlipids.3.2Addchargedlipidstothemembranepatch.WewillnowcreateacombinedDOPC/DOPSmembranebychangingsomeoftheDOPClipidstoDOPS.Theprovidedscript3 cg membrane/mutate-to-dops.tclselects30%ofthelipidsatrandomandchangesthemtoDOPS.1.Tousethisscript,typethefollowingintotheTkConsole:�sourcemutate-to-dops.tcl2.Nowcreateapsfleeitherbyusingtheprovidedpsfgenscript3 cg membrane/build-mixture.tclbytyping�sourcebuild-mixture.tclorbyusingtheAutoPSFplugin.3.LoadtheresultingpdbandpsflesintoVMD-youshouldseethatabout30%ofthelipidsarenowDOPSlipids.Forexample,youcancolorlipidsbyresnametodistinguishbetweenDOPCandDOPS.YouwillneedthismixedDOPC/DOPSmembranepatchforthesimulationsinfollowingsections. 4COMBININGPROTEINSANDMEMBRANEFORASIMULATION314.Takealookatbuild.tcl.Thisscriptcontainsthefollowingsteps:(1)LoadthetwomonomersofaBARdomaindimer.(2)Movethemonomerstoappropriatelocations,toformalattice.(3)CallVMDpluginpsfgenandinputSBCGtopologylesforBARdomains,lipidsandions.(4)InputcoordinatesofthesixBARdomaindimers,lipidmembrane,andions.(5)Generatepsfandpdblesforthecombinedsystem.Moredetaileddescriptionsofthecommandsareincludedinbuild.tclascommentsbeginningwith\#".Youcanviewthecommandsandcommentsinbuild.tclusinganytexteditor,or,e.g.,usinglscommandintheVMDTkConsole.5.LoadtheoutputsystemintoVMDusingthefollowingcommandintheTkConsole:�molloadpsf6bar.psfpdb6bar.pdb Figure12:Combiningproteinsandmembraneforasimulation.Ionsarenotshownforclarity.6.Measurethecenteranddimensionofthesystembyfollowingcommands:�setsel[atomselecttopall]�measurecenter$sel�measureminmax$selRecordtheabovevaluesforuseinthenextsection. 5RUNNINGACOARSE-GRAINEDSIMULATION325Runningacoarse-grainedsimulationWearenowalmostreadytosimulatethesystemofSBCGBARdomainswithSBCGmembrane.InthissectionwewilldiscussrsthowtowriteaNAMDcongurationleforanSBCGsystem.Wewillthenperformthesimulation,anddiscusstheleoutputsandsimulationresult.Toperformexercises,navigatetothefolder5 simulation/.5.1Preparingacongurationle.SinceSBCGwasdesignedtobecompatiblewithNAMD,anSBCGcongura-tionlelookssimilartoanormal,all-atom,NAMDcongurationlethatyoumighthaveusedbefore.1.Asamplecongurationlesim.confhasbeenpreparedforyouinthedi-rectoryexample-output/.Copyittothefolderwhereyouwanttorunthesimulation,andopenitwithatexteditor.Remembertocreateinthesamefoldersubfolderoutputandinput,andaddyouCGlestothefolderinputanalogouslytohowitisdoneinexample-output/.NotethatyouwillneedhereanSBCGparameterleforlipids,whichwehavenotusedbefore.Forthispurpose,copytheleexample-output/input/lipid-ion.partoyourinputfolder.2.Thecongurationlecontainsmanyoptions(entriesintherstcolumn),followedbytheirparameters(entriesinthesecondcolumn)specicallycho-senforthesimulatedsystem.AssumingreadersalreadyhaveexperiencewithNAMDsimulations,herewewillonlygothroughthoseoptionsthatrequirespecialadjustmentsforanSBCGsystem.NewNAMDusersareencouragedtoconsulttheNAMDTutorialandNAMDUser'sGuide.3.Inthetexteditordisplayingthecontentofsim.conf,scrolldowntothesection#Force-FieldParameters.Notealllinesbeginningwith#arecom-mentsignoredbyNAMD.Under#Force-FieldParameters,youwillndsixsimulationoptionsthatmightneeddierentparametersthanthoseofanall-atomsimulation.Theseoptionsdenehowyouwanttheinteractionsbetweenbeadstobecomputed.SinceeachSBCGbeadrepresentsaclusterofatoms,parameterssuchascutoff,switchdist,andpairlistdistwouldtypicallyhavebiggervaluesthanthoseforanall-atomsimulation.ThevalueslistedherehavebeentestedtoworkwellfortheSBCGBARdomainsystem,andcanbeusedasstartingvaluesforotherSBCGsystems.Note,however,thecutoffparametershouldalwaysbebiggerthanthelongestbondlengthinyoursimulationsystem,otherwiseyoursimulationwillcrash. 5RUNNINGACOARSE-GRAINEDSIMULATION334.Scrolldowntothesection#IntegratorParameters.Theparametertimestephasavalueof100.0,implyingthattheintegrationtimestepofthesimulationis100fs/step.Atypicalall-atomsimulationuses1or2fs/step,hencetheSBCGgivesaspeedupof100fromthechoiceofinte-grationtimestepalone.Thechoiceofthetimestepdependsonhowfastbeadsaremovinginthesimulation,and,thus,themaximaltimesteppossible(sothatthesimulationdoesnotcrash)isdeterminedbythestrengthofinteractions,e.g.,stinessofbonds,asmentionedabove.Ifyoursimulationcrasheswithatimestepof100fs/step,startingthesimulationwithashortertimestepmightxtheproblem.Thentimestepcanbeincreasedwhenthesystembecomesstablelaterinthesimulation.5.InthecellBasisVector1,cellBasisVector2,cellBasisVector3,andcellOriginparameters,onespeciestheperiodicboundaryofthesystem.Comparethesevaluestothesystemsizeyouhavemeasuredintheprevioussection.YoushouldseethatonlycellBasisVector2matchesthey-dimensionofyoursystem,whilecellBasisVector1andcellBasisVector3arebothmuchlargerthanthex-andz-dimensionofthesystem.Thisisbecauseweonlywantthesystemtobecontinuousinthey-direction,whileintheothertwodirectionswewanttoallowthemembranetobendfreely.6.ConstanttemperatureismaintainedinthisSBCGsimulationusingLangevindynamics,asusuallydoneinall-atomsimulations.Youcantakealookattheseparametersunder#ConstantTemperatureControl.Inadditiontothetem-peraturecontrol,theLangevindynamicsprovidesmeanstosimulatethesolventeectimplicitly.Namely,theLangevindynamicsintroducesviscousdragandrandomforcesactingoneachCGbead,whichcanbeusedtomimictheviscosityofthesolventandtheBrownianmotionduetorandomhitsfromthemoleculesofthesolvent.Asingleparameter,langevinDamping,isusedtoaccountfortheseeects.Here,langevinDampingissetto2ps�1,asthisvaluewasfoundtoreproducetheviscosityofwaterforthecoarse-graininglevelused(150atomsperCGbead).7.Inthelastfewlinesofsim.conf,youcanseethatthesimulationisdesignedtobeminimizedby1000steps,andthentorunfor50,000,000steps.Thiscor-respondsto50,000,000steps100fs/step=5ssimulationtime.8.Closethetexteditordisplayingsim.conf.Runthesimulationbytypingnamd2sim.conf�sim.loginaterminalwindow. 5RUNNINGACOARSE-GRAINEDSIMULATION345.2Simulationoutputs.Onaone-processormachine,thissimulationwilltakeabouteightdaystocom-plete,butactuallywedonotneedtorunthefull5s.Thegeneraltrendisobviousalreadyafterabouttherst10ns,whichcanbeachievedwithinhalfanhourorso.Ifyoudonotwishtorunthesimulationyourself,youcanusethelesprovidedinexample-output/forthefollowingdiscussiononleoutputsandresults.1.Openthelogleofthesimulation,sim.log,withatexteditor.Ifyoudidnotrunthesimulation,useexample-output/sim.log.Thelogleofasimulationcontainsusefulinformation.Whenyoursimula-tioncrashes,checkingtheloglefortheerrormessageistherststepofxingtheproblem.Theloglecanalsogiveyouanestimateonhowlongasimulationwillrun.Findthewords\Benchmarktime"insim.log,hereyoucanndthespeedofthesimulation.Nowlet'sexaminethesystemviaVMD.2.Closethetexteditor.OpenVMD,andloadthepsfleofthesystem,6bar.psf.Ifyoudidnotrunthesimulation,makesureyouusetheprovidedexample-output/input/6bar.psf.3.Loadtheoutputdcdle,sim.dcd.Ifyoudidnotrunthesimulation,useexample-output/output/sim.dcd.Inthiscase,youwillhave150framesloadedinVMD,oneframeforeachnanosecondofthesimulation.UseVMDtotakealookatthesimulationresult.TheBARdomainsystemoriginallysitsona atmembrane,andafter150nsofsimulationtime,themem-braneiscurvedintoanarch.AsimpleSBCGsimulationusedheredemonstratesverywellhowBARdomainproteinsperformtheirjobofsculptingmembraneshape.FormoreinformationonBARdomain-inducedmembranecurvature,pleaseseeArkhipovetal.,Biophys.J.,95:2806,2008. Figure13:SimulationresultoftheBARdomainsystem.Left:beginningofthesimulation.Right:systemat150ns.4.InyourVMDsession,usetheVMDanimationtooltodisplaythelastframe,whichshouldshowahighlycurvedBARdomain/membranesystem.Openthe