TheMorphologyPredictionofLysozymeCrystalsDeducedfromtheBFDHLawandAttachmentEnergyModelBasedontheIntermolecularInteractionZhanzhongWang,PingpingJiangSchoolofAgricultureandBioengineeringTianjinUniversityTianjin300072,PeoplesRepublicofCLepingDangSchoolofChemicalEngineeringandTechnologyTianjinUniversityTianjin300072,PeoplesRepublicofCAbstractThecrystalmorphologyoforthorhombiclysozymeispredictedusingtheBravais-Friedel-Donnay-Harker(BFDH)andtheattachmentenergy(AE)modelsofmolecularsimulationsoftwareCerius2invacuo.Themorphologypredictedbytwomodelsisapproximatelyconsistent.ThemorphologypredictedbyAEmodelisingoodagreementwiththemorphologyofcrystalsgrownfromsolutionatpH6.5.Themaincrystalfaces011,101and110areobservedinmorphologypredictedbyAEmodel.BycleavingrevealablecrystalfacesinmorphologypredictedbyAEmodel,surfacechemistryvisualizationandtheoreticalanalysisbasedoninteractionofinintra-moleculesorinter-moleculesfortheimportantmorphologicalformsareperformed.TheresultshowsthatsterichindranceandH-bandinteractionplayscriticalrolefortheplate-likemorphologyoforthorhombiclysozyme.Keywords-lysozyme；morphologypredcition；modeling；IntermolecularInteractionINTRODUCTIONTheshapeofacrystalisgovernedbytherelativegrowthratesofeachofthecrystalfacespresent.Themostprominentfaceofacrystalistheslowestgrowing,whilethesmallestfaceisthefastestgrowing.Thus,themorphologicalimportanceofaparticularfaceisinverselyproportionaltothegrowthrateofcrystalface.Identificationofpossiblegrowthdirectionsorfacesisthefirstpartofmorphologyprediction1.EarlyworkincrystalmorphologypredictionwasundertakenbyGibbsin1875inwhichheproposedthattheshapeofacrystalwillbeonetominimizethetotalfreeenergyassociatedwiththesurfaceenergiesofthegrowncrystal.LaterBravais,Friedel,andDannayandHarker1,2proposedmorphologicalsimulationsbasedmerelyoncrystallatticegeometry.TheBFDHlaw,substantiatedbyempiricalobservation,proposedthatthecrystalwillbeformedbyfacesboundingthedirectionsofthegreatestinterplanarspacingofthecrystallattice.Accordingtothislaw,thelargertheinterplanardistancedhklis,thelargerthemorphologicalimportance(MI)ofthecorrespondinghklfaceis.Thus,basedonunitcellparameters,spacegroupandhence,extinctioncondition,andthereciprocaloftheinterplanardistances1/dhkl,usedasthedistancesfromthecentreofthecrystaltotherespectivehklsurfaces,onemayobtainatheoreticalBFDHmorphology.TheBFDHmethodestimatesthemorphologyfromthecrystalsymmetryandthelatticeparameterswithouttakingintoaccountthechemicalnatureandpackingoftheatomsormoleculesthatformthecrystalandneglectingthepossibilityofspecificenergeticinteractionsbetweenthesurfaceatomsinfluencingthecrystalmorphology.Itmaybeusedasaquickscreeningtooltoestimatethehabitofacrystal.In1955,HartmanandPerdokproposedperiodic-bondchain(PBC)theorytoaccountforenergyinteractionsbetweencrystallizingspeciesinthederivationofcrystalmorphology.LaterthistheorywasfurtherdevelopedbyHartmanandHartmanandBennema3.APBCisastrongbondbetweenmoleculesrunningparalleltoacrystallographicdirection.AcrystalismadeofanetworkofPBCshavingdifferentenergiesdependingonthebondenergybetweenthemoleculestheycontain.Consequently,itispossibletoclassifythePBCsasafunctionoftheirenergyanddistinguishstrongPBCsfromweakPBCs4.Growthrateisrelatedtodirectionofbondchainandthefastestdirectionofcrystalgrowthisthatofthestrongestchemicalbond.In1980,basedonPBCmodel,HartmanandPerdokproposedattachmentenergymodel.Buildonincorporatingenergytermsinthecalculationofthetheoreticalcrystalmorphology,advancesinmorphologypredictionwererealizedwhencrystalgrowthwasviewedastheattachmentofslicesorlayersoforderedmoleculestoanexistingcrystalface1.Thisconcept,knownastheattatchmentenergy(AE)method,requiresthedeterminationofthelatticeandsliceenergiesforcalculationoftheattachmentenergyineachimportantcrystallographicdirection.Thisattachmentenergydirectlyinfluencesthemacroscopicshapeofthecrystal4.Thelatticeenergyistheenergycalculatedbysummingpairinteractionsfortheentire,perfectcrystal.Theenergyreleasedontheformationofagrowthsliceofthickness,dhkl,isthesliceenergy,whiletheenergyreleasedontheattachmentofagrowthslicetothecrystalsurfaceistheattachmentenergy.Thetermofinterestformorphologicalpredictionsistheattachmentenergyofeachcrystalface.Subtractingthesliceenergyforeachfacefromthelatticeenergyprovidestheattachmentenergyforeachofthefaces.Therelativegrowthrateforeachfacewastakentobeproportionaltoattachmentenergyandhencefaceswiththelowestattachmentenergieswerepredictedtobetheslowestgrowingsurfacesandhencetohavethehighestmorphologicalimportance5.Thenamecrystallogenesisarosewhenitbecameevidentthatthefieldofcrystallizationofproteinsandotherbiologicalmacromoleculeswasnotrestrictedsimplytocrystalproductionfordiffractionstudies,butitencompassed,infact,allphasesofstructuralbiology,fromproteinexpressionandpurification,torecordingofdiffractiondata.Withregardto978-1-4244-4713-8/10/$25.002010IEEEbiologicalmacromolecule,X-raycrystallographyhasplayedafundamentalroleinconnectingthedotsbetweengenomicdataandbiologicalfunctionbyprovidingaccuratestructuralinformationtoresolveseveralsignificantresearchproblems.TheearliestX-raydiffractionstudiesofthestructuresofbiologicalmacromoleculesbeganintheearlypartofthe20thcentury,verylittleprogresshasbeenmadeinourunderstandingofhowtofacilitatetheprocessofcrystallizingsuchmacromoleculesforstructuralanalyses.Asaresult,obtaininghigh-qualitymacromolecularcrystalsremainsdifficult,unpredictable,andfrustratingandbecomespersistentbottlenecktothegreaterapplicationofX-raycrystallographyinstructuralbiology6,7.SolvingproteinstructuresbyX-raycrystallographyiscontingentupontheavailabilityofordered,diffraction-qualitycrystals8.Inthefieldofcrystalgrowth,inordertoobtainhigh-qualitylaboratory-growncrystals,theresearcherwhoisinterestedincrystalmorphologyoftenneedstovisualizeacrystalhabitresultingfromasetofobservedorcalculateddata,suchasgrowthrates,surfaceenergiesandhabitcontrollingfactors.Crystallizationiseffectedviamolecularrecognitionattheinterfacebetweenthegrowingcrystalanditsmotherphase.Sucheffectshavelongbeenobservedandhavebeenrelatedtogrowthsolutionthermodynamics,specificfacestructureandgrowthmechanism,andmolecularrecognitionprocessatspecificplanes9.Increasedunderstandingofcrystalgrowthfromsolutioncanenhancetheperformanceoftheseparationandpurificationprocessesinmanyindustries.Althoughthecrystalgrowthhabitdiffersfromthetheoreticalmorphologyduetotheinfluenceofcrystalgrowthenvironment,thecrystalmorphologyisverymuchconnectedwiththecrystalstructure.Crystalmorphologyhasbeenthefocusofnumerousresearchefforts10-12.Crystallizationofheneggwhitelysozymehasalreadybeenstudiedforsomeyearssinceitisanidealmodelsystemforcrystallizationofproteinsingeneral.Otherkindsoflysozymecrystalshaveseldombeenused,exceptforthetheorthorhombicform13.Themorphologyanalysisoftheorthorhombiclysozymecrystalsmayincreaseourknowledgeofcrystalgrowthoflysozymetoinstructtoobtainhigh-qualitycrystals,whichcanbeappliedstructuralanlysistoprovideaccurateinformationforgenomicdataandbiologicalfunction.Theaimofthepresentresearchiswastoapplyadvancedmolecularmodellingtechniquestosimulatethetheoreticalcrystalmorphologyoforthorhombiclysozyme,andcomparesthetheoreticalmorphologywithactualhabitoflysozymecrystalgrowninanaqueoussolution.Inthecourseofrefiningthemodel,valuableinformationconcerningmolecularinteractionswithinthelysozymecrystalwasextractedfromthesimulation.EXPERIMENTALANDCOMPUTATIONALMOLECULARMODELINGMETHODOLOGYMaterialsHenegg-whitelysozyme,recrystallizedandlyopholizedwaspurchasedfromSigmaandusedwithoutfurtherpurification.Itsmolecularweightwasassumedtobe14.3kgmol-1.Otherchemicalreagentswereanalyticalpurity.DistilleddeionizedwaterofHPLCgradewasused.Crystallizationexperimentandmicroscopymeasurement.Protein-waterstocksolutionswithproteinconcentrationof10-20%wereprepared,andtheirmeasuredpHwas6.5orslightlyhigher.Ifnecessary,pHwasloweredto6.5bysmalladditionsofHClaqueoussolutions.Supersaturatedsolutionswereobtainedbymixingprotein-waterstocksolutionswithconcentratedsalt-waterstocksolutions.Astocksolutionofsodiumacetatebuffercontaining0.02%sodiumazidewasalsoaddedtominimizepossiblepHchanges.Thesupersaturatedsolutionswerethenleftat4C(3-15daysdependingonsamplesupersaturation)toproducecrystals.Amicroscopicobservationofthecrystalmorphologywascarriedouttakingadvantageofelectronicmicroscopy.DigitalimagesanalysiswasperformedusingaPanasonicLumixDMC-FZ20systemoperatingthePanasonicimageanalysisconnectedtoa3CCDcolorvisioncameramountedonanOlympusBH2opticalmicroscope.Cerius2modelingCrystalstructuresdataoforthorhombiclysozymewasachievedbyProteinDataBanktocalculatetheoreticalmorphology.Experimentalmorphologywasusedtocomparewiththeresultofthesimulatedtheoreticalmorphology.CrystalMorphologyPredictionUsingBFDHandAEmodelClassicmolecularmechanicsanddynamicssimulationswerecarriedoutusingtheCerius2softwarepackage.Thecrystalbuilder,molecularmechanics,andmorphologypredictionmoduleswereemployedtoaccomplishthemodelinggoalsofthisresearch.Universalforcefieldwasused.RESULTSANDDISCUSSIONStructureanalysisThecrystalstructureoflysozymereportedincludedorthorhombic,monoclinic,tetragonalandtriclinicforms,whichhasbeenresolvedusingX-raydiffractionstudies.Inoursimulations,thecrystalstructureoftheorthorhombiclysozymewasobtainedfromtheProteinDataBank14.Thestere-structureoflysozymemoleculeisshowninFigure1.Theunitcellofitscrystalstructureareasfollows:a=30.47,b=59.39,c=68.78,=90,andspacegroupisP212121,whichisshowninFigure2.Figure1.Thestere-structureoflysozymemolecule:ballandstickstyle(left),stickstyle(right)Figure2.TheunitcelloforthorhombiclysozymeMorphologypredictionbyBFDHmodelStructureanalysisThethreefaces110,002,011,101dominatedthecrystalhabitasrevealedfromtheBFDHmorphologicalprediction.TheresultsaresummarizedinTable.AccordingtoBFDHlaw,thelargertheinterplanardistancedhklis,thelargerthemorphologicalimportance(MI)ofthecorrespondinghklfaceis.FromtheTable1,itcanbeseenthatdhklof011faceisthelargestanditsfacetareais63.49%oftotalfacetarea,whichmeans011faceownsthelargestthemorphologicalimportance(MI).Thedhklof101faceisslightlylargerthan110faceanddhklof002isthesmallest.CrystalmorphologypredictedbyBFDHmodelcanbededucedandwasshowninFigure3(a),revealingallfaceswhichbelongtothecrystallographiczones110,002,011,and101,respectively.FromFigure3(a),thereisawellagreementwithcalculationresultinTable1.The011facewasfoundtobethelargestinarea,subsequently101face,110faceand002face.TABLE.CALCUTIONRESULTSOFBFDHMODELhklMultiplicitydhklTotalfacetareaTotalfacetarea/%011444.9590.9763.49002234.399.0406.309101427.8626.8718.75110427.1116.4111.45MorphologypredictionbyAEmodelTheresultsofattachmentenergycalculationswerereportedinTable.Basedonattachmentenergymodel,theMIsequenceisbasedontheassumptionthatthegrowthratesoffacesareproportionaltoattachmentenergy.Hence,thegreaterattachmentenergy,thefasterthecorrespondingfacegrowsandthesmalleritsmorphologicalimportance.Oncetherelativegrowthratesofthesignificantfacesareknown,amacroscopicimageofthecrystalmorphologycanbepostulated.CrystalmorphologypredictedbyAEmodelcanbededucedandwasshowninFigure3(b).Themorphology(Figure3a)predictedbyBFDHmodelisapproximatelyconsistentwiththatpredictedAEmodel.Themaindifferencesexistindisappearanceof002faceinAEmodel.FromTableandFigure3(b),itcanbeseenthatthereisagoodcorrelationbetweengrowthfaceareaandtheattachmentenergyofthedominantface.Themorphologypredictedisplatelike,suggestingthatasinglefaceisindeeddominatingtheoverallcrystalgrowth.Inthesecases,themostdominantfacehasanattachmentenergywhoseabsolutevalueismuchlowerthanthatfortheotherfaces,andtherelativegrowthrateisnotablysmaller.Hence,onefacedominatesthecrystalgrowth.TABLE.CALCULATIONRESULTSOFAEMODELhklMultiplicitydhklEatt(total)TotalfacetareaTotalfacetarea%/(kcal/mol)/2/2011444.95-74.1116130076.80101427.8-148.74285020.40110427.11-167.758782.799(a)(b)Figure3.Predictedcrystalmorphology(a)BFDHmodel,(b)AEmodelComparisonofpredictedmorphologywithexperimentalgrowthcrystalThemorphologicalsimulationswereconfrontedwithexperimentaldataobtainedfromsolutiongrowncrystals.Thecrystalmorphologywasassessedbyopticalmicroscopy.MorphologicalsketchwasshowninFigure4.Figure4.ExperimentalcrystalmorphologyThepredictedmorphologybasedupontheAEmodelandBFDHmodelcomparesfavorablywiththeexperimentalmorphology.Themaindifferencebetweentheexperimentalmorphologyandpredictedmorphologyisthat002facedisappearsintheexperimentalmorphology,whichismoreconsistentwiththemorphologypredictedbyAEmodelthanbyBFDHmodel.Despitedifferencebetweenpredictedandexperimentalmorphology,itshouldberememberedthat,overall,thepredictedandsolutiongrownmorphologyarerathercomparable.Byfurtheranalyzingmorphologypredictedbytwomodelsandexperimentalmorphology,itcanbeseenthat011faceisthemostdominantinarea.Thiswasperhapsduetothefactthatthisfacehadsmallergrowthpromotinghydrogen-bondingcomponentinvolvedintheintermolecularinteractionsinvolvedinitsattachmentenergy,incontrasttothoseonthe110,002,101faces.SurfacechemistryvisualizationfortheimportantmorphologicalformsThesurfacechemistryofthethreemainsurfaceswasinvestigatedtoprovidebetterunderstandingtointeractionandrecognitionamonglysozyme:thethreefaces011,101,and110expecteddominatethecrystalhabitasrevealedfromtheAEmorphologicalprediction.(a)(011)(b)(101)(c)(110)Figure5.Cleavagestructureofmainexposurecrystalplane(a)011,(b)101,(c)110TheresultsaresummarizedinFigure5.The011surface(Figure5a)wasfoundtoberoughonthemolecularlevel.Incontrastto101crystalface,chemicalgrouprevealingisbigger,whichcanbringaboutagreatersterichindrancetoholdbackpackingoflysozymemoleculeinsolutionin011face.Asaresult,thegrowthrateof011crystalfaceiscomparativeslow,showinghighmorphologicalimportance.Examinationofthe101surface(Figure5b)revealsasmoothersurfacecomparedwith011faceonthemolecularlevel.Thechemicalgrouprevealingissmall,whichallowslysozymemoleculeeasilytopackin101surface,leadingto101surfacehaverapidgrowthrate.The110surface(Figure5c)wasfoundtobeveryopenandroughonthemolecularlevelrevealingadiagonalpatterndownthroughthesurfacewithalternatingorientationsofthelysozymemolecule.Thepatternproducedwasdiagonalinnaturewithhydrogenbondinganddonororacceptoratomswereactiveonthesurfaceforbindingoncomingmolecules.Inaddition,withthissurface,bothamino-groupandhydroxylcomponentsoflysozymemoleculewerefoundtoberevealabletopossiblebindingwithappropriatemolecules.Asaresult,thegrowthrateof110surfaceisthegreatest,showingthesmallestmorphologicalimportance.CONCLUSIONSThecrystalmorphologyoforthorhombiclysozymeispredictedusingAEmodelinconjunctionwithBFDHmodel.Accuratemodelingandmorphologypredictionofthiscrystalareachieved.Themorphologypredictedbytwomodelsisapproximatelyconsistent.ThemorphologypredictedbyAEmodelismoreconsistentwiththemorphologyofcrystalsgrownfromsolutionthanBFDHmodel.Themaincrystalfaces011,101and110areobservedanddominantinmorphologypredictedbyAEmodel.Bycleavingthesedominantcrystalfaces,surfacechemistryvisualizationandtheoreticalanalysisbasedoninteractioninintra-moleculesorinter-moleculesfortheimportantmorphologicalformsareperformed.TheresultindicatesthatsterichindranceeffectandH-bandinteractionplayscriticalrolefortheplate-likemorphologyoforthorhombiclysozyme,whichprovidesaimportantinstructioninmolecularlevelforpreparationofhigh-qualitylysozymecrystal.ACKNOWLEDGMENTThisworkwasfundedbytheNationalNaturalScienceFoundationofChina(No.20806053)，DoctoralFundofMinistryofEducationofChina(No.200800561029)andChinaPostdoctoralScienceFoundation(No.20080440677)REFERENCES1J.C.Givand,R.W.Rousseau,P.J.Ludovice,“CharacterizationofL-isoleucinecrystalmorphologyfrommolecularmodeling,”J.Crys