Principles of Protein X-Ray Crystallography Jan Drenth Principles of Protein X-Ray Crystallography ThirdEdition With Major Contribution from Jeroen Mesters University of Lu¨beck, Germany JanDrenth LaboratoryofBiophysicalChemistry UniversityofGroningen Nyenborgh4 9747AGGroningen TheNetherlands [email protected] Coverillustration:CourtesyofAdrianR.Ferre´-D’Amare´ andStephenK.Burley,TheRockefeller University.Thefour-(cid:2)-helixbundlemoietyoftranscriptionfactorMax.Reproducedwithpermission fromNature363:38–45(1993). LibraryofCongressControlNumber:2006926449 ISBN-10:0-387-33334-7 e-ISBN-10:0-387-33746-6 ISBN-13:978-0-387-33334-2 e-ISBN-13:978-0-387-33746-3 Printedonacid-freepaper. (cid:2)C 2007,1999,1994SpringerScience+BusinessMedia,LLC Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Use in connection with any form of information storage and retrieval, electronic adaptation, computer software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,evenifthey arenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare subjecttoproprietaryrights. 9 8 7 6 5 4 3 2 1 springer.com Preface to the Third Edition In the 7 years since the publication of the previous edition, protein X-ray crys- tallographyhasmaderapidprogress.Thiswas,toalargeextent,triggeredbythe sudden growth of interest in structural genomics. Impressive technological ad- vancesfacilitatedthisdevelopment.ItrequiredupdatingChapter2onSourcesand Detectors. Itisnolongeranexceptiontocollectafulldatasetinafewminutesandtosolve the structure in hours. However, one bottleneck remains and that is the growth ofqualitycrystals.Althoughacceleratedbyroboticsystems,itisstillatrial-and- errorprocess.Forthebenefitofthenoviceincrystallization,achapteron“Practical ProteinCrystallization”writtenbyDr.JeroenR.Mestershasbeenadded. Anotheradditionisasectiononsingle-wavelengthanomalousdiffraction.This technique has gained much popularity in recent years, especially in the high- throughputfield.AlsoSHELXD,adual-spacedirectmethodforsubstructurede- termination,equallyusefulasSnB,hasnowbeenaddedtoChapter11onDirect Methods. We are indebted to many colleagues who in some way or another assisted us in the preparation of this edition. Among them are Thomas Barends, Zbigniew Dauter, Rolf Hilgenfeld, Ankie Terwisscha van Scheltinga, Bram Schierbeek GeorgeSheldrick,andSimonTulloch.JanDrenthisespeciallygratefultoBauke Dijkstraforthegeneroushospitalityinhislaboratory. JeroenMesters JanDrenth v Preface to the Second Edition Since the publication of the previous edition in 1994, X-ray crystallography of proteins has advanced by improvements in existing techniques and by addition ofnewtechniques.Examplesare,forinstance,MAD,whichhasdevelopedinto an important method for phase determination. Least squares as a technique for refinementisgraduallybeingreplacedbytheformalismofmaximumlikelihood. Withseveralnewsections,thebookhasbeenupdated,andIhopeitwillbeaswell receivedasthepreviousedition. In the preparation of this second edition, I was greatly assisted by experts who commented on relevant subjects. I acknowledge the contributions of Jan Pieter Abrahams, Eleanor Dodson, Elspeth Garman, Eric de La Fortelle, Keith Moffat,GaribMurshudov,JorgeNavaza,RandyRead,WillemSchaafsma,George Sheldrick,JohanTurkenburg,GertVriend,CharlesWeeks,andmycolleaguesin theGroningenLaboratory. I am especially grateful to Bauke Dijkstra for the generous hospitality in his laboratory. JanDrenth vi Preface to the First Edition Macromoleculesaretheprincipalnonaqueouscomponentsoflivingcells.Among themacromolecules(proteins,nucleicacids,andcarbohydrates),proteinsarethe largestgroup.Enzymesarethemostdiverseclassofproteinsbecausenearlyev- erychemicalreactioninacellrequiresaspecificenzyme.Tounderstandcellular processes, knowledge of the three-dimensional structure of enzymes and other macromolecules is vital. Two techniques are widely used for the structural de- terminationofmacromoleculesatatomicresolution:X-raydiffractionofcrystals andnuclearmagneticresonance(NMR).WhileNMRdoesnotrequirecrystalsand providesmoredetailedinformationonthedynamicsofthemoleculeinquestion, itcanbeusedonlyforbiopolymerswithamolecularweightoflessthan30,000. X-raycrystallographycanbeappliedtocompoundswithmolecularweightuptoat least106.Formanyproteins,thedifferenceisdecisiveinfavorofX-raydiffraction. The pioneering work by Perutz and Kendrew on the structure of hemoglobin and myoglobin in the 1950s led to a slow but steady increase in the number of proteinswhosestructurewasdeterminedusingX-raydiffraction.Theintroduction of sophisticated computer hardware and software dramatically reduced the time required to determine a structure while increasing the accuracy of the results. In recent years, recombinant DNA technology has further stimulated interest in proteinstructuredetermination.Aproteinthatwasdifficulttoisolateinsufficient quantitiesfromitsnaturalsourcecanoftenbeproducedinarbitrarilylargeamounts usingexpressionofitsclonedgeneinamicroorganism.Also,aproteinmodifiedby site-directedmutagenesisofitsgenecanbecreatedforscientificinvestigationand industrial application. Here, X-ray diffraction plays a crucial role in guiding the molecularbiologisttothebestaminoacidpositionsformodification.Moreover,it isoftenimportanttolearnwhateffectachangeinaprotein’ssequencewillhave onitsthree-dimensionalstructure.Chemicalandpharmaceuticalcompanieshave vii viii PrefacetotheFirstEdition becomeveryactiveinthefieldofproteinstructuredeterminationbecauseoftheir interestinproteinanddrugdesign. ThisbookpresentstheprinciplesoftheX-raydiffractionmethod.AlthoughI willdiscussproteinX-raycrystallographyexclusively,thesametechniquescanin principlebeappliedtoothertypesofmacro-moleculesandmacromolecularcom- plexes.Thebookisintendedtoservebothasatextbookforthestudentlearning crystallography, and as a reference for the practicing scientist. It presupposes a familiaritywithmathematicsatthelevelofupperlevelundergraduatesinchem- istryandbiology,andisdesignedfortheresearcherincellandmolecularbiology, biochemistry,orbiophysicswhohasaneedtounderstandthebasisforcrystallo- graphicdeterminationofaproteinstructure. Iwouldliketothankthemanycolleagueswhohavereadthemanuscriptandhave given valuable comments, especially Aafje Vos, Shekhar and Sharmila Mande, BorisStrokopytov,andRistoLapatto. JanDrenth Contents Preface to the Third Edition v Preface to the Second Edition vi Preface to the First Edition vii Chapter 1 Crystallizing a Protein 1 1.1 Introduction 1 1.2 PrinciplesofProteinCrystallization 1 1.3 CrystallizationTechniques 4 1.4 CrystallizationofLysozyme 8 1.5 APreliminaryNoteonCrystals 9 1.6 PreparationforanX-rayDiffractionExperiment 11 1.7 Cryocooling 15 1.8 Notes 17 Summary 20 Chapter 2 X-ray Sources and Detectors 21 2.1 Introduction 21 2.2 X-raySources 21 2.3 Monochromators 30 2.4 IntroductiontoCamerasandDetectors 31 2.5 Detectors 33 2.6 TheRotation(Oscillation)Instrument 38 Summary 43 x Contents xi Chapter 3 Crystals 45 3.1 Introduction 45 3.2 Symmetry 49 3.3 PossibleSymmetryforProteinCrystals 56 3.4 CoordinateTriplets:GeneralandSpecialPositions 56 3.5 AsymmetricUnit 57 3.6 PointGroups 58 3.7 CrystalSystems 58 3.8 RadiationDamage 60 3.9 CharacterizationoftheCrystals 61 Summary 63 Chapter 4 Theory of X-ray Diffraction by a Crystal 64 4.1 Introduction 64 4.2 WavesandTheirAddition 65 4.3 ASystemofTwoElectrons 68 4.4 ScatteringbyanAtom 71 4.5 ScatteringbyaUnitCell 73 4.6 ScatteringbyaCrystal 74 4.7 DiffractionConditions 76 4.8 ReciprocalLatticeandEwaldConstruction 77 4.9 TheTemperatureFactor 81 4.10 CalculationoftheElectronDensity(cid:3)(x yz) 84 4.11 ComparisonofF(hkl)andF(h¯ k¯ l¯) 90 4.12 SymmetryintheDiffractionPattern 91 4.13 IntegralReflectionConditionsforCenteredLattices 95 4.14 IntensityDiffractedbyaCrystal 96 4.15 ScatteringbyaPlaneofAtoms 103 4.16 ChoiceofWavelength,SizeofUnitCell,andCorrection oftheDiffractedIntensity 105 Summary 107 Chapter 5 Average Reflection Intensity and Distribution of Structure Factor Data 109 5.1 Introduction 109 5.2 AverageIntensity;WilsonPlots 111 5.3 TheDistributionofStructureFactorsFandStructure FactorAmplitudes|F| 114 5.4 CrystalTwinning 116 Summary 118 Chapter 6 Special Forms of the Structure Factor 119 xii Contents 6.1 Introduction 119 6.2 TheUnitaryStructureFactor 119 6.3 TheNormalizedStructureFactor 120 Summary 122 Chapter 7 The Solution of the Phase Problem by the Isomorphous Replacement Method 123 7.1 Introduction 123 7.2 ThePattersonFunction 124 7.3 TheIsomorphousReplacementMethod 133 7.4 EffectofHeavyAtomsonX-rayIntensities 139 7.5 DeterminationoftheHeavyAtomParametersfrom CentrosymmetricProjections 142 7.6 ParametersofHeavyAtomsDerivedfromAcentric Reflections 144 7.7 TheDifferenceFourierSummation 146 7.8 AnomalousScattering 148 7.9 TheAnomalousPattersonSummation 152 7.10 OneCommonOriginforAllDerivatives 154 7.11 RefinementoftheHeavyAtomParametersUsing PreliminaryProteinPhaseAngles 157 7.12 ProteinPhaseAngles 160 7.13 TheRemainingErrorintheBestFourierMap 167 7.14 TheSingleIsomorphousReplacementMethod 170 Summary 171 Chapter 8 Phase Improvement 172 8.1 Introduction 172 8.2 TheOMITMapWithandWithoutSimWeighting 173 8.3 SolventFlattening 179 8.4 NoncrystallographicSymmetryandMolecularAveraging 185 8.5 HistogramMatching 187 8.6 wARP:WeightedAveragingofMultiple-RefinedDummy AtomicModels 190 8.7 FurtherConsiderationsConcerningDensityModification 192 Summary 193 Chapter 9 Anomalous Scattering in the Determination of the Protein Phase Angles and the Absolute Configuration 194 9.1 Introduction 194 9.2 ProteinPhaseAngleDeterminationwithAnomalousScattering 194 9.3 ImprovementofProteinPhaseAngleswith AnomalousScattering 196 9.4 TheDeterminationoftheAbsoluteConfiguration 198 9.5 Multiple-andSingle-WavelengthAnomalousDiffraction (MADandSAD) 199 Summary 209