SEDIMENTATION VELOCITY ANALYTICAL ULTRACENTRIFUGATION
Interacting Systems
Peter Schuck
National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, Maryland
Huaying Zhao
National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, Maryland
The Authors’ contribution to the Work was done as part of the Authors’ official duties as NIH employees and is a Work of the United States Government. Therefore, copyright may not be established in the United States. 17 U.S.C. § 105.
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Library
of Congress Cataloging-in-Publication Data
Names: Schuck, Peter (Peter W.), author. | Zhao, Huaying (Biophysicist), author.
Title: Sedimentation velocity analytical ultracentrifugation : interacting systems / Peter Schuck and Huaying Zhao.
Description: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2017] | Includes bibliographical references and index.
Identifiers: LCCN 2017016200| ISBN 9781138035287 (hardback ; alk. paper) | ISBN 1138035289 (hardback ; alk. paper) | ISBN 9781315268705 (e-book) | ISBN 1315268701 (e-book) | ISBN 9781351976831 (e-book) | ISBN 1351976834 (e-book) | ISBN 9781351976848 (e-book) | ISBN 1351976842 (e-book) | ISBN 9781351976824 (e-book) | ISBN 1351976826 (e-book)
Subjects: LCSH: Ultracentrifugation. | Macromolecules--Analysis. | Nanoparticles--Analysis. | Sedimentation analysis.
Classification: LCC QH324.9.C4 S385 2017 | DDC 572--dc23
LC record available at https://lccn.loc.gov/2017016200
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PeterSchuck
HuayingZhao
2.4.1.1Phasesand
3.1THETRANSPORTMETHODANDWEIGHTED-AVERAGESEDIMEN-
3.1.1Isothermsof
3.2.1BasicPrincipleofSolvingCoupledLammEquationsfor
3.4CONSTANTBATHTHEORYANDEXTENDEDEFFECTIVEPARTICLE
3.4.1ConstantBathApproximationofDiffusion
3.4.2ConcentrationGradientsandAverageDiffusionBasedon EffectiveParticleTheory
4.1DIFFUSION-DECONVOLUTEDDISTRIBUTIONS
4.1.1RelationshiptoAsymptoticBoundaries
4.1.2DiscriminationofInteractingComponents
4.1.3Quantifying s
4.1.4EmbeddingPriorKnowledge
4.2APPARENTSEDIMENTATIONCOEFFICIENTDISTRIBUTIONS
4.2.2TheIntegralSedimentationCoefficientDistribution
4.3MULTI-COMPONENTDISTRIBUTIONS
5.1PHENOMENOLOGYOFNONIDEALSEDIMENTATIONVELOCITYOF
5.2SEDIMENTATIONOFHETEROGENEOUSNONIDEALSYSTEMS
5.2.1PredictionsfromStatisticalFluidMechanics
5.2.2TheJohnston–OgstonEffect—StratificationofMultiComponentSolutionswithRepulsiveNonideality
5.3CHEMICALREACTIONSINNONIDEALSEDIMENTATIONVELOCITY
5.3.1StatisticalFluidMechanicsPictureofChemicalInteraction
5.3.2DiscreteChemicalReactionsNotInfluencedbyHydrodynamicInteractions
5.3.2.1NonidealLammEquationofInteractingSystems
5.3.2.2TheTransportMethodandtheWeightedAverage sw-Value
5.3.2.3SlowReactionsandthePopulationIsotherms
5.3.2.4FastReactions:EffectiveParticleTheoryand Gilbert–JenkinsTheory
6.1EXPERIMENTALDESIGN
6.1.1SampleConcentrations
6.1.2OpticalDetectionandSignalIncrementsfortheAnalysis
6.1.2.1AbsorbanceandInterferenceOpticalDetection
6.1.2.2FluorescenceDetection
6.1.3SamplePurity
6.1.4ExperimentalPlanningwithSimulationTools
6.1.4.1LammEquationModeling
6.1.4.2SpeciesPopulationsalongaTrajectory
6.1.4.3SelectingaTrajectoryintheTwo-Dimensionalor Three-DimensionalConcentrationSpace
6.2ASSESSINGWHETHERORNOTTHEREISBINDING
6.3CLASSIFYINGTHEKINETICS—SLOWORFAST?
6.4DETERMININGTHEASSOCIATIONSCHEMEANDSTOICHIOMETRY
6.4.1ApparentMolarMassEstimatesfrom c(s)or c(M )Peaks
6.4.2Interpretingthe s-valuesofComplexes
6.4.3DeterminingtheStoichiometryfromMulti-Component
6.4.4TheJobPlot
6.4.5TransitionPointoftheExcessFreeoroftheUndisturbed
6.4.6DeterminingtheAssociationModebyExplicitFittingwith DifferentLammEquationModels
6.5QUANTITATIVEANALYSISOFAFFINITY,LIFETIME,ANDTHEHYDRODYNAMICPROPERTIESOFCOMPLEXES
6.5.1Signal-WeightedAverageSedimentationCoefficients sw
6.5.1.1Determining
6.5.1.2AssemblingtheIsotherm
6.5.2GlobalAnalysiswithIsothermsofBoundaryFeatures
6.5.2.1GlobalAnalysis
6.5.2.2SpeciesPopulationIsothermsandAverageSedi-
6.5.2.3SedimentationCoefficientsandAmplitudesofRe-
Foreword
ItisapleasureandanhonortowritetheForewordtothethirdpartofthiscomprehensivetrilogybyPeterSchuckandco-authors.Withthecompletionofthisvolume theywillhaveassembled,broughtup-to-dateandgreatlyextendedtheclassictext onthistechniquethatwaspublishedbyHowardSchachmanin1959(1),andwill haveputtogetheraguidetotheimportantscience(andart)ofanalyticalultracentrifugationthatwillservethefieldanditspractitionersformanyyearstocome.
Schachman’sopusmightbeconsideredtorepresenttheculminationanddocumentationofthefirst‘goldenage’oftheultracentrifuge,inwhichtheapplications ofanalyticalultracentrifugationbecamewidespreadwithinthephysicalbiochemistrycommunity.Thatperiodbeganinthelate1940sandearly1950sandwas madepossiblebythecommercialdevelopmentofthefirststableandreliableinstrumentandaccessoriesforanalyticalultracentrifugation,intheformoftheSpinco ModelEAnalyticalUltracentrifugeanditsassociatedrotors,controlsandoptical systems.Theleadingpractitionersofthisfirstcycleofcommerciallysupported methodologyincludedSchachmanhimself,ofcourse,butalsoDavidWaugh,David Yphantis,GersonKegeles,KensalVanHolde,RobertBaldwin,VictorBloomfield andWilliamHarrington,amongothers.Alltheseworkersparticipatedinthedevelopmentofnewmethodstomakeanalyticalultracentrifugationmoreflexibleand adaptabletoawiderrangeofmacromolecularproblemsandsystems,andallalso appliedtheirmethodstothefirstwaveofquantitativecharacterizationofawide varietyofthemacromolecularsystemsthatunderliemodernmolecularbiology.1
Inthelate1970sand1980sanalyticalultracentrifugationbegantofalloutof style,basedinpartonthedevelopmentofotherbiophysicalmethodsfordeterminingthestructuresandinteractionsoftheproteinsandnucleicacidsthatcomprisethemolecularunderpinningsofbiologicalsystems,butalsobecauseSpinco stoppedmakingandservicingtheModelEanditscomponents.Duringthis‘dark’ periodthefieldwaskeptalivebyacadreofdedicatedultracentrifugepractioners,ledbyDavidYphantis,whoorganizedNSF-sponsoredworkshopsonanalytical ultracentrifugationattheUniversityofConnecticuttointroducenewpeopleto thefield,andkepttheinstrumentsgoingbysettingupandoperatinganinformal systemofpartsandmethodologicalknowledgeexchangetosupportthecontinued
1Theseultracentrifugeenthusiastswereahappy,interactiveandnon-competitivelot.Inabrief essaywrittenfortheFestschriftvolume(s)of BiophysicalChemistry honoringDavidYphantis,I sketchedasnapshotofDavidWaugh’slaboratoryasitexistedatMITinthe1950s(2).Asdescribed bySchachmaninanotherarticleintheYphantisFestschrift,theother‘ultracentrifugelaboratories’ ofthaterahadsimilarenvironments(3).
operationoftheworld’sagingstableofModelEs.Theseeffortswerealsofacilitated byanumberofformerSpincoservicerepresentatives,whosetuptheirownsmall servicecompaniesandflewfromlabtolabtohelpkeepmostoftheSpincomachines functional.
Despitethedifficultiesofthisdarkperiod,aloyalcadreofyoungerscientists, trainedbyYphantisandhisgenerationandledby—amongothers—PeterSchuck andtheotherauthorsofthepresentmethodologicaltrilogy,continuedtoappreciate theuniquepoweroftheultracentrifugeasabiophysicaltool,andinthe1990s BeckmanInstrumentsboughtSpincoandbegantoproducenew,simplerandmore user-friendlyanalyticalultracentrifuges,theBeckmanModelsXL,whicharewidely usedtodayandmadethecontinuationofthefieldpossible.
Whatisitabouttheanalyticalultracentrifugationtechniquethatmakesit suchauniqueandflexibletoolforbiophysicsandmolecularbiology?Clearlyit cannotcompetewithx-raycrystallographyandnuclearmagneticresonanceasa methodtosolvethedetailedatomiclevelstructuresofbiologicalmacromolecules. Butwhattheultracentrifugecould(andcan)dowastotakeadvantageofitscentrifugaldesigntoamplifytheforceofgravity,applythisforcetomoveandseparate macromoleculesandtheircomplexesinsolutionunderphysiologicalconditionsof temperature,macromolecularconcentrationsandsolventenvironment,andprovide ingeniousopticaltechniquestoobservethesemovementsinrealtime.
Theutilityofanalyticalultracentrifugationformacromolecularstudiesisdue, inpart,tothehappycoincidencethatthemolecularmassesofbiologicalmacromoleculesandtheircomplexes(rangingfrom104 to107 Daltons)andtheirbiologicalconcentrationswithincells(rangingfrom ∼10 8 to ∼10 5 moles/liter)are wellmatchedtothecentrifugalforcesthatcanbegeneratedinrotorsofaboutone footindiameterspinningatcontrolledratesrangingupto60,000rpm.Advances inrotordesignalsomadeitpossibletoachievetheseforceswithoutfatiguingthe metaloftherotorstothepointwheretheyexploded.Thussolutionboundaries betweenmacromolecularcomponentsandcomplexescouldbeestablishedinultracentrifugecellswithquartzwindows,andthemigrationof,andconcentration changesacross,theseboundariescouldbemonitoredinrealtimeusingcleverabsorbanceandinterferometric(andnowfluorescence)opticalsystems.Thismadeit possibletodeterminethesedimentationcoefficients(s)ofdefinedmolecularspecies, aswellastheirdiffusionconstants(D)astheboundariesspread,andthus—by applyinghydrodynamicinterpretations—determinetheirmolecularweightsand frictionalproperties(aswellastheirlevelsofhomogeneity)underconditionsthat couldbemaintainedclosetothoseof‘real’biologicalenvironments.
Ofcoursemeasuring s and D doesn’ttelloneeverythingonewantstoknow abouttheseparticlesandtheircomplexes,butitisastepintherightdirection. Buildingonthecleverapplicationofothermethodsinparallel,ultracentrifugationrevealsagreatdealaboutthesesystemsthatwecannoteasilylearninother ways.Themethodsbywhichthesephysicalparameterscanbedeterminedinthe analyticalultracentrifugearedescribedindetailbySchucketal.inPartIof thisseries(“BasicPrinciplesofAnalyticalUltracentrifugation”),andthe(relatively)straightforwardapplicationofthesemethodstosystemsof‘non-interacting’
macromoleculesisdescribedbySchuckinPartIIunderthesubtitle:“Discrete SpeciesandSize-DistributionsofMacromoleculesandParticles.”
Bydefinitionanon-interactingmacromolecule,asthetermisusedhere,means onethatdoesnotbindspecificallyornon-specificallytotheothermacromolecular componentspresent(atleastundertheconditionsoftheexperiment).However, thisusagedoesn’tmeanthatthesecomponentscanbeconsideredtobe‘unaware’ ofthepresenceoftheothermacromoleculesinsolution,northatthemeasured parametersarenotperturbedbythemeasurementtechnique,gentlethoughitappears.Thermodynamicissuesofexcludedvolume,macromolecularcrowdingand (forchargedsystems)Donnaneffectsmustbeconsidered.Inadditioninstrumentspecificproblems—includingconcentrationdependenciesduringsedimentation thatareinducedbythesectorshapeoftheultracentrifugecell,theeffectsofpressuredifferences[fromoneatmosphere(atm)atthetopofthecelltoupto ∼ 1000 atmsatthebottom]onmacromoleculesandcomplexes,andthepile-upofmacromoleculesatthebottomofthecellduringsedimentation,allperturbsedimentation velocitymeasurementsandanalysesoftheresultingdataandmustbetakeninto accountasdescribedinPartII.
Ofcoursethesituationgetsevenmorecomplicatedwhenweturntothe‘interactingsystemsofmacromolecules’thatarediscussedinthepresentvolume(Part III)oftheseries.Now,inadditiontoalltheproblemsofnon-interactingsystems describedinPartII,themacromoleculescananddobindspecificallyandnonspecificallytooneanotherwithvaryingaffinitiesbymeansofnon-covalentinteractions,andthepresenceorabsenceoftheseinteractionswilldependonthe concentrationsofthecomponentsinthesolution.Theseconcentrationswillchange acrosstheultracentrifugecellasafunctionofsedimentationtimeandpositionin thecellandalso,ofcourse,asafunctionoftheadditionofsmallmoleculebinding ligandsandperturbantsofvariousothersorts.
If,asdescribedinthisvolume,theinvestigatorhasdevelopedarobustmolecular modelofthespecificandnon-specificbindinginteractionsbetweenthecomponents ofthesolution,andhasknowledgeofthebindingparametersasafunctionof componentconcentrationsasthedifferentmacromolecularcomponentssediment intheultracentrifugecell,thenthemethodsthatSchuckandZhaopresenthere canbeappliedtopredict(atleastapproximately)thetime-dependentdistribution ofmacromoleculesintheultracentrifugecell.Thesemethodsarebasedinpart onnumericalsolutionsoftheLammequationsforthesystemasdefinedbythe interactionmodel,butalso—forrapidlyequilibratingsystems—involvetheuse of‘effectiveparticletheory’todevelopreasonableestimatesofatleastthemore robusthydrodynamicparametersonthebasisofdefinedsimplifyingassumptions.In additionacompleteanalysisfurtherrequires—throughadditionalLammequations —theinclusionofthe‘non-interacting’effects(excludedvolume,concentration changesduetosedimentationinthesector-shapedcell,etc.,asdescribedbySchuck inPartII)onthetime-dependenceofthesedimentationprocess.
Inprinciplesuchanalyseswillwork,anditisveryvaluabletohaveacompletetheoreticaldescriptionoftheinterplayofalltheseinteractionsforwell-defined systemsundergoingsedimentationvelocityintheultracentrifugecell.Inpractice,
however,onerarelyhassufficientbackgroundinformationaboutrealbiologicalsystems,andtoapplytheseapproachesoneneedstogathersignificantadditional informationaboutthesysteminadvance.Thisiswherethemolecularintuitionof theinvestigatorcomesintoplay,basedonhis/herpriorknowledgeofthesystem, becausejusttakinganuncharacterizedcellularextractandloadingitintoanultracentrifugecellandattemptingtoapplythesemodelingapproaches abinitio will obviouslynotyieldusefulresults.Nevertheless,ultracentrifugalanalysesofsuch complexsystemsonthebasisofthemethodologieslaidoutinthesemonographs bySchucketal. can besuccessfullyperformed,and will provideuswithinformationthatwouldbehardtoobtainanyotherway, if weknowsomethingaboutthe systemtostartwith.
Anexampleofasystemofinteractingmacromoleculesaboutwhichonecan obtainsignificantanduniquemolecularinformationbysedimentationvelocityapproaches—againifoneknowssomethingaboutthesystembeforestarting—isthe DNAreplicationcomplexofbacteriophageT4.(Ishouldemphasizethatwhilethis happenstobeasystemthatIamveryfamiliarwithbecauseourresearchgroup hasstudieditformanyyears,thesamepointscouldbeequallywell-illustratedwith theworkofmanyotherinvestigatorsonmanyothermacromolecularsystems.)
AsoriginallyshownbythelaboratoriesofBruceAlbertsandNancyNossal, theT4DNAreplicationsystemcompriseseightdiscretetypesofT4-codedprotein subunitsthatcanbeassembled invitro ontoamodelDNAreplicationforkto formafunctionalreplisomecomplexthatcanperformleadingandlagging-strand DNAsynthesisatratesandfidelitiescharacteristicofthe invivo system(4,5).The complete invitro systemcontainsanucleicacidframeworkontowhichassembletwo oppositely-directedpolymerases,apolymeraseclamp-clamploadersub-assembly thatcontrolsthestabilityofthepolymerasesduringreplication,andahelicaseprimasecomplexthatopenstheDNAaheadoftheleading-strandpolymeraseto exposethereplicationtemplatesandformRNAprimerstoinitiatethesynthesis of‘Okasaki’DNAfragmentsonthelaggingstrandtemplate.Thecomplexalso includesasingle-strandedDNAbindingproteinthatbindscooperativelytothe singlestrandDNAtemplatesthataretransientlyexposedbythehelicasecomplex andregulatestheinteractionsoftheothercomponentsofthesystem.
Detailscanbefoundelsewhere(6,7,8),butitisworthnotingthatthissystemprovidesawonderfulbiophysical‘playground’onwhichsedimentationvelocity analyseshavebeencrucialfortheestablishmentofmanyofthemoleculardetailsof thefunctioningsub-assembliesoftheoverallcomplex.Forexample,suchanalyses wereidealfordeterminingthesubunitstoichiometryofthevarioussub-assemblies oftheT4replicationsystem,includingshowingthattheT4replicationhelicase isahexamerofidenticalsubunitsheldtogetherinaring-shapedconfigurationby sixATPmoleculesthatliebetweenandholdtogetheradjacentsubunits;thatthis helicaseisfunctionallystabilizedbyasingleprimasesubunitthatbindstothe hexamerichelicaseringattheadvancingreplicationfork;andthatthefunctional helicaseisloadedontothereplicationforkwiththecooperationofasinglesubunit ofthehelicaseloaderprotein.SimilarapproachesalsoshowedthattheT4clamp
loadercomplexcontainsfivesubunitsoftwodifferenttypes,andthatthereplication clampitselfconsistsofthreesubunits.
Furthermore,becausesedimentationratesareslow,complexesthatassociate anddissociatewithtimeconstantsoflessthan10minutesorsocanbeconsideredtoremainatequilibriumwithco-sedimentingconstantconcentrations(after takingradialdilutionintoaccount)oftheconstituentproteinsofthecomplexduringasedimentationvelocityrun,whilecomplexesthatdissociatemoreslowlycan beconsideredtobestablespeciesontheultracentrifugetimescale.Itturnedout thatintheT4systemthis‘time-boundary’betweenrapidlyandslowlydissociatingsystemsfallsataconvenientpointtopermitustousetheseapproachesto establishappropriatesubunitassemblymixingprotocols,becausetheslowlydissociatingmetastableaggregatesthatresultedfromtheuseofincorrectorder-ofadditionpathwayscouldbeeasilydiscriminatedfrom“correct”assemblyreaction sequenceswithinwhichcomplexequilibriacouldbemaintained(8).Again,thisT4 DNAreplicationstoryisonlyoneexampleofhowtheuseofsedimentationvelocity approacheshashelpedscientistsallovertheworlduntangleandmorefullydescribe themolecularmechanismsofthecentralprocessesofbiology.
Insummary,theanalyticalultracentrifugecontinuestobeacrucialtoolforthe studyofinteractingmacromolecularsystems,andthematerialscontainedinthese threevolumeswilllongprovideaninvaluableguideforbiophysicallyorientedinvestigatorswhowishtoapplythisimportanttool,bothcorrectlyandimaginatively.
PeterH.vonHippel,UniversityofOregon
References
1. H.K.Schachman,“UltracentrifugationinBiochemistry”,AcademicPress,NewYork,1959.
2. P.H.vonHippel,GraduatestudentdaysatMIT,Biophys.Chem.,vol.108(1),pp.17-22, 2004.
3. H.K.Schachman,ThosewonderfulearlyyearswiththeModelEultracentrifugeandDavid Yphantis,Biophys.Chem.,vol.108(1),pp.9-16,2004.
4. N.NossalandB.M.Peterlin,DNAreplicationbybacteriophageT4proteins.TheT443, 32,44-62,and45proteinsarerequiredforstranddisplacementsynthesisatnicksinduplex DNA,J.Biol.Chem.,vol.254(13),pp.6032-6036,1979.
5. N.K.Sinha,C.F.MorrisandB.M.Alberts,Efficientinvitroreplicationofdouble-stranded DNAtemplatesbyapurifiedT4bacteriophagereplicationsystem.J.Biol.Chem.,vol. 255(9),pp.4290-4303,1980.
6. F.Dong,E.P.GogolandP.H.vonHippel,ThephageT4-codedDNAreplicationhelicase (gp41)formsahexameruponactivationbynucleosidetriphosphate,J.Biol.Chem.,vol. 270(13),pp.7462-7473,1995.
7. T.C.Jarvis,L.S.PaulandP.H.vonHippel,StructuralandenzymaticstudiesoftheT4 DNAreplicationsystem.I.Physicalcharacterizationofthepolymeraseaccessoryprotein complex,J.Biol.Chem.,vol.264(21),pp.12709-12716,1989.
8. D.Jose,S.W.WeitzelandP.H.vonHippel,Assemblyandsubunitstoichiometryofthe functionalhelicase-primase(primosome)complexofbacteriophageT4DNA,Proc.Natl. Acad.Scis.USA,vol.109(34),pp.13596-13601,2012.
Preface
Reversible,non-covalentinteractionsbetweenmacromoleculesorparticlesareimportantinawiderangeoffields,including,forexample,materialsciences,biotechnology,colloidalchemistry,immunology,structuralbiologyandcellbiology.Inparticular,thestudyofreversiblyinteractingsystemsofmacromoleculesisacrucial challengeinthegoaltoobtainphysicalunderstandingofbiologicalprocessesina cell.Interactionscanspanmanyordersofmagnitudeofstrengthandorientation. Volumeexclusionandhydrodynamicinteractionsareobligatoryrepulsiveinteractionsinthecrowdedcellularenvironment[3].Intheeyelens,forexample,these arebalancedbyweaklyattractiveinteractionpotentialsthathelptopreventaggregationofcrystallins[4,5].Weaktransientbindingeventsarealsoimportant, forexample,inthecontextofmulti-valentpatternrecognitionoftheimmunesystem[6–8].Slightlystronger,short-livedandcooperativeinteractionsareatplayin manycasesintheformationofadaptorproteincomplexesinsignaltransduction andotherdynamicmulti-proteincomplexes[9].Specifichigh-affinityinteractions oftenfacilitatetheassemblyofcellularstructures,andenablespecificrecognitionof sequencesintranscription[10,11].Finally,veryhigh-affinityandusuallylong-lived complexesareformed,forexample,inantibody-antigeninteractions[12].Theseare justafewexamplesfromamyriadofsuchinteractionsinthecell.Ubiquitousmotifs inthebiologicalcontextaremulti-siteandmulti-componentinteractions,cooperativity,andandfrequentlytheformationofstructurallypolymorphmulti-protein assemblies[9,13].Thestudyofsuchinteractionsposesaformidablechallenge.
Byobservingthemass-drivenseparationofmoleculesinacentrifugalfield,sedimentationvelocity(SV)analyticalultracentrifugation(AUC)isuniquelysuitedfor thestudyofreversibleinteractionsofpurifiedmacromoleculesinsolution,acrossthe entirespectrum,fromstronglyattractivetorepulsiveinteractions,withequilibrium dissociationconstantsrangingfromtheorderof10pM[14]to10mM[7],andwith thepotentialtocharacterizemacromoleculesorparticlesfrombelowkDa[15,16] intotheGDarange[17]inmolarmass.Animportantvirtueisthestronghydrodynamicresolutionwhichoftenallowsthesize-distributionofmacromoleculesand theircomplexestobedetected,and/ortheirdynamicco-sedimentationprocessto beobserved,suchthatthenumberofdifferentcomplexes,theirstoichiometry,and affinitymaybedetermined.Itisapplicabletoself-associationandmulti-component hetero-associationprocessesalike,andcangenerallybecarriedoutwithouttheintroductionofextrinsiclabels.ThismakesSV-AUConeofthemostpowerfultechniquestostudyreversiblemacromolecularassemblyprocessesinsolution.
ThishasbeenrecognizedearlyoninthedevelopmentofAUC,andafternearly acenturyofmethodologicalevolution,awealthofknowledgehasbeencreated
throughthecollectiveworkofseveralgenerationsofscientists.ExcellentmonographsonAUCandthesedimentationofinteractingsystemshavebeenpublishedbySvedbergandPedersen[18],Schachman[19],Fujita[20,21],Nichol[22], Cann[23],andWilliams[24],priortothehiatusofAUCinthe1970sand1980s. Therenaissanceofthetechniqueinthe1990shasbroughtdifferentinstrumentation, significantadvancesinstatisticalfluiddynamicsofsedimentation,newtheoretical modelsfordynamicallylinkedco-sedimentation,vastlymorecomputationalcapabilitiesbothinhardwareandinnumericalmethodsleadingtoverydifferentdata analysisstrategies,newmethodsforthepreparationofhigh-qualityproteinsamples,andahostofnewfieldsofapplications.Therefore,ourgoalwastoprovidea modernframeworkforAUCthatissolidlyrootedinthefoundationsbuiltbythe scientificgiantsearlierinthe20thcentury,butfromacurrentviewpointembedding thenewcapabilitiesandinterests.
Tothisend,thefirstvolumeofthisseries BasicPrinciplesofAnalyticalUltracentrifugation (referredtoasPartI)[1]comprehensivelydescribesthebasic physicsandthermodynamicprinciplesofsedimentation,instrumentationandopticaldetectors,theirsensitivity,calibrationandnoisecharacteristics,centrifugal runparameters,experimentaldesignprinciples,andoffersusefuldatatables.This providestheconceptualandexperimentalbasisforcarryingoutmeaningfulAUC experiments.Thesecondvolume SedimentationVelocityAnalyticalUltracentrifugation:DiscreteSpeciesandSize-DistributionsofMacromoleculesandParticles (referredtoasPartII)[2]providesthetheoreticalbackgroundandprinciplesfor mathematicaldataanalysis.Itrevolvesaroundthecentralproblemofunraveling sedimentationfromdiffusionandpolydispersitygivennoisysedimentationvelocity data.Thetransportmethodisintroduced,andone-andmulti-dimensionalormulticomponentsedimentationcoefficientdistributionsaredefined,withcriticalviewof theirinformationcontent.Afinalchapterdiscussestheirpracticalapplication.
Usingtheseessentialtools,inthepresentwork,wecantackleouroriginalgoal— studyingtherichphenomenologyofsedimentationofinteractingsystemsintheory andpractice.Inourviewthemostfascinatingaspectsarethemanyseemingly counter-intuitivefeaturesofsedimentationboundariesofrapidlyreversiblesystems, whichweattemptedtoelucidateinaphysicalmolecularperspective,presented alongsidethemathematicaltheory.Asecondaspectkeptinmindthroughoutisthe question,towhatextenttheoreticalresultscantranslateintoreliabledataanalysis, givennoisyexperimentaldata.
Theoutlineofthebookisthefollowing:In Chapter1 weestablishthemasterequationswithprototypicalexamplesofself-associatingandhetero-associating systems.Thisleadstotherecognitionthatblindlysolvingpartial-differentialequationsforthesedimentationprocesswithoutfurtherinsightintothecharacteristic phenomenologyisverylimited.In Chapter2,wetakeamoreempiricallookat thesedimentationpatternsandtheirmajordeterminants.Weshowthatthesedimentationbehaviorcanbeclassifiedaccordingtothechemicalequilibrationtimes relativetothesedimentationtime,andexaminethephysicalprinciplesunderlying dynamicallycoupledsedimentation.Thisisusedquantitativelyin Chapter3 to developinsightfulapproximatemodelsofthesedimentationprocessthatfocuson
differentaspectsofthesedimentationboundaries,includingtheiroveralltransport, theboundarypattern,boundarypolydispersity,anddiffusionalspread.Thisallows ustoestablishtheimportantlinktothetransportmethodand,in Chapter4,the connectiontothediffusion-deconvolutedsedimentationcoefficientdistributionsof non-interactingspeciesofPartII.Ifproperlyinterpreted,theseturnouttobea majortoolalsoforthestudyofinteractingsystems. Chapter5 isdevotedtohydrodynamicnonidealityinthestatisticalfluidmechanicspictureofsedimentation,and itspracticalimpactonthesedimentationprocessanddataanalysisofinteracting systems.Finally, Chapter6 combinesthepreviousconsiderationsinthesystematic discussionofstrategiesforexperimentaldesignandpracticaldataanalysis.
Asinthepreviousvolumes,tofacilitatethepracticalapplicationsoftheconceptsdiscussed,thebookissparinglyexpandedwithspeciallymarkedtextboxes cross-referencingfunctionsinthepublicdomainsoftware SEDFIT and SEDPHAT TheseprogramscanbedownloadedfromthewebsiteofourlaboratoryattheNationalInstituteofBiomedicalImagingandBioengineering.
Infact,theoriginalmotivationforasystematicpresentationarosefromour annualworkshopsondataanalysisforAUCandrelatedbiophysicaltechniquesat theNationalInstitutesofHealth.Goingbeyondthecoursematerial,weintendedto makethebookasself-consistentandcomprehensiveaspossible,withmanycitations totheoriginalliteratureforfurtherreading,suchthatitallowsagrowingnumber ofnewresearchersinterestedinAUCtobecomeacquaintedwithallaspectsofthis powerfulmethodology.Additionally,wehopeitwillalsoprovegenerallyusefulas referenceforexperiencedcolleaguesreadinguponspecificaspectsofsedimentation velocityanalyticalultracentrifugation,andasabasisforcontinuedexpansionof thistechnique.
Bethesda,March2017
ThisworkwassupportedbytheIntramuralResearchProgramoftheNationalInstituteofBiomedicalImagingandBioengineeringattheNationalInstitutesofHealth.
SYMBOLDESCRIPTION
A2 secondvirialcoefficient
a (r,t)radial-andtime-dependentsignal
aλ (r,t)radial-andtime-dependentsignalatwavelength λ
afast signalamplitudeofthereaction boundarydeterminedfromintegrationof c(s)
aslow signalamplitudeoftheundisturbedboundarydetermined fromintegrationof c(s)
apop,i({ck,tot})effectiveloadingsignalof species i asafunctionoftotalloadingconcentrationsofall components
β(t)time-dependentbaselinesignal offsetthatisradiallyconstant (‘RInoise’)
b bottomradius(distancefrom centerofrotationtothedistal endofthesolutioncolumn)
b(r)radial-dependentbaselinesignaloffsetthatistemporally constant(‘TInoise’)
c concentration
c0 loadingconcentrationattime t=0
cp plateauconcentration
cA ineffectiveparticlemodel,the concentrationofthesecondary component A co-sedimentingin thereactionboundary
cu theconcentrationofthesecondarycomponentsedimenting intheundisturbedboundary
...
c componentconcentrationat thephasetransitionintheeffectiveparticlemodel
c(s)sedimentationcoefficientdistribution
c(p)(s)sedimentationcoefficientdistributionwithBayesianprior
{ck,tot} setoftotalloadingconcentrations
χk(r,t)spatio-temporalevolutionof theconcentrationdistribution ofspecies k,inmolarunits
χk(r,t)totalconstituentconcentration ofcomponent k,inmolarprotomerunits
ˆ
χ(v,w)concentrationinvelocityinversetimecoordinatesof Gilbert–Jenkinstheory
χ1,ni Lammequationsolutionofan idealnon-interactingspeciesat 1signalunitloadingconcentration
χ1 monomerconcentrationinmolarunits
χw totalweightconcentration
χnd(r,t)evolutionofthesedimentation profileofaninitiallyuniform solutionofnon-diffusing,inert particles
δ(x)Diracdelta-function ∆ttimeinterval
δi,j Kroneckersymbol, δi,j =1if i = j,else δi,j =0
d opticalpathlength
dˆ c/dv differentialvelocitydistributioninrectangulargeometry
D translationaldiffusioncoefficient
D0 idealtranslationaldiffusioncoefficientinthelimitofinfinite dilution
Dk constituent(average)translationaldiffusioncoefficientof component k
D∗ B apparentdiffusioncoefficientof macromolecularcomponent B intheconstantbaththeory
di subscriptlabelingdimerparametersinself-association
εi,λ molarsignalincrementof species i atwavelength λ
∆εAB molarextinctioncoefficient changeincomplex AB dueto hypo-orhyperchromicity,or changesinfluorescencequantumyield
f translationalfrictioncoefficient
f 0 translationalfrictioncoefficient inthelimitofinfinitedilution
fc translationalfrictioncoefficient atfiniteconcentration
f0 translationalfrictioncoefficient oftheequivalentcompact, smoothspherewiththesame massanddensityastheparticle
f/f0, fr frictionalratio(inlongand shortnotation)
jsed sedimentationflux
jdiff diffusionflux
H(x)Heavisidestepfunction,equals 0for x< 0and1for x> 0
h heightofthesector
j flux
k enumerationofmacromolecularspeciesorcomponent
κ enumerationofmacromolecularcomplexes
kB Boltzmannconstant
K associationequilibriumconstant
K1,i associationequilibriumconstantformonomer-oligomerreaction
KD dissociationequilibriumconstant
K
∗ D effective‘dissociationequilibriumconstant’ K 1/(n 1) ormonomerconcentrationinmonomer-n-merself-association
koff chemicaloff-rateconstant
kon chemicalon-rateconstant
ks non-idealitycoefficientofsedimentation
ks averagenon-idealitycoefficient ofsedimentation
ks,ji mutualnon-idealitycoefficient ofsedimentationforspecies j and i
kD non-idealitycoefficientofdiffusion
λ wavelengthorgeneralizedsignal
l.h.s.left-handside(ofanequation)
ls-g∗(s)apparentsedimentationcoefficientdistributionofnondiffusingparticles g∗(s)determinedbyleast-squaresfitof databystepfunctions
m meniscusradius(distancefrom thecenterofrotationtothe proximalendofthesolution column)
M molarmass
M ∗ apparentmolarmass
Mb buoyantmolarmass
Ni totalnumberofspecies
Nk totalnumberofcomponents
Nκ totalnumberofcomplexes
mo subscriptlabelingmonomerparametersinself-association
ω rotorangularvelocity
φ effectivepartialspecificvolume Φvolumefractionofmacromoleculesorparticlesrelative tothetotalsolutionvolume
p(s)priordistributioninthe Bayesianregularizationofsedimentationcoefficientdistributions
qi chemicalreactionfluxof species i
ˆ q reactionfluxinvelocity/inverse timecoordinatesofGilbert–Jenkinstheory
ρ solventdensity
ρ0 standarddensity(ofwaterat 20◦Cinatmosphericpressure)
r radius(distancefromthecenterofrotation)
r secondmomentpositionofthe boundary
R gasconstant
RS Stokesradius
r.h.s. right-handside(ofanequation) rms rootmeansquare
rmsd rootmeansquaredeviation
s sedimentationcoefficient
s0 idealsedimentationcoefficient inthelimitofinfinitedilution
sk constituent(average)sedimentationcoefficientofcomponent k
s∗ B apparentsedimentationcoefficientofmacromolecularcomponent B intheconstantbath theory
sA...B reactionboundaryvelocityin effectiveparticletheory
sasy averagesedimentationcoefficientoftheasymptoticboundaryinGilbert–Jenkinstheory
sfast sedimentationcoefficientofthe reactionboundarydetermined fromintegrationof c(s)
sfast({ck,tot})isothermofthereaction boundary s-valueasafunction ofcomponentloadingconcentrations
Sk i stoichiometryofcomponent i incomplex(orspecies) k
SA...(B) stoichiometryofeffectiveparticlephase A...(B)
st w instantaneousweightedaveragesedimentationcoefficient
sw,λ({ck,tot})signalweighted-average sedimentationcoefficientasa functionoftotalloadingconcentrationsofallcomponents
s(EPT ) w sw forrapidlyreversiblysystemsbasedoneffectiveparticle theory
SSRsumofsquaredresiduals
σλ errorofdataacquisitionatsignal λ
sw signalweightedaveragesedimentationcoefficient
s20,w sedimentationcoefficientcorrectedtostandardconditionsof waterat20◦C
sxp experimentalsedimentationcoefficientuncorrectedforbuffer densityandviscosity
t time
τ lifetimeorfractionaltimeofa state
T absolutetemperature
v linearvelocityintheapproximationofrectangulargeometry withconstantforce
v partial-specificvolume
vxp partial-specificvolumeunder experimentalconditions
v0 partial-specificvolumeunder standardconditions
WSSRweightedsumofsquaredresiduals
w weightconcentration
x spatialcoordinateintheapproximationofrectangulargeometrywithconstantforce
ExactDescriptionofIdeally SedimentingAssociating Systems
IN thissection,wefocusonthedescriptionofsedimentationprocesseswherethe particlesofinterestexhibitinteractionsthatcanreversiblychangetheirassemblyorconformationalstate.Thisincludessolutionswithasinglemacromolecular componentexhibitingself-associationreactions,wherehomo-oligomersareformed thatcandynamicallydissociatebackintosubunits.Similarly,thisincludessystems withchemicalbindingreactionsbetweendifferentmacromolecularcomponentsthat leadtotheformationofhetero-oligomers,which,inturn,canspontaneouslybreak apartintotheircomponents.Atthesametime,solutionsareassumeddiluteenough forthelimitof‘idealsedimentation’tohold,suchthatrepulsiveinteractionsfrom volumeexclusionandhydrodynamicinteractionscanstillbeneglected.Thereductionofinteractionstosolelyreflecteitherassembledordissociatedstatesneglects intermediaterelativespatialandenergeticconfigurations,whichwillbeconsidered laterinconjunctionwithhydrodynamicinteractionsandmacromoleculardistance distributions(Chapter5).Theutilityofthe‘idealsedimentation’approximationis dictatedbythetime-scaleofsedimentation,aswellastheconcentrationrangeof theavailabledetectionsystems.
Practicalexamplesofsystemsexhibitingreversiblechemicalreactionsinthe ‘idealsedimentation’regimeincludemanyprotein-proteinandprotein-nucleic acidinteractions,assembliesofmulti-proteincomplexesandmolecularmachines, protein-smallmoleculeinteractions,interactionsinvolvingcarbohydrates,reactions betweencompoundsofsupra-molecularchemistry,andmostotherreactionswith dissociationequilibriumconstantsinthemicromolarrangeandbelow.
Wearecondensingparticlecharacteristicstothesamelimited,macroscopic setofparametersasinPartII(Section1.2)[2].Thus,thenatureofthemacromoleculesorparticleswillnotplayanyroleinthepresentworkotherthantheir (effective)mass,density,translationalfrictioncoefficient,andbindingproperties, whichtogetherdeterminetheirsedimentationbehavior.Formorebackgroundon
howthesedimentationparametersderive,forexample,thequestionofwhatcan beunderstoodastheeffectivesedimentingparticle,consideringthecontributions ofmacromolecule-solventandco-soluteinteractions,see Chapter2 ofPartI[1].All pointsdiscussedthereapplyequallytointeractingsystems.
Sedimentationvelocityoffersauniqueopportunitytostudyreversiblebinding reactionsfreeinsolutionduetoitsgeometricconfigurationwherecomplexescan behydrodynamicallyresolved,withhighsize-resolutiongeneratedbytheuniversal mass-baseddrivingforce,butwherethecomplexesarenotseparatedduringtheir migrationfromabathofslower-sedimentingunboundspeciesoftheconstituent components.1 Asaconsequence,anyreversiblyformedcomplexescanbekeptpopulatedandremaininanassociation/dissociationreactionreflectingkineticand equilibriumpropertiesoftheinteraction.Suchdynamicassociation/dissociation reactionscandrasticallychangethesedimentationbehaviorofthemacromolecular components.ThisallowsustouseSVtoelucidatetheassemblyscheme,measure theenergeticsofcomplexformation,learnaboutthelife-timeofcomplexes,and gaininformationonthehydrodynamicshapeoftransientlyformedcomplexes.
Throughoutthisdiscussion,wewillassumethereaderisfamiliarwiththeexperimentalaspectsofanalyticalultracentrifugationoutlinedinPartI[1],thebasic theoryofsedimentation,aswellasthetoolboxfortheanalysisofnon-interacting systemscomprehensivelydescribedinPartII[2].Thesewillprovidethefoundation forthestudyofinteractingsystems.Inparticular,theLammequation—master equationforsedimentationanddiffusion—willserveasthestartingpointforthe descriptionofthereaction/diffusion/sedimentationprocess.
1.1LAMMEQUATIONSOFINTERACTINGSYSTEMS
Webeginbyrecapitulatingthesedimentationanddiffusionofasuspensionofnoninteractingparticles,discussedinPartII,Section2.2.1[2].Thebalanceofsedimentationanddiffusionfluxesintheradialgeometryofcentrifugationleadstothe Lammequation
1Thisisincontrast,forexample,toconventionalchromatography,wheresamplesareinjected asamigratinglamella,suchthatcomplexesandunboundspecieswithdifferentvelocitiesmay separate,leadingtocomplexdissociation.
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times some 60 feet. A very hard wood when seasoned ↑
Aalii (Dodonaea viscosa) valued as a close hard-grained, dark wood. ↑
Known also as lehua ahihi, a variety of the Metrosideros polymorpha. ↑ Hawaii-nei, here in, or of Hawaii ↑
The various named mats here given show eighteen varieties, some of which refer to the material of which they are made, others their fine or coarse mesh or plait, others again plain or colored pattern. ↑
Contrary to the general claim that the pawehe mat was a product of Niihau only, it is here listed among those of Maui and Hawaii. It is a sedge mat of fine quality, worked mostly in colored patterns, though some are found plain. ↑
This designates a pandanus mat, simply, and may refer to the common coarse mesh mat, seeing that most of them are made from this same material ↑
This name, makalii, meaning small eye, indicates a fine-mesh mat, as makanui (large eye) indicates a large mesh, designated as two-fingers’ width Launui also belongs to this class, as it is described as of three-fingers’ width of mesh. ↑ a b c
Pueo is a coarse, thick mat of large size ↑
Puukaio is described as a mat of many layers ↑
Hiialo, end of mat; so called because the end of the mat is brought towards one’s front when the weaving is done ↑
Ne-ki is made of young bulrushes. ↑
Opuu takes this name from the pattern, so called for its rounding edges resembling flower buds. ↑
Kumulua, of two layers, and kumukolu, of three layers. ↑ a b
Alolua, as indicated by the name, is smooth on both sides ↑
Makoloa takes its name from the sedge of which it is made, its length and fine weave; those of Niihau being the finest of mat manufacture, some being plain and some in colored pattern. ↑
The puahala, or hinano mat is the famed product of Puna; from the flower of the pandanus. ↑
Aneenee, sometimes called apeu, and the palaueka, or palau, are small, portable mats, plain and patterned, for sitting on. The pakea is a round coarse mat for the same purpose. ↑
Koa (Acacia koa), a fine furniture wood, termed by some of late, Hawaiian mahogany. Besides the two kinds known as straight-grained and curly koa, there is a variety of harder grain named koaie, as also koalaunui ↑
While koa forests of all the islands furnished canoes, there were certain sections more favorable than
others, both as to size and quality of the tree and convenience of getting the partly-hewn canoe to the shore Hilo and Kona districts of Hawaii and Hana of Maui were such. ↑
An account is given of one Lulana, of Kipahulu, Maui, canoe-maker in chief to Keawenuiaumi, finding two koa trees in the Hilo forest from which he made two canoes, each twenty fathoms long and one and one-half fathoms deep; the largest ever seen. (Au Okoa, Dec 29, 1870 ) ↑
The kind known as ala, clingstone, the principal quarry of which was high up on the slope of Mauna Kea ↑
Other canoe-making countries use fire to facilitate this hollowing of the canoe, though no mention is made of a like method being observed here ↑
These, termed pepeiao (ears), are for the placement of seats. ↑
Hew with, not against the grain in all cases. ↑
Koi wili, a reversible adze, sometimes termed owili; to twist or turn over. ↑
Koi kupa was the gouge-like adze for internal work ↑
Wae is the affixed brace to stiffen and support the sides of the canoe ↑
Niao is the grooved edge of the inside or body of the canoe on which the rim is made to fit. ↑
Aiea (Nothocestrum breviflorum), a yellowish wood of light but tough grain ↑
Hawaiians produced an excellent lampblack from several plants, as shown, which, mixed with the gum (pilali, not hili) of the kukui, furnished a durable black paint. ↑
Akia (Wikstroemia foetida), a small shrub 2–4 feet high ↑
Wauke or waoke (Broussonetia papyrifera), the well-known paper mulberry ↑
Palaholo, not recognized by this name. ↑
Mamaki (Pipturus albidus), furnishing the coarse, heavy kapas. ↑
Kauwila (Alphitonia ponderosa), a hard, close-grained, heavy wood ↑
Kawau (Byronia Sandwicensis) the preferred kapa-log for its sounding qualities ↑
Ohia (Metrosideros polymorpha), one of the commonest of Hawaiian forest trees ↑
Mamane (Sophora chrysophylla), another hard, durable wood. ↑
The face of a kapa log or block is slightly convex, not perfectly flat. The under part is shorter and hollowed, and emits a resonant sound in use, the ends being placed on stones It is said that ownership of kapa blocks, kua kuku, were proved by their tone ↑
The clubs, or kapa beaters, were of round and of four-sided forms, the former with or without longitudinal grooves, the latter grooved or carved in various patterns. These were of the heaviest woods. ↑
Pa-u or skirt The same applied to kapa spreads. ↑
Paiula is said to be a kapa into which particles of red kapa are beaten with the new ↑
This furnishes an insight into the method of utilizing worn and waste material ↑
Pala-a, one of the commonest of Hawaiian ferns (Davallia tenuifolia), the leaves furnishing a red dye ↑
The kapala takes its name from daubing, to produce a black kapa, a funeral garb. ↑
Olena (Curcuma longa), furnishing a yellow dye. ↑
Pili grass (Heteropogon contortus). ↑
Kalamalo, a tufted grass (Eragrostis variabilis) ↑
Kukaelio, not identified under this name. ↑
Ti (Cordyline terminalis), whose leaves are of varied household use, and its roots, when cooked, eaten for its sweet qualities, or furnishing substance for the distillation of okolehao (rum) ↑
Opiko, or Kopiko of which there are two kinds, kea and ula, of the genus Straussia ↑
Olomea (Perrottetia Sandwicensis). ↑
Neneleau, a sumach (Rhus semialata). ↑
Akala (Rubus Hawaiiensis) ↑
Not identified under this name. Probably the hauhele (Hibiscus Arnottianus) ↑
Kowali or koali vine (Ipomea tuberculata). ↑
Hale kukuohi, a house set apart by itself, occupied by persons of high rank. ↑
Fasten, puki, the word used here, refers to tying the different woods of the house together only and not to any other thing. ↑
Kuaiole, lit , rat back ↑
Pi-a, a measure of one hand span distance, or space ↑
Kauhuhu, cover for the ridge-pole. ↑
Hale ohule, bald-headed house ↑
Ama’uma’u, the Sadleria tree-fern of Hawaii ↑
The trimming of the doorway was the final act indicating a finished house and was attended with religious ceremonies and offerings The accompanying feast may be termed the house warming. ↑
The word pilikia (cling to the post), so applicable for all sorts of trouble, is said to have had its origin from the necessity of sleeping with heads to the post (kia) as a safe-guard against night prowler’s thrusts through the thatching. ↑
Aho lolo, batten to hold down the thatch. ↑
Noni, not in general use for house timber, though the variety Morinada trimera grows some 20 feet high. The smaller tree was cultivated for its dyes, the root and wood yielding a yellow, and the bark a red color. ↑
Hale ili koa, koa-bark house. ↑
Ekaha fern (Acrostichum micradenium) ↑
Wailukini, lit., Russian water. From Hawaiian acquaintance with the Russian trade of the northwest in early days, musk was indelibly associated with them in name, the dry product being hua lukini, and the liquid perfume wailukini. ↑
Loulu, Hawaiian palm, of which there are two kinds, loulu lelo (Prichardia Gaudichaudii), and loulu hiwa (Prichardia martii). ↑
Lauhala, lit , hala leaf, though in general use the name is erroneously applied to any part of the pandanus tree. The body of the tree is puhala, by which name it is also known ↑
Lonomuku, known as Hinahanaiakamalama, the woman who leaped to the moon from Hana Her husband seized and tore off a leg in arresting her flight, hence muku, cut off, shortened. ↑
Hana-ua-lani-haahaa, lit , Hana of low heaven, from the supposition of the low clouds being reached from its hills from which the above attempt was said to have been made. ↑
Several parts of the islands lay claim to this tradition. Koolau, of Oahu, among others, held him in high esteem as a cultivator faithful in his offering to the gods, wherefore he was saved from death on being devoured by a shark, and cast ashore on Kauai ↑
The one king of Hawaii of this name was the half-brother of Umi, who overcame and slew Hakau in Waipio, and sacrificed him on the altar of the Pakaalana heiau. ↑
The tradition of Owaia is to the effect that he was named as one of the most cruel kings of earth in answer to an inquiring voice from heaven. ↑
Kahiko-luamea, father of Wakea ↑
Hua figures prominently in Hawaii and Maui traditions, the one here referred to being: in a dispute with his priest and prophet Luahoomoe, on East Maui, about some uwau (Æstrelata phacopygia sandwichensis) birds, he became so angry that he vowed death to the priest. Aware of his coming fate Luahoomoe directed his sons to safety
while he perished in flames. Immediately the rains ceased, streams and springs dried up so that famine and desolation spread, from the continuous drought. Hua died miserably from which comes the saying: “Rattling are the bones of Hua in the sun.” ↑
Ikuwa, September–October, the lunar month. ↑
Poha koeleele, bursting, pattering ↑
Hua, the thirteenth day of the lunar month. ↑
Varieties of sweet potato. ↑
Ikiiki, April–May, the time of light summer showers ↑
Mohalu, the twelfth day of the month. ↑
Kaaona, May–June. ↑
Hinaiaeleele, June–July ↑
Keaonui, large cloud, supposed to personify a deity. ↑
The first Mahoe is August of the Hawaii calendar. ↑
Lono; this is the twenty-eighth ↑
Kau, the sunny season, is from Ikiiki (May) to Ikuwa (October) of Hawaii’s calendar The various islands appear to have differed widely from each other, both in months and seasons. The Kau was also known as the Makalii season with some. Instead of Mahoe-mua and Mahoe-hope representing days of the month, as one Hawaii calendar shows, according to
David Malo, Kauai adopts them for first and second divisions of the year ↑
Mahakea, a wild, uncultivated field. ↑
The days named are from the eighteenth to the twenty-sixth of the month, inclusive. ↑
Welo, March–April ↑
Six named varieties of sweet potatoes ↑
Nana, February–March. ↑
The day of Kane falls on the twentyseventh of the month ↑
Kaulua, January–February. ↑
Seven more varieties of potatoes. ↑
Kaelo, December–January ↑
Mauli, the twenty-ninth day of the month. ↑
Welehu, October–November. ↑
Makalii, November–December ↑
More varieties of sweet potatoes. ↑
Kanepuaa, a god of agriculture ↑
La-i is an abbreviation of two words, la for lau, leaf; and i for ti or ki, the plant; hence, ti or ki-leaf ↑
Puula-i, ti-leaf hill. ↑
Lau fishing is with large joined nets to the top of which are affixed bunches of ti-leaf to frighten and confine the fish. ↑
Paiai, kalo pounded stiff; hard poi ↑
The pithy nature of the wood, never of large size, rendered it light when dry These stalks were called auki ↑
Okolehao, so named from the introduced iron-pot method of its distillation by the beach-comers of early day ↑
Kukui (Aleurites Moluccana), so called for its recognized lightfurnishing properties, as shown in this paper ↑
To ripen bananas, the dry leaves of the kukui were wrapped around the fruit, which is said to effect in three days what would otherwise have required a week’s time to become mellow. Its use in fish roasting was, like the ki-leaf, simply to protect it; not for the imparting of any flavor. ↑
This furnishes the relish known as inamona. ↑
Kukui oil, from experience, is known to be a heavy bodied, slow drying oil, very durable in painting, and said to possess excellent properties for varnish making. Effort has been made of late to start kukui oil making as an industry but so far without success, owing to the uncertainty and high cost of labor ↑
Hamauleo, lit., silent voice. ↑
The writer omits to mention its use ornamentally. The nuts, polished, are strung on a cord, or tape, and worn as a necklace. Young nuts furnish a mottled or plain brown lei, while the old nuts rival black ebony It has use also in
the manufacture of substitute jet jewelry ↑
This furnished the black paint of Hawaii. ↑
The kukui fungus, pepeiao or ears, for a number of years was gathered, dried and exported to China, as a much-desired edible product. ↑
Kaukaweli, possessed by fear. ↑
Ulukukui a Lanikaula, kukui grove of Lanikaula, a famous prophet in the time of Kamalalawalu, who endeavored to dissuade the king from his fool-hardy invasion of Lono’s domain, Hawaii. ↑
Kali kukui, string of kukui kernel ↑
Ala, the fine-grained clingstone, ordinary lava rock being too absorbent ↑
Kane and Kanaloa, two of the four principal gods of Hawaiian mythology. ↑
Kanehunamoku, a mythical land supposed to have been hidden by Kane; its name implies Kane the land hider ↑
The wood of the breadfruit was easily worked, being soft in grain, yet durable in quality. Canoes are made of it in Tahiti, and it has qualities for certain cabinet work ↑
Pahoa is the name of the instrument rather than the stone. The same name is given to a weapon of wood, as also stone, which is described as a short sword ↑
Kalaau, the tree. ↑
Aalii (Dodonaca viscosa), a common hardwood tree, though not of large size. ↑
Hulis are the taro-tops cut off with a thin slice or shoulder of the tuber for its propagation as seed. ↑
Aae and oha are synonymous terms for young taro shoots. ↑
Keaouli, or ao nui eleele, the large black cloud, supposed to embody a watchful deity to whom the farmer appealed for protection and success. ↑
Saying grace at one’s meal ↑
These mounds varied in size sufficient for from say six or eight to maybe as many dozen taros each. ↑
The young taro leaves, cooked, furnish excellent greens, resembling spinach. It is known as luau when cooked, not before. ↑
This account shows the religious character of Hawaiians. ↑
Akolea (Polypodium Keraudreniana). ↑
This starts out with a grave blunder, Haalou being the mother of Namahana, the wife of Keeaumoku, father of Kaahumanu. ↑
Another error, Kamehameha’s birthplace being at Kohala ↑
Kilioopu, name of a wind at Waihee, Maui. ↑
Four waters; the poetic reference to the four adjoining sections of West Maui, viz , Wailuku, Waikapu, Waiehu and Waihee ↑
The peleleu was a special style of canoe, of large size, but short and deep, as a war fleet for the invasion of Kauai. ↑
The mamalahoa edict of protection was proclaimed much earlier in his career, in Puna, Hawaii Some authorities give it as mamalahoe, from the incident of its origin, the splintered paddle. ↑
This person was Kamehameha’s first-born son, but being at this time an adherent of the Keoua party he was liable to the death penalties of the vanquished, hence his call for adequate protection ↑
Papa, a certain class or code of Kamehameha laws. ↑
Here the essayist confuses the events and time of Umi with that of Kamehameha, centuries apart. ↑
Ualakaa, or Roundtop, at entrance of Manoa valley. ↑
Ka niau kani, a mouth-sounding contrivance with a coconut leaf which came into vogue at this time and became thereafter a national chronological era, as here noted, according to ancient custom, which reckoned by events, not years. ↑
[Contents] A S K . H M K .
CHAPTER I.
K T Y . L
S , F D .
C W
A
Kawelo was born at Pupulimu,1 in Waimea, Kauai. Heulu was the father, and Haiamu was the mother, of whom the child, Kawelo, was begotten. During Kawelo’s childhood he was a timid stripling whenever his companions or others challenged him to fight. His elder brother was Kauahoa,2 who was
MOKUNA I.
K , K M W .
A’ , L , H . M W
A
Ua Hanau ia o Kawelo ma Pupulimu i Waimea, Kauai. O
Heulu ka makuakane, a o Haiamu ka makuahine, na laua mai keia keiki o Kawelo. Aia i ko Kawelo wa kamalii, he keiki makau wale ke hakaka mai
kekahi mau keiki, a mea e ae paha. O ko ia nei mua o Kauahoa no ia, na ka makua
born of the same parents. Kauahoa had been previously adopted by Haulili,3 the great one of Hanalei. The purpose for which his elder brother had been taken away was because he was found to be very strong, and, therefore, was feared lest he should kill his younger brother.
Let us turn aside and glance at Kawelo. While Kawelo dwelt peacefully with his parents a desire entered his mind to go sea bathing, which was his favorite pastime from his infancy up to the time of his death. In his eighteenth year a secret longing prompted Kawelo to seek the wives of his half-brother, Aikanaka, the king of Kauai. Said he to Heulu, his father: “How amazing is the greatness of my desire for the wives of my lord brother! By what means may they be obtained?” Whereupon the father asked: “Do you really wish the wives of your lord to be yours?” “Yes,” Kawelo replied. “Here is the means whereby they may be won: let me teach you how to fish.”
hookahi. Ua lawe mua ia o Kauahoa na Haulili, ka mea nui o Hanalei. O ka hana a kona kaikuaana i lawe ia ai, no ka ike ia no ka nui o kona ikaika, a manao ia no hoi o make kona pokii iaia.
E huli ae kakou a nana aku ia
Kawelo. Aia ia Kawelo e hoonanea ana me kona mau makua, kupu mai la ka manao iloko o ua Kawelo nei e hele i ka auau kai, a o kana puni no hoi ia mai kona wa uuku mai a hiki wale i kona make ana. I ka umikumamawalu o kona mau makahiki, kupu mai la ka manao iloko o ua o Kawelo nei e kii i na wahine a kona kaikuaana hanauna, o Aikanaka, ke alii o Kauai. Pane aku i ka makuakane ia Heulu: “Nani mai la ka hoi ka nui o ko’u makemake i na wahine a ko’u kaikuaana haku.
Pehea la auanei e loaa ai?” Ia manawa, ninau mai ka makuakane: “He makemake nae kou e lilo na wahine a ko haku ia oe?” “Ae,” wahi a ua o Kawelo
So they entered upon the task of learning, and not very long after the instruction was begun Kawelo became proficient. Wherefore he immediately went out to fish. In a short period of fishing a great heap of fish was caught. He patiently waited for, but failed to secure the women; so he said to the father: “I can not in the least obtain the wives of my elder brother.” “Then go farming,” answered the father. He went to till the soil, and the things that he planted thrived. He waited, but could not secure [them]; then he meditated: “Indeed! It appeared as though my father’s instructions to me were the wise policy whereby those women may be mine; but lo! they are not.”
Thereafter, he began to learn dancing. In educating himself to dance, and becoming proficient therein, he immediately held a dancing exhibit before a large gathering. When he went to dance Kawelo was arrayed in a
nei. “Eia ka mea e lilo ai, e a’o aku ia oe i ka lawaia.”
O ko laua nei a’o iho la no ia, aole no hoi i emo ia a’o ana iho, o ka makaukau no ia o ua Kawelo nei. O ko ianei hele aku la no ia i ka lawaia. Aole no i emo ia lawaia ana, ku ka paila o ua mea he i’a. Oi kali wale aku keia, aohe no he loaa iki o ua mau wahine nei iaia, ninau aku keia i ka makuakane: “Aohe loaa iki o na wahine a kuu kaikuaana haku ia’u.” “O hele i ka mahiai,” wahi a ka makuakane, hele keia i ka mahiai, a hewahewa ua mea he ai aia nei o ke kanu ana. Oi kali aku keia, aohe no he loaa iki, komo ka manao iloko oia nei: “Ka! kainoa no paha he hana pono ka kuu makuakane e a’o nei ia’u i mea e loaa ai la hoi kela mau wahine ia’u; eia ka aole.”
A mahope iho, hoomaka keia e a’o i ka hula. I ko ianei a’o ana i ka hula a makaukau, hoomaka keia e hula iwaena o ke anaina. I ko ianei hele ana e hula, ua kakua ia ua o Kawelo nei i ke kapa ahuula. Ike mai la ua mau
feather cape. The women saw that Kawelo was very skillful in dancing, so they fell upon him and kissed him. [696]At that moment he mused, “At last here is the means whereby I have secured both, which is dancing.” When he had finished dancing, and when night had come, the women went and met Kawelo; whereupon they lived as husband and wives. Let us leave the narrative of Kawelo with his wives and turn to Aikanaka.
wahine nei i ka lea maoli o Kawelo i ka hula, o ko laua lele mai la no ia e honi. Ia manawa, komo mai la ka [697]manao iloko o ianei: “Eia ka ka mea o olua e loaa ai ia’u, o ka hula.” A pau ka hula ana a ainei; aia ma ka po ana iho, o ka hele mai la no ia o ua mau wahine nei a hui pu me Kawelo. O ko lakou nei noho iho la no ia, noho a kane a wahine. E waiho kakou no ke kamailio ana no Kawelo me na wahine ana, a e huli ae kakou no Aikanaka.
CHAPTER II.
A P B A
K M O .
J M C
F F . O N
W T A
W
While Aikanaka was brooding with love for his wives the thought occurred to him to seek
MOKUNA II.
I A W L . H K O . H M ’
K . L W ’ .
Aia ia Aikanaka e noho ana me ke aloha i na wahine ana, kupu mai la ka manao iloko ona e kii e
the death of his younger brother4 Kawelo. Soon afterwards all the people of Kauai assembled and consulted with their great king Aikanaka.5 The task of spear practice was begun, and the men became highly dexterous in that service. They spent much time in its exercise, and, very long afterwards, a longing took hold of Kawelo to go sightseeing in circuiting Oahu; hence, he said to the father: “How great is my desire to sail and tour all of Oahu!” The father answered: “Go as your desire dictates.”
Upon which he set out; but while he was traveling along the road, young Kamalama6 approached and inquired of Kawelo: “Whither are you bound for?” Kawelo replied, “I am going to sail and tour Oahu and then return.”
Whereupon the former said, “It is well then that I, too, shall accompany you.” The latter gave his consent and boarded the canoe. This canoe, on which they embarked, belonged to Kaulukauloko and Kaulukauwaho.7
pepehi i ka pokii ona, oia o Kawelo. Mahope iho, hui na kanaka a pau o Kauai a kuka pu me ke alii nui o lakou, oia o Aikanaka. Hoomaka ia e a’o i na ihe, a ua nui loa ke akamai o na kanaka ma ia hana. Loihi ko lakou a’o ana ia mea, a liuliu loa, kupu mai la ka manao iloko o Kawelo e hele e makaikai ia
Oahu a puni, a pane aku i ka makuakane: “Lealea mai la ka hoi au i ka holo e makaikai ia
Oahu a puni!” Pane mai ka makuakane: “O hele, e like me kou makemake.”
O ko ianei hele mai la no ia. Iaia, nei nae e hele ana ma ke alanui, ku ana o Kamalamaikipokii, a ninau ana ia Kawelo: “E hele ana kau huakai mahea?” Olelo mai o Kawelo, “E holo ana au e makaikai ia Oahu, a hoi mai.” O ko ianei olelo aku la no ia, “E aho la hoi owau kekahi e hele pu me oe.” Ae mai kela a kau maluna o ka waa, o keia waa a laua i kau ai no Kaulukauloko ame Kaulukauwaho.
Soon they all sailed out for and landed at Oahu. Kou,8 a beautiful woman of Puuloa, Oahu, met him. In due time he started out to call on the celebrated fisherman of Oahu here at that time, who was Makuakeke. Kawelo immediately asked of Makuakeke: “Are the fish of this locality famed for their not being entrapped by the net, caught?” The latter replied: “One has been captured, but the other one is still at large.” “What of it? Let us go out to entrap it; perhaps we may capture it.” So they paddled out until they arrived off the point of Kaena.9
Just as they approached the spot, Makuakeke bent his head down to make observations and saw the fish swimming about. “Here is that fish,” said the fisherman. Let us leave these two awhile and speak relative to the parents.
As the parents were residing on Kauai, every one in their neighborhood, including themselves, were attacked. Moreover, the parents were
O ko lakou holo mai la no ia a hiki ma Oahu. Halawai mai la meia nei o Kou, no Puuloa, Oahu, he wahine maikai. A liuliu iki, hoomaka keia e hele e halawai me ka lawaia nui o Oahu nei ia wa, oia o Makuakeke. Ia wa, olelo aku o Kawelo ia Makuakeke: “Ua make anei na i’a kaulana onei no ka hei ole i ka upena?” Olelo mai kela: “Ua make hookahi, a koe hookahi i’a e noho nei la.”
“Heaha la hoi! e kii kaua e lawaia iaia, malia o make mai ia kaua.” O ko laua nei hoe aku la no ia, a hiki ma ka lae o Kaena. I ko laua nei hiki ana aku, kulou iho la o Makuakeke ilalo e nana ai, a ike i ua i’a nei e holo ana. “Eia no ua i’a nei la,” wahi a ka lawaia. E waiho iki iho kakou no laua nei, a e kamailio ae kakou no na makua.
Aia i na makua e noho ana ma Kauai, luku ia aku la ka poe a pau e pili aku ana i ua mau makua nei, a me ua mau makua nei no hoi kekahi. Kipaku ia aku la nae ua mau makua nei a noho
