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1、Analyzing DoseStep-by-StepExamples:AnalyzingDose-ResponseDatawithPrism3Adose-responsecurveisaplotofresponsetodrugtreatmentvs.drugconcentration.Sensitivitytoadrugactingataspecific,saturablereceptortypicallyspansalargeconcentrationrange,sodose-responsecurvesareusuallysemi-logarithmic,i.e.,theamountofd
2、rugisplottedasthelogofdrugconcentration.Thisexamplewillshowyou(1)howtousePrismtofitasigmoidal(alsoknownaslogistic;)curvetoyourdose-responsedataand(2)onewaytocomparetwodose-responsecurvesstatistically.Supposewewanttoplottwodose-responsecurves,showingtheaverageinvitroresponsetoanagonist,inthepresencea
3、ndintheabsenceofanantagonist,measuredintriplicate.Further,wewishtoincludeonthegraphazero-concentrationcontrolvalue.EntertheDataIntheWelcometoPrismdialogbox,selectCreateanewprojectandWorkindependently.UndertheXColumncategory,selectNumbers,andundertheYColumnscategory,choose3replicatestocalculateerrorb
4、ars.Enterthedataasshownbelow.TheXvalues(agonistdose)aregivenasmolarconcentration,expressedinexponentialnotation.TheYvalues(response,inarbitraryunits)goinsubcolumnsY1toY3Severalpointsaboutthisdataareworthnoting:Thedosageincrement(10nM,30nM,100nM,etc)shownintheXcolumnistypical.Thesevalueswillbelog-tra
5、nsformed,givingroughlyequalhorizontalspacingofdatapointsonthedose-responsecurve.ThesedataareagoodillustrationofPrismsuseofonlyoneXcolumn.AlthoughtheXvaluesfordatasetsAandBarenotthesame,wecancombinealltheXvaluesintoasinglecolumnandleaveY-valuecellsemptywhereappropriate.Thevaluesinrow1representthezero
6、-concentration(noagonist)data.SinceourXcoordinateswillbeplottedaslogarithms,andsincethelogof0isundefined,weapproximatethispointwithanXcoordinateof1.0e-010,about2logunitsbelowthelowestreal;Xvalue.Lateron,wellshowhowtoplaceazeroontheXaxisforthisdatapoint.Forthisexample,wereassumingthattheYvaluesdonotr
7、equirecorrectionbysubtractionofabaselinetheminimumYvaluesarealreadyzeroes.IfyouwishtosubtractabaselinevaluefromeachYvalueinadataset,readaboutautomaticbaselinecorrectionsusingPrismintheGraphPadQuickAnswersDatabase.Laterinthisexample,welldemonstratenormalizationoftheYvalues,whichcanalsoserveasameansof
8、baselinecorrection;.YoucanentertheYvaluesinanyconvenientunits,thentransformtootherunitsifyouwish.WellusePrismtonormalize(i.e.,transformtopercentofmaximalresponse)ourYvalueslater.Particularlywhendosingwithanimpurepreparation,youmaywishtoenterXvaluesintermsofdilutionfactor;orinmass/volume(e.g.,mg/mL)u
9、nits.TheQuickAnswersDatabasehasmoreinformationaboutworkingwithdilutionfactors.Usingmass/volumeunitsisnotaproblem,althoughitmaycausePrismtodisplayanerror;message,whichwelldiscusslater.Log-transformtheXvaluesNote:Therelationshipbetweendoseandresponseinasystemfollowingmass-actionkineticsishyperbolic,no
10、tsigmoidal.Thedose-responsecurvebecomessigmoidalonlywhenresponseisplottedagainstthelogarithmofdose,andPrismsbuilt-insigmoidaldose-responsecurve-fitmodelspresupposethatyourXvaluesareinthatform.Usersoccasionallyfindthattheirdose-responserelationshipsaresigmoidalbeforelogtransformationinthatcase,wereco
11、mmendthisuserdefinedmodel.ToconvertthevaluesintheXcolumntotheirrespectivelogarithms,clickAnalyze.ChooseBuilt-inanalysis.FromtheDatamanipulationscategory,selectTransforms.IntheParameters:Transformationsdialog,choosetoTransformXvaluesusingX=Log(X).Note:Atthebottomofthisdialog,thereisanoptiontoCreatean
12、ewgraphoftheresults.Butwerenotreadytodothat;wehaveonemoremanipulation,namelynormalization,todobeforemakingthefinalgraph.PrismdisplaysanewResultssheet(partlyillustratedbelow)withthelog-transformedXvalues.NormalizetheYValuesInthissection,wellconverttheYvaluesindatasetsAandBtoacommonscale.Thisisusefulw
13、henyouwanttocomparetheshapeorposition(EC50)oftwoormorecurvesanddontwanttobedistractedbydifferentmaximumandminimumvalues.Withthelog-transformedResultssheetinview,clickAnalyze.IntheNewAnalysisdialog,chooseAnalyzetheresultstableyouarelookingat.IntheAnalyzeDatadialog,selecttheDatamanipulationscategory,t
14、henchooseNormalize.IntheParameters:NormalizeYvaluesdialog,specifyhowPrismwillnormalizetheYvalues.Forthisexercise,wellacceptthedefaultsettings,whichwilldefine0%and100%asthesmallestandthehighestvalues,respectively,foreachofthedatasets.NormalizingthedatainthiswayconvertsittoPercentofmaximumresponse.Not
15、etwopoints:(a)Normalizationwillcausethedose-responsecurvetoextendverticallyfrom0to100bydefinition,andwellconstrainthecurvefitlatertoensurethis.Therefore,youshouldbefairlyconfidentoftheaccuracyofyourminimumandmaximumvalues.(b)Inthisexample,theminimumYvalueswerealreadyzeroes,sonoalterationoftheminimum
16、valueswillbemade.Note,however,thathadthesevaluesbeengreaterthan0,thenormalizationwouldeffectivelyhaveproducedabaselinecorrection.ChoosetoPresentresultsasPercentages.Andsincetheresultsofthisanalysis;arethevaluesthatwewillfinallygraph,checktheboxtoCreateanewgraphoftheresults.Overlookingthischeckboxisaverycommonmistake.Thesettingsareshownhere:TheResult