Computer-aided method-development programs require accurate models to describe retention and to make predictions based on a limited number of scouting gradients. The performance of five different retention models for hydrophilic-interaction chromatography (HILIC) is assessed for a wide range of analytes.
Trang 1j ou rn a l h om ep a ge :w w w e l s e v i e r c o m / l o c a t e / c h r o m a
Full length article
a University of Amsterdam, van ‘t Hoff Institute for Molecular Sciences, Analytical-Chemistry Group, Science Park 904, 1098 XH, Amsterdam, The Netherlands
b TI-COAST, Science Park 904, 1098 XH, Amsterdam, The Netherlands
Article history:
Received 29 September 2017
Received in revised form 9 November 2017
Accepted 10 November 2017
Available online 11 November 2017
Keywords:
Hydrophilic-interaction chromatography
Retention model
Gradient scanning
Method development
Gradient equations
Computer-aidedmethod-developmentprogramsrequireaccuratemodelstodescriberetentionandto makepredictionsbasedonalimitednumberofscoutinggradients.Theperformanceoffivedifferent retentionmodelsforhydrophilic-interactionchromatography(HILIC)isassessedforawiderangeof analytes.Gradient-elutionequationsarepresentedforeachmodel,usingSimpson’sRuletoapproximate theintegralincasenoexactsolutionexists.Formostcompoundclassestheadsorptionmodel,i.e.a linearrelationbetweenthelogarithmoftheretentionfactorandthelogarithmofthecomposition,is foundtoprovidethemostrobustperformance.Predictionaccuraciesdependedonanalyteclass,with peptideretentionbeingpredictedleastaccurately,andonthestationaryphase,withbetterresultsfora diolcolumnthanforanamidecolumn.Thetwo-parameteradsorptionmodelisalsoattractive,because
itcanbeusedwithgoodresultsusingonlytwoscanninggradients.Thismodelisrecommendedas thefirst-choicemodelfordescribingandpredictingHILICretentiondata,becauseofitsaccuracyand linearity.Othermodels(linearsolvent-strengthmodel,mixed-modemodel)shouldonlybeconsidered aftervalidatingtheirapplicabilityinspecificcases
©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense
1 Introduction
Hydrophilicinteraction chromatography (HILIC) hasbecome
increasinglyimportantfor theanalysisofhighlypolaranalytes,
such as antioxidants [1], sugars (e.g glycomics [2–4]), (plant)
metabolites[5–7],foodstuffs[8],andenvironmentalpollutants[9]
Theexact mechanismofretentioninHILIChasbeenintensively
investigatedanditisthoughttoberathercomplex.Thecurrently
acceptedmechanismisacombinationof(i)partitioningprocesses
oftheanalytesbetweenawater-poororganicmobilephase and
a water-rich layerabsorbed ona polarstationary-phase
mate-rial[10],and(ii)electrostatic interactionsbetweentheanalytes
andthestationary-phasesurface[11].Therefore,HILICcanbestbe
describedasamixed-moderetentionmechanism
∗ Corresponding author at: University of Amsterdam, van ‘t Hoff Institute for
Molecular Sciences, Analytical-Chemistry Group, Science Park 904, 1098 XH,
Ams-terdam, The Netherlands.
E-mail address: B.W.J.Pirok@uva.nl (B.W.J Pirok).
TodescriberetentioninHILIC,severalretentionmodelshave beeninvestigated.Themodelmostcommonlyusedin reversed-phase LC (RPLC) involves a linear relationship between the logarithmoftheretentionfactor (k)and thevolumefractionof strongsolvent(ϕ) Whenalinear gradientis usedin RPLC this resultsinso-calledlinear-solvent-strengthconditions[12].Already
in1979,LSSconditionshavebeenstudiedanddescribedindetailby Snyderetal.[12]andequationswerealsoderivedforsituationsin whichanalyteselutebeforethegradientcommencesorafterithas beencompleted[12,13].However,duetothemixed-mode reten-tionmechanism,thislinearmodelmaybelesssuitabletoaccurately modelretentioninHILIC
Todescriberetentionmoreaccuratelyacrossawiderϕ-range, Schoenmakersetal.introducedaquadraticmodel[13],including relationsfortheretentionfactorforanalyteselutingwithinand afteragradient.However,anerrorfunctionwasrequiredtoallow partialintegrationofthegradientequation.Thisisanimpractical aspectoftherelationship.Moreover,themodelmayshow devia-tionsfromtherealvalueswhenpredictingoutsidethescanning range.Anempiricalmodel proposedbyNeueand Kuss circum-ventedtheintegrationproblems,allowinganalyticalexpressionsto
https://doi.org/10.1016/j.chroma.2017.11.017
0021-9673/© 2017 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).
Trang 2reten-tionmodelbasedonsurfaceadsorptionhasalsobeenproposedfor
HILIC,predictingretentionacrossnarrowrangesofwater
concen-trationsintheeluent.Toaccountfortheobservedmixed-mode
behaviourfoundinHILIC,Jinetal.introducedathree-parameter
model[15],whichwasfoundtopreciselydescriberetentionfactors
inisocraticmode[16].However,similartothequadraticmodel,
integrationof thecorresponding gradientequation was
signifi-cantlycomplicated,involvingagammafunctionandpotentially
yieldingcomplexnumbers
For efficient method development, an underlying accurate
descriptionoftheretentionmechanismiscrucial.Because
gradi-entelutionisanessentialtoolforanalysingorscanningsamples,
accuratedescription of gradient-elution patterns is also
essen-tial.Computer-aided-optimizationtools,suchasDrylab[17] for
1D-LC, or PIOTR [18] for 1D and 2D-LC, utilize the concept of
so-called “scouting” or “scanning” runs to establish retention
parameters[19],fromwhichtheoptimalconditionsandthe
opti-malchromatogramcanbepredicted.MethoddevelopmentinHILIC
followingtheseprincipleshasextensivelybeenstudiedbyTyteca
etal.[20,21].However,thecurrentlyemployedretentionmodels
forHILICdonotallowaccuratepredictionofretentiontimesof
ana-lyteselutingduringorafterthecompletionofgradientsbasedona
verylimitednumberofscoutingmeasurements.Thishampersthe
applicationofsuchoptimizationtoolsforHILIC
Inthiswork,wepresenttheresultsofanevaluationstudyof
eachofthefiveabove-listedmodelsforpredictingretentiontimes
ingradient-elutionHILICbasedonalimitednumberofscouting
runsforawiderangeofapplications.First,theequationforeach
retentionmodel is addressedinthecontext ofgradient-elution
chromatography.WeuseSimpson’sRule[22]toapproximatethe
integrationofresultinggradientequationswhenanexactsolution
doesnotexist,i.e.forthequadraticandmixed-modemodels.The
performanceofeachofthesemodelsincomputer-aided
method-developmentprogramsisassessed
2 Theory
Inthecasethatasoluteelutesbeforethestartofthegradient,
theretentiontime(tR,before)canbecalculatedfrom
tR,before=t0(1+kinit) (1)
wherekinitdepictstheretentionfactoratthestartofthegradient
andt0thecolumndeadtime.Thegeneralequationoflinear
gradi-entsallowscalculationoftheretentiontimeifacompoundelutes
duringthegradient
1
B
ϕ init +B(t R −)
ϕ init
dϕ
k (ϕ)=t0−tinit+tD
kinit
(2)
Inthisequationk (ϕ) istheretentionmodel,denotingthevariation
oftheretentionfactorkwiththecompositionparameter.The
changeinϕasafunctionoftime(i.e.theslopeofthegradient)is
depictedBϕ=ϕinit+Bt)andisthesumofthesystemdwelltime
tD,thewaitingtimebeforethegradientisprogrammedtostarttinit,
andt0(≈tD+tinit+t0).Forusefulapplicationofgradient-elution
retentionpredictionmodelsinrealcases,it isessentialthatthe
retentiontimecannotonlybeestablishediftheanalyteelutes
dur-ingthegradient,butalsoifitelutesafterthegradientiscompleted
Inthiscase,theretentionisobtainedbyintegratingtheretention
modelinthefollowingequation
1
B
ϕfinal
ϕinit
dϕ
k ()+tR−−tG
kfinal =t0−tinit+tD
kinit
(3)
Here,tGrepresentsthegradienttime.Theapplicationofsomeof theproposedHILICretentionmodelsiscomplicated,becausethe integralsinEqs.(2)and(3)cannotbeanalyticallysolved.The appli-cationofeachoftheHILICmodelsforgradient-elutionseparations
isthemaintopicofthispaperandthiswillbedescribedindetail
inthefollowingsections
2.1 Exponentialmodel
Intheexponentialmodel(Eq.(4)),k0accountsforthe extrap-olatedretentionfactorforϕ=0andSdenotesthechangeinthe retentionfactorwithincreasingmobilephasestrength
Thisequationisoftenreferredtoasthelinear-solvent-strength (LSS)equations,becauseitcorrespondstoLSSconditionsin com-binationwithlineargradients(ϕ=ϕinit+Bt).Schoenmakersetal derivedequationsforacompoundelutingduring(tR,gradient)and after(tR,after)thegradient[13]
tR,gradient= 1
SBln
1+SB·kinit
t0−tinit+tD
kinit
tR,after=kfinal
t0−tD+tinit
kinit
BS
1−kfinal
kinit
Here,kfinalrepresentstheretentionfactorattheendofthegradient andtGthedurationofthegradient
2.2 Neue-Kussempiricalmodel TheempiricalmodelintroducedbyNeueandKuss[14]isgiven by
lnk=lnk0+2ln (1+S2ϕ) −1+S1Sϕ2ϕ (7) wherethecoefficientsS1andS2representtheslopeandcurvature
oftheequation,respectively.Integrationofthegradientequation yields
tR,gradient= lnF
B(S2−S1lnF)−ϕinit
withFdefinedas
F=S2Bk0
t0−tinit−tD
kinit
Similarly,introducingEq.(7)intoEq.(3)andrewritingyields
tR,after=kfinal
t0−tinit+tD
kinit
+S2Bk0(e1 +S1ϕinitS2ϕinit −e1 +S1ϕfinalS2ϕfinal ))+tG+ (10)
2.3 Adsorptionmodel Theadsorptionmodelisbasedonconfinedsurfaceadsorption
asusedinnormal-phasechromatographyandisgivenby
wherendepictstheratioofsurfaceareasoccupiedbyawateranda solutemolecule[16].Intheeventsthatthecompoundelutesduring
orafterthegradientretentioncanbecalculatedfrom[23]
tR,gradient=
k0
t0−tinit +tD
k init
B (n+1)+ϕn+1init
1 n+1 B
−ϕinit
Trang 3
t0−tinit+tD
kinit
− kfinal
Bk0(n+1)
2.4 Mixed-modemodel
Themixed-modeaspectofHILICledJinetal.toproposea
tai-loredmodel[15]
whereS1issaidtoaccountfortheinteractionofsoluteswiththe
stationaryphaseandS2fortheinteractionofsoluteswithsolvents
Whileseeminglyattractivebecauseofitsabilitytoaccountforthe
mixed-modecharacterofHILICretention,therelationdoesposea
practicalproblemuponintegrationofthegradientequation
ThecalculationoftheretentiontimeusingEq.(14),requiresa
gammafunctionandmaypossiblyresultincomplexnumbers.To
circumventthis,weapplySimpsons’Rule[22]toapproximatethe
integral(Eq.(15))
Simpsons
⎧
⎨
⎩
ϕ final +B(tR,gradient−)
ϕ init
eS1 ϕ·eS2dϕ
⎫
⎬
⎭
=Bk0
t0−tinit+tD
kinit
(15)
Thisrule divides theintegral over a function, f,in ourcase
f (ϕ) =eS 1 ϕ·eS 2 inmsegmentsofwidthϕ.Subsequently,each
segmentisapproximatedbya solvablequadratic equationsuch
that,inessence,thecomplexintegral isreplacedbymsolvable
quadraticequations(Eq.(16))
ϕfinal
ϕ init
f (ϕ) dϕ≈ϕ3
f (ϕinit)+4f
1
mϕ+ϕinit
+2f2
mϕ+ϕinit
+ +2f
m−2
m ϕ−ϕinit
+4fm−1
m ϕ+ϕinit
+f (ϕfinal)
(16)
Ofcourse,theapproximationisaccompaniedbyanerror.With
theSimpsons’Rule,themaximumerrordependsonmandcanbe
calculatedfrom
|E|≤D(ϕfinal−ϕinit)5
whereDrepresentsthemaximumvalueofthefourthderivativeof
theretentionmodelintheintegrationrangefromϕinittoϕfinal.In
thisstudy,wesettheacceptablecalculationerrorto0.001,which
ismuchsmallerthanthetypicalexperimentalerror.Rewritingthe
equationyieldsm≥4
|f 4 (ϕ x ) · ϕ 5
0.18 |(18)
Inthecaseofthemixed-modemodel,ϕxequalsϕinit.Likewise,
themixed-moderetentionmodelcanbeappliedinconjunction
withEq.(3),resultingin
tR,after=kfinal
t0−tinit+tD
kinit − 1
Bk0
Simpsons
⎧
⎨
⎩
ϕfinal
ϕ
eS 1 ϕ·eS 2dϕ
⎫
⎬
⎭
⎞
2.5 Quadraticmodel
Incomparisonwiththeexponential(“LSS”)model,thequadratic modeloffersamoreflexiblesolutionacrossabroaderrangeofthe volumefractionofthestrongsolvent.Retentionisgivenby
WhereS1andS2 representtheinfluencesofthevolumefraction
ofstrongsolvent.Similartothemixed-modemodel,integrationof thegradient-elutionequationiscomplex.Effectively,thegradient equationsbecome
Simpsons
⎧
⎨
⎩
ϕ final +B(tR,gradient −tG−)
ϕ init
eS 1 ϕ·eS 2 ϕ 2
dϕ
⎫
⎬
⎭
=Bk0
t0−tinit+tD
kinit
(21)
tR,after=kfinal
t0−tinit+tD
kinit − 1
Bk0
Simpsons
⎧
⎨
⎩
ϕfinal
ϕ init
eS 1 ϕ·eS 2 ϕ 2
dϕ
⎫
⎬
⎭
⎞
ForcalculatingthenumberofpartitionsmfortheSimpson’s approximationfrom(Eq.(18)),]zϕxnowequalsϕfinal,becausethe fourthderivativeislargestatthefinalsolventstrength
3 Experimental
3.1 Chemicals Aqueoussolutionswerepreparedusingdeionizedwater(Arium 611UV; Satorius, Germany; R=18.2 M cm) Acetonitrile (ACN, LC–MS grade)wasobtained fromAvantor Performance Chemi-cals(Deventer,TheNetherlands).Ammoniumformate,formicacid (reagentgrade,≥95%)andthepeptidemix(HPLCpeptidestandard mixture,H2016)wereobtainedfromSigma-Aldrich(Darmstadt, Germany).Theearl-greyteawasobtainedfromMaasInternational (Eindhoven,TheNetherlands).Thedyesusedinthisstudywere authenticdyestuffsobtainedfromthereferencecollectionofthe CulturalHeritageAgencyoftheNetherlands(RCE,Amsterdam,The Netherlands)
3.2 Instrumental AllexperimentswerecarriedoutonanAgilent1100LC sys-temequippedwithaquaternarypump(G1311A),anautosampler (G1313A),acolumnoven(G1316A)anda1290Infinitydiode-array detector(G4212A)(Agilent,Waldbronn,Germany).Infrontofthe column,anAgilent1290InfinityIn-LineFilter(G5067-4638)was installedtoprotectthecolumn.Thedwellvolumewas approxi-mately1.1mL.Theinjectorneedlewassettodrawandejectata speedof10L·min−1 withtwosecondsequilibrationtime. Two
columnswereused,aWatersAcquityBEHAmide(150×2.1mm i.d.,1.7-mparticles,130-Åporesize;Waters,Milford,MA,USA) andaPhenomenexLunaHILICcolumn(50×3mm,3m,200Å; Phenomenex,Torrance,CA,USA),furtherreferredtoasdiolcolumn 3.3 Procedures
3.3.1 Analyticalmethods The mobile phase consisted of acetonitrile/buffer[v/v] 97:3 (MobilephaseA)andacetonitrile/buffer[v/v]1:1(Mobilephase
Trang 4B).Thebufferwas10mMammoniumformate atpH 3 Forall
experimentsrecordedontheamidecolumn,fivedifferentscouting
gradientprogramswereused.Allgradientsstartedfrom0.0until
0.5minisocraticat100%A,followedbyalineargradientfrom100%
Ato100%Bin10(GradientA1),17(GradientA2),30(GradientA3),
52(GradientA4)and90(GradientA5)minutes.Inallcases,100%
Bwasmaintainedfor2min,afterwhichalineargradientof1min
broughtthemobilephasebacktotheinitialcompositionof100%
A,whichwasmaintainedfor20mintothoroughlyre-equilibrate
thecolumn.Theflowratewas0.25mLmin−1
Fortheexperimentscarriedoutonthediolcolumn,thefive
differentscoutgradientseachstartedwith0.0–0.5minisocraticat
100%A,followedbyalineargradientfrom100%A–100%Bin0.67
(GradientD1),1.33(GradientD2),2.0(GradientD3),4.0(Gradient
D4)and6.0(GradientD5)minutes.Theflowratewas1.0mLmin−1
3.3.2 Samplepreparation
Thepeptidemixwasusedataconcentrationof1000ppmin
deionizedwater,andwasdilutedfivetimeswithACNbefore
anal-ysis.Theinjectionvolumewas5L
Themetaboliteswereindividuallypreparedasstocksolutions
inACN/waterwithratios(varyingbetween9:1or8:2[v/v])and
resultingconcentrationsdependingonthesolubilityofeach
com-pound (see Supplementary Material section S-1) For analysis,
mixturesofsevenoreightmetaboliteswerepreparedwith
effec-tivemetaboliteconcentrationsinthesemixturesbetween100and
500ppm.Theinjectionvolumeofeachmixturewas1L.Thepeaks
inthechromatogramswereidentifiedusingindividualinjections,
clearlydistinguishablepeakpatternsandUV–visspectra
Thedyeswerepreparedasindividualstocksolutionsof
approx-imately5000ppminwater/MeOH(1:1)[v/v].Mixturesof20dyes
werepreparedandtheresultingsolutionwasdilutedfourtimesin
ACN.Themixtureswereinjectedatavolumeof3Lwitheffective
individualdyeconcentrationsofapproximately25ppm.Thepeaks
inthechromatogramswereidentifiedusingtheUV–visspectra
For the preparation of the earl-grey-tea sample, 200mL of
deionizedwaterwasheateduntiltheboilingpointwasreached.The
heatingwasturnedoffandtheearl-grey-teabagwassubmergedin
thewaterfor5min.Aftercooling,theresultingsolutionwasdiluted
fivetimeswithACNpriortoanalysis.Theinjectionvolumewas
5L
4 Results and discussion
4.1 Goodness-of-fit
ToestablishagoodrepresentationofHILICbehaviour,asetof
57analyteswascompiledcomprisingorganicacids,peptides,
syn-theticandnaturaldyesandcomponentsfoundinblacktea(Table1)
Thesetmainlycomprisesacidic, basic,zwitterionicand neutral
compoundswithvaryingpolarityand,inmostcases,aromatic
func-tionality.Theretentiontimesforallanalytesontheamidecolumn
wererecordedwithfivedifferentgradientprograms(see
Exper-imentalsection, gradientsA1-A5) Using theobtainedretention
times(see SupplementaryMaterialsection S-2for allretention
time data), allretention parameters were determinedfor each
retentionmodelbyusingthenonlinear-programming-solver
fmin-searchfunctionofMATLABtofittheretentionmodeltothedata
Theresultingretentionparameters aredisplayedinTable1.For
mostanalytes,reasonablevalueswerefound.Peptidecomponent
1exhibitednoretentionandthuswasexcludedfromthisstudy
Toassess theability of thedifferentmodels todescribethe
retentionbehaviour,theAkaikeInformationCriterion(AIC)[24]
wasused.Thiscriterionprovidesameasureforthemean-squared
errorindescribingtheretentionbehaviourbasedoninformation
theoryanditcanberegardedasagoodness-of-fitindicator.The cri-terionhasbeenusedbeforetostudyretentionbehaviourinHILIC [16]andpartitioncoefficients[25].OneattractivefeatureoftheAIC criterionisthatitallowscomparisonofmodelswithdifferent num-bersofterms.Forexample,athree-parametermodelisexpected
todescribethedatabetterthanatwo-parametermodel.TheAIC criterionaccountsforthisbypenalizingthemodelforeach addi-tionallyemployedparameter,allowinganunbiasedcomparison ForcalculationtheAIC,thenumberofparameters,p,thenumber
ofexperiments,n,andthesum-of-squareserror(SSE)fromthefit
oftheretentionmodelareused
AIC=2p+n
In
2SSE
n
+1
(23) Table1liststheAICvaluesobtained.LowerAICvaluesgenerally indicateabetterdescriptionoftheretentionbehaviour.Generally, theadsorptionand Neue-KussmodelsshowfavourableAIC val-ues.InthecaseoftheNeue-Kussmodel,thisisinagreementwith previousstudies[16].ThisisalsoreflectedinFig.1,wherethe num-beroffoundcompoundswithagivenAICvaluearegroupedina histogramperretentionmodel.ItcanbeseenthattheLSSmodel performspoorlyinmostcasesandthatboththemixed-modeand quadraticmodelsarenotrobustacrosstherangeofcompounds Conversely,theplotsuggeststhattheadsorptionandNeue-Kuss modelsperformmorereliably,inparticularforthemetabolitesand dyes(seeSupplementaryMaterialsectionS-3forhistogramsper classofanalytes)
4.2 Predictionerrors Withthisinsight,theabilityofthemodelstoreliablypredict retentiontimesbasedonasmallernumberofgradientswasstudied
toallowautomaticgradientoptimization.Tosimulatesucha situa-tion,theretentiontimesfromgradientsA2andA4wereexcluded, andtheretentionparametersweredeterminedoncemoreusing exclusivelythedatafromgradientsA1,A3andA5.Theobtained retentionparameterswereusedtopredicttheretentiontimesfor gradientsA2andA4
TheresultsareplottedinFig.2Afortheamidecolumn,where theerrorsinpredictionoftheretentiontimesofallanalytesin gra-dientA2arereflectedbythesolidbarsandthedashedbarsreflect thepredictionerrorsforgradientA4.Mostmodelsperformvery similarly,withanaveragepredictionerrorofapproximately2%for retentiontimesofgradientA2and2.5%forretentiontimesof gradi-entA4.Asignificantdeviationofthisimpressionistheperformance
oftheNeue-Kussmodel,whichissurprisingbecauseofthelowAIC valuesfoundforthismodel.Thiscanbeexplainedbyrealizingthat thisisanempiricalmodelnowusingjustthreepoints(A1,A3and A5)insteadofallfivesuch,wasthecaseforFig.1.Toinvestigate
towhichextenttheobservationsobtainedthusfaralsopertainto otherstationaryphases,theretentiontimesfor17oftheanalytes (peptidesandmetabolites)werealsorecordedonacross-linked diolcolumn,usingasimilarsetofscanninggradients(see Sup-plementaryMaterialsectionS-4fortheobtainedretentiontimes, determinedretentionparametersandthecalculatedAICvalues;see Section3.3.1forgradientprogramsandconditions).Again,using exclusivelydatafromgradientsD1,D3andD5,theretentiontimes
ofgradientD2andD4werepredictedandthepredictionerrors areshowninFig.2B.Interestingly,thepredictionerrorsacrossthe rangeofmodelsismuchbetterwith,withpredictionerrorvaluesof approximately0.5%forD2and1.0%forD4.Noteworthyis,however, thedramaticperformanceoftheNeue-Kussmodelforwhichthe box-and-whiskerplotsareoff-scale.Thelowerpredictionerrors suggestamore-regularbehaviourofthediolcolumn.Itisworthto pointoutthattheobtainedretentionfactorsforbothcolumnswere rathersimilar.Toruleoutthatthissignificantlybetterperformance
Trang 5Table 1
Overview of determined retention parameters and calculated AIC values for all 57 analytes and five studied retention models based on five scanning gradients.
tea component 1 3.322 18.069 7.386 −2.217 0.708 1.564 5.225 3.325 −18.253 1.952 9.400 −2.373 1.604 2.940 7.430 249.896 19.696 0.578 tea component 2 3.781 18.941 8.570 −2.790 0.000 1.940 5.768 3.765 −18.717 0.165 10.719 −2.790 1.940 3.767 9.177 282.120 18.957 −0.045 tea component 3 3.975 15.981 6.959 −2.290 0.006 1.951 2.875 3.981 −16.211 1.880 8.983 −2.300 1.955 0.870 6.379 96.118 7.975 1.096 tea component 4 4.830 20.493 9.618 −3.726 0.001 2.801 7.156 7.831 −62.722 133.254 −5.245 −3.729 2.802 5.156 8.452 121.672 7.762 5.553 tea component 5 4.604 17.599 11.171 −2.867 0.088 2.456 8.560 8.625 −72.020 164.111 −3.301 −2.930 2.482 6.518 8.557 132.038 8.858 5.938 tea component 6 5.251 13.292 15.366 −2.011 0.000 2.753 13.394 8.272 −40.755 56.057 7.373 −2.008 2.752 11.394 5.297 14.315 0.160 17.142 nicotinic acid 2.245 11.175 5.807 −0.699 0.000 0.764 5.681 2.296 −12.574 3.847 7.781 −0.693 0.763 3.687 4.871 239.184 26.905 2.576 benzyltrimethylammonium 2.626 12.234 2.614 −0.991 0.000 0.977 −2.923 2.637 −12.644 3.064 4.402 −0.991 0.977 −4.921 4.403 125.560 14.849 −8.292 adenine 2.746 10.943 4.915 −0.708 0.143 0.956 0.966 2.784 −11.849 3.511 6.654 −0.771 0.975 −1.172 4.139 88.312 10.965 −0.413 hypoxanthine 2.731 10.730 8.425 −0.709 0.000 0.953 5.485 2.781 −11.851 3.505 10.254 −0.709 0.953 3.488 5.527 187.602 19.457 −3.392 adenosine 2.783 10.090 4.831 −0.559 0.095 0.939 0.812 2.809 −10.809 3.707 6.420 −0.598 0.950 −1.231 3.773 61.007 8.018 0.743 benzylamine 3.064 12.556 9.744 −1.170 0.000 1.207 6.508 3.069 −12.842 2.479 11.619 −1.173 1.208 4.503 7.528 278.750 22.807 −3.007 tyramine component 1 * 3.228 12.835 7.439 −1.307 0.002 1.321 2.110 3.965 −29.081 68.844 1.422 −1.304 1.319 0.097 5.562 120.642 11.979 −1.056
* Two well−separated peaks were systematically observed for tyramine.
** Excluded from study due to lack of retention.
Trang 6Fig 1. Quality of fit of 56 retained analytes based on the obtained AIC values for each retention model The analytes were classified within distinct ranges of AIC values for clarity See Supplementary Material section S-3 for quality-of-fit histograms per analyte class.
Fig 2. Box-and-whisker plot showing the errors of prediction for (A) 56 analytes on the amide column, (B) 17 analytes on the diol column (C) 17 analytes on the amide and diol column For each column/model combination a plot is provided for the prediction errors of both the second and fourth gradient (A2 and A4 for amide and D2 and D4 for the diol) Plot C reflects results exclusively for gradient 2 for both columns Note the different scales on the y-axes.
ofspecificmodelsiscausedbytheabsenceofthedyesand/ortea
componentsinthedataset,theplotshownasFig.2 compares
exclusivelythepredictionerrorsforthe17selectedanalytes.The
observedtrendssupportthosefoundinFigs.2Aand2B
4.3 Repeatability
Tostudytherobustnessoffittingtheretentionparametersand predictingretentiontimes,tenanalyteswereselectedand
Trang 7mea-Fig 3.Retention curves of 10 selected analytes for the (A): LSS, (B) mixed-mode, (C) quadratic, (D) adsorption and (E) Neue-Kuss models Each curve represents the average
of five sets of retention parameters derived from five sets of gradient retention data The error bars shown represent the uncertainty.
suredfivetimeswithallfivegradientsontheamidecolumn.The
resultingretentioncurvesareshowninFig.3.Theerrorbarssignify
thespreadbasedonthefivedeterminations.Narrowspreadsinthe
retentioncurveswereobservedfortheLSSandmixed-mode
mod-els,butespeciallyfortheadsorptionmodel.Thespreadwaslarger
foranumberofcomponentswiththeNeue-Kussmodel,despite
theuseoffivedatapointsforfitting,anditwasdramaticforthe
quadraticmodel
Onetrendthatcanbeobservedisthatforspecific(mostly
early-eluting)analytesthespreadislargertowardshigherfractionsof
water.ThetypicalHILICconditionsmaynolongerbeapplicablein
thisrange.Earlier-elutingcompoundsaregenerallymoredifficult
tofitwiththerelativelylimitedgradientrangeusedforscouting.To
studytheinfluenceofthenumberofscanninggradientsontheerror
inprediction,retentionparametersweredeterminedforeach
pos-siblecombinationofgradientswherethepredictedgradientwould
fallwithinthescanningrange.Forexample,gradientsA1,A2and
A4couldbecombinedtopredictA3asthelatterfallswithinthe scanningrange,whereasthiswasnotthecaseforpredicting gra-dientA4fromgradientsA1,A2andA3.Theresultsareshownin Fig.4,withtheplotshowingthepredictionerrorsforall56retained analytesplottedagainstthenumberofusedscanninggradients Notethatthemixed-mode,quadraticandNeue-Kussmodelswere notinvestigatedfortheusewithtwoscanninggradientsasthey arethree-parametermodels.Notsurprisingly,alargernumberof scanninggradientsimprovestheaccuracyofthepredictions How-ever,wecanseethatforsomemodelsthistrendismoresignificant thanforotherones.Usingfourscanninggradientsinsteadoftwo providesjustminorimprovementsinpredictionaccuracyforthe adsorptionmodel,whichappearstoperformsolidlyfortheamide column.Itshouldalsobenotedthattheeffectofadditives,which havebeenshowntoinfluencethetypeofinteractionsinHILIC,have notbeenevaluatedhere[26]
Trang 8Fig 4.Plot showcasing the mean error in prediction for all 56 retained analytes as a
function of the number of scanning gradients used To establish this plot, all possible
combinations of scanning gradients (A1–A5) were used with the restriction that the
predicted gradient must fall within the scanning range.
5 Concluding remarks
Wehaveinvestigatedthequality-of-fitandprediction
accura-ciesforfiveretentionmodelsandawidearrayofcompoundsfrom
differentclasses.Formostcompoundclasses,theadsorptionmodel
providesthemostrobustperformancein termsof itsabilityto
describeandaccuratelypredictHILICretentionbasedonalimited
numberofscanninggradients.Predictionaccuracieswere
gener-allybetterforadiolcolumnthanforanamidecolumn,withthe
exceptionoftheNeue-Kussmodelwhichperformedpoorlywhen
usingthreescoutingrunsoneithercolumn
Whiletheadsorptionmodelwasfoundtoperformrobustlyfor
mostoftheinvestigatedanalytes,thedatasuggestastrongeffect
ofthecombinationofanalyteclassandstationary-phasechemistry
onmodelperformance.Thetwo-parametermodelisalsoattractive,
becauseitcanbeusedwithgoodresultsusingonlytwoscanning
gradients.We recommendthattheadsorptionmodelshouldbe
thefirst-choicemodelfordescribingandpredictingHILICretention
data,unlessdataareavailabletodemonstratethatothermodels
(“LSS”model,mixed-modemodel)performadequatelyinspecific
situations.Basedonthepresentdata,wecannotrecommendthe
quadraticandNeue-KussmodelsforuseinHILIC
Acknowledgement
TheMANIACprojectisfundedbytheNetherlandsOrganisation
forScientificResearch(NWO)intheframeworkofthe
Program-maticTechnology AreaPTA-COAST3of theFundNewChemical
Innovations(Project053.21.113).AgilentTechnologiesis
acknowl-edgedforsupportingthiswork.TheDutchInstituteforCultural
Heritage(RCE)iskindlyacknowledgedforprovidingtheaged
syn-theticandnaturaldyesamples
Appendix A Supplementary data
Supplementarydataassociatedwiththisarticlecanbefound,
intheonlineversion,athttps://doi.org/10.1016/j.chroma.2017.11
017
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