Use of individual retention modeling for gradient optimization in hydrophilic interaction chromatography: Separation of nucleobases and nucleosides

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ContentslistsavailableatScienceDirect

Journal

of

Chromatography

A

jou rn al h om ep a g e : 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

Use

of

individual

retention

modeling

for

gradient

optimization

in

hydrophilic

interaction

chromatography:

Separation

of

nucleobases

and

nucleosides

Eva

Tyteca

a,∗

_,

_Davy

_Guillarme

b

_,

_Gert

_Desmet

a

a_Vrije_Universiteit_Brussel,_Department_of_Chemical_Engineering,_Pleinlaan_2,_B-1050_Brussels,_Belgium

b_School_of_{Pharmaceutical}_Sciences,_University_of_Geneva,_University_of_Lausanne,_20,_Boulevard_d’Yvoy,₁₂₁₁_Geneva_4,_Switzerland

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received7August2014

Receivedinrevisedform

24September2014

Accepted25September2014

Availableonline13October2014

Keywords:

Computer-assistedmethoddevelopment

Individualretentionmodeling

Nucleobases Nucleosides HILIC

a

b

s

t

r

a

c

t

Inthisstudy,theseparationoftwelvenucleobasesandnucleosideswasoptimizedviachromatogram simulation(i.e.,predictionofindividualretentiontimesandestimationofthepeakwidths)withtheuse ofanempirical(reversed-phase)non-linearmodelproposedbyNeueandKuss.Retentiontime predic-tionerrorsoflessthan2%wereobservedforallcompoundsondifferentstationaryphases.Asasingle HILICcolumncouldnotresolveallpeaks,themodelingwasextendedtocoupled-columnsystems(with differentstationaryphasechemistries)toincreasetheseparationefficiencyandselectivity.The analyti-calexpressionsforthegradientretentionfactoronacoupledcolumnsystemwerederivedandaccurate retentiontimepredictionswereobtained(<2%predictionerrorsingeneral).Theoptimizedgradient (predictedbytheoptimizationsoftware)includedcouplingofanamideandanpentahydroxy function-alizedsilicastationaryphaseswithagradientprofilefrom95to85%ACNin6minandresultedinalmost baselineseparationofthetwelvenucleobasesandnucleosidesinlessthan7min.Thefinalseparation wasobtainedinlessthan4hofinstrumenttime(includingequilibrationtimes)andwasfullyobtained viacomputer-basedoptimization.Assuch,thisstudyprovidesanexampleofacasewhereindividual retentionmodelingcanbeusedasawaytooptimizethegradientconditionsintheHILICmodeusinga non-linearmodelsuchastheNeueandKussmodel.

1. Introduction

Tospeedupthemethoddevelopment(MD)processin chro-matography,fullyorsemi-automatedMDsoftwareprogramshave beendevelopedforreversedphaseliquidchromatography(RPLC) [1–6].TheseautomatedMDstrategiesforRPLC describedin lit-eratureareeithersearch-based (e.g.usingtheSimplexmethod) [7],model-based(e.g.Drylab[8],Chromsword)[9]orbasedona combinationofboth(designofexperiments(DoE),multiplelinear regression(MLR)[10],predictiveelutionwindowstretchingand shiftingmethod(PEWS2₎_[11]_)._Recently,_the_PEWS2_method_was successfullyappliedforthegradientoptimizationinhydrophilic interactionchromatography(HILIC)[12].

HILICisbecomingmoreandmorepopular,forthedetermination ofhydrophiliccompounds,poorlyretainedinRPLCconditions,and fortheanalysisofionizablecompounds[13].HILICretentioncanbe

∗ Correspondingauthor.Tel.:+3222693617.

E-mailaddress:eva.tyteca@vub.ac.be(E.Tyteca).

consideredasamixed-modemechanism,combininghydrophilic partitioningoftheanalytesbetweentheorganic-richmobilephase andthewaterenrichedlayerpartiallyimmobilizedonthe station-aryphase, compoundsadsorptionthroughhydrogenbonds,and electrostaticandionicinteractions[14].Althoughboththelinear reversedphase(semi-log)(Eq.(1))andthenormalphase(log-log) retentionrelationshipshavebeenusedinliteraturetomodelHILIC retention[15],thedependencyofln(k)onbothϕandlog(ϕ)inthe HILICseparationmodedoesnotfollowastrictlinearrelationship [15,16].Basedontheseobservations,Jinetal.proposedamixed modelcombiningpartitioning andadsorptionterms (Eq.(2))to describetheretentionbehaviorinHILIC[15].JanderaandHájek [17]introducedanextendedmodelincludingoneextraparameter tobetterdescribetheretentionatlowpercentagesofwater.Other (reversed-phase)non-linearmodelssuchasthequadraticmodel andtheempiricalmodelfromNeueandKuss(Eq.(3))havealso beenproposedinliteraturetodescribetheretentionrelationship intheHILICseparationmode[12].

ln(k)=ln(kw)−Sϕ (1)

http://dx.doi.org/10.1016/j.chroma.2014.09.065

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ln(k)=ln(kw)+S1ϕ+S2 ln(ϕ) (2) ln(k)=ln(kw)+2ln(1+S2ϕ)− S1ϕ

1+S2ϕ

(3) whereϕisthefractionofwater,kwistheextrapolatedvaluesofkfor ϕ=0(i.e.,pureACN)andSisthesolventstrengthparameterwhich isaconstantforagivencompoundandorganicsolvent[18,19],S1 theslopeforthenon-linearmodels,S2 thecurvaturecoefﬁcient [21].

Grecoetal.reporteddeterminationcoefﬁcientsR2_above_0.99 for14benzoicacidsusingEq.(2)[14].Inarecentstudy,including severalanalytespossessingdiversephysico-chemicalproperties, wereportedR2

adjustedandQ2-valuesfortheempiricalNeueandKuss (Eq.(3))model,closetothoseofthemixedmodel(Eq.(2))[12]. However,thegradientretentionpredictionsweremuchless accu-rateinHILICthanRPLC,restrictingtheuseofcommercialsoftware packagesrequiringthesimulationoftheretentionofeverypeakin thechromatogram[12].

Theexpressionforthegradientretentionfactorcanbefoundby solvingthefundamentalgradientequation:

t0= tR

−t0

0 dts

k(ϕ) (4)

wheretRandt0arethetotalretentiontimeandthecolumndead time,respectively[20]andtsisthetimeinthestationaryphase. Whereasthemixedmodel(Eq.(2))nolongerhasananalytical solu-tiontothefundamentalgradientequation,itisoneofthevirtues oftheNeueandKuss-model(Eq.(3))thatitiseasilyamenableto ananalyticalsolution,leadingtothefollowingexpressionforthe effectiveretentionfactorkeff=(tR−t0)/t0[21]:

keff=t_tD

0+

[0+(1+S20)/S1ln(1+ˇkwS1(t0−tD/k0)exp(−S10/1+S20))]/[1−(S2(1+S20))/S1ln(1+ˇkwS1(t0−tD/k0)exp(−S10/1+S20))]−0

ˇt0

(5) where tD is thedwell time, ˇis the gradientslope, deﬁned as

(ϕe−ϕ0)/tGandk0istheisocraticretentionfactoratthestartof thegradient,i.e.forϕ=ϕ0.

Inapreviousstudy,involvingsampleswithpteridines,sugars andadrugmixtureofvenlafaxine,tramadolandtheirmetabolites inHILICweobservedstronglynon-linearretentionrelationships, thatweresocomplexthattheycouldnotbemodeledusingany oftheexistingnon-linearretentionmodels.Asaconsequence,the traditionalretentionmodelingapproach[22]thatissosuccessful andwidespreadusedinRPLC,couldnotbeappliedand wehad toswitchtoamodel-guidedsearchapproach(so-calledPEWS2 -technique[11,12]).Forasamplecontainingcompoundsbehaving more“nicely”,individualretentionmodelingusinganon-linear 3-parametermodel(mixedmodelandtheempiricalmodelfromNeue andKuss)couldbeusedtooptimizethegradientconditions.

Inthepresentcontribution,wereportontheoptimizationofa HILICseparationoftwelvenucleobasesandnucleosidesusingthis individualretentionmodelingandthecouplingofcolumns(with differentstationaryphases).IntheadoptedMDworkflow,three differentcolumnchemistriesandtwomobilephasepHweretested. Theseparationofnucleicacidsandanalogsareofgreat inter-estinpharmaceuticalsciences,genomics,geneticsandothers[23]. Massoliniandcoworkersusednarrowborecolumnswith gradi-entelution(ZIC-HILIC,150mm×2.1mm,5␮m)toseparatethe 12nucleobasesandnucleosidesincludedinthisstudyin55min. Nikitasetal.usedreversed-phaseliquidchromatography (with-outionparingreagent)toseparate16nucleobasesandnucleosides usingtwo-segmentgradientprofiles[24].Thelinearlog-log reten-tionrelationshipshowedbetterpredictionaccuracycomparedto thesemi-logretentionrelationship(Eq.(1)),bothforsimplelinear andmulti-lineargradientprofiles.Jinetal.[15]reportedR2_-values around0.999andisocratic predictionerrors smallerthan 5%at

95%ACNforeightnucleosidesonsixdifferentcolumns,usingEq. (2).However,nogradientpredictionswereevermadeusingthis mixedmodel.Pappa-Louisiandcoworkersreportedonthegradient retentiontimepredictionsofaminoacidsinHILICusingthe LSS-model(Eq.(1))forlinear,multi-linearandcurvedelutionproﬁles withthesamestartingconcentration.

2. Experimental

WaterwasobtainedfromaMilli-Qwaterpurificationsystem fromMillipore(Bedford,MA,USA).Acetonitrile(ACN),methanol (MeOH)andformicacidwereofULC-MSgradeandpurchasedfrom Biosolve(Valkenswaald,Netherlands).Ammoniumacetate(>98%, Sigma–Aldrich,Belgium)buffer10mMwaspreparedby weigh-ingadequatemassofammoniumacetate.ThepHwasadjusted to 3.0 or 6.0 with formic acid (FA). All compounds (thymine, uridine, inosine,adenine,uracil, hypoxanthine,cytidine, thymi-dine,adenosine,cytosine,guanineandguanosine)werepurchased fromSigma–Aldrich.Stocksolutionsof1000ppmwereprepared in MeOH except for guanosine and guanine (0.1%FA and KOH solutions,respectively).ThesamplesweredilutedinACN+0.1% FAand injectedat100ppm.Theinjectionvolumewas1␮L.All experimentswereperformedonanAgilentInfinity1290system withadwellvolumeof112␮L.ThecolumnswereSupelcoHILIC and SupelcoOH5, i.e., baresilica and pentahydroxy functional-ized silicarespectively (100mm×2.1mm, 2.7␮m), and Waters AcquityAmide,i.e.,amidefunctionalizedsilica(100mm×2.1mm, 1.7␮m).Thedeadtimesweremeasuredat70%ACN:0.419,0.381 and0.422minonthebaresilica,thepentahydroxyandtheamide stationary phase, respectively. The flow rate was 0.5mL/min.

Temperaturewasset25◦C.UV-detectionwassetat254nm.The isocraticscoutingrunswereperformedusingdifferentsubgroups (seedifferentcolorsinFig.3),toavoidoverlappingpeaksandensure accurateretentiontimedetermination.

2.1. Dataanalysis

Matlabsoftware(2009)wasusedfortheestimationofthemodel parametersandthecalculationoftheoptimalgradientconditions viaanin-housewrittenMatlabcode.Theretentionfactorsofthe isocraticscoutingrunswereusedtoobtainthemodelparameters (Eqs.(2)and(3))vialeastsquaresﬁttingusingtheMatlab® rou-tinelsqcurveﬁt.Gradientretentiontimeswereeitherpredictedby implementingtheanalyticalexpression(Eq.(5),fortheNeue–Kuss model)inMatlab-softwareor,fortheothernon-linearmodel(Eq. (2)),vianumericalintegrationofthefundamentalgradient equa-tionviaanin-housewrittenMatlabroutinebasedonthetrapezoid rule. t0=

tR−t0 0 dts k(ϕ)= tD k0 + 1 ˇ

ϕ_elution ϕ0 dϕ k(ϕ)⇔ˇ·

t0−tD k0

=

ϕ_elution ϕ0 dϕ k(ϕ)=I (6)

ThepercentageofACNatelutionϕelutionisobtainedby minimiz-ingI−ˇ*(t0−tD/k0).Fromϕelution,theeffectiveretentionfactorkeff canbecalculatedvia:

keff =tR−t0 t0 = tD t0 + elution−0 ˇt0 (7)

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Table1

R2

adjustedandQ2valuesandtheretentionparameterskw,S1andS2forthe12nucleobasesandnucleosidesonthepentahydroxystationaryphasecolumnpH=6.

Eq.(3) Eq.(2) R2 _Q2 _ln(k w) S1 S2 R2 Q2 ln(kw) S1 S2 Thymine 1.0000 0.9998 1.96 21.2 2.4 0.9988 0.9911 −0.45 −3.3 −0.6 Uracil 0.9998 0.9996 3.12 39.3 4.2 0.9989 0.9922 −1.54 −1.0 −1.2 Thymidine 0.9991 0.9935 2.88 31.7 3.3 0.9993 0.9985 −0.95 −2.7 −1.0 Uridine 1.0000 1.0000 3.09 42.4 4.7 0.9989 0.9918 −1.84 −0.3 −1.2 Inosine 0.9999 0.9991 3.66 36.7 3.5 0.9994 0.9960 −0.85 −2.9 −1.2 Adenosine 1.0000 0.9999 3.93 50.0 5.0 0.9990 0.9925 −1.93 −0.3 −1.5 Hypoxanthine 0.9999 0.9997 4.30 44.0 4.0 0.9992 0.9938 −1.14 −2.4 −1.4 Cytosine 0.9994 0.9968 1.96 21.2 2.4 0.9998 0.9991 −0.45 −3.3 −0.6 Adenine 1.0000 0.9999 0.93 18.5 2.7 0.9990 0.9929 −1.11 −1.5 −0.5 Cytidine 0.9999 0.9992 1.36 21.7 2.7 0.9994 0.9958 −1.12 −2.4 −0.6 Guanine 0.9994 0.9984 5.08 72.0 6.4 0.9993 0.9987 −2.27 −0.6 −1.7 Guanosine 0.9994 0.9986 5.23 62.9 5.3 0.9989 0.9979 −1.43 −2.9 −1.6

The prediction errors were calculated as (tR,experiment− tR,predicted)/tR,experimentwithtR=t0*(1+keff).

Thegradientoptimizationstrategyconsistsofagridsearch, scan-ningthroughallcombinationsofϕ0andˇ(100×100conditions withln(ˇ)equallyspacedbetween0.001and0.5andϕ0between 0.05and0.35).Forallcompounds,theretentiontimetRispredicted andtheresolutionRs(Eq.(8))estimatedunderallthecombinations ofϕ0andˇ. Rs= √ N 4 k 1+kelution (8) wherekelutionistheaverageretentionfactorofthetwocompounds whenelutingfromthecolumn,i.e.forϕ=ϕelution.Thebestgradient conditionscorrespondtobaseline separation(Rs,crit=1.6)within theshortestpossibleanalysistime(tR,analysis=tR,lastcompound).When multiple good solutions are found, these solutions are ranked, accordingtotheirrespectiveanalysistimes.

Forthecoupledcolumnswithdifferentstationaryphases,the sameapproachcanbefollowed,usingtheanalyticalexpressions fora coupledcolumnsystem(Eqs. (9)–(12)).In Eq.(8) the iso-craticplatenumberNisthesumoftheindividualplatenumbers (Ncolumn1+Ncolumn2)and kelution is theretentionfactor atelution fromthesecondcolumn.

Notethatotherqualitycriterions,suchastheScriterion[25], couldbeusedintheoptimization.

3. Resultsanddiscussion

3.1. Retentionmodeling

Inaﬁrststep,theisocraticretentionrelationshipsforthetwelve nucleobasesandnucleosidesinHILICmodewereestablishedby performing10isocraticmeasurements(95,94,93,92,91,90,88, 85,80and70%ACN),onthreedifferentstationaryphasechemistries at twodifferentpH-values. Subsequently,we performeda least squaresﬁtting of the obtainedisocratic retention factors,using Eqs.(2)and(3),toestimatetheretentionparameters.Thehigh numberof isocraticrunswasbasedonourpreviousexperience withpteridines,sugarsandthedrugmixtureofvenlafaxine, tra-madolandtheirmetabolites,showingthatverystrongcomplex non-linearitiescanoccurinHILIC.

InFig.1,theestablishedmodelsforallcompoundsontwo sta-tionaryphasechemistriesaregiven(pH=6).Thebaresilicashowed lessretentionforallcompoundscomparedtothepentahydroxy column.Bothretentionmodels(Eqs.(2)and(3),resp.redandblue curvesinFig.1)wereabletodescribetheisocraticretentiondata

Fig.1.Isocraticmeasurementsandestablishedretentionmodels(kvs.fractionofACNϕ)foralltwelvenucleobasesandnucleosidesonthepentahydroxyandthebaresilica

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Table2

Averagegradientpredictionerrorsfor12nucleobasesandnucleosidesandfour

gradientruns(95–85%ACNin2and6min,92–85%ACNin2and6min).

Eq.(2) Eq.(3) Pentahydroxy pH3 2.8% 3.0% pH6 3.0% 3.5% Baresilica pH3 3.6% 3.2% pH6 2.1% 1.8% Amide pH6 3.5% 3.6%

veryaccuratelyandthedifferencebetweenbothretentionmodels wasverysmall(Fig.1).InTable1,theR2

adjustedandQ

2_values_and theobtainedretentionparametersareprovidedforallcompounds onthepentahydroxycolumn.

Sinceusingalltenisocraticrunstoestablishtheretention mod-elsforgradientoptimizationpurposeswouldbetoomuchwork inapracticalapplication,weinvestigatedwhethertheretention modelscouldalsobeestablishedusingasmallernumberof scout-ingruns.Forthispurpose,fourscoutingisocraticruns(95,90,85 and80%ACN)wereusedtoinvestigatethepossibilitiesof gradi-entretentiontimemodeling.Subsequently,theretentionmodel parametersobtainedfromtheseisocraticrunswereusedtopredict theretentionunderfourdifferentgradientswithvariousgradient timestGanddifferentstartingcompositionsϕ0(95–85%ACNin2 and6min,92–85%ACNin2and6min).Theexperimentalgradient retentionfactorswerecomparedwiththepredictedonesandthe percentageerrorswerecalculated.

Allabsolutegradientpredictionserrorsweresmallerthan5% withanaverageofaround3%forallpHsandcolumns(seeTable2). Nosigniﬁcantdifferenceinpredictionerrorswasobservedbetween thedifferentgradientrunsandbetweenthemixedmodelandthe empiricalmodelfromNeueandKuss.Fig.2showsthecorrelation plotforkpredicted vs.kexperiment usingthesefourisocraticscouting runs.

3.2. Separationoptimization 3.2.1. Individualcolumns

AsshowninSection3.1boththeempiricalNeueandKuss-model andthemixedmodelgavesimilargradientpredictionerrors. How-ever,sincethecalculationtimeusingtheanalyticalexpression(Eq.

Fig.2.Correlationplotforkpredictedvs.kexperimentfor12nucleobasesandnucleosides

includingfourdifferentgradients(95–85%ACNin2and6min,92–85%ACNin2

and6min)onthepentahydroxystationaryphaseatpH=6.Retentionparameters

obtainedusingfourisocraticscoutingruns(95,90,85and80%ACN).

Table3

Retentiontimepredictions(min)onthepentahydroxystationaryphaseatpH=6.

Gradientconditions:94–90.6%ACNin3.36min.

tR,predicted (min) tR,experiment (min) %error (Eq.(3)) %error (Eq.(1)) Thymine 0.819 0.819 −0.02% −3.80% Uracil 0.881 0.874 0.79% −2.70% Thymidine 1.024 1.024 0.03% −4.40% Uridine 1.497 1.480 1.17% −3.30% Inosine 2.067 2.069 −0.11% −7.30% Adenosine 2.147 2.130 0.79% −5.00% Hypoxanthine 2.212 2.200 0.54% −6.10% Cytosine 2.962 2.987 −0.02% −3.80% Adenine 3.151 3.119 0.79% −2.70% Cytidine 3.967 3.931 0.03% −4.40% Guanine 3.828 3.891 −1.62% −3.56% Guanosine 4.627 4.655 −0.60% 0.60%

(8))viatheNeueandKussisocraticretentionrelationshipis sig-niﬁcantlyreducedcomparedtothenumericalintegrationviathe mixedmodel,gradientoptimizationwasperformedwiththeNeue andKussretentionparameters.Becausethemodelingshowedto bereasonablyaccurate(consistently<5%),allpeakswere individ-uallymodeledintheMDstrategy.Thisisanalternativegradient optimizationapproachcomparedtothePEWS2_strategy_which_has alreadybeensuccessfullyappliedforthegradientoptimizationin theHILICmode[12],whentheretentionmechanismofthe com-poundsistoocomplextobeaccuratelydescribedbythesimple modelfromNeueandKuss.Firsttheretentiontimeandpeakwidth ofeverypeakinthemixtureissimulatedundervariousgradient conditions.Then,thecorrespondingresolutionmapRs(Eq.(8))is constructedfromwhichtheoptimalgradientconditionscanbe obtained.Theoptimalconditioncorrespondstothecasewherethe criticalresolutionRs,critwasmaximal,similartotheresolutionmaps constructedincommercialRPLCmodelingsoftwarebasedonthe linearsolventstrength(LSS)model(Eq.(1)).Asanexample,the bestpossibleseparationonthepentahydroxystationaryphaseis providedinFig.3.Therelativelyhighconcentrations(100ppm), commonforUV-detection,andaninjectedvolumeof1␮Lresulted ingoodchromatogramswithahighsignal-to-noiseratio.Asthe injectedmass(100ng)wasquitelow,noproblemsof overload-ingoccurred.Moreover,sincethereisnoirreversibleadsorptionof thecompoundsatthesurfaceofthestationaryphase,theretention timeswerereliableandidenticalforboththeindividualcompounds andthemixturecompounds.Notethattheseconcentrationsare notcriticalfortheestimationoftheretentionmodelparameters. Incasemoreexpensiveorscarcecompoundswouldbeused,lower concentrationscouldbeobviouslyconsideredduringthescouting runs.Accurateretentiontimepredictions(maximalerrorof1.6%) werefoundforallcompounds(Table2).Comparingtheprediction errorsusingthenon-linearmodelandtheLSS-model,itisclear thatthepredictionaccuracycanbesigniﬁcantlyimproved. More-over,thepredictionerrorsusingthenon-linearmodelinTable3 weremuchbettercomparedtotheaveragepredictionerrorsin Table2.Thelattercouldbeexplainedbythedifferenceingradient rangebetweenthebestpossiblesolution(94–90.6%ACN)andthe gradienttestruns(95–85and92–85%ACN).

We also compared the calculated (experimental) Rs=(tR,2−tR,1)/(w1+w2)andthepredictedRsusingEq.(8)(Fig.4). A similar trend in experimental and predicted Rs was found, immediatelyindicating the critical pairs,although the absolute valuesdifferedsigniﬁcantlyforthelaterelutingcompounds.

3.2.2. Coupledcolumns

Sincenoneoftheconsideredcolumnscouldprovidesufﬁcient separationofallcompounds,weinvestigatedthepossibilitiesto

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Fig.3.Overlaychromatogramof12nucleobasesandnucleosidesonthepentahydroxystationaryphaseatpH=6.Gradientconditions:94–90.6%ACNin3.36min.

Fig.4. ExperimentalandpredictedRsusingEq.(8)forchromatograminFig.3.

performgradientpredictionusingcoupledcolumnswithdifferent stationaryphasechemistriestooptimizetheseparation.

Usingacoupled-columnsystem,gradientelutionretentiontime predictionscanstillbedoneusinganalyticalexpressions.The fun-damentalgradientequationisnowasumoftwointegrals,using bothretentionmodels:

t0 =

tR−t0 0 dts k(ϕ)=

ϕ_{elution,column1} ϕ_0,column1 dϕ kcolumn1_(ϕ) +

ϕ_{elution,column2} ϕ_0,column2=ϕelution,column1 dϕ kcolumn2_(ϕ) (9)

wherethefirstandthesecondintegralsdescribethepartofthe gradientfeltbythecompoundinthefirstandthesecondcolumn, respectively.Thefirstintegralincludesthedwelltimeofthe sys-temtD,thecolumndeadtimet0andtheretentionparameterskw ,S1 andS2fromthefirstcolumntocalculatethefractionofACNat elu-tionfromthefirstcolumnϕelution,column1.Thesecondintegraluses ϕelution,column1asthestartofthegradient(ϕ0,column2=ϕelution,column1) andincludesazerodwelltime,thecolumndeadtimet0andthe retentionparameterskw,S1andS2fromthesecondcolumn.The expressionforϕelutionis:

elution= 0+

[1+S20]/S1ln(1+ˇkwS1(t0−tD/k0)exp(−S10/(1+S20)))

1−[S2(1+S20)]/S1ln(1+ˇkwS1(t0−tD/k0)exp(−S10/1+S20))

(10) whereϕ0isrespectivelyϕ0,column1andϕ0,column2.Fromϕelutionthe retentiontimetRinbothcolumnscanbecalculated:

elution=0+ˇ(tS−tD)=0+ˇ(tR−t0−tD)⇔tR=tD+t0+elution−0

ˇ (11)

Then, thetotal retention time is thesumof both individual retentiontimes.Theresultinganalyticalexpressionforthegradient retentionfactoris:

keff=

(tR,column1+tR,column1)−(t0,column1+t0,column2) (t0,column1+t0,column2)

(12) Thecomputer gridsearchwasextended tothe coupled col-umnsystemsandacombinationoftheamideandthebaresilica stationaryphaseswasproposedbythealgorithm,astheelution order wassimilaronbothcolumns(elution order ofadenosine and hypoxanthinewasreversed comparedtothepentahydroxy column,seeFig.1)directingtowardbetterseparationwhen cou-plingbothcolumnsinseriescomparedtothesinglecolumnsystem. Almostbaseline separation wasobtainedfor the twelve nucle-obasesandnucleosidesinlessthan7min(comparedto55minfrom Massoliniandcoworkers[22]).Itmustbenotedthatfullbaseline separationcouldpossiblybeobtainedbyincreasingthecolumn length(andthecorrespondinganalysistime).

Thepredictionerrorsusingthecoupledcolumnswere some-whatworsethanforthesingle-columnsystem(Table4),which maybeduetothetubingthatwasusedtocouplethecolumns, but(almost)baselineseparationwasobtainedforalltwelve com-pounds(Fig.5).Theworstpredictedcompoundsfortheoptimized gradientonthecoupledcolumnsystemwerehypoxanthineand adenosine.However,nogoodreasonwasfoundforthisbehavioras noneofthesetwocompoundsisthemostionizedandthenumber ofH-bonddonororacceptorgroupsisnotlargerthanfortheother testmolecules.Therefore,nostrongerinteractionsexistbetween thesetwocompoundsandthestationaryphasethanfortheother compounds.

Alsoforthecoupledcolumns,wecomparedtheexperimental andthepredictedRs(Eq.(8)).Asforthesinglecolumnsystem,a

Table4

Retentiontimepredictions(min)usingtwocoupledcolumns(amideandbaresilica

stationaryphase).Gradientconditions:95–85%ACNin6min.

tR,predicted(min) tR,experiment(min) %error

Thymine 1.773 1.804 −1.7% Uracil 1.944 1.971 −1.4% Thymidine 2.177 2.212 −1.6% Uridine 3.185 3.205 −0.6% Inosine 3.693 3.774 −2.2% Hypoxanthine 3.761 3.918 −4.0% Adenosine 3.854 4.071 −5.3% Cytosine 4.764 4.731 0.7% Adenine 4.944 4.921 0.5% Guanine 5.284 5.354 −1.3% Cytidine 5.628 5.673 −0.8% Guanosine 6.177 6.271 −1.5%

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Fig.5. Separation oftwelve nucleobases and nucleosidesusing twocoupled columns(amideandbaresilicastationaryphase).Gradientconditions:95–85%ACN in6min.

Fig.6.ExperimentalandpredictedRsusingEq.(8)forchromatograminFig.5.

similartrendinRswasfoundforallpeaks,indicatingthecritical pairs(Fig.6).Thisagainveriﬁestheuseofindividualpeak model-ing,includingretentiontimeandresolution,usingcoupledcolumn systems to optimize the gradient conditions for HILIC separa-tions.However,theabsolutepredictionerrorswerestillsigniﬁcant. Therefore,attemptstoincludetheseRspredictionswillbeincluded infutureresearch.

Theinﬂuenceofthecolumnsorderwasalsoinvestigatedandno signiﬁcantdifferenceinselectivityandRs,critwasobservedinthis case.

4. Conclusions

Inthisstudy,theseparationoftwelvenucleobasesand nucleo-sideswasoptimizedviachromatogramsimulation,i.e.,prediction ofindividualretentiontimesandestimationofthepeakwidths, withtheuseoftheempirical(reversed-phase)non-linearmodel proposed by Neue and Kuss [21]. As none of the tested sin-glecolumnscouldresolveallpeaks,themodelingwasextended to coupled-column systems (with different stationary phase chemistries)and analytical expressions werederived. The opti-mizedgradientusingacombinationofanamideandabaresilica stationary phase and obtained via the adopted modeling and computer-optimizationapproachresultedinalmostbaseline sep-arationofthetwelvenucleobasesandnucleosideswithananalysis timeoflessthan7min.Theoptimizedseparationconditionswere obtainedinlessthan4hofinstrumenttime(including equilibra-tiontimesof4mincorrespondingtoroughly20columnvolumes). Assuch,thisstudyprovidesanexampleofacasewhere individ-ualretentionmodelingandcomputer-optimizationcanbeusedas awaytooptimizethegradientconditionsintheHILICmode pro-videdanon-linearmodelsuchastheNeueandKussmodelcanbe

used.Forcompoundswhoseretentionmechanismismorecomplex thanthatofthepresentlystudiedset,searchapproachesdepending lessstronglyonanaccurateretentionmodeling,suchasthe pre-dictiveelutionwindowshiftingandstretching(PEWS2₎_method, shouldbepreferredtooptimizethegradientconditionsintheHILIC separationmode[11,12].

Limitationsoftheindividualpeakmodelingapproachinclude theretentiontimerobustnessduetophaseaging,inter-/intra-day methodreproducibilityandsamplematrixeffects.Inworstcase, thismayrequirethepredictiontoberedoneinsomecases(e.g. batch-batchreproducibilityofcolumnswillneedconsideration). Ontheotherhand,theproposedoptimizationalgorithmforHILIC separationscaneasilybeintegratedincommercialreversed-phase softwaresuchasDrylab[26],includingarobustnessmodule,to determinebywhich factorsthecriticalresolution Rs,critis inﬂu-encedmostly.

Acknowledgments

DaveBellisgratefullyacknowledgedforprovidingtheSupelco columns.Theauthorsacknowledgetheﬁnancialsupportfromthe ResearchFoundationFlanders(FWO-Vlaanderen).E.T.isthe recip-ientofaPhD-fellowship(FWO-Vlaanderen).

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