A corneal-PAMPA-based silico model for in predicting cornealpermeability Journal of Pharmaceutical and Biomedical Analysis

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ContentslistsavailableatScienceDirect

Journal of Pharmaceutical and Biomedical Analysis

jo u r n al ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / j p b a

A corneal-PAMPA-based in silico model for predicting corneal permeability

Anna Vincze

^a

, Gerg ˝o Dargó

^a

, Anita Rácz

^c,∗∗

, György T. Balogh

^a,b,∗

aDepartmentofChemicalandEnvironmentalProcessEngineering,BudapestUniversityofTechnologyandEconomics,M ˝uegyetemRakpart3.,1111, Budapest,Hungary

bDepartmentofPharmacodynamicsandBiopharmacy,UniversityofSzeged,Eötvösu.6.,6720,Szeged,Hungary

cInstituteofMaterialsandEnvironmentalChemistry,ResearchCentreforNaturalSciences,MagyarTudósokKrt.2.,1117,Budapest,Hungary

a rt i c l e i nf o

Articlehistory:

Received3February2021

Receivedinrevisedform14June2021 Accepted15June2021

Availableonline17June2021

Keywords:

Cornealpermeability Invitro

Non-cell-basedmodel PAMPA

Insilicomodel QSPR

Quantitativestructure-property relationships

Lipophilicity Polarsurfacearea

a b s t ra c t

Thecapabilitytopredictcornealpermeabilitybasedonphysicochemicalparametershasalwaysbeen adesirableobjectiveofophthalmicdrugdevelopment.However,previousworkhasbeenlimitedto caseswhereeitherthediversityofcompoundsusedwaslackingortheperformanceofthemodels waspoor.Ourstudyprovidesextensivequantitativestructure-propertyrelationship(QSPR)modelsfor cornealpermeabilitypredictions.Themodelsinvolvedinvitrocornealpermeabilitymeasurementsof189 diversecompounds.Preliminaryanalysisofdatashowedthatthereisnosignificantcorrelationbetween corneal-PAMPA(ParallelArtificialMembranePermeabilityAssay)permeabilityvaluesandotherpharma- cokineticallyrelevantinsilicodrugtransportparameterslikeCaco-2,jejunalpermeabilityandblood-brain partitioncoefficient(logBB).TwodifferentQSPRmodelsweredeveloped:oneforcornealpermeability andoneforcornealmembraneretention,basedonexperimentalcorneal-PAMPApermeabilitydata.Par- tialleastsquaresregressionwasappliedforproducingthemodels,whichcontainedclassicalmolecular descriptorsandECFPfingerprintsincombination.Acomplexvalidationprotocol(includinginternaland externalvalidation)wascarriedouttoproviderobustandappropriatepredictionsforthepermeability andmembraneretentionvalues.BothmodelshadanoverallfitofR²>0.90,includingR²-valuesnotlower than0.85forvalidationruns,andprovidequickandaccuratepredictionsofcornealpermeabilityvalues foradiversesetofcompounds.

Abbreviations: ADME,absorption,distribution,metabolism,excretion;API,activepharmaceuticalingredient;Caco-2,celllineofheterogeneoushumanepithelialcol- orectaladenocarcinomacells;clogD7.4,logofcalculateddistributioncoefficientatpH7.4;clogP,logofcalculatedpartitioncoefficient;clogPeCaco-2,logofcalculatedCaco-2 permeability;clogPejejunal,logofcalculatedjejunalpermeability;DOOD,D-optimaloniondesignalgorithm;fbu,fractionunboundinthebrain;GA,geneticalgorithm;HBD, numberofhydrogenbonddonors;HPLC,highperformanceliquidchromatography;ka,absorptionrateconstant;logBB,blood-brainpartitioncoefficient;logD7.4,logof distributioncoefficientatpH7.4;logDI7,65,degreeofionizationatpH7.65;logP,logofpartitioncoefficient;logPe,logofeffectivepermeability;logS,logaqueoussolubil- itymeasuredinmol/L;MR,membraneretention;MW,molecularweight;NN,neuralnetworks;PAMPA,parallelartificialmembranepermeabilityassay;PBS,phosphate bufferedsaline;PC,phosphatidylcholine;PCA,principalcomponentanalysis;P-gp,P,-glycoprotein;PLS,partialleastsquares;PLS,COMP.numberofPLScomponentsinthe model;PPB,plasmaproteinbinding;PSA,polarsurfacearea;Q²CV,goodnessoffitforthecross-validation;R²P,goodnessoffitfortheexternalvalidation;QSAR,quantitative structure-activityrelationship;QSPR,quantitativestructure-propertyrelationship;R²,goodnessoffitforthecalibration;RMSEC,rootmeansquarederrorofcalibration;

RMSECV,rootmeansquarederrorofcross-validation;RMSEP,rootmeansquarederrorofexternalvalidation;TPSA,topologicalpolarsurfacearea;VIP,variableimportance projection;␭max,thewavelengthofmaximumabsorbance;Y-SCR,CVgoodnessofﬁtforthecrossvalidationusingYscrambling;Y-SCRP.,goodnessofﬁtforthetestprediction usingY-scrambling.

∗Correspondingauthorat:DepartmentofChemicalandEnvironmentalProcessEngineering,BudapestUniversityofTechnologyandEconomics,M ˝uegyetemrakpart3., 1111,Budapest,Hungary.

∗∗Correspondingauthor.

E-mailaddresses:racz.anita@ttk.hu(A.Rácz),balogh.gyorgy@vbk.bme.hu(G.T.Balogh).

https://doi.org/10.1016/j.jpba.2021.114218

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1. Introduction

Theeyeisachallengingtargetoftherapy.Becauseofitscompli- catedanatomicstructureandsmallabsorptivesurface,itisdifficult to achievetherapeutic druglevelsin theinterior oftheeye by topical dosageforms (eye drops, ointments,in-situgel-forming systems,etc.).Moreinvasiveonessuchasintraocularinjections orimplantscanbeveryusefulformaintaininghighdruglevelsin both theanteriorandposteriorsegment[1–3].Topicaladminis- trationisthemostcommonwayofanteriorsegmenttreatment asitisnon-invasive,easyandverycomfortable.However,ithas manydrawbacksincludinglowbioavailabilitydespitethefactthat the activepharmaceuticalingredient (API) is usuallyapplied in highdoses[4].Blinking,tearformationandnasolacrimaldrainage causeahugedropindruglevelasthesolutionsarewashedaway withinthefirst15–30secondsfromtheeyesurface [5,6]. Typi- callynomorethan5%bioavailabilitycanbereachedintheanterior segmentbytopicaladministrationduetothesedefensemecha- nisms,andmembranepenetrationissues[4–7].Byusingdosage formswithhighviscosityandmucoadhesivitytheresidencetimeof drugscanbeincreased,however,theseointmentsandinsitugelling systemsoftencauseirritationandblurredvision[1,4,5,8].Higher druglevelscan bereachedin theposteriorsegmentof theeye bysystemicadministrationorintraocularinjectionsandimplants [2,3,5,9].Whilethefirstmayresultinsystemicsideeffectsdueto highdosagethelatterdoesnotrequirefrequentuse,although,it maycauseendophthalmitis,lens damageorretinaldetachment [4,10,11].Despitelow patientcompliance,theintraocularinjec- tions(usuallytargetingthevitreous)arestillthemostcommonly usedposteriorsegmenttherapiessincetherearenootherefficient deliveryroutesforreachinghighdruglevelsintheposteriorwith minimalsystemicsideeffects[9].

The possible routes of absorption are the corneal and non- corneal pathwaysinterms oftopicaladministration [5,6,10].In thecase ofnon-cornealroutesthedrugpenetratesthroughthe conjunctivaand/orsclerawhich isnotveryeffectiveduetothe presenceoflocalcapillarybedsthatcontinuouslyremovethedrug, transferring itintothesystemic circulation.On theotherhand, thecornealrouterepresentsthemainabsorptionpathformost ophthalmictherapeutics(small,lipophiliccompounds)andforthis reason,itisthemoststudiedareabothintermsofdrugdiscovery anddrugformuladevelopment[4,5].Thecorneaisaclearandavas- culartissueconsistingof5layers:cornealepithelium,Bowman’s layer,stroma,Descemet’smembraneandendothelium.Although therelativethicknessesofcornealepithelium,stromaandendothe- liumareabout0.1:1:0.01,thethinnestcornealepitheliumisthe mainbarrierofdrugabsorptionintotheeye[7,10].

Likeinthecaseofothertopicaldosageforms,theinvivohuman pharmacokineticcharacterizationofAPIsinophthalmictreatment isgreatlyhamperedbythedifficultyofdirectlyexaminingtopical drugconcentrations.Furthermore,duetotechnicaldifficultiesno suitableinvivoanimaltestingsolutionisavailableeither[12].For preclinicalophthalmicabsorptionstudiesexvivoandinvitrocel- lularmodelsareavailable.Forexvivostudiesexcisedrabbitcornea isusedmostcommonlybecauseofeasyaccessandanatomicsim- ilaritiesbetweenrabbitandhumaneyes[10,13].However,there arealsosomedifferencesbetweenthetwospeciesandthusthe penetrationisgenerallymuchhigherandcannotbecorrelatedade- quatelytohumans[10].Invitrostudiesapplyrabbitorhumancell cultureswhichareconsideredasamoreethicalalternative.Inthis case,mostlycornealepithelialcellsareusedconsideringthemain roleofcornealepitheliumindrugtransport,however,itisdifficult toisolateoculartissuesforthispurposeandthelifespanofthese primarycellsisveryshort[13,14].Althoughimmortalizedcelllines provideaninexhaustiblesupplyofcellstheymayexhibitabnormal geneexpressionorbiologicalfunctionsespeciallyafterseveraldivi-

sions.Also,penetrationacrosscellculturesisonlyacrudeestimate atbestsinceasingletypeofcellcannotrepresentthecomplexity ofthecornealbarrierasawhole[13].

Thecapabilitytopredictcornealpermeabilitybasedonphysic- ochemical parameters hasalwaysbeena desirable objective of ophthalmicdrugdevelopment.Forthispurpose,greateffortshave beenmadetodeveloppredictivemodelsstartingwiththeworkof SchoenwaldandWard[15].Asummaryoftheearlydevelopment stagescanbefoundinTable1.Thesemodelswerebasedonjust afewphysicochemicalpropertiesbutweretypicallynotgenerally applicable–theirdiversityandperformancewerelimitedtoonly certaingroupsofmolecules.

Inthepastfewdecades,quantitativestructure-propertyrelationship (QSPR) techniques have become a well-established methodforcorrelatingmolecularstructureandphysicochemical propertiesofchemicalcompoundswiththeuseofseveraldescrip- torsandnowadaystheyarecommonlyusedforthefastprediction of differentADME(absorption, distribution,metabolism, excretion)relatedmolecularproperties[21,22].Therehavebeenafew attemptstodevelopQSPRmodelsalsoforthepredictionofcorneal permeability.Kidronetal.usedpartialleastsquares(PLS)regres- sionfor 69 non-congenericcompoundsand concluded thatthe totalnumberofputativehydrogenbonds(HB_TOT)andlogarithmic distributioncoefficients(logDpH7.4,logDpH8.0)werethemostsig- nificantdescriptorsforcornealpermeability[12].Thesignificance oflipophilicityin cornealpenetrationhasbeenrecognizedlong ago,whileforionizablecompounds(mostoftheophthalmicdrugs) thedistributioncoefficientmeasuredatthepHofaqueoushumor andtearfilm(pH7.2–7.6) hasbeenfoundtobeamoreproper descriptorintermsofmembranepermeability[5,8].Inthework ofGhorbanzadeetal.thesamedatasetwasanalyzedbystepwise multivariatelinearregression (MLR),andneuralnetworks(NN) aswell[23].Withthemultilayerperceptron-NNtechnique,they establishedanonlinearmodelforcornealpermeabilitywithmod- erateperformance. AlthoughKidronandGhorbanzade analyzed morecompoundscomparedtotheirpredecessors,thedatacame fromseveralsourceswithdifferentexperimentalconditions.

In2018,Ramsayetal.producedacornealandconjunctivalQSPR modelbyPLSandprincipalcomponentanalysis(PCA)basedonan exvivodatasetof32smallmolecules.Theyfoundthatcornealper- meabilityhasaninverserelationshipwiththepolarsurfacearea (PSA)andthenumberofhydrogenbonddonors(HBD)[24].How- ever,thepredictivepoweroftheirmodelwasrelativelymodest.

Uptothepresentday,therehavebeenseveralmodelsdeveloped forpredictingcornealpermeability, butthere isstillnoreliable QSPRmodelbasedonalargeandhomogeneousdataset.Ofcourse, itisnotaneasymissionsinceexvivoexperimentshaveseriouscon- straintslikethedemandfornumerousanimals,appropriatetissue viabilityandhighcosts.Invitrocellculturemodelsarebetterin termsofcost-effectivenessandthroughput,however,theuseof cell-basedassaysisnotarobustprocess.

To solvethis problem, we have recently developed a novel invitronon-cellularPAMPA-basedmethodforinvestigatingthe cornealpermeabilityofAPIs[25].Corneal-PAMPAisarobust,high- throughputassayusingeasilyaccessiblematerialslikephosphate bufferedsaline(PBS),phosphatidylcholine,dodecane,hexaneand chloroform.Fordevelopingthemethod,exvivorabbitcornealper- meabilitydatawereusedfromheterogeneousdatasetsinterms ofexperimentalconditions.Despitetheuseofheterogeneousdata, thePAMPAmodelwithstandardizedexperimentalconditionspro- videdhighlyreproduciblepermeabilityvaluesthatcorrelatedwell withtheexvivodata(R²=0.88).Thecorneal-PAMPAmethodology canprovidemanycornealpermeabilityvaluesasahomogeneous datasetinashorttimeperiodandthereforeitisasuitablebasisfor thedevelopmentofaninsilicomodel.

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Table1

Detailedsummaryoftheearlymodelsforcornealpermeabilitydetermination.

Equation Typeofmolecules(andnumbers) Molecularproperties Ref.

parabolic steroids(11) logP [15]

parabolic N-alkyl-p-aminobenzoateesters(6) logP [16]

parabolic ␤-blockingagents(12) logP,logDpH7.65,logMW,logDI7.65* [17]

parabolic/sigmoidal ␤-blockingagents(13) logP [18]

parabolic ␤-blockers,steroids,miscellaneouscompounds(32) logD,logP(logPoctanol-logPalkane) [19]

MLRmodel ␤-blockers,steroids,miscellaneouscompounds(30) quantumchemicaldescriptors(3) [20]

*DegreeofionizationatpH7.65.

In the present work, the corneal permeability of 189 APIs selected froma diversechemical spacewasdetermined bythe corneal-PAMPA method [25] experimentally and used to build a robustQSPRmodelfor predictingcornealpermeability,which couldbeausefultool inthedevelopmentoffutureophthalmic agents.

2. Materialsandmethods 2.1. Materials

Analytical grade solvents like acetonitrile, chloroform, hex- ane,dodecaneandformicacidwerepurchasedfromMerckKGaA (Darmstadt,Germany).Phosphatebufferedsaline(PBS)powder,l-

␣-phosphatidylcholine(PC)andallinvestigatedcompounds(See TableA1.,AppendixA)werepurchasedfromSigmaAldrichCo.Ltd.

(Budapest,Hungary)exceptforbetaxololhydrochloride,bevantolol hydrochloride, bromfenac sodium, bufuralol hydrochloride, 11- deoxycorticosterone,ethoxzolamide,flurbiprofen,nepafenacand penbutolol,whichwerepurchasedfromTorontoResearchChemi- calsInc.(NorthYork,Toronto,Canada).Distilledwaterwaspurified bytheMilliporeMilli-Q^®140GradientWaterPurificationSystem.

2.2. Invitropermeabilitystudies

Thecorneal-PAMPAmeasurementswerebasedonourprevi- ousreport[25].BrieﬂyallcompoundsweredissolvedinPBSbuffer (pH7.4)tomakesolutionswith100␮Mnominalconcentration.

DuetothenegativeeffectofusingDMSOasacosolventonthe goodnessofpredictioninthecorneal-PAMPAassaysystem(accord- ingtoourpreviousreport[25]),noDMSOwasusedforthisstudy either.300␮LoftheinitialPBSsolutionswereplacedintoa96- wellpolypropyleneplate(A)(Agilent,Waldbronn,Germany).For thecorneal-PAMPAmembrane,16mgPCwasdissolvedinasol- ventmixtureofchloroform,hexaneanddodecane5:70:25%(v/v) in atotal volumeof600␮L.Eachwelloftheacceptorplate(B) (MultiscreenAcceptorPlate,MSSACCEPTOR;Millipore)contained 300␮LPBSandeachwellofthedonorplate(MultiscreenTM-IP, MAIPN4510,poresize0.45␮m;Millipore)(C)wascoatedwith5␮L ofthelipidsolution.Afterevaporationofhexaneandchloroform, thedonorplatewasinsertedintotheacceptorplate,andeachwell ofthedonorplatewasﬁlledwith150␮LPBSsolutionsofcom- poundsfromplateA.Afterthat,thedonorplatewascoveredwitha sheetofwettissuepaperandplatelidtopreventevaporationofthe solventduringthe4hincubation(35^◦C,HeidolphTitramax1000).

Ineachassay,tworeferencecompoundsweremeasured:buspirone andhydrocortisonewithhighandlowcornealpermeabilityvalues, respectively.

For HPLCanalysisatleast120␮Laliquotsweretakenout of everywellofplatesBandCandtransferredto96-wellpolypropy- lene platesandsealed.TheinitialplateAwasanalyzedaswell.

Theeffectivepermeabilityandmembraneretentionofdrugswere calculatedusingthefollowingequations[26]:

Pe= −2.303

A×(t−ss)×

₁

1+r_v

×lg

−r_v+

₁₊_r

v 1−MR

× c_D(t) c_D(0)

(1) wherePe istheeffectivepermeability (cm/s),Aistheﬁlterarea (0.3cm²),tistheincubationtimeofPAMPAassay(14400s),ssis thetimetoreachsteady-state(s),r_visthevolumeratioofaqueous compartments(V_D/V_A),V_DandV_Aarethevolumesinthedonor (0.15cm³)andacceptorphase(0.3cm³),cD(t)istheconcentration ofthecompoundafterincubationonplateC(mol/cm³),cD(0)isthe concentrationofthecompoundonplateA(mol/cm³)andMRisthe membraneretentionfactor,deﬁnedas:

MR=1− c_D(t)

c_D(0)− V_Ac_A(t)

V_Dc_D(t) (2)

wherecA(t)istheconcentrationofthecompoundafterincubation onplateB(mol/cm³).Intablesandﬁguresweusuallyusethisterm as100*MR(%).

2.3. HPLCanalysis

Quantitativechromatographicanalyseswerecarriedoutusing anAgilent1260liquidchromatographysystem(AgilentTechnolo- gies,PaloAlto,CA,USA)onaKinetex^®2.6␮mC18100ÅLCcolumn (30×3mm)withamobilephaseflowrateof1.1mL/min.Mobile phaseAandBconsistedof0.1%(v/v)formicacidinwater,andace- tonitrile/water(95/5)with0.1%(v/v)formicacid,respectively.A 3.91minlonglineargradientprogramwasused:inthefirst0.3min 0%B,between0.3and1.8min0–100%B,then100%Bwaskept for0.6minand finally,at2.41the100%Bwasdroppedto0%.

Thiswasfollowedbyanequilibrationperiodof1.5minpriorto thenextinjection.Theinjectionvolumewas6␮L.Chromatograms wererecordedbyadiodearraydetectorinthewavelengthrange of200–500nm,andintegrationwascarriedoutatthe␭maxofeach compound.Data acquisitionand analysiswerecarriedoutwith ChemStationB.04.03.

2.4. Datasetgeneration

Theapplieddatasetcontainedtheexperimentalcorneal-PAMPA permeabilityandthemembraneretentionvaluesof189APIsbased onthepreviouslymentionedexperimentalmodel[15].Thedom- inantprotonationstateatpH7.4wasassignedtoeachcompound withtheChemAxonCalculator(cxcalc)[27]andSchrödinger(Lig- Prep)[28,29].Consequently,theappropriate3Dstructureswere usedforthemoleculardescriptorgeneration.

Classical1,2and3Dmoleculardescriptorsandextendedcon- nectivityfingerprints(ECFP)weregeneratedfortheAPIswiththe DRAGON7.0software[30].Thedefinitionoftheappliedmolecular descriptorscanbefoundintheworkofTodeschinietal.[31].More- over,anadditional80physicochemicalpropertieswerecalculated bytheACD/Perceptasoftware[32].Aninter-correlationlimit of 0.997wasusedforthefilteringoftheclassicaldescriptors[33].Con- stantdescriptorswerealsoexcludedfromthedataset.FortheECFP

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fingerprints,defaultparameterswereappliedinDRAGON7.0,with amaximumradiusof4andafingerprintlengthof1024[34].The finalnumberofgeneratedmoleculardescriptorswas3302,which werefurtherusedfortheQSPRmodelbuilding.

2.5. QSPRmodeling

Partialleastsquares(PLS)regressionwasappliedasaclassical andfrequentlyusedregressionalgorithmforthemodelbuilding.

InPLSregression,latentvariablesarecalculated,whichcanbeused for the predictionof theY dependentvariable,in ourcase the corneal-PAMPApermeabilityvaluesandthemembraneretention.

Asawell-establishedtoolinQSAR/QSPRanalysis,thereisnoneed toexplainthePLSalgorithminmoredetailotherthanreferringto thetutorialpaperofGeladiandKowalski[35].Theoptimalnum- berofPLScomponentsforthemodelswasselectedbasedonthe globalminimumoftherootmeansquarederrorofcross-validation (RMSECV).Outlierselectionofthesampleshasbeencarriedoutby theplotoftheﬁrsttwolatentvariables(PLScomponents).The95

%conﬁdenceellipsewasusedforthedeterminationoftheoutliers.

TherangeoftheYvariable(corneal-PAMPAvalues)wasalsomod- iﬁedto0−50×10⁻⁶cm/s,duetothepoorcoverageoutsideofthis range.

In eachmultivariatecalibrationwiththousandsofmolecular descriptors, the use of variable selection techniques [36] is an essentialstepfortheappropriatemodelbuildingwithgoodpredic- tionperformance.Inourcase,thevariableimportanceprojection (VIP)andgeneticalgorithm(GA)methodswerecombinedforthis purpose.First,thenumberofvariableswasdecreasedtothemost important20%basedonVIPvalues,thenageneticalgorithmwas usedontheremainingvariables.Thisformofpre-ﬁlteringwithVIP scoreswasnecessaryinordertodecreasethecalculationtimefor themoretime-demandingGAprotocol.Themajorparametersof thegeneticalgorithmwerethefollowing:thepopulationsizewas 64,thepercentageoftheinitialtermswas30,thealgorithmwas runforahundredgenerationsanddoublecross-overwasused.

ModelbuildingwascarriedoutinPLSToolbox[37].Validation ofthemodelsisindispensableforreliableprediction,thereforeour modelswerevalidatedinthreedifferentways:cross-validation, externalvalidationandY-scrambling[38].Trainingandtestsplits werecarriedoutbytheD-optimaloniondesignalgorithm(DOOD) implemented inPLStoolbox[39].Thedatasplit ratiowas80% Training–20 %Testset.Thetraining sampleswereusedfor7- foldcross-validation,whichmeansthat1/7ofthesampleswere predictedbasedontheother6/7ofthesamples,andthisprocess wasrepeatedwhileallthepartitionshavebeenpredictedexactly once.Thefoldsofsampleswereselectedrandomly,thustwenty iterationswereimplementedintotheprotocol.Seven-foldcross- validationisawell-knownoptionforcross-validationprocesses.

Theoptimalnumberoffoldsshouldbebetween5and10basedon theworkofHastieetal.[40].Thetestsplitsofthesampleswere usedfortheexternalvalidation,wheretheYtargetvaluesofthe moleculeswerepredictedbasedonthecalibrationmodel.Finally, Y-scrambling (randomlyreorderedYvector)canverifythatour modelsarefarbetterthantheuseofrandomnumbers.Thiscan helpustocheck“chancecorrelations”andwhetherthemodelsare overfittedornot.Anadditionalmethod,calledthepermutationtest wasalsoappliedtotestthesignificanceofthedifferencebetween theactualandtherandommodel.Herethemainhypothesisisthat ouroriginalmodelisnotsignificantlydifferentfromtherandomly reorderedYvectorones.Wilcoxon,SignandrandomizationT-tests wereappliedfortesting.

PerformanceparameterssuchasR²(calibration),Q²CV(cross- validation),R²_P(externalvalidation)andQ²_Fn[41],therootmean squared error of calibration, cross-validation and external validation(RMSEC/RMSECV/RMSEPrespectively),themeanabsolute

error(forcalibration,cross-validationandexternalvalidation)the coefﬁcientofconcordance(CCC,likewiseforallcalibrationandval- idationsteps)[42]etc.werecalculatedtoappropriatelydetermine thequalityofthemodels.

3. Resultsanddiscussion 3.1. PreliminaryanalysisoftheAPIs

Inourpreviouswork,weinvestigatedtherelationshipsbetween corneal-PAMPApermeability(logPe)andmembraneretentionvalues(MR) incomparisonwithexperimentalCaco-2 permeability dataandcalculatedphysicochemicalproperties,suchasmolecular weight(MW),topologicalpolarsurfacearea(TPSA)andlipophilic- itydescriptors(logP,logD_pH7.4),inthecaseof50structurallyand physicochemicallydiversecompounds[43].Duetoweakcorrela- tions(R²=0.018−0.506)weconcludedthatcornealpermeability cannotbepredictedbasedononlythesephysicochemicaldescrip- torsandforthisreason,alargermeasuredpermeabilitydataset is needed to be able to carry out a QSPR analysis. As part of ourconclusion,weestablishedthattheweakcorrelationbetween corneal-PAMPApermeabilityandCaco-2(gastrointestinal)permeability(R²=0.125)conﬁrmsthatourmodelisindependentofthe generallyacceptedgastrointestinalpermeabilitymodelandmay supportitsadequacyforcornea-speciﬁcinvitromeasurements.

Inthecurrentwork,189APIs(fromwhich50APIshavealready beenmeasuredinthepreviouswork[43])wereselectedfroma diversechemicalspaceandtestedinthecorneal-PAMPAmodelto producedatasetforinsilicomodeling.(Seeexperimentaldatain TableA1.,AppendixA)Beforecomputationalmodeling,weeval- uatedthemaincharacteristicsofthecompoundsbasedontheir physicochemical properties like logP, logD_pH7.4,MW, TPSA and acid-basecharacteristics(Fig.1).

Weinvestigatedtherelationshipbetweencorneal-PAMPAper- meabilityandtheabove-mentionedphysicochemicalparameters (Fig.2).Forlinearregressionanalysis,theGraphPadPrismsoftware wasused[45].Theresultprovedtobealikeaseachoftheseparam- etersshowedweakcorrelationwithcornealpermeability,onlythe followingtendenciescouldbeobserved:thecornealpermeability decreasedwithincreasingTPSAwhileitincreasedwithincreasing logPandlogD_pH7.4values.However,themolecularweightseemed tohavenoeffectoncornealpermeability.Theneutralandbasic compoundsexhibitedhigherpermeabilityvaluesthantheacidic oramphotericones,which observationcorresponds tothegen- eraltrendformembranepermeabilityofdrugsitashasalsobeen reportedpreviously[46].Thebestsquaredcorrelationcoefﬁcient (R²=0.356)wasobservedinthecaseoflogD_pH7.4,whichisprobably duetothefactthatthemeasurementswerecarriedoutatiso-pH 7.4conditions.

The relationship between membrane retention and these physicochemical parameters hasalso been investigated. In the case ofTPSAand logPonlytrends couldbeobserved withlow squaredcorrelationcoefﬁcients(R²=0.289and0.367respectively).

TheMRvaluesincreasedwithincreasinglogPanddecreasedwith increasingTPSA,whichisinaccordancewiththefactthatthemore lipophilic(andlesspolar)theAPIis,themorelikelyitgetsintothe membrane.Theanalysisresultedinverypoorﬁtswiththeother twoparameters.(SeeFigureB1.,AppendixB).Thecorneal-PAMPA permeabilityvalueswerealsocomparedwithotherpermeability- relatedinsilicovalueslikeCaco-2permeability(pH7.4,at350rpm stirringrate)jejunalpermeability[47]and blood-brainpartition coefﬁcient[48](logBB),whichwerepredictedbytheACD/Percepta software[32]asagoldstandardtoolindrugdiscovery(Fig.3).

The Caco-2 model applies human epithelial colorectal ade- nocarcinoma cells thus, unlike the PAMPA model, it contains

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Fig.1.Histogramsofphysicochemicalpropertiesof189compounds.Physicochemicalpropertiesincludemolecularweight,topologicalpolarsurfacearea,calculated logpartitioncoefﬁcient,calculatedlogdistributioncoefﬁcientatpH7.4,andacid-basecharacteristics.TheTPSA,clogPandclogDpH7.4valueswerecalculatedwiththe ACD/Perceptasoftware[32]andtheacid-basecharacteristicsweredeterminedwiththeChemAxon/MarvinSketchsoftware[44].

activetransporters.Forcomparingthecorneal-PAMPAandCaco- 2permeabilityvalues,9APIs(hydrocortisone,emetine,etoposide, loperamide,quinine,risperidone,sparfloxacin,trimethoprim,ver- apamil)werelabeledwithredstarsonFig.3,whicharepotential substrates of P-gp efflux pump according to the prediction of ACD/Perceptasoftware[32].Forthepropercomparisonbetween thedifferentassays,compoundsthatareknowntobepenetrating viaactivetransportshouldbeavoided.Toclarifythedifferences intheirpenetrationbehavior,squaredcorrelationcoefficientsare representedhere,whichrefertothedatasetswithout(R²)andwith (R²*)theP-gpsubstratesaidedbyactivetransport.Similarly,to ourformer conclusion, onlya weakcorrelationcouldbedeter- minedbetweencorneal-PAMPAandCaco-2permeabilityvalues.

Aweakcorrelationwasfoundinthecaseofjejunalpermeability andblood-brainpartitioncoefﬁcienttoo,whichindicatesthatthe corneal-PAMPAisnotauniversalpermeabilitymodelandthatthe trans-cornealdiffusionprocessispresumablygovernedbydiffer- entfactorsthanintestinalorblood-brain-barrierpenetration.Thus, theresultsofthepreliminaryanalysisclearlyveriﬁedtheneedfor auniqueQSPRmodelforcorneal-PAMPApredictions.

3.2. Corneal-PAMPApermeabilityQSPRprediction

Inthemodel-buildingphase,theoriginalmatrixcontained3302 molecular descriptors(including the predictedphysicochemical ones,classical1,2and3DdescriptorsandtheECFPﬁngerprint)as Xvariables,andcorneal-PAMPAexperimentalresultsastheYvec- tor.ThetotalnumberofAPIswherecorneal-PAMPAexperimental values couldbedeterminedwas151.Outlierselectionwasper- formedonthedataset:a)ﬁrsttheAPIsoutsideofthewell-covered

0−50×10⁻⁶cm/srangewereexcluded,b)thenthefirsttwoPLS componentswereplottedagainsteachotherand95%confidence ellipsewascalculatedtoexcludetheoutliersbasedonthemolec- ulardescriptors.Inthefinalform,143APIswereincludedinthe dataset.

Inthenextstep,thematrixwassplitintotrainingandtestset, whichwasobligatorytocarryoutapropervalidationofthemodel.

WiththeDOODalgorithm,80%ofthecompoundswereselected forthetrainingset.Thus,114APIswereappliedforthecalibration andcross-validationof themodel.Autoscaling(standardization) wasusedasdatapretreatment.Wehaveselected100molecular descriptorswiththecombinationofVIPscoringandgeneticalgo- rithmfromtheoriginaldescriptorset.Inthe7-foldcross-validation part,RMSECVvalueswereusedforthedeterminationofthenum- berofPLScomponents.TheglobalminimumoftheRMSECVvalues wasatﬁvePLScomponents.Cross-validationwasperformedwith arandomizedselectionin20iterations.Theﬁnalcalibrationcurve alongwiththetestvalidationsamplesbasedon5PLScomponents isshowninFig.4ab.

Thesampleswerewell-fittedtothecalibrationcurveandthe errorswerehomogenousalongtherange.Itisclearlyseeninthe performancesaswell:theR²(goodnessoffitforthecalibration)and Q²_CV(goodnessoffitforthecross-validation)were0.953and0.866, respectively.Theperformanceofthetestvalidationwas0.862.The remainingperformanceparametersofthemodelaresummarized inTable2.

Outoftheselected100variables,themostimportantphysic- ochemical descriptors (based on their VIP scores) were the following: absorption rate constant (ka), jejunal permeability (clogP_e_jejunal,pH=7.4), fraction unbound in the brain (f_bu),

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Fig.2. PAMPA-relatedcornealpermeabilityasafunctionofphysicochemicalproperties.Correlationbetweencornealpermeabilityandmolecularweight(a.),topological polarsurfacearea(b.),calculatedlogpartitioncoefficient(c.),calculatedlogdistributioncoefficientatpH7.4(d.)andacid-basecharacteristics(e.)ofthecompoundswiththe squaredcorrelationcoefficient(R²).TPSA,clogPandclogDpH7.4valueswerecalculatedwiththeACD/Perceptasoftware[32]andtheacid-basecharacteristicsweredetermined bytheChemAxon/MarvinSketchsoftware[44].ThecorrelationcoefficientsweredeterminedusingtheGraphPadPrismsoftware[45].Thebluedottedlinesstandforthe95

%conﬁdencebands.

clogDpH7.4,plasmaproteinbinding(PPB).Allthesedescriptorshad VIP(variableimportance)scoresabove1.3.Theresultscorrespond to thekinetic behavior of the permeability parameteras these descriptorsarerelatedtopassivetransportofdrugs.Inaddition, the fact that predicted data of neither thegastrointestinal (ka, clogP_e_jejunal),northeblood-brainbarriertransport(f_bu)insilico modelscoulddescribethecorneal-PAMPA permeabilityprocess, suggeststhecomplexityofourmodel,whichisalsosupportedby ourconclusionsinthepreliminaryanalysis.Ionizationstateand lipophilicityarealsowell-knowndeterminantsofthepermeabil- ity process [46,49,50], which are alsopresent herein theform ofclogD_pH7.4.Additionally,linearregressionanalysiswascarried outinthecaseofka,PPBandf_bu againstlogPe andonlyaweak correlationwasfoundineachcase,whichsupportsourprevious observationthatusinglinearregressionofonlyoneparameterata timecouldnotresultinagoodmodelforprediction(SeeFigureB2., AppendixBandTableA2.,AppendixA).

Yscramblingwasalsousedforthevalidationofthemodeland tocheckthepossibilityofoverﬁtting.Theexperimentalcorneal- PAMPAvalueswererandomizedinthedatasetforthisvalidation.

Thepredictionperformancesat5PLScomponentsweredecreased properlyto0.016and0.14forcross-validationandtestvalidation, respectively.Thepermutationtest(with50iterations)hasfounda signiﬁcantdifferencebetweenourﬁnalmodelandtherandomized one(at␣=0.05level).FortheresultofthepermutationseeTable A3,AppendixA.

3.3. Corneal-PAMPAmembraneretentionQSPRprediction

Inthecaseofmembraneretentionprediction,thesameproto- col(withthesameparameters)wascarriedoutasinthecaseof permeabilityprediction.Theselectedrangeofmembrane reten- tionwasbetween0and100%.Aftertheoutlierselectionprocess, 180APIsoutof189wereincludedinthedataset.Theremaining

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Fig.3.PAMPA-relatedcornealpermeabilityasafunctionofvariousinsilicotransportparameters.CorrelationbetweencornealpermeabilityandcalculatedCaco-2 permeability(pH7.4,at350rpmstirringrate)(a.),calculatedjejunalpermeability(b.)[47]andcalculatedblood-brainpartitioncoefficient(c.)[48]ofthecompounds withsquaredcorrelationcoefficients(R²).InthecaseofCaco-2permeability(a.)recalculatedsquaredcorrelationcoefficient(R²*)wasalsointroducedincludingnineP-gp substrates.clogPeCaco-2,clogPejejunalandclogBBvalueswerecalculatedwiththeACD/Perceptasoftware[32].ThecorrelationcoefficientsweredeterminedusingtheGraphPad Prismsoftware[45].Thebluedottedlinesstandforthe95%confidencebands.

Fig.4. ab.ThePLScalibrationcurve.a)Predictedcorneal-PAMPAvaluesareplottedagainsttheexperimentalones.InFig.4b)themodelistransformedtologarithmic scale.Calibrationsamplesaremarkedwithgreycircles,whiletestvalidationcompoundsaremarkedwithreddiamonds.

ninecompoundswereexcludedduetotheirnegativemembrane retentionvalues(theywereoutofthe0–100%range).Intotal,83 moleculardescriptorswereincludedinthematrixafterthevari- ableselectionprocess(VIPscoresandgeneticalgorithm).Classical physicochemical,two-dimensional,three-dimensionaldescriptors andﬁngerprintbitpositionswereincludedintheselectedsetof variables.ThesameDOODalgorithmwasusedforthetraining-test split.Thetrainingsetcontained144compounds(80%),whilethe remaining36compoundswereusedfortestvalidation.Seven-fold cross-validationwasusedfortheinternalvalidationofthemodel with20iterations,andeightPLScomponentswereappliedbased

ontheglobalminimumoftheRMSECVcurve.Theﬁnalcalibration modelwiththecalibrationandtestsamplestogetherisplottedin Fig.5.Thesampleswerewell-ﬁttedtothecalibrationcurve(even thetestones)andtheerrorswerehomogeneousalongtherange.

TheR² valueofthecalibrationwas0.97,whiletheQ²_CVandQ² predictionwere0.91and0.94,respectively.Alltheperformance parametersaresummarizedinTable2.

Themostimportantphysicochemicalpropertiesamongstthe83 selecteddescriptors(basedontheirVIPscores)werethefollow- ing:logaqueoussolubility(logS),logPandPPB.Thesedescriptors hadVIPscoresabove1.3.Theresultconﬁrmsthethermodynamic

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Table2

SummaryoftheperformanceparametersfortheﬁnalQSPRmodels*.

Model Permeability Membraneretention Permeability(in logsale)

RMSEC 2.87 4.37 0.04

RMSECV 5.06 8.14 0.08

RMSEP 5.15 7.05 0.11

R² 0.95 0.97 0.95

Q²CV 0.87 0.91 0.86

R²P 0.86 0.94 0.85

Q²F1 0.86 0.96 0.75

Q²F2 0.86 0.93 0.75

Q²F3 0.85 0.93 0.79

CCCTrain 0.98 0.99 0.97

CCCCV 0.93 0.95 0.93

CCCExt 0.92 0.97 0.89

MAE_Train 2.15 3.28 0.04

MAECV 3.79 4.90 0.06

MAEExt 3.92 5.74 0.08

r²_m 0.80 0.89 0.58

r¯²_m 0.76 0.88 0.65

r²_m 0.07 0.01 0.13

r₀²−r₀²

0.02 0.00 0.07

k 0.87 0.96 1.09

k’ 0.91 0.99 1.01

Y-SCRCV 0.02 0.02 –

Y-SCRP. 0.14 0.04 –

PLSCOMP. 5 8 –

*RMSEC–rootmeansquarederrorofcalibration,RMSECV–rootmeansquared errorofcross-validation,RMSEP–rootmeansquarederrorofexternalvalidation, R²-goodnessoffitforthecalibration,Q²CV-goodnessoffitforthecross-validation, R²P-goodnessoffitfortheexternalvalidation,QF12–F1typegoodnessoffitforthe externalvalidation,QF22–F2typegoodnessoffitfortheexternalvalidation,QF32– F3typegoodnessoffitfortheexternalvalidation,CCC(Train/CV/Ext)–coefficient ofconcordanceforthetraining/CV/externaltestset,MAE(Train/CV/Ext)–mean absoluteerrorforthetraining/CV/externaltestset,r²_mandr²_m–basedonthe workofRoyetal.[52],

r₀²−r₀²

istheabsolutedifferenceofther²₀valueswithout interceptinthecaseofobservedvs.predictedandpredictedvs.observedvalues, kandk’-theslopeoftheregressionlines(withorwithoutpassingthroughthe origin),Y-SCRCV-goodnessofﬁtforthecrossvalidationusingYscrambling,Y-SCR P-goodnessofﬁtforthetestpredictionusingY-scrambling,PLSCOMP.–numberof PLScomponentsinthemodel.

Fig.5.Predictionofthemembraneretention.Predictedvaluesareplottedagainst theexperimentalmembraneretentionvalues.Thetestsamplesaremarkedwith reddiamondsandthecalibrationonesaremarkedwithgreycircles.Thecalibration curveismarkedwiththeredline.

behavioroftheMRparameterforthetestedcompoundsinthatit relatestotheirdistributionbetweenthedonor,acceptorandlipid membrane.TheprimaryrelevanceofthelogPandlogSparame- terssuggeststhedominanceoftheneutralformofthecompounds, whichalsosupportsthespeciﬁcityoftheinsilicodescription,as theprotondissociationofdrugmoleculesinthemembraneistypi-

callydepressed.ThefactthatlogPismorefavorablethanlogD_pH7.4 asa descriptor for membrane retention confirms theresultsof ourpreliminaryanalysis(SeeFigureB1.,AppendixB).Theweighted appearanceofPPBcanbeexplainedbythelipophilicity-dependent natureofthefreeformofthedrug,whichisconsistentwiththe generalkineticdescriptionofdrugtransport.Additionally,linear regressionanalysiswascarried outin thecaseof logS andPPB againstMRandonlyweakcorrelationswerefoundwiththesquared correlationcoefficientsof0.232and0.189respectivelywhichalso verifiestheneedformorecomplexmodelsthanthelinearregres- sionofonephysicochemicalparameteratatime(SeeFigureB3., AppendixBandTableA2.,AppendixA).

Y-scramblingwasalsousedtocheckthepossibilityofover- fitting.Themodelperformancesstronglydecreasedwiththeuse ofrandomizedYvalues.TheQ²CVwas0.02,whiletheQ²fortest predictionwas0.04.Thepermutationtest(with50iterations)has foundasignificantdifferencebetweenourfinalmodelandtheran- domizedone(at␣=0.05level),verifyingourmodel.

Thedetailedsummaryoftheperformanceparametersofthe ﬁnalmodels(permeabilityandmembraneretention)isshownin Table2.Allparametersaregoodandfulﬁllthesuggestedconditions fortheacceptanceofthemodel:R² >0.7,Q_Fn²>0.6,CCC>0.85, r²_m >0.5,r²_m< 0.2[42,51],and

r₀²−r₀²

<0.2.Based onthe performancesofthemodels,wearerecommendingtheuseofper- meabilityvaluesinlinearscaleforfurthercalculations.

4. Conclusion

Twoquantitativestructure-propertyrelationshipmodelswere developedfortheinvestigationofcornealpermeabilityandmem- braneretention.TheQSPRmodelswerebasedonexperimentally determinedcorneal-PAMPAvalues.Partialleastsquaresregression wasappliedfor theprocess. Theﬁnal models containedclassi- calmoleculardescriptorsandECFPﬁngerprintsin combination.

Themodelsincluded143and180APIsforPeandMRprediction, respectively.Acomplexvalidationprotocol(includinginternaland external phases)was carried outto provide robustand appro- priatepredictionsforthepermeabilityand membraneretention values.Thegoodnessofthemodels(R²)wereabove0.90inboth cases and theywere not lower than0.85 for validation either.

Thepermutationtests showedthatourmodelsare notoverfit- tedandtheyareclearlyapplicabletoprovidegoodpredictionsfor thecornealpermeabilityoftheAPIs.Thisis,toourknowledge,the firstsuchinsilicomodelreportedsofar.Theresultsalsoshowed thattherewasnosignificantcorrelationbetweentheexperimental corneal-PAMPA values and the existing classical in silicophar- macokineticallyrelevantdrugtransport models,suchasCaco-2 permeability,jejunalpermeability andtheblood-brainpartition coefficient(logBB).Thus,ourmodelscanbegoodcandidatestopro- videthecornealpermeabilityandcornealmembraneretentionof compoundsinaveryshorttimewithappropriateprecision.

Authors’contributions

The manuscript was written through contributions of all authors.Allauthorshavegivenapprovaltotheﬁnalversionofthe manuscript.

DeclarationofCompetingInterest

Theauthorsreportnodeclarationsofinterest.