Modeling the Mechanisms by Which HIV-Associated Immunosuppression Influences HPV

20 Pages·2017·2.73 MB·English

RESEARCHARTICLE
Modeling the Mechanisms by Which HIV-
Associated Immunosuppression Influences
HPV Persistence at the Oral Mucosa
MeghnaVerma1☯,SamanthaErwin2☯,VidaAbedi1,RaquelHontecillas1,StefanHoops1,
AndrewLeber1,JosepBassaganya-Riera1*,StancaM.Ciupe2*
1 NutritionalImmunologyandMolecularMedicineLaboratory,BiocomplexityInstituteofVirginiaTech,
Blacksburg,VA,UnitedStatesofAmerica,2 DepartmentofMathematics,VirginiaTech,Blacksburg,VA,
UnitedStatesofAmerica
a1111111111
a1111111111 ☯Theseauthorscontributedequallytothiswork.
a1111111111 *[email protected](JBR);[email protected](SC)
a1111111111
a1111111111
Abstract
Humanimmunodeficiencyvirus(HIV)-infectedpatientsareatanincreasedriskofco-infec-
tionwithhumanpapillomavirus(HPV),andsubsequentmalignanciessuchasoralcancer.
OPENACCESS
TodeterminetheroleofHIV-associatedimmunesuppressiononHPVpersistenceandpath-
Citation:VermaM,ErwinS,AbediV,HontecillasR, ogenesis,andtoinvestigatethemechanismsunderlyingthemodulationofHPVinfection
HoopsS,LeberA,etal.(2017)Modelingthe
andoralcancerbyHIV,wedevelopedamathematicalmodelofHIV/HPVco-infection.Our
MechanismsbyWhichHIV-Associated
modelcapturesknownimmunologicalandmolecularfeaturessuchasimpairedHPV-spe-
ImmunosuppressionInfluencesHPVPersistence
attheOralMucosa.PLoSONE12(1):e0168133. cificeffectorThelper1(Th1)cellresponses,andenhancedHPVinfectionduetoHIV.We
doi:10.1371/journal.pone.0168133 usedthemodeltodetermineHPVprognosisinthepresenceofHIVinfection,andidentified
Editor:GuidoPoli,UniversitaVitaSaluteSan conditionsunderwhichHIVinfectionaltersHPVpersistenceintheoralmucosasystem.
Raffaele,ITALY ThemodelpredictsthatconditionsleadingtoHPVpersistenceduringHIV/HPVco-infection
Received:May3,2016 arethepermissiveimmuneenvironmentcreatedbyHIVandmolecularinteractionsbetween
thetwoviruses.ThemodelalsodetermineswhenHPVinfectioncontinuestopersistinthe
Accepted:November24,2016
shortruninaco-infectedpatientundergoingantiretroviraltherapy.Lastly,themodelpre-
Published:January6,2017
dictsthat,underefficaciousantiretroviraltreatment,HPVinfectionswilldecreaseinthelong
Copyright:©2017Vermaetal.Thisisanopen
runduetotherestorationofCD4+Tcellnumbersandprotectiveimmuneresponses.
accessarticledistributedunderthetermsofthe
CreativeCommonsAttributionLicense,which
permitsunrestricteduse,distribution,and
reproductioninanymedium,providedtheoriginal
authorandsourcearecredited.
DataAvailabilityStatement:ThecompleteSBML
compliantmodelwasdepositedinwww. Introduction
biomodels.netandassignedtheidentifierMODEL
1605030001.Alltheotherrelevantdataarewithin Infectionwiththehumanimmunodeficiencyvirus(HIV)afflictsover35millionpeopleworld-
thepaperanditsSupportingInformationfiles. wideandresultsinimpairedimmuneresponseswhichmayaffectdefensesagainstother
pathogens.Intheabsenceofprotectivevaccines,currentmanagementofHIVconsistsof
Funding:Thestudywassupportedbythefunds
fromtheNutritionalImmunologyandMolecular administrationofcombinationantiretroviraltherapy(cART)—whichsuppressesviralreplica-
MedicineLaboratory(www.nimml.org). tionand,consequently,drasticallyreducesmorbidityandmortality[1,2].cARTsare99%
effective;however,antiviraldrugresistance(mainlycausedbynon-compliance)againstsome
CompetingInterests:Theauthorshavedeclared
thatnocompetinginterestsexist. oftheanti-HIVdrugshasbeenreportedinupto60%ofthepatients[3].Moreover,acurefor
PLOSONE|DOI:10.1371/journal.pone.0168133 January6,2017 1/20
ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
HIVischallengingduetothestrictneedforlifelongtreatmenttoavoidvirusreboundfrom
activationoflatentreservoirs.
Apartfromtheacquiredimmunodeficiencysyndrome(AIDS),HIVincreasestheriskof
developingopportunisticinfectionsbyotherinfectiousagents,includingviruses:papillomavi-
rus,herpesviruses,flaviviruses;andbacteria:Helicobacterpylori,Salmonellatyphimurium,
Chlamydophilapneumonia[4].EpidemiologicaldatasuggeststhatHIVpatientshavean
increasedriskfordevelopinghumanpapillomavirus(HPV)-inducedcancerssuchasoropha-
ryngealcancer,cervicalcancer,anogenitalcancerandanalcancers[5–10].However,thecellu-
larandmolecularmechanismsexplainingthecorrelationbetweenincreasedsusceptibilityof
HPV-associateddiseasesandHIV-inducedimmunesuppressionremainlargelyunknown.
Theoropharyngealcancersareasubsetofheadandneckcancers(HNCs)whichaccount
forapproximately4%ofallthecancersintheUnitedStates.Theincidenceofdiseasewas
twiceashighinmenthaninwomenin2015[11].Theoropharyngealcancers,intheirclini-
callydistinctformofsquamouscellcarcinoma,arecommonlydetectedinHIVpatientswitha
highernumberoflifetimeoralsexualpartners,immunosuppression,smoking,andcurrent
tobaccouse.ThecausalroleoforalHPVinfectionissupportedbysubstantialmolecularand
cellularevidence[5–7,12].
RecentstudiessuggestedthattheinteractionbetweenHIVandHPVmightberesponsible
fortheincreasedriskofcervicalcancers[13,14].Similaritiesinriskfactorsfortheacquisition
ofHIVandHPVinfections,suchashigh-risksexualbehavior,multiplesexualpartners,and
disease-relatedimmunosuppressionmakesthedemarcationbetweentheHPVandHIV-asso-
ciatedmalignancieschallenging.IthasbeenhypothesizedthatHIVpatientswhohavebeen
infectedforalongperiodoftimehaveahigherprevalenceoforalHPVinfectionandsubse-
quentlyareatahigherriskforHPV-associatedHNCs[15].HIV-inducedimmunosuppression
alsoincreasestheriskofHPV-associatedcancer.Otherfactorsthatcanincreasetheriskof
severeHPVinfectionsinHIVpatientsincludeimmunesenescence,aging,impairedimmune
responsetoHPV,anddirectinteractionbetweenthetwoviruses[13,14,16].Theimmunolog-
icalchangescausedbyHIVcreateapermissiveimmuneenvironment,therebydecreasingthe
overallimmuneresponsesagainstHPV.However,themechanismsbywhichHIV-induced
reductioninCD4+TcelllevelsimpairstheimmuneresponseagainstHPVorotherpathogens
remainlargelyunknown.
Besidesimmunologicalfactors,interactionsatthemolecularlevelbetweenHIVgenestat,
revandvprandHPVhavealsobeenreported.Multiplestudiesindicateanup-regulationof
HPVoncogenicgenes(E6andE7)expressionbytat[14,17,18].Tat increasesHPVshedding
whichsuggeststhatHIVinfectionmaycontributetothepathogenesisofHPV-associateddis-
easebymolecularinteractionsthroughtat[16].
Currently,therearetwocommerciallyavailableHPVpreventivevaccines,thequadrivalent
humanpapillomavirusvaccine(QHPV)(Gardasil;Merck)againstHPVtypes6,11,16and18
andabivalentvaccine(Cervarix,Glaxosmithkline)againstHPVtypes16and18.Bothvaccines
areknowntobe98–100%effectiveagainstHPVtypes16and18[19].Recentstudiesdemon-
stratedtheefficacyoftheanti-HPVvaccineCervarixinHIV-infected-oral-HPV-negative
patientswheremorethan90%ofpatientsproducedhighantibodytitersagainstHPV[20].
However,moredataisneededtoaddresscross-reactivitybetweentheinducedantibodyand
otherHPVstrains[21].Moreover,additionalefficacytrialsofQHPVinHIVinfectedindivid-
ualsareneededtoproperlydeterminethecorrelationbetweenvaccinesdose,timingandpro-
tectionagainstallHPVgenotypesinimmunocompromisedHIVpatients.Themechanistic
investigationofco-infectionscenarioisexperimentallychallenging.Thedisadvantagesof
interruptedtreatmentofHIVandlimitedefficacyfortheHPVvaccineagainstalltheHPV
strainsfurtheraddstothecomplexity.Thelimitedclinicalinformationabouttreatmentand
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ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
preventionoptionsagainstHPVinanHIV/HPVco-infectionhasleadustoanalternative
modeofinvestigation.
TogainnewinsightsintotheunderlyingmechanisticinteractionsbetweenHIVandHPV,
inanHIV/HPVco-infectionwedevelopedamathematicalmodelofHIVandHPVinterac-
tions.BuildingonpreviousmodelsofHIV[22]andHPV[23]singleinfections,thisnovel
modelcapturesthemolecularinteractionsbetweenHIVandHPVduetotatandtheeffectof
progressivedepletionofCD4+TcellduetoHIVinfection.Usingthemodel,weaimtoinvesti-
gatewhytheprevalenceoforalHPVinfectionisincreasedinHIV-infectedindividuals.We
demonstratehowthedynamicsofHPVchangesinanHIV/HPVco-infectionwhenthepatient
undergoescombinedantiretroviraltherapy.Thefindingscanbeusedtofurtheradvanceour
understandingofthemechanismsunderlyingoralimmuneplasticity.Lastly,modelingcan
helpproposenewhypothesesforreversingresidualinflammationinindividualsfollowingthe
startofcARTandguideclinicalpractice.
Methods
MathematicalmodelofHIVinfection
WemodeltheinteractionbetweenHIVandCD4+Tcellsasin[22,24].Briefly,weconsider
theinteractionbetweenthreepopulations:i)targetCD4+Tcells(T),ii)productivelyinfected
CD4+Tcells(I),andiii)HIV(V).Targetcellsareproducedatrates,dieatrated,andbecome
productivelyinfectedatrateβproportionaltotheinteractionbetweentargetcellsandthe
virus.InfectedcellsproduceN virionsthroughouttheirlifetime,whicharereleasedthrough
1
bursting,anddieatrateδ.Thevirusisclearedataratec perday.Thefollowingsystemof
1
ordinarydifferentialequations(ODE)representsthesedynamics:
dT
¼s(cid:0) dT(cid:0) bTV;
dt
dI
¼bTV(cid:0) dI; ð1Þ
dt
dV
¼N dI(cid:0) c V;
dt 1 1
withinitialconditionsT(0)=T I(0)=I andV(0)=V
0, 0, 0.
TheeffectofcARThasbeenmodeledasareductionofthevirusinfectivityinthepresence
ofreversetranscriptaseinhibitorstoβ(1-ε )andareductionintheproductionofinfectious
RT
virionsinthepresenceofproteaseinhibitorstoN (1-ε ).Here0(cid:20)ε ,ε (cid:20)1arethedrug
1 PI RT PI
efficacies[24,25].
ThemodelinthepresenceofcARTbecomes:
dT
¼s(cid:0) dT(cid:0) ð1(cid:0) ε ÞbTV;
dt RT
dI
¼ð1(cid:0) ε ÞbTV(cid:0) dI; ð2Þ
dt RT
dV
¼ð1(cid:0) ε ÞN dI(cid:0) c V;
dt PI 1 1
withinitialconditionsT(0)=T I(0)=I andV(0)=V .Notethatmodels(1)and(2)donot
1, 1, 1
takeintoaccounttheHIVlatentreservoirsintheformofrestinglong-livedmemoryCD4+T
cellswithintegratedHIVintheirgenome[26].
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ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
MathematicalmodelofHPVinfection
WemodelHPVin-hostdynamicsasin[23].Weconsidertheinteractionbetweenfourpopula-
tions:i)HPVinfectedbasalepithelialcells(Y ),ii)theHPVinfectedtransit-amplifyingcells,
1
inthesuprabasalepitheliallayer(Y ),iii)HPV(W)andiv)HPV-specificcytotoxicTlympho-
2
cytes(CTL)(E).WeassumethatN isthetotalconcentrationofepithelialcellsatthebeginning
2
ofHPVinfectionandthebasallayerisformedofuninfectedbasalepithelialcells,targetedby
HPV.UponHPVinfection,thebasalepithelialcellsbecomeinfectedY whenHPVinteracts
1
withuninfectedcellsatrateψ.WedenotethedifferenceN -Y astheconcentrationofunin-
2 1
fectedepithelialcells.Thebasalinfectedcells,Y traverseupthroughtheepithelialcolumnand
1
transformintoY cells,whichmovefurtherintothesuprabasalepitheliallayer[27][28].The
2
Y cellsbecometransit-amplifyingcellswhichstartassemblingvirionstobereleasedatthesur-
2
face[29,30].Therefore,bothY andY cellsareHPVinfectedcellsbutdifferentiallylocatedin
1 2
theepithelialcelllayer,whereinY cellsareassumedtohavehigherexpressionoftheonco-
2
genesE6andE7comparedtoY [23].Forsimplification,weassumethattheuninfectedcells
1
andinfectedcellshaveanequalprobabilityofinteractionwiththeHPVvirionsirrespectiveof
thespatialarchitectureofthetissue.Amoregeneralizedmodelwhichtakesintoaccountthe
infectivityandlayertransitionterms,oronewhichwouldconsiderspatialstructuresforepi-
thelialcellsindifferentlayersrequiresextensiveknowledgeofnumerousparameters,which
arecurrentlyunknown.Weassumethattheinfectionisdensitydependentwithφrepresenting
theuninfectedcellconcentrationwheretheinfectionishalf-maximal.Weassumethatinfected
cellpopulationsY andY differintermsoftheoncogeneexpressionsuchthattheY (locatedin
1 2 2
thesuprabasalepitheliallayer)havehigheroncogeneexpressioncomparedtoY cells(locatedin
1
thebasalepitheliallayer)[31].TherateofoncogeneexpressionoftheHPVtypepresentinan
infectedcell,givenbyεcontrolstheconversionofY ,intothetransit-amplifyinginfectedcells,
1
Y Cells,Y ,growatraterε,proportionaltotheirowndensityanddieatrateμ.Duetohigher
2. 2
expressionofoncogenes,thetransit-amplifyingcells,Y dividemorebeforedeath,comparedto
2
thebasalinfectedcellsY .Since,bothinfectedcellpopulationhaveanexpressionofoncogene,
1
asin[23],bothtypesofinfectedcellsproducefreevirions(W),atproductionratesk andk that
1 2,
arereleasedthroughbursting.Forsimplicity,weconsideranequalvirionproductionrateofk =
1
k =k.TheHPVvirionsareclearedatratec [23].Thec clearanceratecapturestheantibody
2 2 2
clearancerateimplicitly.
TheclearanceofHPVintheinfectedcells,isassociatedwithasuccessfulimmuneresponse
thatincludesthetriggerofinnateimmuneresponsestargetedagainstthevirionsreleasedfrom
thesurfaceaswellasinfectedcells[30].Inadditiontotheinnateimmuneresponses,theHPV-
specificCTLsrecruitedduringtheadaptiveimmuneresponseaidintheeliminationofthe
infectedbasalcells[32].Here,weassumethat,afterencounteringtransit-amplifyinginfected
cellsY ,effectorcellsspecifictoHPV,E,expandwithamaximumpercapitarateωandcarry-
2
ingcapacityK.Thiscarryingcapacityisanadditiontotheoriginalwork[23].Inthecurrent
model,theCTLresponseEisinitiatedonlybyY cellswhichhavehigheroncogeneE6expres-
2
sion[33][34]comparedtoY .
1
WedisregardthedifferentialCTLresponseagainsttheinfectedcellpopulationsandcon-
siderthatHPV-specificCTLpopulationEkillsbothclassesofinfectedcellsatthesameratea,
sincebothinfectedcellspopulationsexpressoncogenesE6andE7[30][32].Additionally,the
modeldoesnottakeintoaccountthevirusspecificgeneexpressionatanyparticularepithelial
site.Finally,thefunctionaldifferencesinE6andE7,whicharemajordeterminantsofHPV
pathogenicitybetweenHPVtypes[35],arealsoneglected.
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ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
Thefollowingsystemofdifferentialequationsrepresentsthesedynamics:
dY N (cid:0) Y
1 ¼cW 2 1 (cid:0) εY (cid:0) mY (cid:0) aY E;
dt φþN (cid:0) Y1 1 1 1
2
dY
2 ¼εY þrεY (cid:0) mY (cid:0) aY E;
dt 1 2 2 2
ð3Þ
dW
¼mkðY þY Þ(cid:0) c W;
dt 1 2 2
(cid:18) (cid:19)
dE E
¼oY E 1(cid:0) ;
dt 2 K
withinitialconditionsY (0)=Y Y (0)=Y W(0)=W andE(0)=E
1 10, 2 20, 0 0.
Co-infectionModel
Theeffectoftatprotein. HIV-proteintat,secretedfromHIV-infectedintraepithelial
immunecells,isknowntoplayanimportantroleinthedisruptionofepithelialtightjunctions,
therebyfacilitatingtheentryofHPVintothemucosalepithelium[36].Wemodelthetat-
inducedincreasedlikelihoodofHPVinfectionthroughincreasingthetotalavailableepithelial
cellsfromN toN (1+pV),where(p)istheeffectoftatproteinsecretedbyanHIVvirion(V),
2 2
giveninEq(4).Theterm(1+pV)incorporatestheHIV-associatedepithelialdisruptionasone
ofthemajorunderlyingmechanismsthatincreasesthesusceptibilityofepithelialcellstothe
HIV/HPVco-infection[36].
dY ð1þpVÞN (cid:0) Y
1 ¼cW 2 1 (cid:0) εY (cid:0) mY (cid:0) aY E: ð4Þ
dt φþð1þpVÞN (cid:0) Y1 1 1 1
2
Theeffectofimmunosuppression. InHIV-infectedindividuals,thelossofCD4+Tcells
leadstoconsecutivelossofCD4+Tcell-mediatedimmuneresponsesagainstotherpathogens
suchasHPV.NaïveCD4+TcellsaredepletedinmucosaltissuesinallthestagesofHIVinfec-
tion[26,37],andprogressivedeclineofCD4+Tcellsaffectsthedifferentiationprocessof
naïveCD4+Tcellsintothedifferentsubsets.Suchasubset,Th1,isknowntoplayamajorrole
inimmuneresponsesagainstHPV[34]throughinductionofcell-mediatedimmunityinthe
presenceofIL-2,IL-12andIFN-γcytokines[38].
TomodelthedecreaseintheavailabilityofCD4+TcellpopulationduetoHIV;andthe
subsequenteffectofsuchlossonHPV-specificCTL(E)responses,weassumethatthecarrying
capacityoftheEpopulationdecreasesinanimmunosuppressedpatient.Inparticular,werep-
resentKasthecarryingcapacityofCTLsandthusthemaximumEpopulation.WemakeKa
functionofCD4+Tcellpopulation,suchthatKisgivenby,K=K(T)=bT,whereTarethe
uninfectedCD4+Tcellsinthemodel(1).WhenTdecreasesduringtheprogressivelossof
CD4+Tcells,T,K(T),themaximumcarryingcapacitydecreasesatalinearrate.Weassume
thattheCTLcarryingcapacityisdirectlyproportionaltotheamountofCD4+Tcells.Other
modelingoptions,suchasaTdependentsourcewithadeathtermwereexplored,howeverthe
maximumproliferationtermK(T)bestexplainedthehomeostaticmechanisticbehaviorofthe
CTLs.
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ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
Fig1.HIVHPVDiagram.Adiagramfortheco-infectionmodel(5).TheleftsideofthefigurerepresentstheHIVdynamicswhereintheinteractionbetween
targetCD4+Tcells(T),productivelyinfectedCD4+Tcells(I)andHIV(V)areshown.Thefigurealsoincludestheeffectofreversetranscriptase(RT)and
proteininhibitor(PI)(shownbyredline—inhibition).TherightsideofthefigurerepresentstheHPVdynamicswhereintheinteractionbetweeninfectedbasal
cells(Y ),suprabasaltransit-amplifyingcells(Y ),HPVspecific(E)cellsandHPV(W)areshown.Thesystemsbiologymarkuplanguage(SBML)compliant
1 2
networkofinteractionsbetweenHIV(V)andHPV(W)iscreatedusingCellDesigner[40](S1Fig).
doi:10.1371/journal.pone.0168133.g001
Theco-infectionmodelbecomes(seeFig1):
dT
¼s(cid:0) dT(cid:0) ð1(cid:0) ε ÞbTV;
dt RT
dI
¼ð1(cid:0) ε ÞbTV(cid:0) dI;
dt RT
dV
¼ð1(cid:0) ε ÞN dI(cid:0) c V;
dt PI 1 1
dY ð1þpVÞN (cid:0) Y
1 ¼cW 2 1 (cid:0) εY (cid:0) mY (cid:0) aY E; ð5Þ
dt φþð1þpVÞN (cid:0) Y1 1 1 1
2
dY
2 ¼εY þrεY (cid:0) mY (cid:0) aY E
dt 1 2 2 2
dW
¼mkðY þY Þ(cid:0) c W;
dt 1 2 2
(cid:18) (cid:19)
dE E
¼oY E 1(cid:0) ;
dt 2 KðTÞ
withinitialconditionsT(0)>0,I(0)>0,V(0)>0,Y (0)=Y Y (0)=Y W(0)=W andE
1 10, 2 20, 0
(0)=E wheret=0isthetimeofco-infection.
0
PLOSONE|DOI:10.1371/journal.pone.0168133 January6,2017 6/20
ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
ThecompleteSBMLcompliantmodelwasdepositedinBioModels[39]andassignedthe
identifierMODEL1605030001.
Results
Analyticalresults
Analytically,wecanfindanecessaryconditionfortheHPVinfectiontobecleared(datainS1
File).WeassumethatwehaveachronicallyinfectedHIVsubjectwhoreachedsteadystateval-
ues(T,I,V).Undertheseconditions,thecarryingcapacityforpopulationEbecomesK¼bT.
System(5)reducesto:
dY ð1þpVÞN (cid:0) Y
1 ¼cW 2 1 (cid:0) εY (cid:0) mY (cid:0) aY E;
dt φþð1þpVÞN (cid:0) Y1 1 1 1
2
dY
2 ¼εY þrεY (cid:0) mY (cid:0) aY E;
dt 1 2 2 2
ð6Þ
dW
¼mkðY þY Þ(cid:0) c W;
dt 1 2 2
(cid:18) (cid:19)
dE E
¼oY E 1(cid:0) :
dt 2 K
Then,HPVwillclearwhen:
ckmð1þpVÞN ðεþmþaEÞð(cid:0) εrþaEþmÞ
2 < ; ð7Þ
c ðφþð1þpVÞN Þ ðεþmþaE(cid:0) rεÞ
2 2
whereEisanyCTLlevel(datainS1File).Biologically,thismeansthatwhentheproduct
betweenHPVinfectionrateandtheHPVproductionrate(inthepresenceofHIV)islessthan
thecombinedeffectofeffectorcellsandnaturaldeathrateofHPV,clearanceofHPVwillbe
observed.
Numericalresults
Usingtheco-infectionmodel(5),wenumericallysimulateddiseasescenariosinordertounder-
standthedynamicsofHPVinfectioninaco-infectedindividual.Arecentclinicaltrialhasinvesti-
gatedtheeffectofHIVinHPVinfectioninthepresenceandabsenceofcombinationantiretro-
viraltherapy[41].ThelevelsoforalHPVDNAintheco-infectedpatients,whichwasmonitored
for24weeksafterthestartofcART,remainedelevatedthroughouttherapy.Todeterminethepos-
siblemechanismsofHPVpersistence,weinvestigatemodels(5)and(6)fortherelativecontribu-
tionsofco-infectionfactors:tat,asgivenbypV,andimmunosuppressionasgivenbyK(T).
Parametervalues. Parametervaluesfrompreviouslypublishedstudiesareutilizedhere,
asfollows.EquilibriumvaluesforHIVRNApermlandHIV-specificuninfectedCD4+Tcells
permlwerereportedinanHIV/HPVco-infectionstudytobeV =4.8x104virionspermland
T=3.3x105cellsperml[41].SincethepatientisinachronicHIVsteadystate,wederiveI,β
andsfromsteadystateconditionsI¼cN11Vd,b¼ c1 ands¼dT þTV,tobeI =2.4x103cells
N1T
perml,β=1.5x10-7mlpercellsperdayands=5.6x103cellspermlperday.Theremaining
parametersaresummarizedinTable1.
Weassumethatthetat-effect,givenbypV,rangesbetweenzeroand20,toaccountforuptoa
20-foldincreaseinthetargetepithelialcellpopulationduetoco-infection.Theimmunosuppres-
sionfactor,givenbyKðTÞ¼bTrangesbetweenKðTÞ=35cellsandKðTÞ=1celltoaccount
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ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
Table1. Parameters.
Parameter Value Description Reference
s 5.6x103cellsml-1day-1 CD4+Tcellrecruitmentrate Seetext
β 1.5x10−7mlvirions-1day-1 HIVinfectionrate Seetext
d 0.01day-1 UninfectedCD4+Tcelldeathrate [42]
δ 1day-1 InfectedCD4+Tcellsdeathrate [43,44]
N 467virionscells-1 HIVburstsize [45]
1
c 23day-1 HIVclearancerate [46]
1
ε varied Reversetranscriptaseefficacy Seetext
RT
ε varied Proteaseinhibitorefficacy Seetext
PI
T 3.2x105cellsml-1 UninfectedCD4+Tcellsatequilibrium [41]
I 2.4x103cellsml-1 InfectedCD4+Tcellsatequilibrium Seetext
V 4.8x104virionsml-1 HIVatequilibrium [41]
N 104cells Totalconcentrationofepithelialcells [23]
2
φ 106cells Epithelialcellconcentrationforwhichinfectionishalfmaximal [23]
Ψ 0.0067cellsvirions-1day-1 HPVinfectionrate [23]
μ 0.048day-1 Epithelialcelldeathrate [23]
r 0.1 Transit-amplifyingcellsrecruitmentrate [23]
ε varied Oncogenicexpression Seetext
ω 10−3cell-1day-1 CTLexpansionrate [23]
K varied CTLcarryingcapacity Seetext
a 0.01day-1cells-1 CTLkillingrate [23]
k 1000virionscells-1 HPVburstsize [23]
c 0.05day-1 HPVclearancerate [23]
2
doi:10.1371/journal.pone.0168133.t001
forchangesinavailableCTLconcentrationsbetweenanHPVinfectionandHIV/HPVco-infec-
tion.Lastly,theoncogeneexpressionεrangesfromzerotoone.
TheviraldynamicsofHPVinfectedindividuals. WefirststudythedynamicsofHPV
infectionintheabsenceofHIV,asgivenbymodel(6)withI=V =0cellsperml,andT=106
cellsperml.Weletε=0.5perday,KðTÞ=35cells,b=3.5x10-5andtheotherparametersare
listedinTable1.Undertheseassumptions,model(6)predictsHPVandCTLlevelssimilarto
thosein[23].Inparticular,HPVreachesamaximumof1.4x105copiesatday174andeventual
clearance(seeFig2,panelb,greensolidline).TheCTLexpansionisdelayedby80days,and
reachesanequilibriumvalueof27cellsbyday240(seeFig2,panelb,purpledashedline).
Transit-amplifyingcells,Y withhighoncogenicgeneexpression,are12-timeshigherthan
2
cellswithlowoncogenicexpression,Y (seeFig2,panela).Thisresultisdependentonthe
1
oncogeneexpressionrateε(notshown).
TheviraldynamicsofHIV/HPVco-infectedindividuals. Westartbyassumingthatthe
tateffectleadstothedoublingofavailabletargetepithelialcells,i.e.N ð1þpVÞ¼2N .We
2 2
thenaccountforHIVinducedimmunosuppressioninanHIV/HPVco-infectedindividual,by
changingKðTÞasfollows.WehaveshownintheprevioussectionthatanHIV-naïveindivid-
ualhasaCTLcarryingcapacityKðTÞ=35cells,whereT=106CD4+Tcellspermland
b=3.5x10−5.Wekeeptheb=3.5x10-5anddecreasetheTnumbertoi)T=5x105cellsperml,
correspondingtoaveragechronicHIVCD4+Tcellnumbers[47];ii)T=3.3x105cellsperml
asintheHIV/HPVco-infectionstudy[41];andiii)T=2x105cellsperml,correspondingto
AIDS.
PLOSONE|DOI:10.1371/journal.pone.0168133 January6,2017 8/20
ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
Fig2.HPVinfection.(a)InfectedbasalcellsY (bluesolidline)andsuprabasal,transit-amplifyingcells,Y (reddashedline);(b)HPVW(greensolid
1 2
line)andCTLE(purpledashedline)forε=0.5perdayandKðTÞ=35cells.AlltheotherparametersarelistedinTable1.
doi:10.1371/journal.pone.0168133.g002
UndertheseassumptionsandparametersinTable1,model(6)predictsHPVclearancein
cases(i)andHPVpersistenceincases(ii)and(iii).Incase(i),HPVlevelsreachesamaximum
of2.4x105copiesatday128andclearsbyday1050.Incases(ii)and(iii),HPVreachessteady
statevaluesof3.5x106and6.7x107DNAcellsafter20and2.1years,respectively(seeFig3,
panela).CTLlevelsdecreaseto17.5,11.5and7cellspermlforcases(i),(ii)and(iii),respec-
tively(seeFig3,panelb).
Todeterminetherelativecontributionsofthetat-effectandimmunosuppressioninthe
transitionbetweenHPVclearanceandHPVpersistence,wederivedabifurcationdiagram
showingtheasymptomaticdynamicofHPVasgivenbymodel(6)whenbothpV andKðTÞ
arevaried.Asexpected,anincreaseintheavailableepithelialcellsrequiresalargerCTLpopu-
lationfortheclearancetooccur(seeFig4,reddashedlines).Inparticular,ifthetateffectis
increasedto100%suchthatð1þpVÞ=2,thentheCTLcarryingcapacityhastobeK>11.9
cellsforclearancetooccur.Moreover,acarryingcapacityaslowasKðTÞ=7cellsisenoughto
ensureHPVclearanceintheHIV-naïvecase(80%lowerthantheconsideredbasevalueof
KðTÞ=35cells).
Changingoncogeneexpressionrates. Wehaveconsideredthattheoncogenicexpression
isε=0.5.InanHIV-naïvehost,thiscorrespondstotransit-amplifyingcells,Y exceedingthe
2
infectedbasalcells,Y by12-times(seeFig2,panela).Inthemathematicalmodelfrom[23],
1
theauthorsshowedthatinanHIV-naïve,HPV-unvaccinatedindividual,adecreaseinthe
oncogenicexpressionεleadstoaslowergrowthofY ,Y andW,adelayedandweakCTL
1 2
responseEand,consequently,adelayedHPVclearance.Todeterminewhetherthiseffectis
carriedoverinanHIV/HPVco-infectedindividual,wecomparedclearanceregionsforε=0.1
perday,ε=0.5perdayandε=0.9perdayforvaryingpV andKðTÞvalues(seeFig4,panel
a).Wefindthattheclearanceregions(definedastheareaunderthecurve)arehigherforlow
εvalues,similartotheresultsfromanHIV-naïvepatient[23].
PLOSONE|DOI:10.1371/journal.pone.0168133 January6,2017 9/20
ModelingMechanismsbyWhichHIV-AssociatedImmunosuppressionInfluencesHPVPersistence
Fig3.HIV/HPVco-infection.(a)HPVWand(b)CTLEasgivenbymodel(6)forε=0.5perday,parametersarelistedinTable1,andT=106cells
perml(bluesolidlines);T=5x105cellsperml(reddashedlines);T=3.3x105cellsperml(greendottedlines);andT=2x105cellsperml(purple
dashed-dottedlines).
doi:10.1371/journal.pone.0168133.g003
Fig4.Varyingoncogeneexpressionrates.(a)BifurcationdiagramshowingclearedW(areabelowthecurve)versuschronicW(areaabovethe
curve)asthetateffectpVandCTLcarryingcapacityKðTÞvary.Here,thecriterionforHPVclearanceisgivenbyEq(7);(b)HPVW;and(c)CTLEas
givenbymodel(6)forparameterslistedinTable1andε=0.1(bluesolidlines),ε=0.5(reddashedlines),andε=0.9(greendottedlines).
doi:10.1371/journal.pone.0168133.g004
PLOSONE|DOI:10.1371/journal.pone.0168133 January6,2017 10/20