G. T. Huynh and F. R. Adler. - Department of Mathematics, University

17 Pages·2011·0.53 MB·English

Mathematical Medicine and Biology Advance Access published June 22, 2011
MathematicalMedicineandBiologyPage1 of 17
doi:10.1093/imammb/dqr007
MathematicalmodellingtheagedependenceofEpstein–Barrvirusassociated
infectiousmononucleosis
GIAOT.HUYNH∗
DepartmentofMathematicsandStatistics,OaklandUniversity,2200N.SquirrelRoad,
Rochester,MI48309-4401,USA
Correspondingauthor:[email protected]
∗ D
o
w
AND n
lo
a
FREDERICK R.ADLER de
d
DepartmentsofMathematicsandBiology,UniversityofUtah,155South,1400East, fro
m
Room233,SaltLakeCity,UT84112-0090,USA h
ttp
[email protected] ://im
[Receivedon29September2010;revisedon19April2011;acceptedon4May2011] am
m
b
.o
MostpeoplegetEpstein–Barrvirus(EBV)infectionatyoungageandareasymptomatic.PrimaryEBV xfo
infectioninadolescentsandyoungadults,however,oftenleadstoinfectiousmononucleosis(IM)with rd
jo
symptomsincludingfever,fatigueandsorethroatthatcanpersistformonths.Expansioninthenumberof u
rn
CD8+Tcells,especiallyagainstEBVlyticproteins,arethemaincauseofthesesymptoms.Wepropose als
a mathematical model for the regulation of EBV infection within a host to address the dependence of .o
rg
IMonage.Thismodeltracksthenumberofvirus,infectedBcellandepithelialcellandCD8+ T-cell a/
responsestotheinfection.Weusethismodeltoinvestigatethreehypothesesforthehighincidenceof t U
n
IMinteenagersandyoungadults:salivaandantibodyeffectsthatincreasewithage,highcross-reactive iv
e
T-cellresponsesandahighinitialviralload.Themodelsupportsthefirsttwoofthesehypothesesand rs
ity
suggeststhatvariationinhostantibodyresponsesandthecomplexityofthepre-existingcross-reactive o
T-cellrepertoire,bothofwhichdependonage,mayplayimportantrolesintheetiologyofIM. f U
ta
h
Keywords:infectiousmononucleosis;mathematicalmodel. o
n
J
a
n
u
a
ry
1
8
, 2
1. Introduction 0
1
2
Epstein–Barrvirus(EBV)isamemberoftheherpesvirusfamilyinfectsover90%ofhumansworldwide
andcanpersistforthelifetimeoftheperson(Rickinson&Kieff,2001).EBVistransmittedbyintimate
contact,mainlythroughsalivaandoropharyngealsecretion(Andiman,2006).Withinahost,thevirus
primarily targets two cell types, B cells and epithelial cells. EBV enters B cells and epithelial cells
through different routes using different glycoprotein complexes on its envelop (Hutt-Fletcher, 2007).
Hostsalivaandantibodies,likeIgAandIgG,toviralglycoproteinscandecreasetheinfectionofBcells
butenhancetheinfectionofepithelialcells(Sixbey&Yao,1992;Turketal.,2006).
EBV can establish long-term infections in B cells, driving an infected B cell through stages of
latentinfectionwheretheviralgenomeremainsinsidethecell.Thevirusstaysquiescentandremains
invisible to the immune response within memory B cells. These latently infected memory B cells can
c TheAuthor2011.PublishedbyOxfordUniversityPressonbehalfoftheInstituteofMathematicsanditsApplications.Allrightsreserved.
(cid:13)
2of17 G.T.HUYNHANDF.R.ADLER
beactivated,becomingplasma-likeBcellswithinwhichvirionsreplicateandburstout(lyticinfection).
Infectionofepithelialcellstypicallyresultsinlyticreplicationwithvirusesburstingoutandcelldeath
(Hutt-Fletcher,2005).Infectionsofbothcelltypesareimportant,asinvitroexperimentshowsthatvirus
producedfromonecelltypepreferentiallyinfectstheother(Borza&Hutt-Fletcher,2002).
MostpeoplegetEBVinfectionatyoungageandareasymptomatic.Adolescentsandyoungadults
infected with EBV develop infectious mononucleosis (IM) in up to 50% of cases, with symptoms
including fever, fatigue and sore throat that can persist for months (Andiman, 2006; Cohen, 2005).
These symptoms are caused mainly by expansion in the number of CD8 T cells, especially against
+
EBVlyticproteinsexpressedduringlyticreplicationandproductionofvirions(Hislopetal.,2007).
Sinceitsdiscoverymorethan40yearsago,EBVhasattractedmanyempiricalstudiesofitsabilityto
persistwithinonehostanditsassociationwithcancers.However,EBVinfectsonlyhumansandalim- D
o
w
itedrangeofhostcellsandlacksagoodanimalmodelstoinvestigateEBVinfectioninvivo(Rickinson, n
lo
2005). Most hypotheses and conclusions about EBV infection are based on studies of cell cultures in a
d
e
ecpoiltlhecetleiadlfarnodmBincfeelcltelidnepse.oVpliera.lMloaandysaasnpdecitnsfeocfteEdBcVelilndfeactatiomnussttilblereombtaaiinneodpefnroqmuessatliiovnasainndclbuldoiondg d from
whatfactorsaffectingthedynamicsofinfectionthatmayleadtoIM. http
In our previous work, we developed a mathematical model of the within-host dynamics to study ://im
EBVlong-terminfectionandviralevolution(Huynh&Adler,2010).Inthisstudy,weextendthewithin- a
m
hostmodeltoincludefeaturesofimmunesystemthoughttobeimportantinIM:theroleofantibodies m
b
in shifting infections between the two cell types and the effect of specific and cross-reactive T-cell .o
x
responses.Themodeltracksthenumberofviruses,infectedBcellsandepithelialcells,specificCD8 + ford
Tcellsandcross-reactiveCD8 Tcellsrespondingtotheinfection. jo
+ u
Weusethismodeltoinvestigatethefollowingthreehypotheses: rna
ls
.o
rg
• SHaolsivtasaalinvdaaanndtibanotdibyoedfifeescttsoEBVproteinspromoteinfectionofepithelialcellswhich,inturn,can at U/
n
induceanelevatedCD8 T-cellresponseagainstlyticinfection.Thishypothesiscomesfromobser- iv
+ e
vationsthatsomeunknownfactorinhostsalivaandantibodiestoviralproteinshavebeenobserved rsity
toenhanceepithelialcellinfectionandthatsalivaryIgAlevelincreaseswithage(Jafarzadehetal., o
f U
2008;Sixbey&Yao,1992;Turketal.,2006;Weber-Mzelletal.,2004). ta
h
o
• Cross-reactiveT-cellresponses n Ja
Continuous exposure to different pathogens as people age can increase the complexity of the pre- n
u
a
existing memory T-cell repertoire. Adolescents infected with EBV may recruit large numbers of ry
1
cross-reactivememoryTcellspreviouslycreatedinresponsetootherviralinfections.Thesecross- 8
, 2
reactivememoryT-cellresponsesmaybeeasiertobeactivatedthannaiveTcellsbutlessefficient 0
1
2
incontrollingtheinfectionthanprimaryresponsesfromnaiveTcells(Cluteetal.,2005;Rickinson
&Kieff,1996).
Theinitialviralload
•
Highviralchallengesinadolescents,oftenacquiredviakissing,mayinduceaggressiveCD8+T-cell
response(Hislopetal.,2007).
InonestudyusingdatacollectedfromthreeIMandthreeasymptomaticdonors,thelevelsofCD8
+
Tcellsduringtheprimaryinfectionwereobservedtobebetween4and26foldshigherinIMcasesthan
inasymptomaticcases(Silinsetal.,2001).Ourgoalofapplyingthemodelinstudyingthesehypotheses
is not to predict the exact level of antibody effect, cross-reactive memory CD8 T-cell response or
+
MATHEMATICALMODELLINGTHEAGEDEPENDENCEOFEBV 3of17
initialviralloadthatinducesIMbuttohelpinformulatingquestionsandprovidinginsightsforspecific
biologicalstudyofIMinthelaboratory.
2. Model
AddressingthethreehypothesesforthecausesofIMrequiresconsiderationofantibodyeffectsandstate
variables representing cross-reactive T-cell responses to latent and lytic infection. Our mathematical
model(Fig.1and(2.1))trackstwotypesoftargetcells,Bcellsandepithelialcells,viruses,twotypesof
specificcytotoxicTcells(CTLs)attackinglatentlyinfectedBcells( T )andlyticallyinfectedcells(T ),
2 4
respectively, and two types of cross-reacting CTLs against latently (T ) and lytically (T )-infected
2c 4c
D
cells. B cells is classified further into four state variables: naive B cells ( B ), latently infected B cells o
1 w
(B2),latentlyinfectedmemoryBcells(B3)andlyticallyinfectedBcellsorplasmacells(B4).B2andB3 nlo
a
representdifferentstagesoflatency. B arenewlyinfectedcells,expressingEBVlatentgenes(Thorley- d
2 e
d
Lawson,2005)andthuscanberecognizedandkilledbyeffectorTcells.B3representsthenextstage fro
oflatencywithnoexpressionofviralgeneandhencenoTcellresponsetotheseinfectedmemorycells m
h
(Thorley-Lawson,2005). ttp
Infectionofepithelialcellsoftenresultsinvirusreplicationandproduction.Epithelialcellsdonot ://im
ordinarily harbour latent virus, which has been observed only in the cases of cancer like nasopharyn- am
m
gealcarcinoma.Themodelthusincludesonlytwostatevariables:uninfectedepithelialcells(E1)and b
.o
lytically infected epithelial cells (E4). Viruses are classified into virus derived from B cells ( VB) and xfo
virus derived from epithelial cells (VE) since virus produced from one cell type preferentially infects rdjo
the other (Borza & Hutt-Fletcher, 2002). Cytotoxic T-cell responses against viral latent and lytic pro- u
rn
teinshavebeendetectedinEBVpositiveindividuals(Cluteetal.,2010).ExpressionofEBVproteins als
can also stimulate cross-reactive response from CD8+ T cells specific to influenza virus ( Clute et al., .org
2005). Four state variables for T-cell responses are included to examine the effect of these responses a/
t U
n
iv
e
rs
ity
o
f U
ta
h
o
n
J
a
n
u
a
ry
1
8
, 2
0
1
2
FIG.1.ModelofEBVinfectionofBcellsandepithelialcells.AntibodieslikeIgAcanshifttheviraltargetfromBcellsto
epithelialcells.Activationofcross-reactivememoryTcells(T2c,and T4c)thatarenotefficientinkillinginfectedcellsmay
contributetothepathologyofIM.
4of17 G.T.HUYNHANDF.R.ADLER
on the dynamics of infection. The model consists of a system of twelve ordinary differential
equations:
dB
1
d (B B ) f(a)μ V B f(a)μ V B ,
1 0 1 Eb E 1 Bb B 1
dt = − − −
dB
2
ρ(f(a)μ V B f(a)μ V B ) (d c)B k B T χ k B T ,
Eb E 1 Bb B 1 2 2 2 2 2 2 2 2 2c
dt = + − + − −
dB
3
cB rB srB ,
2 3 3
dt = + −
D
dB4 ow
rB d B k B T χ k B T , n
dt = 3− 4 4− 4 4 4− 4 4 4 4c loa
d
e
ddEt1 =de(E0−E1)−h(a)μBeVBE1−h(a)μEeVEE1, d from
h
ddEt4 =h(a)μBeVBE1+h(a)μEeVEE1−(de+γ)E4−k4E4T4−χ4k4E4T4c, (2.1) ttp://im
a
m
dV m
B b
dt =nd4B4−dvVB, .ox
fo
rd
dVE jo
nγE d V , u
dt = 4− v E rn
a
ls
ddTt2 =(1−σ2)φ2TNw(B2)+θ2T2w(B2)−δT2, at U.org/
dT2c niv
σ mφ T w(B ) mθ T w(B ) mδT , e
dt = 2 2 M 2 + 2 2c 2 − 2c rsity
dT4 (1 σ )φ T [w(B E )] θ T [w(B E )] δT , of U
dt = − 4 4 N 4+ 4 + 4 4 4+ 4 − 4 tah
o
dT4c n J
σ4mφ4TM[w(B4 E4)] mθ4T4c[w(B4 E4)] mδT4c. an
dt = + + + − u
a
ry
1
ThedynamicsofBcellsobeytheseassumptions: 8
, 2
0
Naive B cells have an initial population size of B0 and turnover rate d1. They encounter and are 12
•
infectedbyV andV withrates f(a)V μ and f(a)V μ ,respectively,where f(a)represents
B E B Bb E Eb
theinhibitingeffectofhostsalivaandantibodyresponsesoninfectionofBcells(2.3).
Aninfectionofanaivecell, B ,maygiverisetooneormorelatentlyinfectedcells, B ,duetothe
1 2
•
limitedproliferationofthesenewlyinfectedcells,whereρ istheproliferationfactor.These B cells
2
dieatrated andarerecognizedandkilledbyspecificorcross-reactiveeffectorTcellsatrate k or
2 2
χ k , respectively. They can also enter the latently infected memory state, driven by EBV turning
2 2
offitsgeneexpression,atratec.
Infected memory cells, B , obey homeostatic regulation similar to normal memory B cells. They
3
•
areinvisibletotheimmunesystemandundergocelldivisionwithrater,whereonecellgoesinto
MATHEMATICALMODELLINGTHEAGEDEPENDENCEOFEBV 5of17
lytic infection and one stays in the memory state. The rate sr represents the death of B due to
3
homeostaticregulationofmemorycells,wheres istheregulationfactor.Foranormalhomeostasis,
s 2balancestheproliferationrateof2r (Macallanetal.,2005).
=
LyticallyinfectedBcells, B ,arisefromlyticreactivationofmemoryinfectedBcellsatrater,die
4
•
andreleasevirusesatrated andcanbekilledbyspecificorcross-reactiveeffectorTcellsatrate k
4 4
orχ k ,respectively.
4 4
Here, χj (j 2 or 4), with 0 6 χj 6 1, characterizes the efficiency of cross-reactive T cells in
=
killinginfectedcells,comparedtospecificTcells.Thesmaller χ isthemoreinefficientcross-reactive
j
Tcellsareinkillinginfectedcells.
Thedynamicsofepithelialcellsassumethefollowing: D
o
w
n
• aUnndinafreectiendfeecpteitdhebliyalVcBellasnhdavVeEinwitiitahlrpaotepsulha(tiao)nVsBiμzeBoefaEnd0 wh(itah)VtuErnμoEvee,rrreastpeedceti.vTelhye.yHeenrceo,uhn(tae)r loaded
represents the enhancement effect of host saliva and antibody responses on infection of epithelial fro
m
cells(2.4). h
ttp
• Lytically infected epithelial cells, E4, die at natural rate de, die due to virus bursting out at rate γ, ://im
andcanbekilledbyspecificorcross-reactiveeffectorTcellsatrate k4orχ4k4,respectively. am
m
Theeffectsofhostsalivaandantibodyresponsesontheinfectionofthetwocelltypesarerepresented b
.o
bythefunctions f andh andincludedasparametersinthecell-specificinfectionterms.Thisisbased xfo
ontheobservationthatsalivafrominfectedpeopleandantibodiestoviralglycoproteinsinterferewith rd
jo
infectionofBcellsandenhanceinfectionofepithelialcells(Turketal.,2006).Fromlimiteddatainthis urn
invitrostudy,weobtainthelinearrelationshipbetween f andh thatcanbedescribedinthefollowing als
.o
equation: rg
a/
h 1 λ λf , (2.2) t U
n
= + − iv
e
wanhteibreodλy≈eff3e2c.tTs,hef fduenccrteiaosnessftoarnedphrecseanrrtydneocruenaistesd.WefifictiheonuctythineiannfteibctoidoyneofffeBctc,eflls=an1dandhhin=cre1a.sWesittoh rsity o
represent increased efficiency in infection of epithelial cells. To model the dependence of f and h on f Uta
h
antibodyresponse,weassumethatthetwofunctionstakeontheforms o
n
J
a
a2 nu
f(a)=1− A2 a2 , (2.3) ary 1
+ 8
λa2 , 20
h(a) 1 , (2.4) 12
= + A2 a2
+
where a represents the strength of saliva and antibody effects. We will refer to a as the antibody
effectfromnowonbecausethefactor(s)insalivathatcanenhanceinfectionofepithelialcellsremain
unknown.Thefunctions f(a)andh(a)taketheformofHillfunctions,whereλisthemaximumlevel
of the antibody effect on the infection of epithelial cells and A is the level of a where the effect on
theinfectionofBcellsandepithelialcellsishalfmaximal.Asa increases, f(a)decreaseswhileh(a)
increases before saturating. This saturating form assumes that a certain level of antibody response is
requiredtohavestrongeffectsontheinfectionofbothcelltypes.
Freeviruses,V andV ,areproducedfromBcellsandepithelialcellsatratesnd andnγ,respec-
B E 4
tively,wheren istheaverageburstsize.Thesevirusesdieatrated .TomodeltheCTLresponse,we
v
6of17 G.T.HUYNHANDF.R.ADLER
separatethespecificresponsesagainstlatent( T )andlytic(T )infectioncomingfromnaiveTcellsand
2 4
thecross-reactiveresponses(T andT )comingfromthememoryTcellsspecifictootherencountered
2c 4c
pathogens.
Weassumethatthenaiveandmemorypopulations, T and T ,arefixedatconstantlevelsdueto
N M
homeostatic regulation of these two pools of T cells (Stockinger et al., 2004) and also for the mathe-
maticalconvenienceofthemodel.Uponstimulationbyviralantigens,T becomeeffectorcellsagainst
N
latentorlyticinfectionatrate(1 σ )φ or(1 σ )φ ,respectively,whereσ isthefractionofcross-
2 2 4 4 j
− −
reactive T-cell response. With further stimulation by viral antigens from infected cells, the activated
effectorcells,T andT ,canproliferatewithratesθ andθ ,respectively.Eachtypeofeffectorcelldies
2 4 2 4
atasimilarrateδ.ActivationandproliferationofCTLssaturateasafunctionoftheavailableinfected
cells D
o
w
n
w(Bj)= K BjBj , (2.5) loaded
+ fro
m
where K is the number of infected cells at which activation or proliferation is half maximal and is
h
assumedtobethesameforbothresponses. ttp
Cross-reactive responses, T2c and T4c, are activated from the memory population at rate σjmφj, ://im
a
wherem > 1isameasurementofhowmuchfasteraresponsecanbeactivatedfrommemoryTcells m
m
comparedtoactivationfromnaiveTcells.Thesecross-reactivememorycellsareassumedtohavefaster b
.o
dynamics than specific T cells. Although they may be activated quickly and proliferate rapidly, they xfo
die faster (by a factor m). This comes from observations that memory cells respond with fast kinetics rd
jo
(Kedl&Mescher,1998)butarealsomoresusceptibletodeath(Cerwenkaetal.,1999).Furthermore,T urn
cellsobtainedfromacuteIMpatientshavebeenshowntohavehighexpressionofprogrammed-death-1 als
.o
(Hislopetal.,2007). rg
Thesystem(2.1)hastwoequilibria:aninfection-freeequilibriumandapersistentequilibrium.The at U/
infection-freeequilibriumisgivenby n
iv
e
rs
B1∗ = B0, E1∗ = E0, ity o
f U
withotherstatevariablesequalzero.Thestabilityoftheinfection-freeequilibriumisdeterminedbythe ta
h
basicreproductiveratio,ofEBVinanaivehost(Heffernanetal.,2005): o
n
J
a
n
R0 = 2ndv2 (cid:18)(ρsf−(a1))μ(dB2b+B0cc) + h(ad)eμ+EeγE0γ(cid:19) uary 18
, 2
0
n ρf(a)μBbB0c h(a)μEeE0γ 2 4ρf(a)μEbB0ch(a)μBeE0γ 12
. (2.6)
+ 2dv2s(cid:18)(s−1)(d2+c) − (de+γ) (cid:19) + (s−1)(d2+c)(de+γ)
Infections of both B cells and epithelial cells contribute to the basic reproductive ratio of EBV. The
antibody effects, f(a) and h(a), shift the weight of R contribution from B cells to epithelial cells.
0
If R <1, the infection-free equilibrium is stable and the infection cannot establish within a host. If
0
R >1,theinfection-freeequilibriumisunstableandEBVcanestablishapersistentinfection,whereall
0
statevariablestakeonpositivevalues.Tables1and2presenttheparametervaluesusedforsimulations
andanalysisofthemodel.
Assuming no cross-reactive responses (σ ,σ 0), the dynamics of viruses and T cells for the
2 4
=
caseswithoutantibodyeffect(a 0)andwithantibodyeffect(a 10)areshowninFig.2(iandii),
= =
MATHEMATICALMODELLINGTHEAGEDEPENDENCEOFEBV 7of17
TABLE1 Parameters for the dynamics of B cells and antibody effect used in the model simulations
(2.1).WeusemanyparametersfromPathSim,wheretheratesareestimatedandgiveninaunitofper6
min(Shapiroetal.,2008)andconvertthemintotheunitofperminute
Parameter Description Value Value Reference
d TurnoverrateofnaiveBcells 1/6000 min 1 (Shapiroetal.,2008)
1 −
μ Bcellinfectionrateper 3.3 10 10 min 1virus 1 (Shapiroetal.,2008)†
Eb − − −
×
epithelialcellvirus
μ Bcellinfectionrateper μ /100 min 1virus 1 (Hutt-Fletcher,2005)
Bb Eb − −
B-cellvirus
D
ρ Proliferationfactor 2 Nounit (Shapiroetal.,2008) o
w
d Deathrateoflatentlyinfected 1/11520 min 1 (Shapiroetal.,2008) n
2 − lo
Bcells ad
e
c gRoaitnegoifnltaotemntelmyoinryfescttaegdecells 0.001 min−1 (Shapiroetal.,2008)‡ d from
k2 Rateoflatentlyinfected 3.8×10−8 min−1cell−1 (Shapiroetal.,2008)§ http
r RBacteellosfkreilalecdtivbaytiTonceolflslytic 8.3 10 5 min 1 (Shapiroetal.,2008) ://im
− − a
× m
infectionfromlatentinfection m
s Regulationfactorof 2 Nounit (Macallanetal.,2005) b.o
x
memoryBcells fo
d4 Deathrateoflyticallyinfected 1/4320 min−1 (Shapiroetal.,2008) rdjo
cellsduetovirusesburstingout urn
k4 Rateoflyticallyinfected 7.6×10−8 min−1cell−1 (Shapiroetal.,2008)§ als.o
BcellskilledbyTcells rg
a Thestrengthofantibodyeffect Variable(0–40) Nounit a/
t U
A Levelofawhereantibodyeffect 10 Nounit n
ishalfmaximal ive
λ Maximallevelofantibodyeffect 32 Nounit (Turketal.,2006)¶ rsity
onepithelialcellinfection of U
†Probabilityofvirusandcellencounterperminutemultipliedbyprobabilityofinfectionanddividedbythenumberof tah o
v‡Wiruesetask(e≈th1i0s7to).bethesamerateastheestimationof0.1%oflymphocytesleavingtheWaldeyer’sringperminute. n Jan
n§PumrobbearboilfitTyio(fly1m04p)h.ocyteencounterperminutemultipliedbytheprobabilitythatTi killsitstargetanddividedbythe uary 1
¶Estimatedfro≈mlimiteddatagiveninaninvitrostudy(Borza&Hutt-Fletcher,2002). 8, 2
0
1
2
respectively.Theantibodyeffectgreatlyincreasesthenumberofvirusesbeingproduced,withmostof
thisincreasecomingfromepithelialcellviruses.ElevatednumberofTcellsagainstvirallyticproteins
areinducedduringprimaryinfection.
3. ApplicationtoIM
EBVinfectioninchildrenofyoungageisusuallyasymptomatic.Adolescentsandyoungadultsinfected
with EBV may develop flu-like symptoms referred to as IM. These symptoms result from a massive
T-cell response to EBV a few weeks after the initial viral infection that can last from a few weeks to
severalmonths(Cohen,2005).TheT-cellresponsesagainstvirallatentproteinsaregenerallysmallerin
8of17 G.T.HUYNHANDF.R.ADLER
TABLE2 Parametersforthedynamicsofepithelialcells,virusandT-cellresponsesusedinthemodel
simulations(2.1)
Parameter Description Value Unit Reference
d Turnoverrateofepithelialcells 1/6000 min 1 (Shapiroetal.,2008)†
e −
μ Epithelialcellinfectionrate 3 10 11 min 1virus 1 (Shapiroetal.,2008)‡
Be − − −
×
perB-cellvirus
μ Epithelialcellinfectionrate μ /5 min 1virus 1 Hutt-Fletcher(2005)
Ee Be − −
perepithelialcellvirus
γ Deathrateofinfectedepithelial 1/6000 min−1 Dow
cellsduetovirusesburstingout (Shapiroetal.,2008)§ n
lo
ndσvj VDFriearaactlthiborunartsoetfoseiffzfveeicrutosrcellsactivated Var1ia1/b20l10e60(00–1) virNmuosi∙ncu−enl1ilt−1 SShhaappiirrooeettaall..((22000088)) aded from
fromcross-reactivememoryTcells h
ttp
m FfraocmtomroefmfoasryterTrceespllosnse 5 Nounit Kedl&Mescher(1998) ://im
a
φ2 RateofT-cellactivation 1.95 10−5 min−1 Shapiroetal.(2008)¶ mm
againstlatentinfection × b.o
φ4 RagaatienostflTy-tcicelilnafcetcitviaotnion 4.48×10−5 min−1 Shapiroetal.(2008)¶ xfordjo
θ2 RateofT-cellproliferation 3.25 10−5 min−1 Shapiroetal.(2008)k urn
× a
againstlatentinfection ls
.o
θ4 RagaatienostflTy-tcicelilnpfreocltiifoenration 3.25×10−5 min−1 Shapiroetal.(2008) at Urg/
K Numberofinfectedcellswhen 105 Cell Jones&Perelson(2005) n
iv
T-cellactivationishalfmaximal ers
δ DeathrateofTcells 1/156000 min−1 Shapiroetal.(2008) ity o
†Estimated,takentobethesameasd1. f Uta
‡EstimatedtakentobelessthanμEb(Turketal.,2006). h o
§Estimatedtakentobelessthand4(Borza&Hutt-Fletcher,2002). n J
¶kPPrroobbaabbiilliittyyooffllyymmpphhooccyytteeeennccoouunntteerrppeerrmmiinnuutteemmuullttiipplliieeddbbyytthheepfrreoqbuaebnilciytyooffcTeliladcitviivsaitoinon(ebvyerByi8,–w1h2erhe).i=2or4. anuary
1
8
, 2
0
magnitudethantheT-cellresponsesagainstvirallyticproteinsduringtheacutephaseofIM.Theacute 12
phase is followed by convalescence and eventually a virus carrier state where the CD8 population
+
resolvestoalevelcomparabletothatinasymptomaticcarriers(Hislopetal.,2007).
Weusenumericalsolutionsofourmodeltoinvestigatethethreehypothesesforthehighprevalence
ofIMinteenagersandyoungadults:salivaandantibodyeffects,cross-reactiveT-cellresponsesandthe
initialviralload.ThetotalnumberofTcells(bothspecificandcross-reactiveones)andthelyticT-cell
ratioatthepeakofinfectionareusedasthetwokeymeasurementsofIM.ThelyticT-cellratioisthe
ratiobetweeneffectorTcellsrespondingagainstlyticinfectionandeffectorTcellsrespondingagainst
latentinfection,(T T )/(T T ).Awiderangeofvaluesofthesetwomeasurementshasbeen
4 4C 2 2C
+ +
observedinIMpatients.Individualepitoperesponsesagainstlatentandlyticinfectionscanaccountfor
0.1–5%and1–40%ofthetotalCD8 T-cellpopulation,respectively(Hislopetal.,2007).
+
MATHEMATICALMODELLINGTHEAGEDEPENDENCEOFEBV 9of17
D
o
w
n
lo
a
d
e
d
fro
m
h
ttp
://im
a
m
m
b
.o
x
fo
rd
FIG.2.DynamicsofvirusesandTcellsinthecaseofnocross-reactiveT-cellresponses(σj 0).(i)Withoutantibodyeffect jou
(a 0).(ii)Withantibodyeffect(a 10).Theinsetsshowthelevelofpersistentvirusforthe=twocases.Parametervaluesused rn
are=showninTables1and2. = als.o
rg
a/
3.1 Antibodyeffects t U
n
iv
Race, sex and age are at least in part responsible for individual differences in antibody responses e
rs
(Buckley & Dorsey, 1971; Childers et al., 2003; Jafarzadeh et al., 2008), which may influence the ity
o
outcomes of EBV infection. Titers of antibody responses specific to EBV viral capsid antigen, IgA f U
andIgG,havebeenobservedtoincreasewithageandIgAattainsitshighestlevelduringtheonsetof ta
h
diseasewithinIMpatients(Edwards&Woodroof,1979;Oberenderetal.,1986).Furthermore,individ- on
J
ualsareexposedtomorepathogensastheyage.EBVinfectioninyoungadultsmayactivateantibody an
u
responses that are specific to other viruses but cross-reactive to EBV. As IgG and IgA responses to ary
EBVglycoproteinscanenhancethelyticinfectionofepithelialcells,theprobabilityofgettingIMmay 18
increasewithage. , 20
1
To examine this hypothesis with our model, we vary the strength of the antibody effect (a) and 2
studyitsinfluenceonthetotalnumberofTcellsandthelyticT-cellratio(Fig. 3)measuredatthepeak
of infection. The total number of T cells increases with the level of a but then decreases when a is
large. At high levels of antibody response, infection of B cells is strongly suppressed while the effect
on enhancement of lytic infection of epithelial cells saturates, leading to a decreased total number of
Tcells(Fig.3(i))andincreasedlyticT-cellratio(Fig.3(ii)).
3.2 Cross-reactiveT-cellresponses
Massive expansion of CD8 T cells responding to EBV causes the symptoms of IM (Silins et al.,
+
2001). It has been proposed that the high susceptibility of teenagers and young adults to IM may be
10of17 G.T.HUYNHANDF.R.ADLER
D
o
w
n
atFehvtIeGapla.euba3ask.tee:Andrncaaettitibootohfbdeceyrptoweesafesfk-eerncoetafsthcionteinfvneetcuhTtmeiocbtnoee.tlralPsloan(frσuaTmmjc=ebeteelrl0rs)ov.afa(gTliau)iecTnseoslattlasrlley(ntTsiuh2cmo+iwnbfTneer2cicontif+oTCnaTbD(4lT8e+4s+)1TTa4ancncd)edaltlh2nse.dantthutehmelbypeteircaokTf-ocTfeilcnlefrlealcstitoaiog(na(.iTn(4isit+)lTaTth4eecn)lt/yi(tniTcf2eTc+-tcioTenl2lc(r)Ta)2tii)on, loaded fro
m
h
ttp
duetoamorecomplexmemoryCD8repertoirethaninyoungchildren.Asindividualsage,thememory ://im
CD8 repertoire gets more complex due to exposure to different pathogens. Adolescents infected with a
m
EBV may recruit a large number of cross-reactive memory T cells previously created in response to m
b
otherviralinfections(Rickinson&Kieff,1996).Infact,ithasbeenshownthatmemoryCD8+ Tcells .oxfo
specific to influenza virus can be activated and respond to stimulation by EBV lytic proteins ( Clute rd
etal.,2005).Boththemagnitudeandtheefficiencyofcross-reactiveTcellsinkillinginfectedcellsmay jou
rn
contributetotheetiologyofIM.Thelevelofcross-reactivememoryTcellcanincreasewithage.These a
ls
memorycellsmaybefasteratactivationandproliferationcomparedtonaiveTcells(Veiga-Fernandes .o
rg
etal.,2000)butlessefficientincontrollingtheinfection( Thorley-Lawson,2005). a/
AlargefractionofCD8 TcellscreatedduringthecourseofIMrespondtolyticinfection(5–50% t U
+ n
comparedto1–3%forTcellsrespondingtolatentinfection)(Callanetal.,1998;Hislopetal.,2002). ive
rs
SinceEBVhasmanymorelyticgenesthanlatentgenes(Robertson,2005),itislikelythattherearemore ity
cross-reactiveTcellstoEBVlyticinfectionthantolatentinfection.Wefirstassumecross-reactionof of U
onlyT-cellresponsesagainstlyticinfection.Toaddressthisassumptionwithourmodel,wesetσ2 0 ta
= h
andconsidervfi edifferentvaluesof σ4,0,0.3,0.6,0.8and1.Asσ4increases,thefractionoflyticT-cell on
Tre-scpeollnrseespcoonmsien;galflrloymticcTrocsse-lrlseaacrteivceromsse-mreoarcytivTe.cells increases. At σ4 = 1, there is no specific lytic Janua
ry
To facilitate comparison with the antibody effect (Fig. 3), we present the effects of cross-reactive 1
8
T cells on the development of IM using similar plots, with vfi e curves in each representing different , 2
0
valuesofthelevelofcross-reactivelyticTcells(σ4)(Fig.4).Thisfigurealsoillustratestheimpactof 12
χ , the efficiency of cross-reactive T cells in killing lytically infected cells, on the two measurements
4
ofIM.Acrossalllevelsofantibodyeffects(a),theincreaseinσ greatlyelevatesthetotalnumberof
4
T cells and the lytic T-cell ratio. This effect, however, diminishes as χ increases. At χ 1, cross-
4 4
=
reactivelyticTcellsareasefficientasspecificTcellsinkillinginfectedcells.Infact,duetotheirfaster
response,cross-reactiveTcellsreducetheoverallT-cellresponsesandtheprobabilityofIM.
Wenowaddthepossibilityofcross-reactiveT-cellresponsesagainstlatentinfection.Figure5shows
the effects of this addition on the two measurements of IM. For each level of σ , we set σ 0.2σ
4 2 4
=
toassumelowerlevelsofcross-reactiveTcellsagainstlatentinfectioncomparedtolyticinfection.We
analysed and observed only minimal impacts of variation in the efficiency of cross-reactive T cells in
killinglatentlyinfectedcells(χ )ontheresults.Wethusfix χ 0.5forthisanalysis.Incomparison
2 2
=