Centering the Organizing Center in the Arabidopsis thaliana Shoot Apical Meristem by a

28 Pages·2016·4.1 MB·English

RESEARCHARTICLE
Centering the Organizing Center in the
Arabidopsis thaliana
Shoot Apical Meristem
by a Combination of Cytokinin Signaling and
Self-Organization
MiladAdibi1¤a*,SaikoYoshida2¤b,DolfWeijers2,ChristianFleck1*
1LaboratoryofSystemsandSyntheticBiology,WageningenUniversity,Wageningen,theNetherlands,
2LaboratoryofBiochemistry,WageningenUniversity,Wageningen,theNetherlands
¤a Currentaddress:MaxPlanckinstituteforplantbreedingresearch,Cologne,Germany
¤b Currentaddress:InstituteofScienceandTechnology(IST)Austria,AmCampus1,Klosterneuburg,
Austria
*[email protected](MA);[email protected](CF)
Abstract
Plantshavetheabilitytocontinouslygenerateneworgansbymaintainingpopulationsof
stemcellsthroughttheirlives.Theshootapicalmeristem(SAM)providesastableenviron-
mentforthemaintenanceofstemcells.AllcellsinsidetheSAMdivide,yetboundariesand
OPENACCESS patternsaremaintained.Experimentalevidenceindicatesthatpatterningisindependentof
celllineage,thusadynamicself-regulatorymechanismisrequired.Apivotalroleintheorga-
Citation:AdibiM,YoshidaS,WeijersD,FleckC
nizationoftheSAMisplayedbytheWUSCHELgene(WUS).Animportantquestioninthis
(2016)CenteringtheOrganizingCenterinthe
ArabidopsisthalianaShootApicalMeristembya regardisthathowWUSexpressionispositionedintheSAMviaacell-lineageindependent
CombinationofCytokininSignalingandSelf- signalingmechanism.Inthisstudywedemonstrateviamathematicalmodelingthatacombi-
Organization.PLoSONE11(2):e0147830.
nationofaninhibitoroftheCytokinin(CK)receptor,Arabidopsishistidinekinase4(AHK4)
doi:10.1371/journal.pone.0147830
andtwomorphogensoriginatingfromthetopcelllayer,canplausiblyaccountforthecellline-
Editor:HenrikJönsson,LundUniversity,SWEDEN
age-independentcenteringofWUSexpressionwithinSAM.Furthermore,ourlaserablation
Received:May6,2015 andmicrosurgicalexperimentssupportthehypothesisthatpatterninginSAMoccursatthe
Accepted:January8,2016 levelofCKreceptionandsignaling.ThemodelsuggeststhattheinterplaybetweenCKsig-
naling,WUS/CLVfeedbackloopandboundarysignalscanaccountforpositioningofthe
Published:February12,2016
WUSexpression,andprovidesdirectionsforfurtherexperimentalinvestigation.
Copyright:©2016Adibietal.Thisisanopen
accessarticledistributedunderthetermsofthe
CreativeCommonsAttributionLicense,whichpermits
unrestricteduse,distribution,andreproductioninany
medium,providedtheoriginalauthorandsourceare
credited.
Introduction
DataAvailabilityStatement:Allrelevantdataare
withinthepaper. Alltheaerialplantpartsaregeneratedbytheshootapicalmeristem(SAM)situatedatthe
Funding:Theauthorshavenosupportorfundingto plantapex.TheSAMisformedduringembryogenesisandindicotyledonousangiosperms,
report. suchasthemodelplantArabidopsisthaliana,itcontainsthreelayersofstemcellsinthethree
outermostcelllayers[1,2].Clonalstudiesindicatethateachlayercontainsaboutthreelong
CompetingInterests:Theauthorshavedeclared
thatnocompetinginterestsexist. livedstemcells[3]inthecentralzone(CZ),whichismarkedbyalowercelldivisionrate.
PLOSONE|DOI:10.1371/journal.pone.0147830 February12,2016 1/28
PositioningtheOrganizingCenterinArabidopsisMeristem
DaughtercellsofthestemcellsthatstayintheCZreplenishthestemcellpool,whereasdaugh-
tercellsthatareplacedtowardstheperipheralzone(PZ),whichismarkedbyahighercelldivi-
sionrate,enterdifferentiationandformorganprimordia.Theshapeandthedomainstructure
oftheSAMarekeptunchanged,althoughallcellscontinuouslydivideanddifferentiatingstem
celldaughtersleavethemeristem.Celltrackingandablationexperimentsdemonstratethatthe
fateofeachcellisdeterminedbyitscurrentpositionandnotbylineagespecificheritage,
highlightingtheimportanceofcell-cellcommunication[4].Duetoitschangingcellularcon-
text,patternformationoftheshootmeristemdoesnotrelyonastablepointofreference,but
ratheroccursinaselforganizedmanner[1].
GeneticstudiesmainlyinArabidopsisrevealthattheWUSCHEL(WUS)andCLAVATA3
(CLV3)feedbackloopisapivotalregulatorofstemcellnumber[1,2,5,6].Asmallcellgroup
underneaththestemcellsnamedorganizingcenter(OC)expressesthetranscriptionfactor
WUSthatmaintainsthestemcellintwoways.First,WUSproteinmovesintothestemcells,
presumablythroughintercellularplasmaticbridges,calledplasmodesmata[7].Inthestem
cells,WUSdirectlybindstothepromoterofCLV3andpromotestranscription,inadditionto
maintainingpluripotencythroughayetunidentifiedmechanism[1].CLV3encodeasmall
extracellularsignalpeptidethatbindstoreceptorkinasecomplexes,includingCLV1,andtrig-
gersanintracellularsignalcascadethatdownregulatesWUStranscription[1,8].Thisnegative
feedbackloopbetweenOCandstemcellsprovidesamechanisticframeworktokeepthenum-
berofstemcellsconstant[1],seeFig1A.Second,intheOCcells,WUSdirectlyrepressestran-
scriptionofARABIDOPSISRESPONSEREGULATOR7(ARR7)and15(ARR15)genes[9],
whichencodesintracellularinhibitorsofresponsetotheplanthormoneCytokinin(CK),
therebypromotingcellularCKresponse[10].Hence,thequestionofhowWUSexpressionsis
centeredandrestrictedwithintheSAM,becomesakeyquestioninstudyingthestemcell
homeostasisintheSAM.SeverallinesofevidencefurtherindicatethatCKisanimportant
factorinshootmeristemregulation:first,mutantsdeficientinCKbiosynthesis,reception,or
overexpressingCKdegradingenzymes,haveareducedSAMsize[2,11,12].Second,theCK
receptor,Arabidopsishistidinekinase4(AHK4),isexpressedinthemeristemcenter,overlap-
pingwiththeOCinitsdistalpart[13].ThereceptorisinvolvedintheupregulationofWUS
expressionviaexogenouslysuppliedCKatrelativelyhighlevels,andithasbeenassumedto
conferWUSregulationalsoatendogenousCKlevels.CKresponse,measuredbythereporter
pTCS,peaksattheOC[14]inagreementwithWUSenhancingCKresponseinthesecells.
BasedontheexpressionpatternofthetranscriptionfactorSHOOTMERISTEMLESS(STM)
thatpromotesexpressionoftheCKsynthesisgeneISOPENTENYLTRANSFERASE7(IPT7),
CKisprobablyproducedbroadlythroughouttheshootmeristem,althoughdirectevidenceis
stillmissing[15].Furthermore,immunodetectionofCKssuggestaratherbroadanduniform
distributionthroughouttheshootmeristeminSinapsisalba[16].Recentfindingsinriceindi-
catethatactivationofCK(clippingofariboseresidue)bytheLONELYGUY(LOG)enzyme
isconfinedtothe2-3outermostcelllayersoftheshootmeristem,andithasbeendiscussed
whetheractiveCKislocallyproducedintheshootmeristemandmovesfromthetopdown-
wards[2,17].InArabidopsis,thereareeightLOGhomologs.Oneofthem,LOG4isspecifi-
callyexpressedintheL1layer,buttheexpressionpatternsoftheotherLOGgenesare
unknownandatleastsomeoftheotherLOGgenesseemtobealsoexpressedintheshoot
meristem[13,18,19].
Previousmodelingapproaches
Thepresenceofcelllineage-independentself-organizationsuggeststhattheinternalstructure
ismaintainedbyanetworkofsignalsthatinteractwitheachotherandcancreatestableisolated
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peaksofconcentration.Onetheoreticalapproachthatwassuccessfullyappliedtoexplainself-
regulatedpatternformationindevelopmentalbiologyisthereaction-diffusionschemefirst
introducedbyTuringin1952[20],andhassincebeenappliedtovariousfieldsofdevelopmen-
talbiology[21–23].Mostoftheapplicationsofthereaction-diffusionschemeinpatternforma-
tioninbiologyhavebeenintheformofactivator-inhibitorsystems.Initssimplestforman
activator-inhibitorsystemconsistsoftwointeractingdiffusingmolecule[24].Modelingthe
self-organizedpatternformationintheSAMhasbeensubjectedtovariousmodeling
approachesamongwhich,activator-inhibitormodelshavebeenthemainapproach.Jönsson
etal.[25]werethefirsttomodelthestemcellregulationintheSAMusinganactivator-inhibi-
tormodel.Thispioneeringworkdemonstratedthatanactivator-inhibitorbasedsystemcan
accountfortheobservedexpressionofWUSintheSAM.Hohmetal.(2010),developedthe
firstmodelthatincorporatescompletefeedbackbetweenCLV3andWUS.Thismodelnotonly
reproducedtheexpressionpatternsofWUSandCLV3observedinthewildtypeSAMbutalso
somemutantsandgeneupanddown-regulationphenotypes,furtherdemonstratingthecapa-
bilityofactivator-inhibitormodelsinaccountingforSAMorganization[26].In[27]Fijuta
etalimplementanactivator-inhibitor-basedmodelofWUS/CLV3regulationinagrowingand
dividingcellulartemplate.Theirworkpresentsamodelthatisstableagainstperturbations
causedbycellulargrowthanddivision.,albeitlackofdatahasledtovariousassumptions,The
activator-inhibitorbasedmodelscanaccountforsomefundamentalaspectsofstemcellregula-
tionwithintheSAM.Thesemodels,likeotherspatialmodelsofcellulardevelopment,have
restrictionsregardingthelevelofdetailandthescopeofthemodel.Oftenitisunavoidableto
considertheinputofotherprocessesaspre-patternsorhypotheticalcomponents.Despite
theselimitationthesemodelshavebeensuccessfulinprovidinganintegratedviewoftheavail-
ableexperimentaldataregardingSAM.patterning.Thehypotheticalcomponentsofthese
modelspointoutgapsinourbiologicalknowledgethatneedtobeaddressedinordertoobtain
amechanisticunderstandingoftheSAMstemcellregulatorymechanism.
TheaforementionedmodelsfocusonhowtheWUSexpressionpatterncanemergefrom
theinteractionofnetworkcomponentswithintheSAM.ThecomputationalmodelsofSAM
organizationhowever,havenotbeenlimitedtoself-organizingsystems,othermodelshave
focusedoninvestigatingtheinterplaybetweengeneexpressionpatternsratherthanself-orga-
nizedpatternformation[13,14,28].Thesemodelsfocusontheexperimentallydemonstrated
interactionsbetweentheWUS/CLV3patternsandCKsignaling/perceptionnetwork[13,14,
28].Forinstance,Yadavetal.[28]investigateamodelthatrelatesCKperceptionviaAHK4
receptortopatternformationintheSAM.InthismodelCKisinducedbyanAHK4/CKsignal,
whichisproducedatthecenterofOC.Theexpressionzones(i.e.binaryexpressiontemplates)
ofWUS,CLV3,andKAN1arerestrictedtoCZ,OC,andPZ,respectively.Giventheseinputs
themodelcanrobustlyestablishthespatialpatternsofWUS,CLV3andKANDI1.Further-
more,thesepatternscanwithstandperturbationscausedbycellgrowthanddivision.Inthe
aforementionedworkthelocalizedexpressionofAHK4atthecenteroftheOCisfundamental
forcorrectpatterningofWUS.Thisgroupofexperimentalandcomputationalworks,consis-
tentlyproposethatthepatterningofOCtakesplaceatthelevelofCKreceptionandsignaling.
Consequently,thisimpliesthattheself-organizingpropertiesoftheOC,canarisefromthe
underlyingCKsignaling/perceptionpattern.
Aimofthisstudy
Thecapabilityofactivator-inhibitornetworksinaccountingforSAMpatterninghasbeen
alreadydemonstrated.Ingeneral,theexperimentalidentificationofnetworkcomponentshas
beenamajorchallengeinapplicationofreaction-diffusionmodelsinbiology.Particularlyin
PLOSONE|DOI:10.1371/journal.pone.0147830 February12,2016 3/28
PositioningtheOrganizingCenterinArabidopsisMeristem
theplantfield,itremainsamajorchallengetodemonstratetheexistenceofreactiondiffusion
networksexperimentally.
Inourcontextthishighlightstheimportanceofmotivatingthepre-patternsofamodelby
knownbiologicalknowledgeasmuchaspossible;whenpre-patternsareabstractandcannot
bedirectlylinkedtotheknownbiologicalmechanisms,thetaskofexperimentalidentification
ofnetworkcomponentsiscomplicated.Incontrast,whentheseassumptionsaremotivatedby
experimentalobservations,theycanbemorereadilyinvestigatedviaexperimentation.Asdis-
cussedearlier,theoreticalandexperimentaldatapointtowardsCKsignalingandperceptionas
afundamentalfactorinpatterningoftheSAM[13,14,28].Hereweaimtoexpanduponthe
currentstateofresearchandavoidincorporationofabstractassumptionsinourmodel,byuti-
lizingtheavailabledataasmuchaspossible.OurmodellinksWUS/CLV3feedbacklooptoan
activator-inhibitorsystembasedonCKsignaling.Wedemonstratethatthesecomponents
functiontogethertopositionWUSexpressionattheOC.
Results
TheModel
Inordertoinvestigatetheapical-basalpositionandthelateralextensionoftheOCwithinthe
shootmeristem,wechoseatwodimensionalmodelofalongitudinalsection.Inourmodel,
mobilesignalsarefreetodiffuseoutoftheSAMandintothesurroundingcells(Fig1).Thesys-
temisdescribedbyasetofcouplednon-linearordinarydifferentialequationsonadiscrete
grid,wherethegridpointsrepresenttheindividualcells.Hence,cellsareassumedtobespa-
tiallyuniformandintracellularconcentrationgradientsarenottakenintoaccount,whichis
consideredareasonablesimplificationduetothedifferenceintimescalebetweencytosolic
Fig1.SAMarchitectureanditsrepresentationinthemodel.(A)AnimageoftheSAMandtheimmediatesurroundingarea.Theregionsofinterestare
markedwithcoloredboundaries.(B)SchematicrepresentationofWUSandCLVdomains;thethreedimensionalSAM,consistingofcellsofvariousshapes
andsizes,ismodeledbyatwodimensionalgridconsistingofidenticalblocksrepresentingcells.Thefieldofcellsextendfartherinlateralandbasal
directions.S2Figdepictsthecompletecellulartemplateusedforsimulations.
doi:10.1371/journal.pone.0147830.g001
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PositioningtheOrganizingCenterinArabidopsisMeristem
mobility(fast)andtheactualpatternformationprocess,i.e.,geneexpression(slow).Therefore,
weusethetermdiffusionnotinitsactualphysicalbutratherinaneffectivesense,meaning
unbiasedbi-directionalspreadofmoleculesbetweencellsthroughspecialopeningstermed
plasmodesmataorviatheapoplast.Moreover,forsimplicity,weassumethatthedynamicsof
theWUS/CLV3regulatorysystemarisingfromtheassumedreaction-diffusionsystemaresuf-
ficientlyfasterthanthecelldivisionrateintheSAM.Therefore,theessentialfeaturesofthe
patterningprocessoftheaforementionedsystemcanbewelldescribedbyastaticmodelthat
doesnotincorporatecelldivisionorgrowth.
Factsandassumptionsunderlyingthemodel
Theproposedmodelisbasedonthefollowingpublishedresults:
(cid:129) CKbindstotheAHK4receptor,whichinturncausesphosphorylationofbothtype-Aand
type-BARRsviaarabidopsishistedinephosphotranferproteins(AHPs)[29].Inabsenceof
CKthereceptorfunctionsasaphosphatase.[30,31].
(cid:129) Type-BARRsaretranscriptionfactorsthatactivatetranscriptionofCKresponsegenes,
includingtype-AARRs[32].
(cid:129) Type-Ainhibittype-BARRfunction,theprecisemechanismshasyettobedetermined[10,
33].Ingeneraltwohypothesesexistregardingtheinhibitionoftype-BARRsviatype-A
ARRs.Evidencesuggeststhattype-AARRsinhibittype-BARRsviarepressionofupstream
CKsignaling.Inaddtitionithasbeenproposedthattype-Brepresstype-Aviacompetition
forphosphatemolecules[34].
(cid:129) ThereisfeedbackloopbetweenWUSandCLV3genes,whereWUSmovesfromtheOCinto
thestemcellsandactivatesthetranscriptionoftheCVL3gene.TheCLV3peptideismobile
andinhibitstheexpressionofWUS[1,35].
(cid:129) ExpressionofWUSisactivatedbyCKsignaling[13],presumablyviacanonicaltype-BARRs
effectorgenes.AdditionallyWUSrepressestheexpressionoftype-AARRs[9],thuspromot-
ingCKsignaling.
Inaddition,ourmodelincorporatesthefollowingassumptions:
(cid:129) TheSAMconsistsofequivalentcellsthathavethepotentialtoexpressallgenesincludedin
themodel.Theexceptionistheepidermis(L1layer),whichisassumedtobedifferentfrom
therestofthecellsintheSAM.ThismeansthatinourmodeltheidentityoftheL1celllayer
isnotdeterminedviatheproposedself-organizingmechanism.
(cid:129) Wehypothesizeamolecule(L1signal)thatissuppliedbytheuppermostcelllayer(L1)and
diffusesdownwardlyestablishingagradient.Thepresenceofthismoleculeisnecessaryfor
thecellstobeabletorespondtoWUSsignalbyproducingCLV3.Suchamoleculehasbeen
identifiedbyKnaueretal(2013),whocharactrizedamicroRNA,miR394,thatisproducedat
theL1layerandisrequiredforestablishmentofCLV3expression.InourmodeltheL1signal
isnecessaryforcellstobeabletorespondtoWUSandestablishstemcellidentity[36].
(cid:129) Adiffusinginhibitorandaself-activatingcomponentareessentialpartsofpatternforming
activator-inhibitormechanisms[24].Currentlythereisnoevidenceofsuchaninhibitor
involvedinSAMpatterning;ourtrialsshowthatseveralmoleculeswithinthemodelcanbe
assumedtoactasaninhibitorortoinduceaninhibitor.Forexample,type-AARRsappearas
aplausiblecandidatefortheinhibitorwithinthemodel.Itisknownthattype-AARRsinhibit
CKsignaling[10].Inthemodeltheinhibitorisassumedtobedownstreamofthetype-A
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PositioningtheOrganizingCenterinArabidopsisMeristem
ARRs.Thisisbecausethetofulfilltheroleoftheinhibitorwithinanactivator-inhibitorsys-
tem,type-AARRshavetobehighlymobilesignals.Inabsenceofevidenceregardingthe
mobilityofthesemolecules,weassumedthattheinhibitoryfunctionisconveyedviaahighly
mobileintermediate,factorX.Thusinourmodeltwomechanismsexistforinhibitionof
type-Bbytype-AARRs,viaphosphatecompetitionandviafactorX.
(cid:129) Weassumetype-BARRspromoteCKsignalingviadirectinductionofAHK4.Experimental
resultspresentedonArabidopsiseFPbrowser[37],(datafromAtGenExpressproject[38])
showthatapplicationofZeatinleadstosignificantup-regulationofAHK4levels.Forthe
model,thisassumedinteractionconstitutestheautocatalyticloopoftheactivator-inhibitor
subnetwork.
(cid:129) Inourreductionistapproach,wedonotdistinguishbetweenmRNAandproteinofthegenes
unlessitisessentialinaddressingthequestionathand.Consideringtheexpressionpattern
ofCLV3mRNA[1]anditsdemonstratedinhibitoryeffectattheOC,itbecomesapparent
thatCLV3elicitsasignalthattravelsfurtherthanititsmRNA.Thisisreflectedinthemodel
bydistinguishingCLV3mRNAandprotein.ThemRNAisassumedtobeimmobilewhile
theproteinisabletodiffuse.
(cid:129) InthemodelweassumethatphophotransferfromthereceptortotheARRsaresufficiently
fastprocessescomparedtogeneexpression.Thereforethephosphotransferisimplemented
usingaquasi-steady-stateassumption.SeedetailinMaterialandmethods.
Reaction-diffusionmodelingoftheSAMhasahistoryofmorethanadecadeandthemodel
presentedinthisworkisinspiredandmotivatedbyearliermodelingefforts.Itutilizesconcepts
andcomponents(experimentallyverifiedaswellashypothetical)putforwardinearlierworks
Inparticular,factorXisauniversalcomponentofactivator-inhibitormodelsoftheSAM[25–
27,39].Astheinhibitorinanactivator-inhibitorsystems,modelsconsistentlypredictittobea
fastdiffusingmoleculewithanexpressionpatterncenteredaroundSAM.Todateevidencefor
amoleculethatfulfillstheroleofsuchinhibitorandmatchesitspredictedexpressionpattern
hasnotemerged.SimilarlytheconceptofL1signalwasfirstestablishedbyJoenssonetalin
[25].InlaterworksthiswasutilizedasasignaldefiningthelateralexpressionofWUS[40],as
wellasinanapical-basalsetting,asacofactorthatalongwithWUSisrequiredforproduction
ofCLV3,inbothtwo-dimensional[7],andthree-dimensional[28]settings.Inourmodelthe
L1signalisessentiallythesameastheinlatter;anapicalbasalsignalrequiredforCLV3induc-
tioinresponsetoWUS.Asalreadypointedoutin[28],thestrongestevidencefortheexistence
ofsuchasignalcomesfromtheobservationthatinpCLV3::WUSbothWUSandCLV3are
expressedintheuppermostthreecelllayersoftheSAM[41].
Modelequations
Integratingtheabovestatedexperimentalobservationsandadditionalassumptionsinamathe-
maticalmodel,wearriveatthefollowingsystemofnon-dimensionalizedcoupledordinarydif-
ferentialequations:
dB k G B
ij ¼ 1 ij ij (cid:2)k B ð1Þ
dt ð1þk X Þ 7 ij
6 ij
dA k G B
ij ¼ 8 ij ij (cid:2)k A ð2Þ
dt ð1þk X Þð1þk W Þ 10 ij
6 ij 9 ij
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PositioningtheOrganizingCenterinArabidopsisMeristem
dR k G B
ij ¼ 11 ij ij (cid:2)k R ð3Þ
dt 1þk X þk G B 13 ij
6 ij 12 ij ij
dX
ij ¼ k G A (cid:2)k X þd D^X ð4Þ
dt 14 ij ij 15 ij 1 ij
dW k G B
ij ¼ 16 ij ij (cid:2)W þd D^W ð5Þ
dt ð1þk X Þð1þk Cs Þ ij 2 ij
6 ij 17 ij
dC k L W
ij ¼ 18 ij ij (cid:2)k C ð6Þ
dt 1þk W 20 ij
19 ij
dCs
ij ¼ k C (cid:2)k Cs þd D^Cs ð7Þ
dt 21 ij 22 ij 3 ij
wherewedefined:
A:¼½type(cid:2)A ARR(cid:3); B:¼½type(cid:2)B ARR(cid:3)
C :¼½CLV3 mRNA(cid:3); Ck :¼½Ck(cid:3)
Cs :¼½CLV3 peptide(cid:3); R:¼½AHK4(cid:3)
W :¼½WUS(cid:3); X :¼½Inhibitor(cid:3)
L:¼½L1signal(cid:3)
and
Ck R
G :¼ ij ij : ð8Þ
ij ð1þk Ck þk R Þð1þk A þk B Þ
2 ij 3 ij 4 ij 5 ij
Thesubscriptijdenotesthepositionx=x onthegrid,whereiandjrefertorowandcolumn
ij
indicesrespectively.L andCk refertotheL1signalandtheCKexpressionprofilesderivedin
ij ij
materialandmethods.ThefunctionΓisthetransferfunctionforthetwostepphosphorelay
fromCKbindingtothephosporylationoftheARRs.Itcomprisesthekinaseandphosphatase
activityoftheAHK4receptor,thephosphorelayviatheAHPsandthecompetitionbetween
thetype-Aandtype-BARRsfortheAHPs,forthederivationseematerialandmethods.The
^
spatialcouplingbetweenthegridpointsisachievedbythediffusionoperatorD(seematerial
andmethods).Weusereflectingboundaryconditionsfortheapicalside.Thebasalandlateral
boundaryisnotwelldefined;weuseboundaryconditionswhichare,forsimulationpurposes,
equivalentwithusinganinfinitedomainfortheapical-basaldimension;inthenumericalsimu-
lationsthegridisextendedinbasalandlateraldirectionsuntiltheconcentrationsdecayto
almostzero;thismakestheboundaryconditionatthebasalandlateralendofthegridirrele-
vantandprovidesagoodapproximationfortheinvivoSAM.Weclosethedomainbasallyand
laterallyusingreflectingboundaryconditions.Allsimulations,unlessstatedotherwise,were
carriedoutinacellgridwherethemeristemicdomeisrepresentedbythreecelllayersthatare
9,11and13cellswide.Theuppermostcelllayerandthelaterallyoutermostcellsoftheother
twolayersmakeuptheL1layer(Fig1B).Wealwayscheckedthatthegridislargeenoughto
approximateaninfinitedomaininthedescribedmanner.Inthefollowingfigures,theareaof
thegridthatcontainsnoinformationhasbeencropped.
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PositioningtheOrganizingCenterinArabidopsisMeristem
Mobilityofmoleculesinthemodel. Inamodel,the‘assigned’mobilityofmoleculescan
occuratthelevelofanyintermediatecomponentsthatarenotexplicitlypresentinthemodel.
Moreover,insuchacase,often,mRNAandproteinofageneareconsideredasingleidentity,
henceinreality,theassignedmobilitycanoccuratthelevelofeithermRNAorthegene.
ThecorrectpatterningofthemodeldependsonmobilityofWUS,CLV3peptide,L1signal
andfactorX.inthemodelWUSneedstomemobiletoreachL1layerandtriggertheexpres-
sionofCLV3.ThemobilityofWUSproteinhasbeendemonstratedpreviouslyandWUSpro-
teinisdetectedatL1layer[35].InordertoinhibitWUSattheOC,CLV3isrequiredtobe
mobileinthemodel.SimilarlytheintercellularmovementofCLV3peptidehasbeenestab-
lished[8].Asaninhibitorinanactivator-inhibitorsystem,themobilityoffactorXisrequired
formodelfunctionality.Asmentionedearlier,afeasiblecandidatefortheroleofL1signalis
miRNA394,whichhasbeenshowntoactasamobilesignal.[36]
Modelanalysis
WetestedwhethertheproposedmodelcanaccountfortheobservedpatternsofCLV3and
WUSintheSAMandwhetheritcanreproduceknownexperimentalresults,whicharerelevant
tothepatterningprocess.Tothisend,weperformednumericalexperiments:weexamined
whetherthemodeliscapableofreproducingtheobservedphenotypeswildtypeSAMaswellas
variousnon-wildtypescenariosincludingmutantsandoverexpressionlines.Becauseweusea
mechanisticmodel,wecanmapexperimentalmanipulationsdirectlytotheparametersofthe
model.Thereforethenon-wildtypescenarioscanbeimplementedbychangingthemodelcom-
ponentthatcorrespondstothespecificmutation,overexpression,etc.Forinstance,aknock
outmutationisimplementedbysettingtheproductionrateoftheaffectedgenetozero.To
simulatetheablationscenarios,theappropriatechangesareappliedtothewildtypesystemat
thesteadysate.Oncethesystemreachesasteadystateagain,theresultingexpressionpatterns
arecomparedagainsttheexperimentalobservations.
Modelsubnetworkstructure. Themodelinessenceconsistsoftwocoupledsubnetworks:
WUS/CLV3(Fig2A,greenshaded)andtheCKsignaling(Fig2A,blueshaded).Inaddition
boundaryinformationissuppliedbyCKandtheL1signal(Fig2A,redarrows;alsoseeS1Figfor
theprofiles).PartsoftheCKsignalingnetworkcorrespondtocomponentsofaclassicalactivator/
inhibitorsystem(Fig2A).TheAHK4/B/B partofthenetworkactsasanautocatalyticactivator
p
(Fig2C),whilethepathwayleadingfromB toX,fulfillstheroleofinductionoftheinhibitorby
p
theactivator(Fig2D).TheCKgradientconfinesthedomainofpatternformationtotheupper
partofthemeristem.Theactivator-inhibitornetworkiscoupledtotheWUS/CLV3subnetwork
viaanincoherentfeed-forwardloop(B /WUS/A)whichspecifiesWUSexpressionbytype-B
p
ARR.TheWUS/CLV3subnetworkgeneratestheexpressiondomainofCLV3.Boundaryinforma-
tionsuppliedbytheL1signaldeterminesthecorrectorientationoftheCLV3expressioninapical-
basaldirection.S2Figcontainsexamplesofthemodeloutputintheuncroppedsimulationgrid.
Robustreproductionofthewildtypeexpressionpatternsofthegenesincludedinthe
model. Thesinequanonforthemodelisofcoursewhethertheobservedwildtypepattern
canbeestablishedandmaintained.ThesimulatedwildtypepatternisshowninFig3.WUSis
presentinahighconcentrationinasmallregionatthecenterofSAM,whichinbothlateral
andapicalbasaldirectionscorrespondstotheobservedexperimentalpattern[1].Inourmodel
thelateralpositionofasingleWUSpeakisalwaysatthecenter,whereastheapicalbasalposi-
tiondependsontheregiondefinedbyCK.ThesizeoftheWUSdomaindependsonthe
dynamicsoftheactivator-inhibitorsubnetworkaswellasinhibitionfromCLV3.
WeinvestigatedtheeffectofWUSmobilityonmodeloutputbysettingWUSdiffusionto
zero.Thiscell-autonomousversionofWUSisonlydetectedintheOCandisabsentfromthe
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PositioningtheOrganizingCenterinArabidopsisMeristem
Fig2.Twocoupledsub-networksandboundaryinformationdefineWUSandCLV3expressiondomainsintheSAM.AandBstandfortype-band
type-AARRs.ApandBpdenotephosphorylatedtype-Bandtype-BARRs.(A)ThemodelcanbedividedintotheCKsignaling(blue)andWUS/CLV3(green)
sub-networkscombinedwithboundarymorphogens(L1andCK).TheformerdeterminesthepositionoftheWUSdomainviaaself-organizingsystemwhile
thelatterspecifiestheCLV3domain,takingtheWUSdomainasaninput.Thenetworkconsistsofinteractionsandmoleculesthatarebasedonpublished
experimentaldata(blackarrowsandletters)andhypotheticalinteractionsandmolecules(redarrowsandletters).PartsoftheCKsignalingsub-network
correspondtothecomponentsofthe(B)classicalactivator/inhibitorsystem;(C)thenetworkcomponentcorrespondingtotheautocatalyticactivatorand(D)
totheactivation/inhibitioninteractions.
doi:10.1371/journal.pone.0147830.g002
uppercelllayersoftheSAM,S3AFig.ThisresultsinsignificantreductionofCLV3levelsand
misplacementofitsdomain,S3CFigincomparisontowildtype,S3BandS3DFig.Thissimu-
latedWUSpatterncloselyresemblestheobservedtranscriptionalpatternofWUSintheSAM
[35,42].Incontrast,whenWUSmobilityisconsideredinthemodeltheresultingexpression
extendstotheL1layer,S3BandS3DFig.ThepredictedpatternsofAHK4andWUSbythe
model,overlapintheOC.Thishasbeenobservedexperimentallyandreproducedbyprevious
modelsofWUS/CLV3interactions[14,43].FurthermorethemodelpredictstheWUSexpres-
siondomaintoconstituteasub-sectionofthebroaderAHK4domain.Thisisinagreement
withtheobserveddistributionofWUS::DsRed-N7intheapicalhalfoftheAHK4receptor
domainmarkedbyAHK4::GFP,ininflorescencemeristem[13].Patternsoftype-Aandtype-B
ARRs,seeFig3Cand3D,arecomparabletothepatternsreportedby[14].Itshouldbenoted
thatthepatternoftype-AARRexpressioninthemodelrefertothephohporylatedportionof
theseproteins,whiletherelevantexperimentaldataprimarilyconsistsofGUSreporterand
transcriptionalmarkergeneexpressions[9,14,44].Thiscomplicatesthecomparisonofmodel
outputintermsoftype-AARRexpressionagainstexperimentaldata.Neverthelessthemodel
predictsthatWUSexpressiondomainandthedomainsassociatedwithCKsignaling(AHK4,
type-Aandtype-BARRexpressiondomains),largelyoverlap.Thisisinagreementwithexperi-
mentalobservationsofARR5[13]andAHK4[13,14]transcriptionalreportersintheSAM,as
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PositioningtheOrganizingCenterinArabidopsisMeristem
Fig3.Wildtypeexpressionpatternofthemoleculesinthemodel.Therelativelevelsineachfigurearedepictedbyacolorspectrumshownbythecolor
barinthefigure.ForexamplesofmodelsoutputinanuncroppedtemplateseeS2Fig.
doi:10.1371/journal.pone.0147830.g003
wellaswithpreviousmodelsofmutualinteractionsbetweenCKsignalingandWUSinthe
SAM[13,14].
CLV3(mRNA)expressionislimitedtothetipofthemeristem,withanexpressionzonethat
iswiderattheapicalendandnarrowstowardsbasallimitofCLV3expression,Fig3E.Thisis
inagreementwiththeCLV3(mRNA)patternsobservedexperimentally.
WeinvestigatedtheeffectsofourchoiceofrepresentationofmeristemandL1layeron
modeloutput.Weobservedthatthemodelisnotdependentonthisparticularrepresentation;
modelsimulationsusingseveralotherrepresentationsofmeristemicgeometryandL1layer,
producethecorrectoutput,seeS4Fig.
SensitivityAnalysis. Inordertoanalyzethemodelperformancewecarriedoutaparame-
tersurveyinwhichwecomparedthesimulatedpatternsagainstexperimentalobservationsof
WUSandCLV3patternintheSAM(seeMaterialandMethods,S5Fig).Forthesubsetof
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