Manuscript
bioRxiv preprint first posted online Jun. 3, 2016; doi: http://dx.doi.org/10.1101/057091. The copyright holder for this preprint (which was not
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Title(working):AFacilitatedDiffusionMechanismEstablishestheDrosophilaDorsalGradient
Authors:SophiaN.Carrell1,MichaelD.O’Connell1,AmyE.Allen1,2,StephanieM.Smith1andGregoryT.
Reeves1,*
1
DepartmentofChemical&BiomolecularEngineering,NorthCarolinaStateUniversity,Raleigh,NC
27605,USA
2
Currentaddress:CurriculuminBioinformaticsandComputationalBiology,UniversityofNorthCarolina,
ChapelHill,NC27599,USA
*Correspondence:[email protected]
Summary
ThetranscriptionfactorNF-κBplaysanimportantroleintheimmunesystemasanapoptoticand
inflammatoryfactor.IntheDrosophilamelanogasterembryo,ahomologofNF-κBcalledDorsal(dl)
patternsthedorsal-ventral(DV)axisinaconcentration-dependentmanner.Duringearlydevelopment,
dlissequesteredoutsidethenucleusbyCactus(Cact),homologoustoIκB.Tollsignalingattheventral
midlinebreaksthedl/Cactcomplex,allowingdltoenterthenucleuswhereittranscribestargetgenes.
Hereweshowthatdlaccumulatesontheventralsideoftheembryooverthelast5cleavagecyclesand
thatthisaccumulationistheresultoffacilitateddiffusionofdl/Cactcomplex.Wespeculatethatthe
predominantroleforCactinDVaxisspecificationistoshuttledltowardstheventralmidline.Giventhat
thismechanismhasbeenfoundinother,independentsystems,wesuggestitmaybemoreprevalent
thanpreviouslythought.
Introduction
Inadevelopingorganism,tissuesarepatternedbylong-rangesignalingenactedthroughmorphogen
concentrationgradientsthatcarrythepositionalinformationnecessarytocontrolgeneexpressionina
spatially-dependentfashion.IntheDrosophilablastoderm,thetranscriptionfactorDorsal(dl)actsasa
morphogentoregulatethespatialpatterningofgreaterthan50genesalongthedorsal-ventral(DV)axis
(MoussianandRoth,2005;ReevesandStathopoulos,2009).However,despiteitscentralityto
development,themechanismthatcontrolstheformationofthedlnuclearconcentrationgradientatthe
whole-embryoscaleisnotwellunderstood.
Atthesinglenucleus/celllevel,dlissequesteredtothecytoplasminaninactivecomplexwiththeIκB
homologCactus(Cact).Ontheventralsideoftheembryo,Tollsignalingresultsinthedegradationof
Cact,freeingdltoenterthenucleuswhereitregulatestranscription.Thismechanism,combinedwitha
ventral-to-dorsalgradientofTollsignaling,wouldseemsufficienttodevelopagradientofnucleardl
concentration(Rothetal.,1989).However,takenalone,thismechanismwouldresultinalocal
depletionofdlfromthecytoplasmsurroundingtheventralnucleitocreateacounter-gradientin
cytoplasmicdl,whichisincontrasttotheobservationthatdlaccumulatesbothinthenucleiandinthe
cytoplasmontheventralsideoftheembryoovertime(Reevesetal.,2012)(seeFigure1A-D).
Inthisstudy,weinvestigatethemechanismofdlnuclearconcentrationgradientformationatthe
whole-embryoscale.Weuseacomputationalmodeltoguidethedesignandinterprettheoutcomeof
experimentsthatdistinguishbetweencompetinghypotheses.Ourexperimentalandcomputationaldata
1
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supportthehypothesisthatamechanismoffacilitateddiffusionisresponsiblefortheglobalformation
ofthedlnuclearconcentrationgradient.Underthis“shuttling”hypothesis,adorsal-to-ventral
concentrationgradientofcytoplasmicdl/CactcomplexdevelopsastheresultofToll-mediated
degradationofCact,whichdrivestheoverallfluxofdltowardstheventralsideoftheembryo.Besides
ventrally-directeddlaccumulation,ourcomputationalmodelpredictsthattheshuttlingmechanismcan
accountforseveralotherpreviouslyinadequatelyexplainedphenotypes,suchasduplicateddlgradient
peaks,regionsofdepleteddl,dlheterozygousphenotypes,andwideneddl-GFPgradients(Huangetal.,
1997;Libermanetal.,2009;Reevesetal.,2012;RothandSchüpbach,1994).Wehaveexperimentally
verifiedthesepredictionsthatafacilitateddiffusionmechanismisresponsiblefortheformationofthe
dlnuclearconcentrationgradientinthedevelopingDrosophilaembryo.
Themechanismoffacilitateddiffusionhasbeenpreviouslydescribedandisresponsibleforgradient
formationinothersystems,suchastheDpp/BMPsignalingpathway(Ben-zvietal.,2008;Eldaretal.,
2002;Marquésetal.,1997;Mizutanietal.,2005;Shimmietal.,2005)andhasalsobeensuggestedfor
theformationoftheSpätzlegradientupstreamofTollsignaling(Haskel-Ittahetal.,2012).Thedl/Cact
systemhaseachofthefeaturesrequiredforfacilitateddiffusion(Shiloetal.,2013):(1)theprimary
molecule(dl)bindstoa“carrier”molecule(Cact)thatprotectsitfromcapture,(2)theprimary/carrier
complexisdiffusible(duetothesyncytialstateoftheearlyembryo),and(3)thecomplexisbrokenina
spatially-dependentmanner(throughTollsignalingontheventralsideoftheembryo).Ifthesefeatures
areinplace,theprimarymolecule(dl)accumulatesovertimeatthesiteofcomplexdegradation(the
ventralsideoftheembryo).Therefore,weconcludethatCactperformsaroleindlgradientformation
additionaltoregulatingdl’sentryintothenucleus:shuttlingdltotheventralsidetoformthemature
gradient.
Results
Dorsalaccumulationontheventralsideoftheembryoresultsfrommovementofthedl/Cactcomplex
Initially,DorsalisuniformlydistributedalongtheDVaxisofthedevelopingembryo(Figure1C);during
nuclearcycles11-14,itaccumulatesontheventralside(Figure1B,D).Thisobservationisconsistent
withpreviously-publishedfluorescentimagesofanti-dlimmunostainingsinfixedembryosandinimages
ofdl-GFPfluorescenceinliveembryos(Kanodiaetal.,2009;Libermanetal.,2009;Reevesand
Stathopoulos,2009;Reevesetal.,2012).Themechanismforthisoverallpolarizationoftotaldlinthe
embryocouldbeasymmetricdegradationorproduction;however,ourmodelingworkandexperiments
favoranoverallfluxofdltotheventralsideoftheembryo.UsingaphotoactivatableGFP(paGFP)tag
(PattersonandLippincott-Schwartz,2002),wenoticedthatdlappearsinregionsoftheembryoover810nucleiawayfromthesiteofpaGFPactivationinthetimespanof90minutes.Givenacelldiameter
(i.e.,theaveragedistancebetweenthecentroidsoftwoneighboringnuclei)ofroughly7μm,this
translatestoaneffectivediffusivityof∼0.5-0.9μm2/sandatimescaletocrossonecelldiameterthatis
ontheorderofminutes.Whenactivatedneartheventralmidline,dl-paGFPdiffusesfromitslocationof
activationandfillsadjacentnuclei(Figure1E,MovieS1).Whenactivatedonthedorsalsideofthe
embryo,dl-paGFPdiffusesandshowsatypicalpatternofexclusionfromnucleiinmoredorsalregions
andmoderateuptakeintothenucleiinmorelateralregions(Figure1F,MovieS2).Asdiscussed
previously,thisfluxofdlcouldbeduetodiffusionoffreedl,dl/Cactcomplex,orbothspecies(O’Connell
andReeves,2015).
2
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Todeducewhichprocess(es)mayberesponsiblefortheoverallfluxofdltotheventralsideofthe
embryo,weusedamodelofdl/Cactinteractions(Figure2A,B;seealsoSupplementaryExperimental
Procedures)andexaminedtheequationfortotaldl(seeExperimentalProcedures).Fromthisequation,
weseethatonlytwospeciesmaybecontributingtotheoverallmovementofdltotheventralsideof
theembryo:freecytoplasmicdlandCact-boundcytoplasmicdl.Notethatthisisagenericpredictionof
ourmodelequationsanddoesnotrelyonanyspecificmodelparametervalues.
Modelanalysisandexperimentalpredictions
Todeterminewhichspecies,freedlordl/Cactcomplex,isresponsiblefortheaccumulationofdlonthe
ventralsideoftheembryo,weanalyzedthefullsetofmodelequations(Equations1-8inSupplemental
ExperimentalProcedures)andmadethemodelconsistentwithspatiotemporaldataofdlgradient
dynamics(Reevesetal.,2012)usingevolutionaryoptimization.Analysisoftheresultingparametersets
revealsthat,tobeconsistentwiththedata,therateofdl/Cactcomplexdiffusionisgenerallymuch
fastercomparedtothatoffreedl(Figure2C).
Wethenanalyzedthedirectioninwhichdlanddl/Cactcomplexdiffuseinthemodel.AccordingtoFick’s
law,diffusiveflux(typicallydenotedJ)referstothemovementofasolutefromareasofhigh
concentrationtoareasoflowconcentrationatarateproportionaltoitsconcentrationgradient,𝑑𝐶 𝑑𝑥,
yielding𝐽 ∝ − 𝑑𝐶 𝑑𝑥.Thenegativesignaccountsforthefactthatdiffusivefluxisinthedirectionof
decreasingconcentration.Byconvention,wedefineourx-axistobeequaltozeroattheventralmidline
andoneatthedorsalmidline(seeFigure2A,B);thus,anegativevalueforthefluxindicatesmovement
towardtheventralmidline,andapositivevalueindicatesmovementtowardthedorsalmidline.
Ourmodelingresultsindicatethatdl/Cactcomplexpreferentiallymovestowardstheventralmidline,
whilefreedlmovesaway(Figure2D).Therefore,theventrally-directedfluxoftotaldlmustbedueto
diffusionofdl/Cactcomplex,whichresultsfromTollsignalingactingasasinkattheventralmidline(see
alsoFigure1A,B).Inthisway,Cactshuttlesdlagainstitsconcentrationgradient,therebyallowingan
accumulationofnucleardlattheventralmidlinewhereitisrequiredforproperformationofthedl
gradient.
Themodelusedhereisanextensionofapreviouslypublishedmodel(O’ConnellandReeves,2015),in
whichthecatalyticactivityofTollsignalingwasmodeledphenomenologically(Figure2A,B).Weupdated
themodeltoexplicitlyaccountforbothactivatedTollreceptorsandTollreceptorsboundtodl/Cact
complex(Equations7&8,respectively)toallowforthepossibilitythatTollactivityislimiting.This
possibilitywasprecludedinthepreviousmodel,becausetherateofToll-mediatedCactusdegradation
wasproportionaltotheconcentrationofdl/Cact,whichcreatedapotentiallyunlimitedsink.
Furtheranalysisofourmodelshowedthatthemechanismoffacilitateddiffusioncanbetestedby
alteringthreeexperimentally-tunablebiophysicalparameterstoslowthemechanismoffacilitated
diffusion:(1)decreasingthedldosage,(2)loweringthediffusivityofdlorCact,and(3)increasingthe
widthoftheactiveTolldomain(Figure2E-G).Themodelpredictsthattheseperturbationswilleach
resultinahallmarkprogressionofphenotypes(dependingonthestrengthoftheperturbation):thedl
gradientfirstwidens,thenbecomesflatatthetop,thensplitsintotwopeaks(Figure2H-J).
Furthermore,combinationsoftheseperturbationshavesynergisticeffects.Weconductedexperiments
toaddressallthreeparameters,andfoundthattheysupportedourhypothesis.
3
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Decreasingdldosagewidensandflattensthedlgradient
Inembryosfrommothersheterozygousnullfordl(hereafterreferredtoasdl/+embryos),theshapeof
thegradientbecomesslightlywider,flatter,andlowerinamplitude,withtheslopemaintainedinthe
lateralregionsbutpeaklevelsofthegradientflattened(Libermanetal.,2009)(Figure3).Froma
functionalityperspective,thisphenotypeisstrikingbecausetheportionofthedlgradientthatislost
(thepeakconcentration)issuperfluousasanylevelabovethethresholdlevelforhigh-concentration
targetgeneswillresultinexpression,whiletheportionofthegradientthatisnecessaryforpatterning
geneexpressionboundaries—thegradedportionbetween20%and45%DVposition—ismaintained.
Toexplainthiseffect,onesimplehypothesisisthattheventral-mostnucleiwouldhavereachednormal
dllevels,butonlyiftherewereenoughdlpresent.Sincethetotalamountofdliscompromised,the
ventralmostnucleireachalower-than-normalconcentrationofdl.However,modelsofdlgradient
formationthatlacktheshuttlingmechanismpredictthelossof50%dlnuclearconcentrationgloballyin
dl/+embryos,ratherthanaspatiallypatternedloss(FigureS1).
Incontrast,amodelbasedontheshuttlingmechanismmakessenseofthisphenotype.Inwildtype
embryos,thesmoothpeakofthedlgradientisobtainedduetoasaturationeffect.Thereisenough
dl/CactcomplextosaturateactiveTollreceptorsintheventral-lateralregionsoftheembryo,which
allowsasignificantfluxofdl/Cactcomplextoreachtheventralmidlineandresultsinasmoothlypeaked,Gaussian-likecurve.Inembryoswithhalfthenormaldldosage,activeTollreceptorsinthetails
ofthegradientarenotsaturated;therefore,lessdl/Cactcomplexarrivesattheventralmidline,and
theseembryosneveraccumulateasmoothpeakofthedlgradient(Figure3B,D).
Decreaseddiffusionofdl/Cactcomplexwidensthedlgradient
OtherresearchershavegeneratedseveralGFP-taggedversionsofdlinordertostudyitsdynamicsin
livingembryos(Delottoetal.,2007;Reevesetal.,2012).Ineachcase,taggingdlwithanextraprotein
moietycausedthedlgradienttoexpand.Ifthegradientdevelopsviaadiffusionmechanism,thisresult
wouldseemcounterintuitive.Onewouldexpectthatincreasingthesizeofamoleculewoulddecrease
itsdiffusivity,andthusrestrictthespatialrangeofthegradient.Ontheotherhand,ashuttling
mechanismwouldpredicttheopposite:thatloweringthediffusivityofdl/Cactcomplexwouldwidenthe
gradient.Totestthisprediction,weanalyzeddlandCactconstructstaggedwithproteinsthateither
dimerizeortetramerizeinordertoformlargeclustersofdl/Cactcomplex.
OtherstudieshaveshownthattaggingdlwithamonomericVenus(dl-mVenus)causesthedlgradientto
widen(widthparameterσ=0.16±0.01;comparetoσ=0.14±0.01forwildtype),whileaGFPtag
causesamuchgreaterwidening(σ=0.20±0.02)(Libermanetal.,2009;Reevesetal.,2012).We
surmisedthatthedifferencebetweenthesescenariosisthatVenusisanobligatemonomerwhilethe
GFPconstructweaklydimerizes(Zachariasetal.,2002).Tocarefullymeasuretheeffectofdimerization
oftheproteintagonthewidthofthegradient,werepeatedtheseexperimentsinordertocontrolfor
differencesinfluorescentproteintag,protocol,researcher,andequipmentsoastohaveadirect
comparisonforourworkinnewflylines.First,weanalyzedthegradientinembryosthathadone
endogenouscopyofdlreplacedwithdltaggedwiththeweakly-dimerizingGFP(dl-dGFP)(Reevesetal.,
4
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2012).Wefoundthatthedlgradientintheseembryoswidenedsignificantly(σ=0.21±0.03)as
comparedtowildtype(Figure4A,B).
TheweakdimerizationofGFPcanbeabolishedbytheA206Kmutation(Zachariasetal.,2002);
therefore,wedesigneddl-GFPconstructswiththeobligatemonomerversionofGFP(dl-mGFP)inorder
toinvestigatetheeffectofincreasingthemassofdlwithoutcausingdimerization.Embryoscarrying
theseconstructshavegradientsslightlywiderthanwildtype(σ=0.19±0.03),comparabletoour
measurementsinembryoswiththemonomericVenustag(σ=0.18±0.03)(Figure4B,seealsoFigure
S2A,B).Weexpectthatthewideningeffectinembryosthatcarryamonomerictagislikelyduetothe
increasedmassofthedlproteinandnotthedimerizationofthetag.Wealsodesigneddl-Venus
constructsthathadweakdimerizationrestoredduetoaK206Amutation(dl-dVenus);embryoscarrying
thisdl-dVenustransgenehaddlgradientsthatweresignificantlywiderthanthoseinembryoscarrying
thedl-mVenustransgene(σ=0.19±0.02),matchingthetrendseenindl-mGFPanddl-dGFPembryos
(seeFigureS2A,B).Takentogether,thesedataindicatethattheweakdimerizationofthefluorescent
tags,whichpresumablyslowsdiffusionofdl/Cactcomplex,isthekeyfactorinwideningthegradient.
Itwasalsoobservedthatasinglecopyofdl-dGFPwasunabletocomplementnullmutationsinthe
endogenousdlgene;twocopiesarenecessarytorescuethemutant(Libermanetal.,2009;Reeveset
al.,2012).Thisresultcontrastsdl-mVenus,whichcomplementsatonecopy.Ourshuttlinghypothesis
explainsthisphenotype,asembryosfromdlmotherscarryingonecopyofdl-dGFPhavetwodefectsin
shuttling:alowercopynumberofdlandareduceddiffusivityofthedl/Cactcomplex.Theseembryos
havehighlywidenedgradients(σ=0.22±0.04)(seeFigure4A,BandFigureS2C,D).Wesurmisedthat
thesegradientsareperturbedenoughtoseverelydisruptgeneexpression,perhapsnotbecoming
strongly-peakedenoughtoturnonhigh-thresholdgenes,suchassnail(sna).Therefore,weanalyzed
snaexpressioninembryosfromdl;dl-dGFP/+mothers,andfoundthattheseembryoseitherlackedsna
expressionorexpressedsnainaverynarrowdomain(Figure4C-E,seealsoFigureS2D),confirmingour
hypothesisthatthedoubleperturbationresultsinabreakdownofthetypicallyrobustpatterning
system.
Toinvestigatetheeffectoflargercomplexesondl/Cactdiffusion,weevaluatedtheeffectofadl-lacZ
transgeneonthedlgradient(Govindetal.,1992).AstheproteinproductoflacZ,β-galactosidase(β-gal),
tetramerizes,weexpectthatthisfusionwillslowthediffusionofdltoagreaterextentthandGFP.
However,wefoundthattwocopiesofthistransgeneinadl/+backgroundwereneededinordertosee
aneffectonthewidthofthedlgradient,whichwidenedaspredictedbytheshuttlingmodel(SeeFigure
S2B,E).Thisislikelyduetothefactthatdl-lacZactsasanantimorphicallele(Govindetal.,1992);such
dl-βgalfusionproteinsaresuspectedtobeexpressedatverylowlevelsinsurvivingflylines(Govindet
al.,1996).
InordertostudytheeffectofdecreasedCactdiffusionondlgradientformation,weexaminedembryos
frommotherscarryingasinglecopyofacact-lacZtransgeneinaheterozygouscactbackground
(Fernandezetal.,2001).Weexpectthatthisfusionwillslowdiffusionofthedl/Cactcomplexwithout
affectingthediffusionoffreedl.Intheseembryos,thedlgradientisexpanded(Figure4B,F),indicating
aninabilityofCacttoproperlyshuttledltotheventralmidline.Inanaïvemodel,whereCactdoesnot
shuttledlandthereisnofluxtowardtheventralmidline,wedonotexpectchangingthediffusionof
Cacttohavesuchaneffectonthedlgradient.Itisimportanttonotethat,underthetypicalmorphogen
gradientphenomenon,decreasingthediffusivityofthemorphogenwouldresultinanarrower(more
5
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concentrated)gradient.Sinceourresultsconsistentlyshowthatthedlgradientwidensratherthan
narrowswhenthediffusivityofdlorCactisreduced,weconcludethatdl/Cactcomplex,andnotfreedl,
isthedominantdiffusivespecies.
IncreasingthewidthoftheactiveTolldomainresultsinasplitpeakofdl
TheshuttlinghypothesispredictsthatwideningtheactiveTolldomainresultsfirstinawidened,then
flattened,thensplitdlgradient(Figure2H-J).AstheextentoftheTolldomainiscontrolledby
Gurken/EGFRsignalingduringoogenesis(Schüpbach,1987;Senetal.,1998),weanalyzedembryosfrom
motherscarryingahypomorphicEGFRallele(egfrt1)(RothandSchüpbach,1994).Wefoundthat
embryosfrommothersheterozygousforthisallelehavesignificantlywideneddlgradients,andmost
(10/12)embryosfromhomozygousmothershavegradientssowidethatasplitpeakforms(seeFigure
5).Thisresultisconsistentwithpreviousreportsthatvariousgurkenandegfrmutationsgeneratea
duplicateddlgradientasmeasuredbydlstaining,Twiststaining,andsitesofventralfurrowformation
(RothandSchüpbach,1994),whichisnotreadilyexplainedintheabsenceofashuttlingphenomenon
(Meinhardt,2004;MoussianandRoth,2005).
Ananteroposteriorgradientofdlsupportstheshuttlinghypothesis
IthasbeensuggestedthatashuttlingphenomenonalsooccursthroughtheprocessingofSpätzle(Spz),
theligandforTollsignaling(Haskel-Ittahetal.,2012),whichmayexplainsomeofthephenotypes
describedhere.Todeterminewhetherthehallmarkphenotypesofshuttlingcouldoccurwithout
assistancefromtheproteasecascadeorSpzprocessing,weexpressedaconstitutivelyactiveformofToll
(Toll10b)attheanteriorpoleofthedevelopingembryousingthebicoid3’UTRandthebicoidpromoter
(Huangetal.,1997).Embryosfrommotherscarryingthisconstruct(bcd>toll10b:bcd3'UTR)havean
anterior-posterior(AP)dlgradientinadditiontothenativeDVgradient.Naïvely,onemayexpectthat
theexistenceoftwogradientsinactiveTollsignalingwouldresultinhigherconcentrationsofnucleardl
wherethesetwogradientsoverlap.Incontrast,theshuttlinghypothesispredictsthatdlnuclear
concentrationwouldbelowerintheregionofoverlap,asthetwocompetingdl/CactsinkscauseCactto
shuttledltowardboththeanteriorpoleandtheventralmidline(seeFigure6A-C).Thispredictionis
borneoutinexperiment,astheseembryosshowadecreasedintensityofthedlgradientintheregionof
overlap.Furthermore,64%(9/14)oftheseembryosshowavisiblenarrowingofthesnaexpression
domainatroughly30%egglength,consistentwithpreviouslypublishednumbers(Huangetal.,1997).
Thereisadipindlnuclearintensityatthislocationaswell(Figure6B,C).
Ourmodelingresultsfurthersupportthattheshuttlingmechanismisresponsibleforthisphenomenon
(Figure6C).Weexpandedourmodelsystemfromaone-dimensionalarrayofnuclearcompartmentsto
atwo-dimensionalarrayandaddedasecondTollsignalingdomainperpendiculartothefirst.Our
simulationresultsshowthattheoverlapbetweentheAPandDVTolldomainscreatesalowpointin
nucleardlconcentration,similartoourexperimentalresults.Wethenapproximatedathresholdforsna
expressionbasedontheDVdlgradient,andfoundthelocalminimumindlconcentrationresultsin
reducedorabolishedsnaexpressioninthatregion(Figure6C’).
Wealsoexaminedembryosfrommotherscarryingahomozygousmutationingastrulationdefective
(gd7),whicheliminatestheendogenousventral-to-dorsalgradient.Swappingthebicoidpromoterfor
thestrongerhsp83promoter(hsp83>toll10b:bcd3'UTRconstruct)(Huangetal.,1997),wewereable
createawiderdlgradientattheanteriorpole.Halfoftheseembryos(7/16)showtwopeaksofdlboth
6
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byeyeandwhenthenuclearintensityisplotted(Figure6D,E).Furthermore,theseembryoshavea
doublepeakofsna(Trisnadietal.,2013).Inordertodeterminewhetherornotthisdoublepeak
phenomenonwasaresultoftheembryo’sgeometryatthepole,weanalyzedembryoswithanAPdl
gradientinitiatedbytheweakerbicoidpromoter.Theseembryosshowednosuchdoublepeakeffect
(seeFigureS3).Theseresultsfurthersupportourshuttlinghypothesisasthedlgradientprogressesfrom
narrow(weakpromoter)todoublepeak(strongpromoter)muchasitdoesinthenativeDVsystem
whentheTolldomainexpands.
Discussion
Inthisstudy,weinvestigatedtheformationofthedlmorphogengradientintheearlyDrosophila
embryo.Basedonourmodelandexperimentalverification,weconcludethatthedlgradientis
establishedbyafacilitateddiffusion,or“shuttling”mechanism,inwhichdl/Cactcomplexdiffuses
towardstheventralmidlinewhereCactisdegraded.Furthermore,ourhypothesizedmechanismmakes
senseofseveralpreviouslyunexplainedphenomenaintheliterature.
BesidesdlbindingtoCact,theshuttlingmechanismrequirestwophenomenatooccur.First,dl/Cact
complexmustbeabletomovethroughouttheembryo.Ourexperimentswithdl-paGFPshowthatdl
doesindeedmovethroughtheembryoinamannerthatappearstobeconsistentwithdiffusion.In
contrast,apreviousreportshowedthateachnucleushasitsownwell-mixedcytoplasmicpoolofdlto
drawfrom,andthatdldoesnotreadilydiffusefrompooltopool(Delottoetal.,2007).Thisobservation
wasconfirmedbyastudywhichshowedthatbarrierstodiffusionexistintheearlyembryo,despitethe
lackofcellmembranes(Mavrakisetal.,2009).However,theseresultsdonotcontradictour
hypothesizedmechanism,whichreliesonmovementofdlfromonepooltoanother,becausethetime
scalesaredifferent(secondsvs.minutes).Furthermore,observationalevidencesupportsadiffusionbasedshuttlingmechanism,asloweringthediffusivityofeitherdlorCactwidensthegradient(Figure
7A),ratherthanthenarrowingthatonemightexpectfromamorphogengradientestablishedby(nonfacilitated)diffusion.TheshuttlingmechanismexplainswhydltaggedwithaweaklydimerizingGFP
widensthegradientmorethanonetaggedwithmonomericVenus(Reevesetal.,2012),andalso
explainstherelatedobservationthatonecopyofdl-mVenuscomplementslossofendogenousdlwhile
onecopyofdl-dGFPdoesnot(Libermanetal.,2009;Reevesetal.,2012).Similarly,thismechanism
makessenseoftheobservationthatdltaggedwithβ-galactosidase,whichformstetramers,isantimorphic(Govindetal.,1992),asthedlmoietiesintetramersofdl-βgaldimerizewithendogenousdlto
disrupttheformationoftheendogenousdlgradient.
Second,theshuttlingmechanismrequirestheventralmidlinetobeasinkforthedl/Cactcomplex.This
becomesespeciallyclearinembryosthathaveanectopicAPdlgradientinadditiontotheendogenous
DVgradient(Huangetal.,1997).Intheseembryos,asecondsinkforthedl/Cactcomplexisestablished,
andthetwocompetingsinksformalocalminimuminthedlgradientwherethetwooverlap,rather
thantheglobalmaximumonemightexpectifthetwogradientswereadditiveastheywouldbeina
modelwithoutfacilitateddiffusion(Figure6B,C).Thisresulthasbeenpreviouslyobservedasa"gap"in
thesnadomainwherethetwogradientsoverlap(Huangetal.,1997),similartoour2Dsimulation
results.TheseresultsarguethattheTolldomaindoesactasasink,anecessaryconditionforshuttling.
Inthissystem,itappearsthatactiveTollreceptorsaresomewhatlimitingastheyareeasilysaturated
withdl/Cactcomplex.Thissaturationisnotessentialtotheshuttlingmechanismperse,butitis
necessaryforthemechanismtoexplainseveralobservationsofthedl/Cactsystem.Underwildtype
7
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conditions,asignificantfluxofdl/CactcomplexcanbypassthesaturatedactiveTollreceptorsinthetails
ofthegradient,whichresultsintheaccumulationofasmooth,intensepeakofdlsignalingattheventral
midlineoftheembryo.However,inembryosfromdl/+mothers,thereisnotenoughdl/Cactcomplexto
saturateactiveTollreceptorsinthetailsofthegradient,andthusthereislessaccumulationofdlatthe
ventralmidline(Libermanetal.,2009)(seeFigure7B).Similarly,whentheTollgradientisgreatly
expanded,asinembryosfromegfrt1mothers(RothandSchüpbach,1994),thedomainsofsaturatedToll
receptorsmovefurtherfromtheventralmidline,resultinginasplitpeak(Figure7C).Additionally,the
split-peakphenomenonhasalsobeenobservedinthedlgradientinabnormallylargeembryos(Garcia
etal.,2013).ThisspecificphenotypecouldbeexplainedbytheshuttlingoftheTollligandSpz(HaskelIttahetal.,2012);however,weobservedthesamephenomenoninembryoswithanectopicAPdl
gradientestablishedbyconstitutivelyactiveToll.Inbothcases,ventrally-(anteriorly-)diffusingdl/Cact
complexdoesnotmakeittotheventralmidline(anteriorpole)beforebeingdissociated,leavingthe
ventral-(anterior-)mostnucleisomewhatdevoidofdl.Asimilarmechanism,inwhichtheremovalrate
ofBMPligandssurpassestherateofBMPfluxtothedorsalmidline,hasbeensuggestedtoexplainthe
computationally-predictedsplit-peakphenotypefortheBMPsystemintheearlyembryo(Umulisetal.,
2006).
Theshuttlingmechanismhasbeenproposedinseveralothercontextsandinmultipleorganisms(Benzvietal.,2008;Eldaretal.,2002;Haskel-Ittahetal.,2012;Marquésetal.,1997;Mizutanietal.,2005;
Shimmietal.,2005).Forexample,duringthesamestageofDrosophiladevelopment,shuttlingofthe
BMPligandsDppandScwthroughtheactionofSogandTsgisresponsiblefortheconcentrationofBMP
signalingtoanarrow,intensestripeatthedorsalmidlineoftheembryo.Asimilarmechanismisalso
presentinBMPsignalinginvertebrateembryostospecifytheDVaxis.Inlightoftheseexamples,we
speculatethatthismaybeamoreprevalentmechanismofmorphogengradientformationthan
previouslyappreciated.
ExperimentalProcedures
Flylines
ywflieswereusedaswildtype.dl-paGFP,dl-mGFP,anddl-dVenuswerecreatedbyBACrecombineering.
Forliveimaging,fliescarryingdl-paGFPwerecrossedtofliescarryingH2A-RFPonthesecond
chromosome(BS#23651).dl/+flieswerecreatedbycleaningupdl1viatwohomologousrecombinations
withywtogeneratedl1.2.5.cact/+;cact-fulllacZ25flieswereobtainedfromDavidStein(Fernandezet
al.,2001).dl-lacZflieswereobtainedfromShubhaGovind(Govindetal.,1992).dl-dGFPanddl-mVenus
fliesandtheoriginalBACsusedtocreatethemwereobtainedfromAngelaStathopolous.dl-mGFP,dl1.2.5
flieswerecreatedbyhomologousrecombination.Presenceofdl-mGFPwasconfirmedbyw+.Presence
ofdl1.2.5wasconfirmedviasequencingbyGENEWIZ,ResearchTrianglePark,NC.egfrt1/CyOflieswere
obtainedfromtheBloomingtonStockCenter(#2079).Fliescarryingthebcd>toll10b:bcd3’UTRconstruct
wereobtainedfromAngelaStathopolous.TheplasmidcarryingFRT-stop-FRThsp83>toll10b:bcd3’UTR
wasalsoobtainedfromAngelaStathopoulos.ToremovetheFRT-stop-FRTcassette,wecrossedflies
carryingthisconstructintoalinecarryinghsFLPontheXchromosome(BS#8862).Toremovethenative
DVdlgradient,fliescarryingthetoll10b:bcd3’UTRconstructwerecrossedintoagd7background.See
SupplementalExperimentalProceduresformoredetails.
8
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
BACRecombineering
WefollowedProtocol3oftheNCIatFrederickRecombineeringwebsite
(http://ncifrederick.cancer.gov/research/brb/recombineeringinformation.aspx)togeneratedl-paGFP,
dl-mGFP,anddl-dVenusinpACMAN(Venkenetal.,2006).NEB’sproofreadingQ5DNApolymerasewas
usedtoamplifysequencesatahighlevelofauthenticity.UsingaGalKselectionprotocol(Warminget
al.,2005),singleaminoacidmutationswereintroducedatresidue206inpreviouslyestablishedBACs
(Reevesetal.,2012)togeneratedl-mGFP(A206K)anddl-dVenus(K206A).dl-paGFPwascreatedby
addingtheopenreadingframeofpaGFP(Addgeneplasmid#11911),(PattersonandLippincott-Schwartz,
2002)inframetothe3’endofthedlopenreadingframeinadlrescueconstruct(Reevesetal.,2012)in
pACMAN(Venkenetal.,2006)usinga6x-Glylinker.SeeTableS1foralistofprimersused.
FluorescentinsituHybridization
Allembryoswereagedto2-4hours,exceptfor“young”ywembryos,whichwereagedto0-2hours,
thenfixedin37%formaldehydeaccordingtostandardprotocols(Kosmanetal.,2004).Acombination
fluorescentinsituhybridization/fluorescentimmnuostainingwasperformedaccordingtostandard
protocols(Kosmanetal.,2004).Briefly,fixedembryoswerewashedinTween/PBSbuffer,then
hybridizedwithanti-senseprobesat55oCovernight.Theembryoswerethenwashedandincubated
withprimaryantibodiesat4oCovernight.Next,theembryoswerewashedandincubatedfor1-2hrs
withfluorescentsecondaryantibodiesatroomtemperature.Theembryoswerethenwashedand
storedin70%glycerolat-20oC.Embryoswereimagedwithinonemonthofcompletingtheprotocol.
SeeSupplementalExperimentalProceduresformoredetails.
MountingandImagingofFixedSamples
Embryoswerecrosssectionedandmountedin70%glycerolasdescribedpreviously(CarrellandReeves,
2015).Briefly,arazorbladewasusedtoremovetheanteriorandposteriorthirdsoftheembryo,leaving
acrosssectionroughly200µmlongby200µmindiameter.Thesesectionswerethenorientedsuchthat
thecutsidesbecamethetopandbottom.Theywerethenimagedat20xonaZeissLSM710
microscope.15z-slices1.5µmapartwereanalyzed.EmbryoswithanAPDorsalgradientweremounted
laterallyin70%glycerolusingonepieceofdouble-sidedtape(weakbicoidpromoter)ortwopiecesof
double-sidedtape(stronghsp83promoter).Imagesweretakenat2.5µmintervalsfromjustabovethe
topoftheembryotothedepthatwhichtheembryoreachedmaximalsizeinthexyplane,whichwas
assumedtobethemidsagittalsection.Stacksrangedfrom15-25slices.
DataAnalysis
Imagesofembryocrosssectionswereanalyzedusingpreviouslyderivedcode(Trisnadietal.,2013).
Briefly,theborderoftheembryowasfoundcomputationally,thenthenucleiweresegmentedusinga
localthresholdingprotocol.Theintensityofdlineachsegmentednucleuswascalculatedastheratio
betweentheintensityinthedlchanneldividedbytheintensityinthenuclearchannel.Theintensityof
mRNAexpressionwascalculatedasaverageintensitywithinanannulusroughly18μmwidearoundthe
perimeteroftheembryo.Adescriptionoftheimageanalysisofwholemountembryoscanbefoundin
theSupplementalExperimentalProcedures.
AlldlgradientswerefittoaGaussian,andthesefitswereusedtodeterminethewidthparameter,σ.
Normalizedintensityplotsweregeneratedbyfittingeachembryo’sdatatoitsownGaussianby
9
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
subtractingtheBvalueand70%oftheMvalue,thendividingbytheAvalue.(X=(x–B–0.7M)/A)).The
averagenormalizedintensityplotwasgeneratedbyaveragingtheplotsofallembryosinthespecified
genotype.
Statisticalsignificancewascalculatedusingtwo-tailedhomoscedastict-tests.
ActivatingpaGFPinLiveEmbryos
Embryosweredechorionatedbyhandorfor30sin100%bleach.Theywerethenmountedlaterallyona
slidecoatedwithheptaneglue.Deionizedwaterwasusedasamountingmedium.Twopiecesof
double-sidedtapewereusedtoattachthecoverslip.Imagesweretakenusinga40xwaterimmersion
objectiveonanLSM710confocalmicroscope.Activationbox:9000pixels(300micronsx30microns),
numberofactivationpasses:10,resttime:15s,numberofcycles:40,laserpower:3%forembryo
activatednearventralmidline,2.5%forembryoactivatedneardorsalmidline.A405nmlaserwasused
foractivationanda488nmlaserwasusedforexcitationoftheactivatedGFP.
Modelofdl/Cactinteractions
Weconstructedamodelofdl/Cactinteractionsconsistingofeightdifferentialequations,representing
nuclearandcytoplasmicdl,Cactanddl/Cact,aswellasactivatedTollreceptorsandTollreceptorsbound
todl/Cactcomplex(Toll:dl/Cact).Theequationswerethennon-dimensionalized,resultinginamodel
with20freeparameters.Interactionsweresimulatedduringnuclearcycles10-14,aspreviously
published(O’ConnellandReeves,2015).OptimizationwasperformedinMATLAB®usinganevolutionary
optimizationalgorithmwithstochasticranking(RunarssonandYao,2000,2005),yielding114parameter
setsthatweregenerallyconsistentwiththespatiotemporaldatapublishedbyReevesetal.(2012).
FurtherdetailonmodelequationscanbefoundintheSupplementaryExperimentalProcedures.
Addingtogetherthemodelequationsfordlanddl/Cact(Eqns1-4inSupplementalExperimental
Procedures),weobtainthefollowingequationfortotaldl:
𝜕 1 𝑑𝑙 23*
𝜕 1 𝑑𝑙/𝐶𝑎𝑐𝑡
𝜕 𝑑𝑙 *+*
= 𝐷/0
+
𝐷
/05672*
𝜕𝑡
𝜕𝑥 1
𝜕𝑥 1
23*
where𝐷; representsthediffusioncoefficientforspecies𝑖.
AuthorContributions
SNC,AEA,andSMSconductedexperiments.MDOconductedmathematicalmodeling.SNC,MDO,and
GTRwrotethemanuscript.SNCandMDOgeneratedfigures.
Acknowledgments
ThankstoAngelaStathopoulosandLeslieDunipaceforprovisionofdl-dGFPanddl-mVenusfliesand
BACs,bcd>toll10b:bcd3'UTRflies,andtheDNAusedtogeneratehsp83>toll10b:bcd3'UTRflies.Thanks
toImmunoReagentsforprovidingtheirgoatant-biotinantibody.WearegreatfultoAlexThomasfor
generatingthesna-biotinprobe.ThankstoParvGondaliaforgeneratingthesna-fitcprobe.Thanksto
DavidSteinforprovidingthecact-lacZflyline.WearegratefultoShubbaGovindforprovidingthedllacZflies.Duringthiswork,SNCandGTR(partially)weresupportedbyaCAREERawardfundedbythe
UnitedStatesNationalScienceFoundation(www.nsf.gov),grantnumberCBET-1254344;MDOwas
10
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
supportedbyaGraduateAssistanceinAreasofNationalNeedFellowshipinComputationalScience
fromtheUnitedStatesDepartmentofEducation(www.ed.gov),grantnumberP200A120047.
11
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
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bioRxiv preprint first posted online Jun. 3, 2016; doi: http://dx.doi.org/10.1101/057091. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
FigureLegends
Figure1:DorsalAccumulatesontheVentralSideoftheEmbryo.(A)Currentresearchsuggeststhatdl
doesnotrapidlydiffusefromnucleustonucleusandthereforeitislocallydepletedfromthearea
aroundeachnucleus.(B)Weproposethattotaldlaccumulatesattheventralmidlineduetodiffusion.
"TollDomain"indicatesthatactiveTollreceptorsarebeingproducedontheventralsideoftheembryo.
(C)and(D)Cross-sectionsofwildtypeembryos,stainedfordlandnuclei.(C)dlisequallydistributed
throughoutwhentheembryoisyoung.(D)Totaldlhasaccumulatedattheventralmidlinebylatenc14.
Compareto(B).(E)and(F)dl-paGFPresultsindicatethatdldiffusesthroughouttheembryo.Activation
areainthewhitebox.Anteriortotheleft.(EandE’)Activationneartheventralmidlineapprox.(E)3
minutesand(E’)90minutesafterfirstactivation.(FandF’)Activationnearthedorsalmidlineapprox.(F)
3minutesand(F’)90minutesafterfirstactivation.SeealsoMoviesS1andS2.
15
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
Figure2:TheModelPredictsaShuttlingMechanismandMutantPhenotypes.(A)Thepreviously
publishedmodelofdlgradientdynamicsinwhichtheactiveTollregionwasmodeled
phenomenologically(catalyticactivitylabeled𝑓(𝑥)).(B)Expandedmodelusedinthecurrentstudy.
ActiveTollreceptorsareexplicitlyaccountedfor(producedatarate𝑓(𝑥)).(C)Evolutionaryoptimization
favorshighvaluesfordl/Cactdiffusion(dimensionlessparameterλdl/Cact)andlowvaluesforfreedl
diffusion(λdl).(D)Themodelpredictsdl/Cactdiffusiontowardtheventralmidline(negativevalues)isfar
greaterthanfreedldiffusionawayfromtheventralmidline(positivevalues).(E-G)Perturbingasetof
representativeparameterstoreducerateofshuttlingresultsinahallmarkprogressionofphenotypes.
Thedlgradientfirstwidens(widthparameterσincreases),thenflattensatthepeak,thenobtainsasplit
peakbydecreasingthedosageofdl(E),increasingdl/Cactdiffusion(F),andincreasingthewidthofthe
activeTolldomain(G).Arrowsindicatedirectionofchangeupondecreasingtherateofshuttling.(H-J)
Illustrationsofthehallmarkprogressionofphenotypesassociatedwithshuttling:thepeakexpands(H),
thenflattens(I),thensplitsintotwopeaks(J).Arrowsindicatethedirectionoffluxoftotaldl.
16
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
Figure3:EmbryosfromMothersHeterozygousfordlHaveaDifferent-ShapeddlGradient.(A)CrosssectionofaNC14embryofromamotherheterozygousfordlstainedfordl.(B)Plottednuclearintensity
ofembryoin(A)asafunctionofDVcoordinate(eachbluedotisonenucleus).ErrorbarsindicateSEM
ofnuclearintensity.Pinkcurveisthesmootheddata;blackcurveisafitofthedatatoaGaussian.(C)
Boxplotofgradientwidths(σ)forembryosfrommotherswith2(wt)and1(dl/+)copiesofdl.Hereand
elsewhereinthepaper,boxesindicateinterquartilerange(IQR):fromthe25thtothe75thpercentileof
thedata,whiskersextendamaximumof1.5timesthewidthoftheIQRfromthebox,andoutliers(plus
signs)aredefinedaspointsthatlieoutsidethewhiskers.Numbersindicatesamplesize.Asterisk
indicatesstatisticalsignificanceofp<10-4.(D)Normalizedaverageplotofdlgradientinembryosfrom
(C).SeealsoFigureS1.
17
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
Figure4:DecreasingDiffusionofdl/CactIncreasestheWidthofthedlGradient.(A)Normalizedaverage
plotsofthedlgradientinembryoswith2copiesofwtdl(wt),1copyofwtdland1copyofdl-mGFP
(mGFP),1copyofwtdland1copyofdl-dGFP(dGFP),and1copyofdl-dGFP(1xdGFP).(B)Boxplotof
gradientwidths(σ)forembryosshownin(A)and(F).(C)and(C’)snadomaininwt(C)and1xdGFP(C’)
embryos.Grayarrowheadsindicatethewtdomainofsna;whiteindicatethesnadomainin1xdGFP
embryo.(D)Normalizedaverageplotsofthesnaintensityinwtand1xdGFPembryos.(E)Boxplotof
snadomainwidthforembryosshowninD.(F)Normalizedaverageplotsofthedlgradientinembryos
frommotherswith2copiesofwtcact(wt)and1copyofwtcactand1copyofcact-lacZ(cact-lacZ).
Insetshowsmoreclearlythatcact-lacZisslightlywiderthanwt.Asterisksindicatestatisticalsignificance
(*p<0.02;**p<10-3;***p<10-11)fromwtunlessotherwisenoted.Numbersindicatesamplesize.Seealso
FigureS2.
18
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
Figure5:TheHypomorphicAlleleegfrt1SignificantlyWidensthedlGradient.(A)Cross-sectionofan
embryofromamotherhomozygousforegfrt1stainedfordl.Bracketsindicatepeaksofnucleardl.(B)
Plottednuclearintensityofembryoin(A)asafunctionofDVcoordinate(eachpinkdotisonenucleus).
Theshapehaschangedsignificantlyfromwildtype,astheGaussiancurve(black)doesnotrepresentthe
gradientwell.ErrorbarsindicateSEMofnuclearintensity.(C)Boxplotofgradientwidths(σ)for
embryosfrommotherswith0(wt),1(t1/+),and2(t1)copiesofegfrt1.Numbersindicatesamplesize.
Asterisksindicatestatisticalsignificance(*p<0.01,**p<10-8)fromwt.(D)Normalizedaverageplotofdl
gradientinembryosfrom(C).
19
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peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
Figure6:AnEctopic,Anterior-PosteriorDorsalGradientExhibitsShuttlingPhenomena.(A)and(A’)dl
andsnaexpressioninawildtypeembryo.(B)and(B’)dlandsnaexpressioninanembryowithan
anteroposteriorgradientofdldrivenbythebcdpromoterinadditiontothewildtypeDVgradient.
Whitearrowheadsindicateanarrowingofeachdomainat~30%EL.(C)and(C’)A2-Dversionofthe
modelfeaturingAPandDVactiveTolldomainsexhibitsacompetingsinkphenotype,wherealowpoint
inthedlgradientleadstoagapinsnaexpression.(D)and(D’)dlandsnaexpressioninanembryowith
ananteroposteriorgradientofdldrivenbythehsp83promoterandtheDVgradientabolishedbya
homozygousmutationingd.(E)Plotofdlandsnadomainsfromtheembryoin(D).Eachgreendotsis
onenucleusandtheblackcurveisasmoothingofthedldata.Embryoimagesaremaximalintensity
projections.SeealsoFigureS3.
20
bioRxiv preprint first posted online Jun. 3, 2016; doi: http://dx.doi.org/10.1101/057091. The copyright holder for this preprint (which was not
peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.
Figure7:TheShuttlingMechanismExplainstheFlatandDoublePeakPhenomena,IllustratedinThree
Ways:(A)slowingdl/Cactdiffusion(coloredarrows,fromgreentored),(B)halvingthedosageofdl
(bluedots),and(C)expandingtheTolldomain(fromgreentored).Cartoonrepresentativeofembryo
crosssection.Arrowsindicatediffusionofdl/Cactcomplex,Tolldomainhighlightedinorange,nuclear
concentrationindicatedbyblue-pinkgradient.
21
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