material’. Inthelegend toFig.3,line6,‘(K 3, ‘tenths’shouldread‘tens’;line22,‘Fig.S2Ainthesupplementarymaterial’2A,seeTable S1inthesup On p.894,therearefourcorrectionstobemade.Intheleftcolumn,line12,‘Fig.2D,E’shouldread2E-G’.righ In addition,anumberofothererrorswerenotcorrectedbeforepublication. is printedbelow. Development 133,1411(2006)doi:10.1242/dev.02337 CORRIGENDUM switch, andtheotherinfirstbarofgraph(k There areacoupleoferrorsinFig.2C,onethekey, whereblackshadingshouldindicatemonostablebehaviour andlightgre Krishanu SahaandDavidV. Schaffer Signal dynamicsinSonichedgehogtissuepatterning The authorsapologisetoreadersforthesemistakes. chick embryo,oranadditionalsignalaccumulation,dispersalshuntingmechanism’. wild-type chickembryo:asignalaccumulationregime, asignaldispersalregime, orashuntingmechanism’shouldread‘...thew On p.898,therearetwo corrections.Intherightcolumn,line5,‘Fig.S2’shouldreadS1’.legend toFig.8,li On p.895,onecorrectionshouldbemade.Intheleftcolumn,line9,‘I-VIIinFig.1A’ shouldread‘I-VIinFig.1B’. ptc Development K Gli3 Pin )’ shouldread‘(K ), inwhichthetoptwo portionsofthebararereversed incolour. Thecorrectedfigure 133 , 889-900. ptc /K Gli3 )’. nes 4and5,‘...the t column,line y thebistable plementary ild-type

DEVELOPMENT from secretingcells,andmutatingsuchtransportersdisruptstissue essential foractively transportingmorphogens upontheirrelease example, studiesin morphogen transportatvarious timesinthepatterningprocess.For the steadystateconcentrationgradient,but also therateof Specifically, eachtransportmechanismpotentiallymodifiesnotonly of ‘accessory’mechanismsthatmodulateligandtransport. and cellularresponse. hypothesis doesnotaccountforsuchdynamicsingradientformation determinants ofShhtissuepatterning.Theclassicalmorphogen the timingofShhsourcesecretion(Ericsonetal.,1996)arecrucial al., 1998;Park etal.,2004;Wolff etal.,2003;Yang etal.,1997)and concentration (AhnandJoyner, 2004;Harfeetal.,Kohtz et patterning. Boththetimeofexposure ofacellto given Shh that Shhconcentrationgradientdynamicsplayacrucialroleintissue the morphogenhypothesis.However, very recentstudiessuggest during vertebrate development, isostensibly acanonicalexample of forebrain (Ericsonetal.,1995)andspinalcord(Roelink limb bud (Riddleetal.,1993),midbrain(Britto2002), hedgehog (Shh),whichformsaconcentrationgradienttopatternthe over thetimewindow oftissuepatterning (i.e.atsteadystate).Sonic rapid morphogentransportcreatesaconcentrationgradientinvariant center spatiallyorganizes andpatternstissuearchitecture.Thatis, extracellular morphogenconcentrationgradientemanating fromthe secreted fromsignalingcenters,andthattheresultingstatic hypothesis statesthatchemicalsignals,termed‘morphogens’,are range oftissuepatterningprocesses(Crick,1970;Turing, 1952).The For decadesthemorphogenhypothesishashelpedtoexplain awide INTRODUCTION KEY WORDS:Morphogen,Sonichedgehog,Diffusion, Transport, Modeling during patterningcanshapeatissuepattern. ligand degradation.Thismodelingapproachelucidateshowindividualmodularelementsthatoperatedynamicallyatvarioustimes Shh, suchasPatchedandHedgehog-interactingprotein,significantlylimititssignalingrangebyslowingtransportpromotin signaling rangeofthemorphogenbyconcentratingitnearsecretionsource.Furthermore,severaltranscriptionaltargets proteoglycans, orbythemoderateupregulationofdedicatedtransportmoleculeslikeDispatched,canactuallyincrease predicts thatslowingthetransportofamorphogen,suchasbylipidmodificationligandShh,bindingto work yieldsseveralnovelinsightsintohowdifferent transportmechanismsor‘modules’controlpatternformation.Themodel studies, themodelelucidateshowdynamicsofgradientformationcanbeakeydeterminantcellresponse.Inaddition,th hedgehog (Shh),cooperateinmodularfashiontoregulatetissuepatterningtheneuraltube.Consistentwithnumerousrecent model thatanalyzesdynamicallyhowtheintricatetransportandsignaltransductionmechanismsofamorphogen,Sonic highly complexandaretypicallyanalyzedonlyatlongtimesaftersecretion(i.e.steadystate).We havedevelopedatheoretic the mechanismsthatmorphogensystemsemploytoestablishapreciseconcentrationgradientforpatterningtissuearchitecture During development,secretedsignalingfactors,calledmorphogens,instructcellstoadoptspecificmaturephenotypes.However, Krishanu SahaandDavidV. Schaffer* Signal dynamicsinSonichedgehogtissuepatterning Development 133,889-900doi:10.1242/dev.02254 Accepted 5December 2005 *Author forcorrespondence (e-mail:[email protected]) Berkeley,University ofCalifornia, CA94720-1462, USA. Neuroscience Institute, Department ofChemicalEngineeringand theHelenWills Beyond passive diffusion, morphogensystemscanhave anumber Drosophila have identifiednumerousgenes phenotypes [e.g.fromV3 target cellsswitchatthresholdvalues frommatureventral todorsal 15 nMatthefloorplateto0.5dorsaledgeofneuraltube, within thetissuefromapproximately as itsconcentrationdecreases floorplate, diffuses intotheneuraltube(Roelinketal.,1995),and, laying (RicklefsandStarck,1998)].Shh,secretedfromthe embryonic development stages10-26[~33-116hoursafteregg model Shhregulation ofdorsoventral spinalcordpatterninginchick state concentrationgradient. overlooked bythefocusofmorphogenhypothesisonsteady evolution ofconcentrationgradientsindeveloping tissue,whichis range signaling.Any ofthesemechanismscanaffect thetemporal or immobilizingextracellular-diffusing morphogenstolimitlong- components (Theetal.,1999)serve theputative rolesofdepleting (Chuang andMcMahon,1999)extracellular matrix (ECM) Also, highaffinity interactionsofmorphogenswithcellsurface patterning (Chenetal.,2004;HanTakei etal.,2004). multimers, andthe transmembraneproteinDispatched (Dis)islikely Furthermore, Shhandits space (ChenandStruhl,1996; MarigoandTabin, 1996). internalization ofShhdepletes theligandfromextracellular Shh signaling,anditssubsequent bindingandreceptor-mediated source. Inaddition,theShhreceptor Patched (Ptc)isupregulated by signaling atalarge distance,upto20celldiameters,away fromits significantly reduceitsdiffusivity. However, Shhisstillcapableof which mayanchortheligandtocellmembranesandthereby N-terminal palmiticacid(Pepinsky etal.,1998;Porter1996), by hydrophobicmoieties,includingaC-terminalcholesteroland a establishes agradientduringthisprocess.Shhiscovalently modified has complicatedasimpleunderstandingofhow itstransport (V3) andmotoneurons(MN)thatoccursthroughstage26. subsequently trackthecellfate switchbetweenV3interneurons stage 10,whenShhisfirstsecretedfromthefloorplate. We the neuralfoldappearsandessentiallyastubecloses at previously reviewed (Perssonetal.,2002)].Ourmodelbegins after To investigate temporaleffects oftransport and signaling,we The structureofShh,aswellitsvarious interactingproteins, Drosophila r MN r V2 RESEARCH ARTICLE homolog Hedgehogcanform r V1 inFig.1A,ashasbeen al is 889 g re

DEVELOPMENT positive feedback,whereas transmembrane protein Smo andtherefore actsasarepressor ofShh signalingasdescribedpreviously (Laietal.,2004). switching byinteractingwithitstransmembrane receptor, Patched(Ptc).InabsenceofShh,Ptc represses thesignalingactivit and arrows from proteins togenesindicateactivationorrepression. vitronectin; Vit, Smo,Smoothened.Atthecellularlevel, shown around arepresentative cell.Arrows betweenproteins represent bindingordissociation,arrows from genestoproteins re ( the FEMmesh,eachblackcircle represents ameshboundary, andeachgray‘x’represents anodewhere concentrationsare defined interneurons. Ontheright,cellsA-Care depictedwithasurfacemembrane(orange),nuclei(dashedovals),andextracellulars (Ericson etal.,1997b)].Whitelabelsindicatesubsequentmature stage26cellfates.MN,motoneurons; V1-3,distinctpopulati transverse cross sectionofastage16chickembryodepictsexpression of 890 Fig. 1.Finiteelementmodel(FEM)ofthevertebratedeveloping neuraltube. B ) TheShhcore signalingnetwork(redlabeledasI)andhypothesizedaccessorymechanisms(lab dashedlinewith internalization RESEARCH ARTICLE ptc upregulation yieldsnegative feedback. shh (green) and ( A One-dimensionalprojection ofneuraltubetissue.A ) pax6 (red) [adapted,withpermission,from Ericsonetal. gli upregulation represents Shh inducescellfate y ofthe Development 133(5) pace (lightgray).In ons ofventral present expression, eled II-VI)are inthemesh.

DEVELOPMENT MATERIALS ANDMETHODS the needsofspecifictissues. fashion todynamicallypatternamorphogengradientaccording suggests thatdifferent componentscanbeassembledinamodular formation andcellularsignaling(Fig.1B).Thisinvestigation potential rolesofsixmodularmechanismsinvolved inShhgradient are abletoreproducetheexperimental profilesand clarify the morphogen bindingtoECMandgeneexpression. Modeling results modified byseveral longtimescalemechanisms,including the concentrationgradientinitiallyestablishedbydiffusion canbe analyze Shhpatterningofthedeveloping spinalcordandfindthat and tissuepatterning. dynamics andgeneregulation dynamicsonShhgradientformation biology analysistoexplore theeffects ofdiffusion, receptor-ligand synthesize, andguideexperimental work, wehave appliedasystems mechanisms (Dillonetal.,2003).Therefore,tocomplement, mechanism withoutconsiderationoftheseaccessorytransport thevertebrate limbbud, usingasimplesignal transduction in are unclear. Shhtransportviadiffusion was previously modeled these highlycomplex elementstotheabilityofShhpatterntissue et al.,2002).Theindividual andsynergistic contributions ofeach The etal.,1999),andShhhasalsobeenshown tobind HSPG(Rubin proteoglycans (HSPG)(Bornemannetal.,2004;Takei etal.,2004; Hedgehog dependsupontheactivity ofheparan sulfate Marti,2000).Finally, theeffective transportof and proper presentationofShhtodifferentiating motoneurons (Pons to vitronectinintheneuraltubehasbeensuggestedaid proteins alsoregulate Shhtransport,ashigh-affinity bindingofShh modulate itssignalingactivity (ChuangandMcMahon, 1999).ECM Hedgehog-interacting protein(Hip),bindsShhwithhighaffinity to (Kawakami etal.,2002).Moreover, amembraneglycoprotein, to beinvolved inregulating theirassemblyandintercellulartransport Signal dynamicsinShhtissuepatterning notochord cells(at embryos couldreadily beincorporatedbyaddingextra elementsforthe commitment (JeongandMcMahon, 2005),andsuchscenariosinchick from thenotochordmaydiffuse far intotheneuraltubetoaffect MN (Fig. 1A).Recentwork inmouseembryosindicatesthatearlyShhsecretion seen inwild-typeembryosafterstages 26(>80hoursafterlaying)isshown phenotype switch(Laietal.,2004). Thepositionofthematurephenotypes receptors orothercomponents,and highShhsignallevels induceacell diffuses dorsallyfromitsfloorplatesourcethroughthemeshandbindsto have thesameinitialgeneexpression profile.Astimeprogresses,Shh 10-12 (~34hoursafteregg laying).Atthistime( expression isinitiatedexclusively inthefloorplate(Fig.1A)during stages At theventral-most region ofthechickneural tube,highlevel Shh Developmental timewindow and partitionstheneuraltubeintoameshofdiscrete10 diffusion ofShhaway fromitsfloorplatesourceandthroughtheneuraltube, Shh transportinonedimension.Thespatialaxisofourmodeltracksthe We considerdorsoventral patterningofthechickneuraltubearisingfrom Geometry oftheneuraltube each containingonecell(Fig.1A).Inside10 membrane element/barrier. volume compartment, whichissurroundedbyasmall10nmplasma receptor-ligand complexes) arecompletelyrestrictedwithintheircellular By contrast,allcellsurface andintracellularspecies(e.g.receptors smoothly diffuse throughtheextracellular regions incubesA,BandthenC. moving throughthecontinuousextracellular space ofthemesh(Fig.1A)can was modifiedtoaccountfortortuosity(Lander etal.,2002).AShhmolecule fractions ofneuraltissue(Incardonaetal.,2002).Thediffusion coefficient in sumoccupy 20%ofthevolume basedonempiricallymeasuredvoid space consistsofinterconnectedchannelsunspecifiedgeometry, but that We build uponaprevious singlecellmodel(Laietal.,2004)to x <0), withappropriate Shhsecretiondynamics. ␮ t m cube,theextracellular =0), allcellsinthetube ␮ m cubicelements, Drosophila dimensionalized bythecorrespondingparameters:concentrationsK the model.Asaresult,following typesofvariables werenon- reduces thenumberofindependentparametersthatarenecessarytodescribe to interpretthanindividual parameters.Inaddition,groupingvariables However, relationshipsbetweengroupsofvariables canbeintuitively easier qualitatively thesame. secretion, andallconclusionstrendsdiscussedbelow remained state from1to10nMandpatternevolution timefrom30to150hoursShh parameter values thatchanged the3nMShhswitchingthresholdatsteady response toShhvaried (Fig. 2C).Modelbehavior was investigated for values over fourordersofmagnitudetoobserve whetherthesinglecell the core-signalingpathway, weconductedsensitivity analysisforparameter experimentally inandnearthefloorplate(Fig.3B).For eachparameterin this model,accountsforthedecreasein due toadditionaldownstream targets of Shh concentration(Briscoeetal.,2000).Suchfloorplateinduction,probably space by1cm,andtime1/k floorplate induction,marked byanincrease in floorplate (Ericsonetal.,1997b).For theventral-most cells(closeto pattern matchedtheNkx2.2switchinginterface seenat70 floorplate hasnotbeenquantitatively determined,wechoseitsuchthatour 1997b)]. To satisfythelastcriterion,becauseShhsecretionratefrom wild-type chickembryo[seefigure3BinEricsonetal.(Ericsonal., fluorescenceintensityspatialprofileina al., 1997b)];andaNkx2.2protein timescales forMNspecificationfromfigure3DinEricsonetal.(Ericson hour kinetictimescaleofShhsecretionfromthefloorplate[basedupon threshold atsteadystate(Ericsonetal.,1995;Ericson1997b);~50- gli1 observations: switching‘on’ ofhomeodomain estimates werechosentomeetthethreefollowing experimental (Fig. 2legend, seealsoTable S1inthesupplementarymaterial).Parameter from theliteratureorestimatedbaseduponanalogousbiologicalsystems Kinetic, diffusive andbindingparametervalues wereeitherdirectlytaken Parameters andcomputationaltechniques boundary. output, astheon/off and aGli3term.We reporttheGli1 concentrationastheimportantsystem Thus, inthemodel,effects ofGli2areeffectively lumpedintoaGli1term transcription factor ofbothrepressorandactivator functions,the‘Gli3’type. two types:eitherapuretranscriptionalactivator, the‘Gli1’type,ora Altaba, 1999).Asaresult,wehave effectively parsedtheeffects ofGli2into progenitor cellsrequirefurthercharacterization(Baietal.,2004;Ruizi highly context dependent,anditsmolecularinteractionsintheneuraltube The activities ofGli2,whichoverlap withthoseofbothGli1andGli3,are expression andrapidlyswitchesthestateofnetwork to‘on’(Fig.2B). Gli productiontothepointwherepositively feedsbackuponitsown material). AsShhisincreasedabove athresholdconcentration,itstimulates cellular internalizationeffects (seeFigsS3,S4inthesupplementary the Shhsignalingnetwork derived bypreviously (Laietal.,2004)toinclude and degradation (Fig.1B,Fig.2A).Atthesinglecelllevel, webuild upon and whoseindividual termsrepresentratesofdiffusion, proteinsynthesis that tracktheratesofchangeinconcentrationsnetwork constituents, The Shhsignalingnetwork isrepresentedasasetofdifferential equations receptor kinetics Mathematical formulationofShhtransportbydiffusion and region and Pax6 intheremainder ofthetube.Inthiswork, we among theearliestofwhichare themarkers Nkx2.2intheV3 homeodomain proteins(Briscoe etal.,2000;Jessell,2000), process experimentally analyzedbystainingfornumerous governs theV3/MN/V2/V1 patternoftheneuraltube(Fig.1A),a Dynamic expression of transcriptionfactors (e.g.Glifamily) RESULTS coded intotheFEMLABsoftware. equations areshown inFigsS3,S4(inthesupplementarymaterial)andwere The setofequationsinFig.2Aarepresenteddimensionalform. domain marker inthecaseofmodel) expression ata~3nMShh gli1 expression interface demarcatestheV3/MN deg . Thecorrespondingnon-dimensional gli1 RESEARCH ARTICLE or othersignalsnotincludedin hnf3 nkx2.2 nkx2.2 ␤ , occursabove a10nM (which serves asthe expression seen ␮ m fromthe x 891 =0), Gli3 ,

DEVELOPMENT 892 Fig. 2. G E A C k See nextpageforlegend. perturb RESEARCH ARTICLE k lit 0.001 100 0.1 10 1 k Pin Perturbed Parameter k g3r k Gmax Bistable Switch Irreversible Switch Monostable Behavior t =43hr t =43hr at k Pout at D F H [Gli1] B Off Monostable Behavior [Shh] On t =43hr t =43hr [Gli1] at Bistable f Off Off Cell FateSwitch Irreversible Sh [Shh] [Shh] 5.7 On >2-fold [Gli1] change [Gli1] >2-fold

V3/MN interface V3/MN [Gli1] t =43hr at 70 70 at Cell FateSwitch at Development 133(5) Bistable μ Bistable m On

DEVELOPMENT 2004). ( ‘Promoter’ and‘basal’termshavebeenpreviously defined(Laietal., levels ofconcentrations(steadystates)corresponding toa Shh modelasdescribedpreviously (Laietal.,2004).Two time-invariant conditions were: [Shh]=0;[PtcShh V3/MN developmentaltimewindow( each figure correspond toconcentrationprofiles attheendof concentration; and(H)Gli1intracellularconcentration.Boldedlinesin intracellular concentration;(G)Ptc-Shhcomplex Ptc type embryoisshown:(E)Shhextracellularconcentration;(F) spatiotemporal evolutionofvariousShhnetworkconstituentsinawild- various constantextracellularShhconcentrations.( (i.e. toachieveagreater than7-foldincrease inGli1concentration)at behavior ofthemodelisplotted;k min Signal dynamicsinShhtissuepatterning (Wijgerde etal.,2002),Shh signaling [e.g.Shh expression areentirelylostinmutantswithcompromisedShh ladder ofcellfates. Given thatthe V3domainandNkx2.2 work toevolve themodel behavior fromabinaryswitchinto 2000), events thatcanbeincorporatedinto themodelinfuture regulated byBMP, FGFandretinoidsignals(reviewed byJessell, demarcation. Homeodomainproteinexpression patternsarealso V3/MN boundary, whichresultsintheNkx2.2/Pax6 histological focus ontheventral-most binarycellfate switchdelineatingthe nM. Parametersforcore pathway:D ( Fig. 2.SpatialandtemporalevolutionoftheShhsignal. and shadedinBare shown.k single cellbehaviorfallsintothethree classesschematicallyrepresented the bestavailableliterature value.Rangesofparametervaluesatwhich behavior asparticularparametersare varied100-foldaboveandbelow the on/off switch.Thisgraphshowsthechangesinsteady-state each parameterwhileholdingothersconstantandobservedchangesin single cellstoShh,weperformedasensitivityanalysis,i.e.varied determine whichparametersmoststrongly control theresponse of a Gli1 [Ptc min k min k connect GlitoNkx2.2. knowledge ofthe mechanistic andmolecularinteractionsthat used asamarker ofShh signalingactivity, withoutrequiring upregulated following Shhsignaling,weassumethatitcanbe Gli ispresumablyexpressed. Also,becauseNkx2.2israpidly a robust marker of cellswhereShhsignalingisactive, and where and Chiang,2000),Gli3 x ( Boundary conditionsforallspecieswere impermeableatthesource in thesupplementarymaterialforparameterdescriptionsandsources). k K range ofvalues(e.g.k Notice thatseveralparametersneedtobecontrolled withinanarrow ( and anintermediatebistableregime where eitherstateisstable. concentration: onlythe‘off’stateisstable,‘on’ 2004). There are three distinctregimes controlled byextracellularShh A Ѩ C =300 Pdeg Pbas Pout g3rc gli1 / SensitivityanalysisofparametersinthesinglecellShhnetwork.To ) Reaction-diffusion equationsforthecore Shhsignalingnetwork. ) Ѩ in x –1 –1 –1 ). ( =1.73 =0.12; K =0.09 min =0 at ]=0.33 nM;[Gli1]=1.63[Gli3]=5.81and[Gli3R]=61.2 –/– ; k ; k ; k ‘off’ statecanexist,aswehavepreviously described(Laietal., D ␮ /Gli2 B deg Cdeg on m). ) Thetimeforasinglecelltoswitchfrom aV3toMNfate ) Three classesofsteady-statebehaviorinthecore singlecell =120,000,000 M ϫ =0.009 min x =0 =0.00198 min 10 ptc –/– –11 –1 ␮ =3.32 (Park etal.,2000)mice], weuseNkx2.2purelyas m) andzero atlargedistances(concentration=0 ; k min M Gmax ϫ Gmax –/– –1 10 =2.74 ; r –1 –11 (Litingtung andChiang,2000),Smo –1 ; k g3b ) andseveralcanvaryoverawiderange(e.g. –1 ; k –/– Pin =3.1 M; andK ϫ min perturb –/– Pmax /Smo =0.03 min 10 /Gli3 –1 ϫ in –10 =2.25 lit , valueofparameterforwhichthe ; ]=0; [PtcShh 10 , valueofparameterinliterature. k Shh –/– min M Cin t –19 =83 hours).Simulationinitial –/– Gli3 =1.0 =0.2 min (Wijgerde etal.,2002),and ϫ –1 M =8.3 (Bai etal.,2004;Litingtung 10 ; k 2 –1 ϫ –9 min ; k Pout 10 ϫ min M out Gbas 10 –7 =0.00036 min –1 –1 ]=0; [Ptc ; k ; k –10 cm E-H =2.11 g3r Cout –1 2 M (seeTable S1 ) The /s; k ; =0.0117 min =0.00181 ϫ out gli1 off 10 ]=2.0 nM; =0.10 –12 ‘on’ and –1 ; M –1 –/– ; state levels at60-80hours (Fig.2E).NotethatShhrapidly ( a highconcentrationwithin5hours, but thenfelltoapproachsteady cells (Fig.2;seealsoMovies 1-8inthesupplementarymaterial). wild-type tissuepatternwithdistinct regions of the dashedlineinFig.1B), simulationcorrectlyreproduceda intracellular signaltransduction andligandinternalization(within spatial model.For thecoreShhsignalingpathway, whichincludes the concentrationsofShhnetwork constituentsinamulticellular, the Shhsignalpropagatesinneuraltube,wedynamicallytracked To gaincomprehensive spatialaswelltemporalinsightsintohow Spatiotemporal evolutionoftheShhsignal during thisdevelopmental timewindow. dynamically varying theShhconcentrationacellisexposed to transport mechanismswillmodulatecellphenotypepatterning by and 3.5nMforsteadystate,respectively, inFig.2D).Accessory to steadystate(5.7nMforaswitchat43hours,4.583 within earlytimewindows thanifthetissuewereallowed toproceed Shh concentrationthresholdmustbepresenttoswitchcellfate morphogen gradienthasachieved steadystate.Notethatahigher shown tohave amatureV3/MNdemarcation,but beforethe hours, thetimeatwhichneuraltubehasbeenexperimentally and probablybeforeShhreachesasteadystategradient. changes (i.e.theV3/MNboundary)atdifferent timesafterexposure, complex sequenceofShhconcentrationsthatwilldrive cellfate the gradientevolves, cellsintheneuraltubewillbeexposed toa increases suchasthreefoldtotenfold,datanotshown). Inreality, as (Fig. 2D,resultswerequalitatively similarforotherthreshold different Shhconcentrationswillswitchfate after different durations initial basalconcentration,themodelpredictsthatacellexposed to once itachieves asevenfold increaseinGli1concentrationfromits studies. Ifweconservatively assumethatacellcanswitchphenotype 2004; Wolff etal.,2003;Yang etal.,1997).Themodelsupportsthese and Joyner, 2004;Harfeetal.,Kohtz etal.,1998;Park etal., of Shhexposure isanimportantdeterminantofcellresponse (Ahn recent studieshave shown thatnotjustthelevel but alsotheduration gradient reachessteadystate.Insupportofthishypothesis,numerous cells begin tointerprettheShhgradientinformation beforethe and Gurdon,1999),indicatingthatitispossibleoreven likely that transcription factor canswitchcellfate (Niwa etal.,2000;Shimizu indicate thataslittleatwofold increaseintheconcentrationofa a cellphenotypeswitch.Quantitative resultsfromothersystems a target transcriptionfactor above akey thresholdvalue, itcaninduce That is,assoonmorphogensignalingincreasestheexpression of concentration toreachasteadystateinorderundergo patterning. hypothesis, thetissuemaynotneedtowait forthemorphogen embryos (Fig.2D).Incontrasttothecanonicalmorphogen the 3-daytimewindow forV3/MNpatterncompletion inchick switching behavior beforereachingsteadystate,particularlywithin we foundthattheShhsignalingnetwork alsoundergoes robust switch inGli1expression atsteadystate(Laietal.,2004).However, via Ptcupregulation, thissignalingnetwork exhibits arobust on/off binding siteswithinitsown promoter, andanegative-feedback loop material). Asaresultofpositive-feedback loop,arisingfromGli1- complexes (Fig.2A,seealsoFigsS3,S4inthesupplementary cellular internalizationoftheShhreceptorPtcandPtc-Shh first built uponasinglecellShhsignalingnetwork modeltoinclude To analyzethedynamicsofV3/MNbinarycellfate switch,we expression varieswithextracellularShh Dynamic approach tosteadystategene During thispatterningprocess, extracellular Shhrapidlybuilt to For allsubsequentanalysis,weanalyzetheShhgradient at83 RESEARCH ARTICLE gli1 ‘on’ and‘off’ 893 t <5

DEVELOPMENT where (K between Nkx2.2andGli1.Simulationinitialconditionsparametersare thesameasthoselistedinFig.2,exceptwithin The dashedlineindicatestheexperimentallymeasured Nkx2.2profile atstage18, of theGli1concentrationinbothwild-typeandtransfectedsidesembryoafter63hoursShhsecretion matchexper and cellstransfectedwithasignaling-defectivePtc(green) [adapted,withpermission,from Briscoeetal.(Briscoeal.,20 of allthecorepathway componentsatvarious timesduring patterning (Fig.2E-H).Theresultingintricateconcentrationprofiles developmental timewindow of3daysforwild-typechickV3/MN neural tubeapproachbut donotreachsteady-statelevels inthe cells(Fig.2H).Allconcentrationsinthe versus thedorsal‘off’ fold higherGli1proteinlevel was seenfortheventral ‘on’cells Gli1 concentration,andafter83hoursofShhsecretion,an8-to10- interface exhibited atransientincreasefollowed byadecreasein due tohighShhsignalingnearthefloorplate. Incardona etal.,2000).After20hours, consistent withprevious observations (Incardonaetal.,2002; predominant formofPtcwas aninternal,complexed form(Fig.2G), rapidly internalizedbut degraded more slowly, sothatthe elevated andboundfreePtc.TheresultingPtc-Shhcomplexes were free Ptcinitiallydecreasedasextracellular Shhlevels rapidly above theShhswitchingthreshold(Fig.2D,E).Nearfloorplate, exhibited discreteon/off regions due toinduced continuous Shhprofilethatissmoothenedbytransport,Ptcprofiles receptor-mediated endocytosis (Fig.2F).In contrasttothemore portions oftheembryoandbegan tomediateShhdegradation via a directShhtranscriptionaltarget, increasedintheventral-most concentration profile.Shhlevels thenmorerapidlydeclinedasPtc, passive diffusion alonegoverned theearlyevolution of theShh this relatively shorttimescale,receptor-ligand internalizationand expression fromShhtarget genesdoesnotbuild appreciablywithin phenotype switch[~3nM(Ericsonetal.,1997b)].Becauseprotein hours) rosewellabove thestaticlevels foundtoinduceaMNV3 Fig. 3.Modelpredictsresults. experimentalpatterning 894 A Shh alsodrove adynamicGliexpression pattern.Cellsatthe RESEARCH ARTICLE ptc K Gli3 ) у 10 6 . Seetextfordetails. Shunting ptc was highlyupregulated B ptc expression ( A ) Across sectionofastage20-24chickembryoindicatesexpression of k signaling [i.e.bysettingtheratio(K insensitive toPtcinthedifferential equationsgoverning intracellular were suppliedwithasignaling-defective PtcbymakingSmoactivity transfection inFig.3A,cellsbetween40-60 then imagedatstages20-24( at stages10-12weretransfectedononesideoftheneuraltubeand inhibits Smosignaling(Briscoeetal.,2001).Inthisstudy, embryos negative Ptcmutantthatlacksthecapacity tobindShhyetstill which theneuraltubewas transfectedtoexpress adominant- to predictexperimental resultsbysimulatingaprevious studyin profiles seenexperimentally. We next testedtheabilityofmodel satisfy Shhthresholdswitchinglevels andgeneexpression spatial analysis ofparameterswas conducted,andvalues werechosento As describedabove (Materialsandmethods/Results),sensitivity Prediction ofmutantPtcphenotype (1/k and geneexpression andproteindegradation over anumberofhours cm over acelldiameterover tenthsofseconds[(10 mechanisms occurringatmany different timescales:liganddiffusion patterning would bedifficult topredictintuitively duetothemultiple (green inFig.3A)lacked supplementary material].Briscoeetal.foundthattransfectedcells (1/K model capturedtheeffects ofthemutantPtconpatternformation, previously describedwild-typepattern(Ericsonetal.,1997b).The whereas thecontralateral,untransfectedsideexhibited the Hipmax 2 /s], ligandbindingandinternalizationontheorderofminutes deg shh t Shunting , 1/k =~50 hours(Ericsonetal.,1997b).Seetextforrelationship k on and 1/k Pout and 1/k Cin ; seeTable S1inthesupplementarymaterial), Cdeg ). nkx2.2 induced rateofHipsynthesis,k concentration and( at variouslevelsof( interface positionat ventrally.pattern interacting-protein (Hip)shifts Fig. 4.ShhbindingtoHedgehog- material). (see Fig.S4inthesupplementary equations andparameterswere added in Fig.2;however, Hipmechanism parameters are thesameas thoselisted Simulation initialconditionsand t =39-63 hours).To simulatethe expression (Briscoeetal.,2001), Gli3 /K ptc 01)]. ( ) r Development 133(5) ␮ B A transfectedregions The Gli1protein ϱ ϫ t maximalGli1- ) B m and80-110 initialHipsurface ) =83 hoursisshown imental profiles. 10 in Fig.S2Athe ) Modelingresults –4 cm) nkx2.2 Hipmax 2 /1 ϫ (red) . 10 ␮ m –7

DEVELOPMENT hours. Simulationinitialconditionsandparametersare thesameasthoselistedinFig.2,exceptD concentration are shownat ␮ modeling resultsforthetransfectedside(transfectedrange~90 as theShhsignalingrangeincreasedinbothexperimental and Signal dynamicsinShhtissuepatterning Fig. 5.Restricteddiffusion ofShhcanpropagate amorphogensignal. sense Shhsignal,andthereforedonotupregulate simulated Gliupregulation ofHipandallowed ittobindShh (Chuang andMcMahon,1999;Jeong2005). We transcriptional target ofShhsignaling thatbindsandsequestersShh antagonist ofShhsignaling,becauseitisanon-signaling Hip isatransmembraneglycoproteinthatfunctionsasaninducible shifts causes ventralpatterning viaHedgehoginteractingproteinInternalization which leadsustoclassifypatterningintothreedistinctregimes. analyze various mechanismsthatretardorpromoteShhdiffusion, patterning byactingonbothshortandlongtimescales.Then,we negative-feedback loopisshown torestricttherangeofShh to negative-feedback loopsoperating atlongtimescales.First,theHip mechanisms thatexert rapideffects onthedeveloping Shhgradient over awiderangeoftimescales,rangingfromtransport-hindering and tissuepatterning(I-VIIinFig.1A).Thesemechanismsoperate accessory mechanismslikely tohave astrongeffect onShhtransport by dominant-negative Ptc,itwas usedtoanalyzetheeffects ofseveral untransfected sideserves asabarriertoShhtransport. A A m>~70 After themodelhadsuccessfullyreproducedpatterningperturbed ␮ m forwildtypeinFig.3B).Thetransfectedcellscannot Accumulation Signal t =83 hoursatvariousShhdiffusivities. ( Dispersal Signal B ptc , whichonthe B C TheGli1protein interfacepositionisshownatvariousdiffusivities at ) tissue. Therefore,astheinitial( extracellular Shh,Hipactsasa‘shunt’toremove freeShhfromthe when Hipisaddedtothemodel(Fig.4).Bysequestering degradation (Fig.1B,II).Ventral shiftsinthewild-typepatternoccur reversibly, aswelltoundergo internalizationtoaccelerateShh cm concentration atmostpointswas toolow tochangecellphenotype establishavery shallow morphogengradientwherethe to once theShhdiffusion coefficient reachedahighvalue [>10 near itssource,leadingtoadeeperpatterning(Fig.5A,B).However, morphogen concentrationrapidlyincreasedwithinalarge region switched. However, asthediffusivity was graduallyincreased,the the floorplate,yieldingonlyasmallregion inwhichthe cellfate Shh diffusion coefficients (Fig.5),thesignaldidnotdiffuse far from phenotype switchingdeeperintothetissue.For example, atvery low mechanisms thatslow ligandtransportcouldactuallyinduce The mostunanticipatedresultofoursimulationswas that opposing regimes Shh diffusivity dictatesbehaviorbetweentwo (Stamataki etal.,2005). the interface ventrally, consistentwithrecentexperimental results extracellular Shhconcentrationprogressively decreasedandshifted the maximalHipsynthesisrate(Fig.4B)was increased,the ( A Accumulation 2 ) ExtracellularShhconcentrationand( /s], themorphogenrapidlydiffused away fromitssource Signal Dispersal Shh Signal C was varied. t =0) Hipconcentration(Fig.4A)or RESEARCH ARTICLE Accumulation material). S4 inthesupplementary equations were added(see Fig. mechanism parametersand 2;however, Dispatched Fig. the sameasthoselistedin conditions andparametersare aggregate. Simulationinitial ( intracellular concentrationand levels of( t protein interfacepositionat diffusion limitations. Dispatched canovercome Fig. 6.Shhaggregation by B =83 hoursisshownatvarious B ) diffusivity ofaShh Signal ) intracellularGli1 A ) initialDispatched Dispersal t The Gli1 Signal =83 895 –6

DEVELOPMENT equations andparameters were added(see Fig.S4inthesupplementarymaterial). HSPG extracellularconcentration. Simulation initialconditionsandparametersare thesameas thoselistedinFig.2;however, shown atvariouslevelsofinitialHSPG extracellularconcentration.( (>10 to signaldeeperintothetube.However, athighDisconcentration (10 yielded abiphasicresponse(Fig.6A,B).Atlow Disconcentration Similar totheShhdiffusivity results,varying bothoftheseparameters effects ofDisconcentrationandaggregate diffusivity onpatterning. constitutively expressed ECMcomponent, HSPG[mechanismIVin tube pattern,weanalyzedtheeffects ofreversible Shhbindingtoone Because suchinteractionshave beenproposed tomodifytheneural As Shhdiffuses, itcanencountervarious componentsoftheECM. signal diffusivity Extracellular matrixeffectively modifiesShh diffusivity (Fig.5). (Fig. 6B)occursforthesamereasonsasmonomericShh response toDisconcentration(Fig.6A)andaggregate diffusivity aggregates andshiftedtheinterface ventrally. Inaddition,thebiphasic counteracted thebenefitsofenhanceddiffusion ofthese resulting netdecreaseinthenumberofsignalingmoleculestherefore position near10 Note thatsmallchangesindiffusivity donotinfluencetheinterface whereas highdiffusion constantsyielda‘signaldispersal regime’. diffusion constantsconstitutesa‘signalaccumulation regime’, of aparametersuchasShhdiffusivity (Fig.5B,C).Patterning atlow position (i.e.Gli1level) undergoes amaximumvalue asafunction (Fig. 5A).Theresultisbiphasicbehavior, wherethepatterninterface 896 Fig. 7.Extracellularmatrixcomponents functioneffectively tomodulateShhdiffusivity. interface at70 evolved toberobust inthisregime andtoconsistentlypatternan Shh insolution.Thesignalingsystemthereforemayhave the diffusivity ofmonomericShhto10 signaling (Fig.1B,III).To mimicmembrane-boundShh,wereduced et al.,2001)],whichcanthenmorereadilydiffuse dorsally andinduce bound Shhintofreelydiffusing aggregates [sixShhunitslarge (Zeng is incorporatedinourmodelasacatalystforcomplexing membrane- in packaginglipid-modifiedShhintoclusters(Zengetal.,2001).Dis Hh (Kawakami etal.,2002)andhasbeenhypothesized tobeinvolved The transmembraneproteinDisinteractswithcholesterol-modified modifies Shhsignaldiffusivity Shh aggregation viaDispatchedeffectively as wellatsteadystate. –4 1 -10 nM), mostShhwas absorbedintothehexameric form.The RESEARCH ARTICLE –1 nM), asufficient aggregate ofhighdiffusivity was formed ␮ m. Thisbiphasicbehavior isobserved at –7 A cm 2 /s, anestimateforthediffusion constantof –10 cm 2 /s andobserved the t =83 hours B ) TheGli1protein interface positionat Gli3R andGli3Agradient(Fig.2H,F, andMovies 1-8inthe for Initially, Shhlevels rapidlyescalateandextend deepintothetissue profiles canhelptobothinterpretandguideexperimentation. and extracellular Shhnetwork constituents.Fullknowledge ofsuch simulation predictsahighlydynamicprofileforbothintracellular 26) (Ericsonetal.,1996;Ericson1997b;Roelink1995). analyzed duringacrucial~3-daydevelopmental window (stages10- with theShhsignalingsystemonpatterningdynamicswere influence ofanumberparametersandmechanismsassociated aggregate formationondevelopmental patternformation.The surface andECMcomponents,intracellulartrafficking, and investigate therelative impactsoffreediffusion, bindingtocell We have simulatedShhtransportandsignalingintheneuraltubeto DISCUSSION modify thepattern. nM (Looetal.,2001),relatively highlevels ofHSPGarerequiredto transport. However, foranestimatedShhaffinity for HSPGof350 increases therangeofeffective Shhsignalingbyhinderingits functions analogouslytoreduceShhdiffusivity and,paradoxically, Adding immobilizedHSPGtothesystem[5-30 broad region nearitssource,leadingtoadorsalshiftintheinterface. HSPG, thisECMcomponentcanconcentrateShhwithinarelatively effectively signal(asinFig.5). However, atintermediaterangesof large distances,leadingtoadilutionofthefactor tolevels toolow to Shh diffusion isunhindered,andthemorphogenrapidly spreadsto effectively signal.Bycontrast, atvery low HSPGconcentrations, that prevents freeShhfrombuilding uptolevels sufficiently highto HSPG concentrationsactasahigh-capacitymorphogen‘sponge’ a functionofHSPGextracellular concentration(Fig.7A,B).High Fig. 1B(Gouldetal.,1995)].Abiphasicresponsewas observed as steady statemorphogenprofiles(Eldaretal.,2003). from thesource,consistentwithprevious theoreticalstudiesof decay closetothemorphogensourceandaslow decayfurtheraway profile (approximatelyshown inFig.2Efor thereby misinterprettheligandsignalingrange.ThesteadystateShh profile onlyatlatertimescouldmisstheearlyShhbuild-up and (Fig. 2E).Therefore,experimental analysisoftheShhconcentration in ourpatterningresults(0-24hours), B With thecore-signalingpathway (dashedcircleinFig.1B),the t <20 hours,followed bysubstantialreductionsatlongertimes ( Accumulation A ) Gli1intracellularconcentrationat Signal t =83 hoursisshownatvariouslevels of Dispersal Signal there isasmoothGli1,Ptc, Development 133(5) HSPGmechanism t >60 hrs)hasarapid Note thatearly ␮ M] therefore t =83 hoursis

DEVELOPMENT transducing asignal. Ashuntinanelectricalcircuit isanalternate target, yetHipmediatesShhendocytosis anddegradation without Ptc, HipalsobindsShhwithhigh affinity andisaShhtranscriptional Ptc isnottheonlyreceptorthat mediatesliganddegradation. Like Vertebrate Shhpatterningcanbefurthercomplicated bythefact that Intracellular degradation canshunttheShhsignal match orpredictfuturepatterningresults. interactions arefurtherelucidated,would helpupdatethe modelto the transcriptionfactors Gli1-Gli3,Nkx2.2,Pax6 andothers,asthese incorporation ofmoredetailedmechanismsinteractionbetween of markers ofdifferent cellfates (Laietal.,2004).Finally, future into thisspatialmodel,mayaccountforthetransientco-expression model, stochasticeffects, whichcaninthefuturebeincorporated to anMNfate. Aswehave previously discussedinasinglecell express MNmarkers (Ericsonetal.,1996)orpermanentlycommit downstream ofGlimayreveal whetherthesecellstransiently induction kineticsforthenext generationsoftranscriptionfactors threefold increasesinGli1,andadeeperinvestigation ofthe certain borderlinecells(Fig.2H)experience transient two- or that have beenfoundtotriggercellfate switching.Itisnotablethat complexes ina stem cells(Niwa etal.,2000)andthethreefoldincreaseinSMAD with thetwofold increaseinOct3/Oct4expression inembryonic t difference acrosstheV3/MNinterface position atapproximately Gli expression levels corresponds toatwo- tothreefoldGli1 same (datanotshown). Thesevenfold increaseabove basal/initial nM) increases,andallofourconclusionsremainqualitatively the occurring atarangeofthresholdsfromthree-totenfoldGli(4.9-16.3 t time ofV3specification>11nM(or7 from itsinitialbasalconcentration[i.e.aGli1atthe specification couldbeestablishedatasevenfold increaseinGli1 Materials andmethods),themodelpredictsthatV3cellfate chick V3/MNpatterningusedforourparameterestimates(see neural tube;however, given theShhthresholdandkineticdatafrom been experimentally testedforV3/MNpatterninginthe vertebrate Shimizu andGurdon,1999).Quantitative differences inGlihave not gradient canoccuratthetranscriptionfactor level (Niwa etal.,2000; role ofgeneexpression dynamicsintissuepatterning. time. However, thisimportantwork provides strongevidence forthe and exogenously introducedGli3isexpressed atlevels thatvary over endogenous Gli1,Gli2orGli3expression isnotdirectlymeasured, comparison betweentheseresultsandoursimulations.Inparticular, although several experimental detailsprecludeadirect,quantitative for agradedGli3profileinearlypatterning(Stamatakietal.,2005), especially inthemoredorsalsections.Recentwork supportsarole uncharacterized Ptcpromoter)arelikely tomodulate in themodel(e.g.Shh-independentsignalsinfluencingrelatively supplementary material),andatlatertimesprocessesnotincluded graded profileconsistentwithourresults(seeFig.S5inthe the Ptcprofileinneuraltubeindicateahighlydynamic,initially (Lei etal.,2004;Stamataki2005).Inparticular, snapshotsof consistent withsmoothconcentrationgradientsintheMNdomain stains forGliorPtcexpression attimesbeforesteady-stateare accurately predictstheirexpression patterns,andmany experimental stage 12through26canfurthertestdirectlywhetherourframework the expression ofGli1,Gli3orPtcatabroadrangetimesfrom discrete interface at72hours(stage16-26).Quantitative assaysof supplementary material),but thisprofilebegins tosharpenintoa Signal dynamicsinShhtissuepatterning =50 hours(Fig.2H).Therefore,themodelbehavior isconsistent =0)]. We testedmodelbehavior forV3cellfate specification The mechanismbywhichasinglecellinterpretsmorphogen Xenopus blastula cell(ShimizuandGurdon,1999) ϫ Gli1 concentrationat ptc expression, concentrates the ligand. experimental threshold of detection,whereasthelipidmodification form mayberapidlydilutedwithin thetissuetofall below the our resultsindicatethattherapidly diffusing, non-lipid-modified modification was necessary forlong-rangetransport.Bycontrast, (see Lewis etal., 2001).Theinterpretationwas thatlipid ligand detectiononlyatlower levels andmuchclosertothesource the source,whereasknock-inofanon-lipidmodifiedShhled to In onestudyinthevertebrate limb,Shhwas detected~200 range two additionalcelllayersfurtherfromthefloorplate (Fig.5C). 1992). ThisreductionmayactuallyhelpShhtoextend itssignaling the diffusivity toarangebetween10 ~1 a typical20kDaproteininsolutionhasdiffusivity oforder tube andtherebyextend itssignalingrange(Fig.5A).Specifically, constants canactuallyconcentratethesignalinventral neural 2001; Ericsonetal.,1997a;Gritli-Linde2001). the neuraltubeover 20celldiameters(>200 studies have demonstratedthelongrangesignaling abilityofShhin the reduceddiffusivity accompanying membraneassociation,many al., 1998)andaC-terminalcholesterol(Porteret1996).Despite tethers duringitssynthesis,aN-terminalpalmiticacid(Pepinsky et associates withthemembranethroughadditionoftwo lipid anchorage oftheligandbyhydrophobicmodification.Shh to reconcile:thelong-rangesignalingabilityofShhandmembrane ostensibly opposingexperimental observations have beendifficult range, othermechanismsmayunexpectedly enhance it.Two Although receptorbindingcanrestrictthemorphogensignaling signal Restricting diffusion canpropagate amorphogen the cellsurface Hipvariant, Ptc,oreven HSPG(datanotshown). extend theShhsignalingrangebyprotectingfrom bindingto modeling resultssuggestthatthisnew mechanismmaypotentially been foundinthematurebrain(Coulombeetal.,2004).Our 2005). Interestingly, soluble,diffusible formsofHiphave recently very consistentwithrecentexperimental work (Stamatakietal., (Fig. 4),andthenon-cell-autonomousnatureofthisexpansion, is The ventralization ofthetubeobserved whenHipisoverexpressed slow (ChuangandMcMahon,1999;Jeong2005). neural tubewhereHip-Shhcomplex internalizationappears tobe pathway maybemodulatedindifferent organisms, asinthemouse concentration andextent ofHipupregulation, otherratesintheHip regions oftheoralaxis(Coulombeetal.,2004).Otherthanbasal in toothdevelopment, thusrestrictingtheShhsignalingtospecific the spreadofexcess Shhligandbeyond odontogenicmesenchyme Chuang etal.,2003;Tojo etal.,2002).For example, Hipprevents Hedgehog signalingwithgreatspatialprecision(Chiangetal.,1999; signaling arebothparametersthatvertebrates mayusetoregulate centers, itsbasalconcentrationandextent ofupregulation uponShh gradients (Eldaretal.,2003). patterning, amechanismpreviously proposed for morphogen molecules like Hip,limitShhpenetrationandcan‘stabilize’ 2005). Negative-feedback loops,whichestablishshuntsvia organisms (ChuangandMcMahon,1999;Jeong attenuates Shhsignaling,consistentwithseveral studiesinvarious shunting byPtcandHip,asseeninthemodelingresults(Fig.4A,B), degradation thatdivert amorphogenfromsignaling.Intracellular analogous tothereceptor-mediated endocytosis andensuing pathway thatdiverts currentaway fromtheremainderofcircuit, The simulationcounterintuitively predicts thatlower diffusion Although Hipexpression hasbeendetectednearallShhsignaling ϫ 10 –7 cm 2 /s, andhydrophobicmodificationislikely todecrease RESEARCH ARTICLE –8 and 10 –10 ␮ m) (Briscoeetal., cm 2 /s (Creighton, ␮ m from 897

DEVELOPMENT 2001). AsHSPGisactively remodeledbyproteasesinmany tissues, patterning (Gouldetal.,1995;Inatani2003;Yamaguchi, theirfunctionalrolesinneuraltube nervous system,suggesting mannerinthemammaliancentral developmentally regulated involved intheirsynthesis areabundantly expressed ina HSPG concentration(Fig.7A).BothHSPGsandtheEXTgenes can eitherlengthenorrestrictthesignalingrangedependingon a very simplemechanism,thereversible bindingofShhtoHSPG, 2000; Rubinetal.,2002;The1999).Ourresultsindicatethat (Bornemann etal.,2004;Giráldez2002;PonsandMarti, presentation, stabilizationandaccumulationhasbeendifficult et al.,2004). operating in Shh aggregation maybeageneraltransportmodulatingmechanism have additionalfunctionsintheHedgehogpathway, Dis-catalyzed significant controlover therangeofsignaling.AlthoughDismay (Kawakami etal.,2002),indicatingthatthismechanism exerts producing cellsintheventral neuraltube,somiteandlimb specified, andShhimmunoreactivity isdetected onlyinShh- neural tubeof aggregate andtheDis-catalyzedrateofaggregate generation.Inthe response intheV3/MNpatterntobothdiffusivity ofthe Analogous tothemonomericShhresults(Fig.5),thereisabiphasic diffusible Shhaggregates canpropagateaShhsignal(Fig.6A,B). modeling resultsshow thatDis-catalyzedaggregation ofhighly quantify aspatialprofileforShhaggregates intheneuraltube,our the signalingrangeofShh.First,althoughexperiments have yetto Via independentmechanisms,bothDisandECMcanalsoextend Mechanisms modulatingliganddiffusion 898 are active. particular distance from thesource depending onwhichmechanisms above the2.5nMShhsignalingthreshold andcanbetunedtoa tissue, thereby decreasing extracellularShh.V3specificationoccurs the entire tissue.Shunting mechanisms degradeShhovertheentire transport alongtheaxis,thereby creating ashallowShhgradientover By contrast,mechanismsthatinduce signaldispersalpromote Shh transport, thereby causing high accumulationofShhnearthesource. Mechanisms thatpromote thesignalaccumulationregime hinderShh regime, asignaldispersalregime, orashuntingmechanism. mechanisms ofthewild-typechickembryo:asignalaccumulation concentration versusdistanceprofile isshownforcellsthathave gradient. Fig. 8.Three classesofmechanismsmodifytheShhextracellular Distinguishing amongthepotentialrolesofECMinligand RESEARCH ARTICLE An intermediatesnapshot(~30hoursaftersecretion) ofthe Drosophila dis mutant mice,ventral fates arenotproperly (Burke etal.,1999)andzebrafish(Nakano throughput siRNA approaches have recently identifiednovel mechanisms canaccountforanovel phenotype.For example, high experimentation, andthey cantestwhetherseveral hypothesized that iscurrentlyknown aboutasystem,they canguide/suggestfuture they testwhichexperimental resultscanbeaccountedforwithall important instudyingtissuepattering bymorphogens. reasons, accuratemonitoringofcellfate asafunctionof timeis loses competenceareirrelevant totissue patterning.For allofthese signals, steadystatemorphogengradientsestablishedaftera cell considered inourmodel,canbetransientandregulated byseveral cellular competencetoamorphogen,phenomenonnot yet similar tothoseofShh(LeGoodetal.,2005).Lastly, because regulated byitshydrophobicmodifications,whichareintriguingly range, asthestabilityandthereforesignalingrangeofNodal are morphogen degradation duringtransportcandetermineitssignaling Shh concentrationlevels maybeimportant forspecification.Third, determinants ofMNspecification,suggestingthatthesequence of secretion intheneuraltube(Ericsonetal.,1996)werecrucial entire morphogentransportprocess.Second,waves ofShhsource clearly doesnotonlyoccuratoraftersteadystatebut throughoutthe Wolff etal.,2003;Yang etal.,1997)indicatesthatspecification Joyner, 2004;Harfeetal.,Kohtz etal.,1998;Park etal.,2004; to thetimeacellisexposed toagiven Shhconcentration(Ahnand morphogen systemssupports.First,inthevertebrate limb, sensitivity patterning, ahypothesisthatemerging evidence inavariety of can overlook many oftheprocessesthatcontribute totissue Correlating patterningwithmorphogengradientsonlyatsteadystate Dynamic informationthrough modeling to thefarthest transport. sensitivity would indicatethatsignaldispersal mechanismsgive rise result inthedeepestShhtransport,whereasanassaywitha0.5nM sensitivity would indicatethatsignalaccumulation mechanisms sensitivity. For example, immunostainingforShhwitha2.5nM that experimental interpretationsarehighlydependent onassay interpreting experimental results,astheintersectingprofiles indicate spatial Shhconcentrationprofile.Finally, cautionshouldbetaken in degradation oftheShhsignalacrossentireprofileto decreasethe Furthermore, shuntingmechanismspromoteintracellular source. Signalingrangeismaximizedbetweenthesetwo extremes. concentration issufficiently hightochangecellfate onlynearthe a shallow signalgradientover thedeveloping field,suchthatthe signal dispersalmechanismspromotehighShhdiffusion toprovide restricting morphogenaccumulationtonearthesource.Bycontrast, (Fig. 8).SignalaccumulationmechanismslimitShhdiffusion by in whichaccessoryShhtransportmechanismsmodulatepatterning to concentratethesignal. whereas ECMcomponentsfunctionasadditionaldiffusion barriers freely diffusible compoundsallows ittoovercome diffusion barriers, a key parameter. Thisbehavior occursbecauseaggregating Shhinto the effective signalingrangeundergoes amaximumasfunctionof ‘biphasic’ behavior (asseeninFig.5withShhdiffusivity), where mechanism (Fig.6)andECMfunction7)indicateasimilar supplementary material). target, canalsomodulateligandtransport(seeFig.S2inthe results alsoindicatethatvitronectin,adirectShhtranscriptional parameters tomodulateligandsignalinginparticulartissues.Our HSPG concentrationandaffinity canserve asrobust, tunable and theligandaffinity forHSPGcanbecorrespondinglymodulated, Mechanistic modelsserve several rolesindevelopmental biology: This analysishasledtotheidentificationofthreemajorregimes Simulations ofboththeDis-catalyzedligandaggregation Development 133(5)

DEVELOPMENT propagate theHedgehogsignalwhenrequired. have beenevolutionary ‘plugged’intoparticulartissuestorestrictor may intriguinglysuggestfurtherexperiments onhow thesemodules of numerousmodularmechanismsintheHedgehogpathway, and neural tubepatterning.Futuremodelingwork canexplore theeffects on how thesemechanismswork inconcertto provide robust Shh tissue patterning.Theresultsguideandsuggestfurtherexperiments acting atvarious timesregulate morphogentransportandmodulate respectively, totestthepredictedbiphasicresponses. in Figs4,6and7,Fig.S1(inthesupplementarymaterial), levels ofactive Hip,Dis,HSPGandvitronectintothelevels shown vitronectin. Theconcentrationofsuchantibodieswould tunethe can beincubatedinblockingantibodiesagainstHip,Dis,HSPGor V3 neuronswithincreasingsecretion.Finally, neuraltubeexplants of theV3/MNinterface asmoreMNareproducedattheexpense of promoter, andthemodelcanbeusedtopredictpreciseposition Shh canbevaried inthefloorplatethroughuseofaregulable induce Shhsignaldispersal(Fig.8).Second,thesecretionrateof increased (Nguyenetal.,2001),highlevels ofsolubleHSPGwould the spreadofmoleculeswithanHSPGinteractiondomainhave been injecting solubleHSPG.Similartoexperiments inthe brain where diffusivity (Fig.5).Likewise, Shhdiffusivity canbetunedby 2004) ispredictedtopatterndiffering depths,asafunctionofShh forms ofShhwithvarying extents oflipidmodification(Fengetal., tissues whereShhtransportisinvolved. First,knock-inofvarious to analyzeShhpatterningintheneuraltube,andpotentiallyother parameter thatshouldbeexperimentally measured. not yetmodeled(Epsteinetal.,1999),isahighlyimportant patterning processthroughtheactivity ofahighlycomplex promoter the rateofShhsecretionfromfloorplate,whichfeeds geometries andatvarious times.Finally, thesimulationindicatesthat elements areadded(orsubtracted)asthey arise(ordie)inirregular expand thecurrentstaticmodelgeometrytoa‘living mesh’,sothat effects ofcelldivision anddeathduringpatterning.Futurework can this finiteelementnumericalapproachisthatitcanincorporatethe complexes (datanotshown). Furthermore,auniqueadvantage of even withextremely fast intracellular transportratesofShh-Megalin (McCarthy etal.,2002),aslong-rangesignalingisnotobserved, Megalin asanactive Shhtransporterthroughthecytoplasm our preliminarymodelingwork doesnotsupportafunctionof yet known (Carpenteretal.,1998;Ding1998). For example, proteins, whoseprecisemechanismintheHedgehogpathway isnot Bai, C.B.,Stephen,D.andJoyner, A.L. can alsobeincluded,suchasPtc2 be usedtotesttheirpotentialmechanismsofaction.Othermolecules components oftheHhpathway (Lumetal.,2003),andmodelingcan Signal dynamicsinShhtissuepatterning Bornemann, D.J.,Duncan,J.E.,Staatz,W.,Bornemann, Selleck, S.andWarrior, R. Ahn, S.andJoyner, A.L. References http://dev.biologists.org/cgi/content/full/133/5/889/DC1 Supplementary materialforthisarticleisavailableat Supplementary material Committee Award andNIHNS048248toD.V.S. CancerResearchFellowship toK.S.andaUniversityofCalifornia Coordinating This workwassupportedbyaNationalScienceFoundationGraduate 1938. Hedgehog andDecapentaplegic signalingpathways. Abrogation ofheparansulfatesynthesisinDrosophila disruptstheWingless, Gli3. by hedgehogisglidependentandinvolvesanactivatorfunctionof patterning positive hedgehogsignalingduringmouse limbpatterning. In conclusion,wehave analyzedhow complex mechanisms The modelguidesandpredictsnumerousadditionalexperiments Dev. Cell 6 , 103-115. (2004). Dynamicchangesintheresponse ofcellsto (2004). Allmouseventralspinalcord , Megalin, andtheYou classof Development Cell 118 131 , 505-516. , 1927- (2004). Burke, R.,Nellen,D.,Bellotto,M.,Hafen,E.,Senti,K.-A.,Dickson,B.J.and Gould, S.E.,Upholt,W. B.andKosher, R.A. Ericson, J.,Muhr, J.,Placzek,M.,Lints,T., Jessell,T. M.andEdlund,T. Epstein, D.J.,McMahon,A.P. andJoyner, A.L. Ding, Q.,Motoyama,J.,Gasca,S.,Mo,R.,Sasaki,H.,Rossant,J.andHui,C. Crick, F. Chiang, C.,Swan,R.Z.,Grachtchouk,M.,Bolinger, M.,Litingtung,Y., Chen, Y. andStruhl,G. Carpenter, D.,Stone,D.M.,Brush,J.,Ryan,A.,Armanini,Frantz,G., Britto, J.,Tannahill, D.andKeynes,R. Briscoe, J.,Chen,Y., Jessell,T. M.andStruhl,G. Dillon, R.,Gadgil,C.andOthmer, H.G. Coulombe, J.,Traiffort, E.,Loulier, K.,Faure, H.andRuat,M. Chuang, P.-T., Kawcak,T. N.andMcMahon,A.P. Briscoe, J.,Pierani,A.,Jessell,T. M.andEricson,J. Ericson, J.,Briscoe,Rashbass,P., vanHeyningen,V. andJessell,T. M. Ericson, J.,Morton,S.,Kawakami,A.,Roelink,H.andJessell,T. M. Han, C.,Belenkaya,T. Y., Wang, B.andLin,X. Gritli-Linde, A.,Lewis,P., McMahon, A.P. andLinde,A. Giráldez, A.J.,Copley, R.andCohen,S.M. Feng, J.,White,B.,Tyurina, O.V., Guner, B.,Larson,T., Lee,H.Y., Karlstrom, Ericson, J.,Rashbass,P., Schedl,A.,Brenner-Morton, S.,Kawakami, A.,van Eldar, A.,Rosin,D.,Shilo,B.Z.andBarkai,N. Creighton, T. E. Chuang, P.-T. andMcMahon,A.P. Chen, M.-H.,Li,Y.-J., Kawakami,T., Xu,S.-M.andChuang,P.-T. transducing hedgehog. to therelease ofcholesterol-modified hedgehogfrom signalingcells. Basler, K. 110. signaling intheearlyexpansionofdevelopingbrain. motor neuron identity. Two criticalperiodsofSonicHedgehogsignalingrequired forthespecificationof process. control thecell-to-cellmovementofHedgehogbyadynamin-independent activity ofhedgehogsignalingpeptides. whereabouts ofamorphogen:direct evidenceforshort-andgradedlong-range embryogenesis. chicken syndecan-3asaheparansulfate proteoglycan anditsexpression during 2 the secreted enzymenotum shapesthewinglessmorphogengradient. withintheneuraltube. common signalforventralpatterning Sonic hedgehoginducesthedifferentiation ofventralforebrain neurons: a mechanisms. central nervoussystemisregulated byHnf3-dependentand-independent Sonic hedgehogtranscriptionalongtheanteroposterior axisofthemouse 646. differentiation inGli2mutantmice. (1998). DiminishedSonichedgehogsignalingandlackoffloorplate 10157. Sonic hedgehoginlimbdevelopment. W. H.Freeman. soluble forms. Hedgehog interactingprotein inthemature brain:membrane-associated and modulated byinductionofaHedgehog-bindingprotein. morphogenesis. et al. Robertson, E.K.,Cooper, M.K.,Gaffield, W., Westphal, H.,Beachy, P. A. 659. protein complexandlong-rangesignalinginvertebrates. Palmitoylation isrequired fortheproduction ofasolublemultimericHedgehog 95 receptors forthevertebratehedgehogprotein family. Rosenthal, A.andSauvage,F. J.d. 803-815. sonic hedgehogintheneuraltube. form ofpatchedprovides evidencefordirect long-rangemorphogenactivityof neural tube. protein codespecifiesprogenitor cellidentityandneuronal fateintheventral Dev. modulates Fgfsignalingduringbranchingmorphogenesisofthelung. mammalian HedgehogsignalingbytheHedgehog-bindingprotein, Hip1, the ventralneuraltube. (1997a). Gradedsonichedgehogsignalingandthespecificationofcellfatein hedgehog N-andC-terminallipids. R. O.andKohtz,J.D. 180. cell identityandneuronal fate inresponse togradedShhsignaling. Heyningen, V., Jessell,T. M.andBriscoe,J. degradation underliesrobustness ofmorphogengradients. , 667-676. , 13630-13634. 17 (1999). Essentialrole forSonichedgehogduringhairfollicle (1970). Diffusion inembryogenesis. , 342-347. Development (1999). Dispatched,anovelsterol-sensing domainprotein dedicated Cell Development (1992). Mol. Cell.Neurosci. Dev. Biol. Dev. Biol. 101 , 435-445. Proteins: StructuresandMolecularProperties 131 (1996). Dualroles forpatchedinsequesteringand Cell (2004). Synergisticandantagonisticroles oftheSonic Cell Cold SpringHarb.Symp.Quant.Biol. 168 205 , 73-82. 87 126 87 , 438-451. , 661-673. , 1-9. , 553-563. , 281-292. (1999). Vertebrate Hedgehogsignaling 25 Mol. Cell Development Development , 323-333. (1998). Characterizationoftwopatched Proc. Natl.Acad.Sci.USA (2002). Acriticalrole forsonichedgehog (2003). Short-andlong-rangeeffects of Dev. Biol. RESEARCH ARTICLE Nature 7 (1995). Characterizationof , 1279-1291. (1997b). Pax6controls progenitor (2002). HSPGmodificationby (2003). Self-enhancedligand (2004). Drosophila glypicans (1999). Regionalizationof (2001). Ahedgehog-insensitive 255 131 125 236 (2003). Feedbackcontrol of (2000). Ahomeodomain , 40-42. , 4357-4370. , 2533-2543. Proc. Natl.Acad.Sci.USA , 364-386. Nat. Neurosci. Nature Genes Dev. (2001). The Dev. Cell Cell 62 (2004). , 451-466. 397 100 81 (2004). . NewYork: Cell , 617-621. , 747-756. , 10152- 18 Cell 5 (1996). Genes , 635- Dev. Cell 5 , 641- 90 , 103- (1995). 99 , 169- 899 ,

DEVELOPMENT Jeong, J.andMcMahon,A.P. Park, H.C.,Shin,J.andAppel,B. McCarthy, R.A.,Barth,J.L.,Chintalapudi,M.R.,Knaak,C.andArgraves,W. Harfe, B.D.,Scherz,P. J.,Nissim,S.,Tian,H.,McMahon,A.P. andTabin, C.J. 900 Nguyen, J. B., Sanchez-Pernaute, R.,Cunningham,J.andBankiewicz,K.S. Nguyen, J.B.,Sanchez-Pernaute, Martinez-Morales, J.R.,Barbas,A.,Marti,E.,Bovolenta,P., Edgar, D.and Marigo, V. andTabin, C.J. Jessell, T. M. Incardona, J.P., Gruenberg,J.andRoelink,H. Incardona, J.P., Lee,J.H.,Robertson,C.P., Enga,K.,Kapur, R.P. and Kawakami, T., Kawcak,T. N.,Li,Y.-J., Zhang,W., Hu,Y. andChuang,P.-T. Inatani, M.,Irie,F., Plump,A.S.,Tessier-Lavigne, M.andYamaguchi, Y. Niwa, H.,Miyazaki,J.andSmith,A.G. Nakano, Y., Kima,H.R.,Kawakamib,A.,Roya,S.,Schierb,A.F. and Le Good,J.A.,Joubin,K.,Giraldez,A.J.,Ben-Haim,N.,Beck,S.,Chen,Y., Lander, A.D.,Nie,Q.andWan, F. Y. Lai, K.,Robertson,M.J.andSchaffer, D.V. Kohtz, J.D.,Baker, D.P., Corte,G.andFishell, Litingtung, Y. andChiang,C. Lum, L.,Yao, S.,Mozer, B.,Rovescalli,A.,Von Kessler, D.,Nirenberg, M.and Loo, B.-M.,Kreuger, J.,Jalkanen,M.,Lindahl,U.andSalmivirta,M. Lewis, P. M.,Dunn,M.P., McMahon,J.A.,Logan,M.,Martin,F., St- Lei, Q.,Zelman,A.K.,Kuang,E.,Li,S.andMatise,M.P. the developingneuraltube. hedgehog antagonistspatched1andHhip1. neural tubearebypartiallyoverlappingfeedbackactivitiesofthe governed 995. the segregation ofpatchedandsmoothenedinendosomes. S. and transcriptionalcodes. vertebrate digitidentities. (2004). Evidenceforanexpansion-basedtemporalShhgradientinspecifying Genet. 3/4 definesdifferentiation, dedifferentiation orself-renewal ofEScells. increases TKgenetransferin theratbrain. (2001). Convection-enhanceddeliveryofAAV-2 combinedwithheparin 381-392. Chem. Development the neuraltubeandpromotes thedifferentiation ofmotorneurons. Rodriguez-Tebar, A. 12049. tethered SonichedgehogbyPatched-1. Roelink, H. signaling systemasabistablegeneticswitch. defective inhedgehogsignaling. (2002). Mousedispatchedmutantsfailtodistributehedgehogproteins andare heparan sulfate. (2003). Mammalianbrainmorphogenesisandmidlineaxonguidancerequire mutation disruptsHedgehogsignallinginthezebrafishembryo. Ingham, P. W. Chem. Binding ofheparin/heparansulfatetofibroblast growth factor receptor 4. functions inthedevelopingspinalcord. of gradedHedgehogsignalingbyacombinationGli2andGli3activator range. Schier, A.F. andConstam,D.B. diffusion? Sonic Hedgehog. the mammaliantelencephalonismediatedbychangesinresponsiveness to in Drosophila cultured cells. Beachy, P. A. 979-985. mediated byanantagonisticinteractionbetweenshhandgli3. of signalingbyPtc1. hedgehog isrequired forlong-rangesignalingactivityand effective modulation Jacques, B.andMcMahon,A.P. (2002). Megalinfunctionsasanendocyticsonichedgehogreceptor. RESEARCH ARTICLE Curr. Biol. 277 276 24 , 372-376. Dev. Cell , 25660-25667. , 16868-16876. (2000). Neuronal specificationinthespinalcord: inductivesignals (2000). Receptor-mediated endocytosisofsolubleandmembrane- 124 (2003). IdentificationofHedgehogpathwaycomponentsbyRNAi (2004). Inactivationofdispatched1bythechameleon Science 15 Development , 5139-5147. 2 , 31-36. Cell , 785-796. (1997). Vitronectin isexpressed intheventralregion of 5647 105 Cell (1996). Regulationofpatchedbysonichedgehogin Nat. Rev. Genet. Science Proc. Natl.Acad.Sci.USA , 599-612. (2000). Specificationofventralneuron typesis (2005). Growthofthemammalian andpattern , 1044-1046. 118 125 Development (2004). Spatialandtemporalregulation of , 517-528. (2005). Nodalstabilitydeterminessignaling (2001). Cholesterol modificationofsonic , 5079-5089. 299 (2002). Domorphogengradientsariseby Development , 2039-2045. (2000). Quantitativeexpression ofOct- Proc. Natl.Acad.Sci.USA NeuroReport 1 (2004). Thesonichedgehog , 20-29. Development Biophys. J. 129 (2002). Sonichedgehoginduces (1998). Regionalizationwithin , 5753-5765. 131 93 12 86 , 9346-9351. , 3593-3604. (2004). Transduction , 1961-1964. , 2748-2757. 132 Curr. Biol. Nat. Neurosci. , 143-154. Dev. Biol. 97 , 12044- 12 (2001). Nat. J. Biol. , 983- J. Biol. 269 3 , , Wijgerde, M.,McMahon,J.A.,Rule,M.andA.P. Pepinsky, R.B.,Zeng,C.,Wen,P., D.,Rayhorn, Baker, D.P., Williams,K.P., Park, H.L.,Bai,C.,Platt,K.A.,Matise,M.P., Beeghly, A.,Hui,C.C., Wolff, C.,Roy, S.andIngham,P. W. Persson, M.,Stamataki,D.,teWelscher, P., Andersson,E.,Bose,J.,Ruther, Zeng, X.,Goetz,J.A.,Suber, L.M.,Scott,W. J.,Schreiner, C.M.and Yang, Y., Drossopoulou, G.,Chuang,P.-T., Duprez, D.,Marti,E.,Bumcrot, D., Yamaguchi, Y. Riddle, R.D.,Johnson,L.,Laufer, E.andTabin, C. Ricklefs, R.E.andStarck, J.M. Porter, J.A.,Young, K.E.andBeachy, P. A. Pons, S.andMarti,E. Turing, A.M. Shimizu, K.andGurdon, J.B. Tojo, M.,Kiyosawa,H.,Iwatsuki,K.andKaneko,F. The, I.,Bellaiche,Y. andPerrimon,N. Takei, Y., Ozawa,Y., Sato,M.,Watanabe, A.andTabata, T. Stamataki, D.,Ulloa,F., Tsoni, S.V., Mynett,A.andBriscoe, J. Ruiz iAltaba,A. Rubin, J.B.,Choi,Y. andSegal,R.A. Roelink, H.,Porter, J.A.,Chiang,C.,Tanabe, Y., Chang,D.T., Beachy, P. A. progenitor domainsinthepresumptive mammalianspinal cord. requirement forHedgehogsignalingnormalspecification ofallventral Chem. Identification ofapalmiticacid-modifiedformhumansonichedgehog. Bixler, S.A.,Ambrose, C.M.,Garber, E.A.,Miatkowski,K.etal. Development have defectsinSHHsignalingcombinationwithaGli2mutation. Nakashima, M.andJoyner, A.L. 131 ventral spinalcord precursor specificationbyHedgehogsignaling. Dev. Biol. diverse roles inneurogenesis, axonguidance,andsynaptogenesis. embryo. induced bydistinctlevelsandtimingofhedgehogactivityinthezebrafish 2849-2864. Spectrum Avian theAltricialPrecocial GrowthandDevelopment.EvolutionWithin cord requires Gli3transcriptionalrepressor activity. U., Ericson,J.andBriscoe, long-range signaling. Robbins, D.J. 4404. regulation ofanteroposterior polarityinthechicklimb. Relationship betweendose,distanceandtimeinSonicHedgehog-mediated Vargesson, N.,Clarke,J.,Niswander, L.,McMahon,A.etal. Lond. Ser. BBiol.Sci. sulfate proteoglycans. Drosophila EXTgenesshapemorphogengradientsthrough synthesisofheparan tube. gradient ofGliactivitymediatesgradedSonicHedgehogsignalingintheneural gradient interpretation. transduction from activinreceptor tonucleusanditsrelevance tomorphogen mediates thepolarizingactivityofZPA. hedgehog signalingproteins inanimaldevelopment. Development matrix protein vitronectin toinducespinalmotorneuron differentiation. basal cellcarcinoma. sonic hedgehogsignaltransducer, hedgehog-interactingprotein, byhuman 126 negative functions:implicationsfordevelopmentanddisease. sonic hedgehogresponses duringdevelopment. Cell through toutvelu-dependentsynthesisofaheparansulfateproteoglycan. autoproteolysis. concentrations oftheamino-terminalcleavageproduct ofsonichedgehog and Jessell,T. M. , 5959-5969. , 3205-3216. 4 , 633-639. Genes Dev. 273 Curr. Biol. 12 (ed. R.E.RicklefsandJ.M.Starck). NewYork: Oxford UniversityPress. , 14037-14045. (1952). Thechemicalbasisofmorphogenesis. , 99-106. (2001). Heparansulfateproteoglycans inthenervoussystem:their 127 127 (2001). Afreely diffusible formofSonichedgehogmediates (1999). Gliproteins encodecontext-dependentpositiveand Cell 19 , 1593-1605. , 333-342. (1995). Floorplateandmotorneuron inductionbydifferent 13 , 626-641. 81 Br. J.Dermatol. (2000). Sonichedgehogsynergizeswiththeextracellular 237 Nature , 1169-1181. Development , 445-455. Proc. Natl.Acad.Sci.USA , 37-72. 411 (1999). Aquantitativeanalysisofsignal (1998). Seriesofembryonicchickengrowth. In (2002). Dorsal-ventral patterning ofthespinal (2002). Dorsal-ventralpatterning , 716-720. (2000). MouseGli1mutantsare viablebut (2003). Multiplemusclecellidentities 131 146 (2002). Cerebellar proteoglycans regulate (1999). Hedgehogmovementisregulated , 73-82. , 69. Cell (1996). Cholesterol modificationof 75 Development , 1401-1416. 96 Genes Dev. , 6791-6796. Science (2002). Expression ofa Development 133(5) (1993). Sonichedgehog Development Philos. Trans. R.Soc. 274 (2004). Three Development 129 16 (2002). Adirect Genes Dev. (2005). A (1997). , 2865-2878. , 255-259. Development , 2223-2232. Semin. Cell 124 (1998). , 4393- J. Biol. Mol. 16 ,

DEVELOPMENT