Deconvolving the roles of Wnt ligands and receptors in sensing and amplification.

2.2 MB·English

by  Tan, Rui Zhen

MolecularSystemsBiology9;Articlenumber631;doi:10.1038/msb.2012.64
Citation:MolecularSystemsBiology9:631
www.molecularsystemsbiology.com
Deconvolving the roles of Wnt ligands and receptors
in sensing and amplification
RuiZhenTan1,6,NiJi2,RemcoAMentink3,HendrikCKorswagen3andAlexandervanOudenaarden3,4,5,*
1 HarvardUniversityGraduateBiophysicsProgram,HarvardMedicalSchool,Boston,MA,USA,2 DepartmentofBrianandCognitiveSciences,Massachusetts
InstituteofTechnology,Cambridge,MA,USA,3 HubrechtInstitute,RoyalNetherlandsAcademyofArtsandSciencesandUniversityMedicalCenterUtrecht,Utrecht,
TheNetherlands,4 DepartmentofPhysics,MassachusettsInstituteofTechnology,Cambridge,MA,USAand5 DepartmentofBiology,MassachusettsInstituteof
Technology,Cambridge,MA,USA
6Presentaddress:BioinformaticsInstitute,A*STAR,Singapore138671,Singapore.
* Correspondingauthor.DepartmentofPhysics/Biology,MassachusettsInstituteofTechnology,31AmesStreet,Room68-371B,Cambridge,MA02139,USA.
Tel.: þ16172534446;Fax: þ16172586883;E-mail:[email protected]
Received13.2.12;accepted16.11.12
Establishmentofcellpolarityiscrucialformanybiologicalprocessesincludingcellmigrationand
asymmetriccelldivision.Theestablishmentofcellpolarityconsistsoftwosequentialprocesses:an
external gradient is first sensed and then the resulting signal is amplified and maintained by
intracellularsignalingnetworksusuallyusingpositivefeedbackregulation.Generally,thesetwo
processes are intertwined and it is challenging to determine which proteins contribute to the
sensing or amplification process, particularly in multicellular organisms. Here, we integrated
phenomenological modeling with quantitative single-cell measurements to separate the sensing
andamplificationcomponentsofWntligandsandreceptorsduringestablishmentofpolarityofthe
Caenorhabditis elegans Pcells. By systematically exploring how P-cell polarity is altered in Wnt
ligand and receptor mutants, we inferred that ligands predominantly affect the sensing process,
whereas receptors are needed for both sensing and amplification. This integrated approach is
generallyapplicabletoothersystemsandwillfacilitatedecouplingofthedifferentlayersofsignal
sensingandamplification.
MolecularSystemsBiology9:631;publishedonline8January2013;doi:10.1038/msb.2012.64
SubjectCategories:development;signaltransduction
Keywords: Caenorhabditiselegans;cellpolarity;phenomenologicalmodeling;Wntsignaling
Introduction
feedback regulation (Meinhardt, 1999; Weiner, 2002). For
Cellpolarityisimportantformanycellularfunctions,suchas example,duringtheestablishmentofcellpolarityinbudding
migration, axis formation, and asymmetric cell division yeast, activated Cdc42 orients the actin cytoskeleton and
(Strutt, 2001; Nelson, 2003; Silhankova and Korswagen, directsthedeliveryofmoreCdc42tomembranesiteswithhigh
2007).Conceptually,theestablishmentofcellpolarityinmost concentrations of the protein (Pruyne and Bretscher, 2000;
cellscanbethoughtofasatwo-stepprocess:sensingfollowed Wedlich-Soldner et al, 2004). These vesicles are thought to
by amplification (Weiner, 2002). The sensing machinery is contain Cdc42 therefore reinforcing the polarity axis via
usedtodetectanexternalcue.Examplesofexternalcuesfor positivefeedback(Wedlich-Soldneretal,2003).Amplification
unicellular organisms include a pheromone gradient that through positive feedback has also been reported to be
inducescellpolarityinbuddingyeastandcAMPgradientsthat involved in planar cell polarity in multicellular organisms
directsthechemotacticresponseofDictyosteliumdiscoideum (Tree et al, 2002). In this case, positive feedback serves to
(Klein et al, 1988; Arkowitz, 1999). Remarkably, many cells polarize a field of cells by amplifying differences between
are able to polarize in response to very shallow chemoat- proteinlevelsonadjacentcellsurfaces.Amplificationensures
tractant gradients as small as a 1% change in concentration robustness and is responsible for the dramatic sensitivity of
across the cell diameter (Zigmond, 1977; Baier and gradient sensing and the generation of spontaneous cell
Bonhoeffer, 1992). This shallow gradient induces a steep polarization.
intracellulargradientofsignalingmoleculesandcytoskeleton Many mathematical models have been proposed to model
componentsallowingthe cell to polarize (Parentet al,1998; theprocessesofcellpolarization(Wedlich-Soldneretal,2003;
Servantet al,2000).Afterthesensingmachinerydetectsthe Jilkine and Edelstein-Keshet, 2011). Although these models
external cue, an amplification mechanism sets in to convert haveyieldedvaluableinsightsintotheunderlyingmolecular
this spatial information into a stable polarity axis. These mechanisms required for sensing and amplification, they
amplification mechanisms are often based on positive cannotbeusedtoseparateandquantifythecontributionsof
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the different molecular components to these processes, loss of receptors phenotypically mimick the effects of ligand
particularlyintheinvivocontextofamulticellularorganism. loss.Forexample,bothlossofligandsandreceptorscauseloss
Furthermore, construction of such mechanistic models ofpolarityintheEMScell(Thorpeetal,1997).Intriguing,the
remains challenging and is only possible for a few well- phenotypeislesssevereintheligand/receptordoublemutant
studiedsystemduetothelackofdetailedknowledge.Onthe thantheligandmutant(Beietal,2002).Thissuggeststhatin
otherhand,phenomenologicalmodelsthatdescribethemain theabsenceofligands,receptorsmayberespondingtosignals
featuresofasystemthroughafewimportantparametershave thatinterferewithsettingupofthecorrectpolarity.
beenusedsuccessfulinunderstandingthegeneralfeaturesof Here, we found that Wnt signaling also regulates the
many systems (Alon, 2007; Mallavarapu et al, 2009). Here, division of the P cells, which are six pairs of symmetrically
throughtheintegrationofquantitativecellpolaritymeasure- placed cells, P1–P12, found at the left and right sides of the
ments with a phenomenological model, we separated the worm after hatching. During the first larval stage, P cells
contributions of Wnt ligands and receptors to sensing migrate to the ventral side and form a single row of cells
and amplification during establishment of polarity in the (Sulston, 1976). After migration, they divide to produce
Caenorhabditiselegans’Pcells. anterior neuronal blast cells, Pn.a, and posterior epithelial
Wnt signaling plays an important role in regulating cell daughters,Pn.p,n¼1,2,y12(Figure1A).Pcellsprovidea
polarity in many organisms and Wnts have been found convenient model system to study cell polarity for the
to be expressed in a gradient (Yoshikawa et al, 2003; following reasons. First, the establishment of cell polarity
Harterink et al, 2011). In C. elegans, loss of Wnt signaling leads to a clear observable phenotype of different cell fates
leadstocellmigrationandcelldivisiondefects(Thorpeetal, (neuronalversusepithelial)inthedaughtercells.Second,this
1997;Whangboetal,2000;SilhankovaandKorswagen,2007). is an approximate one-dimensional system with anterior–
ManyoftheseasymmetricdivisionsarecontrolledbytheWnt/ posteriorpolarity. Third,the presence of manyPcells in the
b-catenin asymmetry pathway. In this pathway, Wnts first sameanimal,allowustostudyhowtheestablishmentofcell
regulate the polarity of the mother cell through asymmetric polarityvariesalongtheanterior–posterioraxis.
protein localization (Mizumoto and Sawa, 2007a). After
division,theasymmetricproteinlocalizationleadstodifferent
Results
nuclear levelsof POP-1 and SYS-1 in daughtercells (Phillips
et al, 2007; Mizumoto and Sawa, 2007b). This mechanism
lag-2 and lin-31 reliably mark the Pn.a and Pn.p
convertsthepolarityinformationsetupinthemothercellinto
cells, respectively
differentialgeneexpressioninthedaughters(Mizumotoand
Sawa, 2007b). Although major progress has been made in ToidentifyamarkerofP-cellpolarity,wequantifiedthemRNA
uncovering new Wnt pathways and components, the exact expression of a panel of 26 genes using single-cell transcript
functionsofligandsandreceptorsremainunknown.Inmany counting(Rajetal,2008).Thispanelincludesgenesthatwere
cases,itwasfoundthatlossofligandsandreceptorsleadsto previously reported to be expressed in P cells and their
different phenotypes (Sternberg and Horvitz, 1988; Herman descendantsandalsogenesfromthemajorsignalingpathways
andHorvitz,1994).Thisisunexpectedforcomponentsacting (Wnt, Notch, FGF, EGF, and TGF). A set of about 48 single-
in the same pathway, suggesting that ligands and receptors stranded 20-mer oligonucleotides were designed for
mayhavedifferentfunctions.Buttherearealsocaseswhere visualization of each transcript. These fluorescently labeled
Figure1 IdentificationofPn.aandPn.pexpressionmarkers.(A)LineagediagramofPcells.PcellsdividetoformPn.aandPn.p.Pn.adividestogiverisetofive
differentneuronsinL1.Pn.pdoesnotdividetilltheL3stage.(B)Plotoflag-2(red)andlin-31(green)mRNAinPn.pversusPn.a.(C)(Top,left)ImageofL1larvaafter
insituhybridizationwithlag-2(red)andlin-31(green)probes.Dapiisshowninblue.(Top,bottom)Maximumprojectionimageofmultiplez-stacksthatshowslag-2(red)
andlin-31(green)expressioninPn.aandPn.pfromtheP3–P10lineages.(Right)Zoominimageofasinglestackshowingindividuallag-2andlin-31transcriptsinP8.a
andP8.p.
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oligonucleotidesarecomplementarytothetranscriptandbind levelofPOP-1andhighlevelofSYS-1intheposteriordaughter
each individual transcript. This becomes visible as a diffrac- leadstotranscriptionofWntresponsivegenes.Theamountof
tion-limited spot using fluorescence microscopy. Using a nuclearPOP-1intheposteriordaughterisregulatedbyMOM-4
custom-writtensoftware,wemanuallysegmentedtheindivi- andLIT-1proteins,whichfunctioninexportingPOP-1fromthe
dual cells and computationally determined the transcript nuclearintothecytoplasm.
number in each cell. The ratio of the expression in the Pn.a To test if the Wnt/b-catenin asymmetry pathway plays a
versusPn.pdaughterswasusedtoquantifythespecificityof similarroleinPcells,weexaminedthenuclearlevelsofPOP-1
theputativemarkers(SupplementaryTableS1).Weidentified inthedaughtercellsafterdivisioninaPOP–GFPtranslational
lag-2, a transmembrane protein of the Delta/serrate/lag-2 fusionstrain.Wefoundthattheanteriordaughterhasahigher
family,asthemostpromisingPn.amarkerhavingthelargest levelofnuclearPOP-1thantheposteriordaughter(Figure2C).
expressionratio(37.3).lin-31,agenepreviouslyreportedasa This differential level of POP-1 is also observed in other
Pn.p marker (Tan et al, 1998), was found to be the most daughter cells regulated by the Wnt/b-catenin asymmetry
promising Pn.p marker with lowest expression ratio (0.08). pathway(MizumotoandSawa,2007b).Next,wedisruptedthe
Usingthese markers,the anteriorand posteriordaughters of POP-1 branch in the asymmetry pathway by a temperature
theP3–P10cellscanbescoredwithhighconfidence(Figures shift in mom-4; lit-1 mutant worms (Takeshita and Sawa,
1Cand2C;SupplementaryFigure1). 2005).SimilartoWTanimals,bothPn.aandPn.pinmom-4;
Although both daughter cells initially inherit lag-2 mRNA lit-1mutantwormsinheritedlag-2mRNAfromthePcells.But
from the P cell, lag-2 is rapidly degraded in the Pn.p cells unlikeWTanimals,Pn.pcellscontinuetoexpresslag-2some
(Figure 2C). We quantified lag-2 and lin-31 expression by timeafterdivision(Figures2Band3B).Thislag-2expression
counting individual transcripts in the Pn.p and Pn.a cells is sustained even after Pn.p cells go on to divide in L1.
excludingcellsimmediatelyafterdivision.Weobservedthatin (Figure2D).InWTanimals,Pn.pcellsdonotdivideuntilthe
wild-type (WT) animals lag-2 and lin-31 expression is L3 stage. This suggests that upon inhibition of the Wnt/
mutually exclusive (Figure 1B). In WT animals, the lag-2 b-catenin asymmetry pathway, the Pn.p cells have adopted
countinPn.acellsisalwaysmuchlargerthanthelag-2count Pn.a-like fates where they expressed lag-2 and divide in L1.
inPn.pcells(Figure1B). This effect is similar to that observed in othercells whereby
disruption of the Wnt/b-catenin asymmetry pathwaycaused
the posteriordaughter to take on anteriorcell fate (Bertrand
and Hobert, 2009; Gleason and Eisenmann, 2010). These
Role of the Wnt/b-catenin asymmetry pathway
experiments confirm the role of Wnt/b-catenin asymmetry
in regulating P cells’ divisions
pathwayinpolarizingPcellsandshowthatlag-2expressionin
ManyasymmetricdivisionsinC.elegansareregulatedbythe the daughter cells after division is a good reflection of the
Wnt/b-catenin asymmetry pathway through polarization of polarityofthemotherPcellbeforedivision.
themothercellbeforedivision(MizumotoandSawa,2007b).
In this pathway, asymmetry localization of many regulatory
proteins(includingWRM-1andAPR-1)inthemothercellisset
NotchsignalingisnotinvolvedinsettingupP-cell
upbyWntligandsandreceptors,leadingtodifferentnuclear
polarity
levelsofPOP-1andSYS-1inthedaughtercellsafterdivision.A
high level of POP-1 and low level of SYS-1 in the anterior Since Pn.a and Pn.p express high levels of lag-2 and lin-12,
daughterleadstoinhibitionofWntsignaling,whereasalow respectively (Figure 2A), we tested for the role of Notch
Figure2 InhibitionofWnt/b-cateninasymmetrypathway.(A)InWTanimals,lag-2transcript(red)andlin-12transcript(green)arefoundinthePn.aandPn.p
respectively.(B)Inmom-4;lit-1wormsthathavebeentransferredto251Cfor9hpriorfixationtoinhibittheWnt/b-cateninasymmetrypathway,lag-2transcriptis
observedinboththePn.aandPn.p.(C)POP-1localizationishighinthePn.aandlowinPn.pafterP-celldivision.(D)BoththePn.aandPn.pdivideinL1,leadingtothe
increaseinnumberofcellsintheventralnervecord.
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signaling in P-cell polarity. To determine if Notch signaling ligand mutant (egl-20; cwn-1; cwn-2), and quintuple-ligand
mayberequiredformaintainingdifferentfatesinthePn.aand mutant(egl-20;cwn-1;cwn-2;lin-44;mom-2),somePn.pcells
Pn.p,weinhibitedNotchsignalingusingalag-1temperature- expressed lag-2 and their corresponding Pn.a cells expressed
sensitivestrain(Qiaoetal,1995).However,wedidnotobserve lin-31, suggesting that the P cell had been polarized in the
anyaberrantdevelopmentinthePn.aandPn.pcells.Wealso oppositedirection (Figure 3C;Supplementary Figure S3). We
examined animals with lin-12 loss of function mutation, found that in the triple-ligand mutant, 47.9% correctly
lin-12(n941),andsemi-dominantmutation,lin-12(n137),and polarized, 44.0% exhibited a polarity reversal, and 8.1%
didnotobserveanychangeincellfatesandtheexpressionof showedsimilarlevelsoflag-2inbothdaughtersindicativeofa
lag-2 in Pn.a and Pn.p cells (Greenwald et al, 1983). These symmetricP-celldivisionandthereforelossofP-cellpolarity.A
resultssuggestthatnotchsignalingisnotinvolvedinsetting very different phenotype was observed in the Wnt receptor
upP-cellpolarity. mutants (Figure 3D).Inthemom-5; lin-17mutant, lag-2was
often observed in both daughter cells (53.5%) and a smaller
fraction of cells correctly polarized (38.6%) or reverse
polarized (7.9%). The different phenotypes observed in the
Mutations in Wnt ligands induce polarity reversal,
ligand and receptor mutants suggest that they may play
whereas mutations in Wnt receptors induce
differentrolesinestablishingcellpolarity.Todetermineifthe
polarity loss
different phenotypes observed is due to the different roles of
To explore which Wnt ligands and receptors are involved in receptors and ligands in sensing and amplification and to
P-cellpolarity,weexaminedlag-2andlin-31expressioninPn.a further quantify the phenotypes presented in Figure 3, we
andPn.pcellsinligandandreceptormutants.WTpolaritywas constructedaphenomenologicalmodel.
observedinmostsingle-anddouble-ligandmutants,consistent Cell–cellsignalinghasbeenfoundtobeimportantinplanar
withpreviousobservationsontheredundantroleoftheWnt cell polarity models (Tree et al, 2002). Since pairs of P cells
ligands (Zinovyeva et al, 2008) (Supplementary Figure S2). (P3/P4, P5/P6, P7/P8, and P9/P10) are in contact before
However, in the double-ligand mutant (egl-20; cwn-1), triple- division,cell–cellsignalingmayplayaroleintheirdivisions.
Figure3 lag-2expressionindifferentmutants.Plotoflag-2mRNAcountsinPn.pversusPn.ainWTanimals.(A)InanimalswithinhibitionofWnt/b-catenin
asymmetrypathway,mom-4;lit-1(B),multiple-ligandmutant,egl-20;cwn-1;cwn-2,(C)anddouble-receptormutant,mom-5;lin-17(D).Dottedlinesdividetheplotof
lag-2expressioninPn.pversusPn.aintoregionsforcorrectpolarity,lossofpolarityandreversepolarity.Fractionsofcellsthatfallintothesethreeregionsareindicated
ontheplots.
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Ifcell–cellsignalingoccursbetweenpairofPcells,wewould reversepolarity)is((1þg)/2)r Dtand((1(cid:2)g)/2)r Dt,respec-
T T
expectthepolarityofdivisionbetweenthesepairsofPcellstobe tively. Here, g reflects the external gradient that ranges from
correlated. In WTanimals, all the divisions are correct hence (cid:2)1to1,r isthetotalreactionratethatsetsthetimescaleof
T
WT animals cannot be used for this analysis. Hence, we thedynamics,Dtisthetimestepofthenumericalsimulation.
calculatecorrelationinthetriple-ligandmutant(egl-20;cwn-1; To understand the behavior of the model, we ran stochastic
cwn-2) where many of the divisions are polarized in the simulationstodeterminethebehaviorofindividualcells.The
reversed direction. If there is cell–cell signaling, we would chemical master equation is also solved to obtain the
expectpairsofPcellstobothdividecorrectly,leadingtoboth distribution forapopulation of cellsattimeT.In absenceof
Pn.a daughters having high lag-2 levels, or to both divide an external gradient (g¼0), y(t) has equal probability of
with reverse polarity, leading to low levels of lag-2 in both increasing or decreasing at each step of the simulation
Pn.adaughters.Whenweexaminedthelag-2expressionlevels (Figure4A)andperformsanunbiasedrandomwalkresulting
in the anterior daughters for the anterior P cell versus the in an approximatelyGaussian distribution (symmetric about
posterior P cell in each pair (Supplementary Figure 4), no 451)atthetimeofP-celldivision(Figure4B,green).Ifg40or
significantcorrelationisfoundbetweentheirexpressionlevels go0, the probabilities of taking a left and right step are
(correlation value¼(cid:2)0.029, P-value¼0.70). This suggests unequal,resultinginabiasedrandomwalktowards901(blue)
that cell–cell signaling does not play a significant role in or01(red),respectively(Figure4AandB).Tosummarizethe
P–celldivision. informationencodedinthehistogramsofy(T)foreachsetofg
and r , we determinethefractionof thecells thatundergoes
T
correct, reverse or loss of polarity based on the following
A phenomenological model for cell polarity
classification rules: y(T)4751 (correct polarity), y(T)o151
ThepolarizationstateofthePcellisdenotedbythedynamic (reverse polarity), and 151oy(T)o751 (loss of polarity). A
variabley(t),whichisananglethatrangesbetween01(reverse coordinate on the phase diagram corresponding to the
polarity)and901(WTpolarity).WeassumethatthePcellhas particular set of g and r , will be colored with different
T
initially no polarity (y(t¼0)¼451). For subsequent times, intensitiesofblue,red,andgreendependingonthefractionsof
until the P cell divides at time T, we describe the dynamic correct,reverse,andlossofpolarity,respectively.(Figure4C)
behavior of y(t) as a one-dimensional random walk. In the As expected for g40 and high r , values of most cells are
T
simplestmodel thatonly involvesthe sensing of an external correctlypolarized.Forvaluesofgcloseto0andlowvaluesof
gradient, the probability of taking a right step (increasing y; r , most of the cells are unpolarized. However, this simple
T
towards WT polarity) or left step (decreasing y; towards model is unable to explain the coexistence of correct and
Figure4 Stochasticmodeling.Withoutfeedback(A)Schematicsshowingthedependenceofraandrpong.Forg¼0,ra¼rpandfor0ogo1,ra4rp.Valuesofra
andr donotdependony.(B)(Left)Stochasticsimulationofy fromt¼0tot¼T(divisionofPcell)(Right)Histogramsofy(T)forconstantr ¼0.05withdifferent
p a a a T
valuesofg¼0.3(blue),g¼0(green),andg¼(cid:2)0.3(red).(C)Phasediagramshowingtheparametersspaceofgandr givingrisetocorrectpolarity(blue/C),reverse
f
polarity(red/R),andunpolarizeddivisions(green/U).Dottedlinesshowtheregionofparameterspacegivingriseto35%correctpolarity(top)or35%reversepolarity
(bottom).Withfeedback(D)Schematicsshowingthedependenceofraandrpongandy.Forg¼0,ra¼rpatya¼451.For0ogo1,ra4rpatya¼451.Forboth
cases,r increaseswithy whereasr decreaseswithy.(E)(Left)Stochasticsimulationofy fromt¼0tot¼T(divisionofPcell)(Right)Histogramsofy(T)for
a a p a a a
g¼0.3andr¼0.06(blue),forg¼(cid:2)0.3andr¼0.06(red),forg¼0andr¼0.06(magneta)andforg¼0andr¼0.01(green).(F)Phasediagramshowingthe
f f f f
parametersspaceofgandr givingrisetocorrectpolarity(blue/C),reversedpolarity(red/R),unpolarizeddivisions(green/U),andcoexistenceofcorrectandreverse
f
polarity(magneta/C/R).Dottedlinesshowtheregionofparameterspacegivingriseto35%correctdivisions(top)or35%polarityflips(bottom).Theintersectionofthe
twodottedlinesshowsthecoexistenceofcorrectandreversepolarity.
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reverse polarity observed in the triple-ligand mutant catenin asymmetry pathway, which sets up polarity of the
(Figure3C). Pcell,ledtoexpressionoflag-2inbothdaughtercells.Hence,
To expand beyond this simple model, we included a y isagoodapproximationofthepolarizationstateofthe
lag-2
mechanismthatreinforcesadeviationfromthenon-polarized motherPcellatthetimeofdivisiony(T)ascalculatedbythe
state.Biologically,thisreinforcementcouldbeestablishedby, modelabove.
for example, positive feedback regulation. To introduce Todeterminethevalueofr ,weexaminedthedistributionof
b
amplification, we let the probability of taking a right step y in the mom-4; lit-1 strain and observed a Gaussian
lag-2
increasewithyandtheprobabilityoftakingaleftstepdecrease distribution (Figure 5B). Although ligands and receptors are
withy.Thesimplestwaytoreinforcedeviationistointroduce functioningproperlyinthemom-4;lit-1strain,Pn.aandPn.p
lineardependenciesonyintotheprobabilitiesoftakingaright are unable to execute different cell fates as the MOM-4 and
orleftstep.Inthisexpandedmodel,theprobabilityoftakinga LIT-1proteins,requiredforthedaughtercellstohavedifferent
right step (increasing y; towards WT polarity) or left step amount of POP-1, lost their function. We observed that the
(decreasing y; towardsreversed polarity) is ((1þg)/2)(yr þ distributionfory is centered at601.Thebiasofthey
f lag-2 lag-2
r )Dt and ((1(cid:2)g)/2)([901(cid:2)y]r þr )Dt, respectively. g per- distribution is likely to be due to the differential amount of
b f b
forms the same role here as in the simple model and SYS-1inthetwodaughtercells.Sinceinformationdetermining
characterized thegradient.Onthe otherhand, r isreplaced throughsensingandamplificationarenotconveyedeffectively
T
bytworatesr andr .Intheabsenceofagradient(g¼0),y(t) tothedaughtercellsasthePOP-1branchisinhibited,wecan
f b
hasequalprobabilityofincreasingordecreasingwhenthecell usethismutanttoobtainanestimateforr ¼0.006bysetting
b
isunpolarized(y¼451)similartothebehaviorofthesimple r ¼0. This is likely to be an overestimation as the SYS-1
f
model.However,ifthereisanyfluctuationthatdrivesthecell branchisunaffected.Usingthisestimationforthevalueofr ,
b
away from the unpolarized state, this fluctuation will be we determined the values of g and r that yields maximum
f
reinforced.Inotherwords,theprobabilitythatywillmovein likelihoodfitsfortheWTandmutantsstrains’distributions.
the same direction as the fluctuation does,is largerthan the When we fit the WT distributions, we obtained large
probabilitytomoveintheoppositedirectionofthefluctuation uncertainties in the fit parameters. This is expected because
(Figure 4D and E, green traces). The parameter r quantifies the parameter range over which WT polarity is observed is
f
this reinforcement. A basal rate independent of y(t), r , is large.AlthoughtheWTdistributioncannotbefitteduniquely,
b
included and set to be a constant. The external gradient is weknowthattheparameterslieintheparameterspacewhere
superposed on this process and further biases the random 100%correctdivisionsareobservedwhichisboundedbythe
walk (Figure 4D and E, blue, red, and magenta traces). dashed line in Figure 5D and E. Next, the experimental
Anotherwaytoviewthepolarizationprocessisthatinitially distributionofy forthedifferentPcellsintheligandand
lag-2
whenthecellisunpolarized(y¼451),thecontributionsofr to receptormutants(Figure5C,bluehistograms)werefittothe
f
theprobabilitiesoftakingarightorleftstepareequal.Hence, model(Figure5C,redlines).Thedistributionsforeachofthe
thesensingprocess,representedbyg,playsamoreimportant individual P cells are significantly different; hence, the fit
roleissettinguppolarization.Oncesensinghasoccurredandy parametersgandr weredeterminedforeachPcellintheligand
f
is no longer close to 451, contributions of amplification mutants and receptor mutants independently. The model is
representedbyr willbecomeimportantandactsynergistically able to reproduce the main features of the experimental
f
withthegradientto furthersetupthepolarization.Amodel distributions. Interestingly, these two parameters segregated
assuming additive effects of gradient sensing and amplifica- outinparameterspace(Figure5D).Wefoundthatthegradient
tion is alsounable toproducethe coexistence of correctand parametergwasalwayslowercomparedwithWT(Figure5D),
reversepolarity(SupplementaryFigureS5). suggestingthatbothWntligandsandreceptorsareimportant
Werepeatedtheanalysisfortheexpandedmodel,settingr for the sensing of the gradient. However, the feedback
b
asaconstantandfoundaregioninparameterspace(gversus parameter r was significantly smaller when receptors were
f
r), which allows for the coexistence for correct and reverse mutatedcomparedwithligandmutations,suggestingthatthe
f
polarity(Figure4F,magenta),whichwasabsentinthesimple receptorsmightbeinvolvedinamplifyingthesignal.
model(Figure4C).Wethenusedthismodeltofurtherquantify
the experimental results and explore where the different
mutants are located in this parameter space. Note that the
Decreasing ligand results in symmetric divisions
present model is a purely phenomenological model (in
at low r
contrasttoamechanisticmolecularmodel)thatallowsusto f
extractparameters,gandr,fromtheexperimentaldata. From the above analysis, we inferred that Wnt ligands are
f
primarilyinvolvedinsensingwhereasWntreceptorsfunction
in both sensingand amplification. Mutations in Wnt ligands
primarilyleadtopolarityreversalswhereasmutationsinWnt
Loss of Wnt ligands reduces the parameter g,
receptorscauselossofpolarity.Verysimilarresultshavebeen
whereas loss of Wnt receptors results in a
reportedformanytailblastcellsin C.elegans, includingthe
decreased value of both g and r
f Tcell,suggestingthatourmodelmaybegenerallyapplicable
Tocomparethepredictionsofthemodeltotheexperimental (Sternberg and Horvitz, 1988; Herman and Horvitz, 1994).
data, we converted the lag-2 transcript count in each pairof However,incontrast,ithasbeenreportedfortheEMScellin
daughter Pcell to a single angle y (Figure 5A). From the C.elegansthatlossofligandscauseslossofpolarityapparently
lag-2
earlierexperiments,weobservedthatinhibitionoftheWnt/b- inconsistent with our interpretation (Thorpe et al, 1997).
6 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited
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RZTanetal
Figure5 Fittingofligandsandreceptorsmutantsdistributions.(A)Plotoflag-2mRNAcountsinP3.pversusP3.ainegl-20;cwn-1;cwn-2strainandillustrationofhow
y iscalculated.(B)Histogramsfory (blue)andmaximumlikelihoodfits(red)formom-4;lit-1straingrownat251Cfor9h.(C)Histogramsfory (blue)and
lag-2 lag-2 lag-2
maximumlikelihoodfits(red)forP3–P10inegl-20;cwn-1;cwn-2andmom-5;lin-17strains.(D)Fitparameter,gandr obtainedusingmaximumlikelihoodfortriple-ligand
f
mutant(egl-20;cwn-1;cwn-2strain)(white)andreceptormutant(mom-5;lin-17strain)(black).Whitedottedlineshowstheregionofparameterspacegivingrisetoabove
99.9%correctdivisions.AlthoughtheparametersofWTPcellscannotbedeterminedexactlyasmanycombinationsofparameterscangiveriseto100%correctpolarity,
theparametersofWTPcellsmustlieabovethewhitedottedline.Hence,valuesofgobtainedforbothligandsandreceptorsmutantsarelowerthanthatofWTPcells.
(E)Abstractionofparameters’movementinphasespaceasaresultofmutations.(i)DecreasingligandsinWTPcellsleadstoreductionofgandconvertscorrectpolarityinto
thecoexistenceofcorrectandreversepolarityobservedinthetriple-ligandmutant.(magneta)(ii)Decreasingreceptorsslightlywillleadtoreductionofr andcellsthatstill
f
polarizecorrectlyiftheparametersliewithintheregionofcorrectdivision(whitedottedline).(iii)Decreasingligandsinstrainswithreducedr wouldleadtolossofpolarity.
f
However,uponcloserinspectionofthepolarityphasediagram mutant,divisionsoftheP3andP4cellsaresymmetricwhereas
(Figure 5E), we hypothesized that in the EMS cell, the WT the divisions of the P5–P10 cells are correct (Figure 6A).
parametersarelikelytobedifferent.Forexample,theEMScell Reducing ligand levels in the mom-5; cwn-1 strain led to
mightexperienceadifferentgradientorhasreducedamplifi- symmetric divisions in the P5 and P6 cells (Figure 6A)
cationpotentialcomparedwiththePcells. confirmingourprediction.Thisbehaviorwasalsoreproduced
TheparameterrangeoverwhichWTpolarityisobservedis inthemom-5;egl-20andmom-5;egl-20;cwn-1mutants,where
largeandisboundedbythedashedlineinFigure5DandE.If divisionsinallP3–P10cellswereaffected(Figure6A).
wewouldreducer slightlysothatmostPcellsstillcorrectly
f
polarize(movingfromWTtoCinFigure5E)andsubsequently
removeligand(movingfromCtoUinFigure5E)itshouldbe
Positivecorrelation between receptor levelsand r
possibletoinducelossofpolarityuponlossofWntligand.To f
testthispredictionandaccesstheparameterspaceoflowr, Inthemom-5;egl-20andmom-5;egl-20;cwn-1strains,where
f
we looked for mutants for which r is lower than WT but divisionsinallP3–P10cellswereaffected,weobservedahigh
f
sufficientlyhightoyieldcorrectdivisions.Wechosethemom- fraction of symmetric divisions in the P3–P6 cells, lower
5singlereceptormutantasourcandidateastherearemanyP fractions of symmetric divisions in the P7–P8 cells and
cells with correct divisions in this mutant. In the mom-5 coexistenceofcorrectandreversepolarityintheP9andP10
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 7
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RZTanetal
Figure6 Effectsofreducingligandinmom-5backgroundandcorrelationbetweenreceptorlevelandr.(A)Histogramsofy (blue)andmaximumlikelihoodfits
f lag-2
(red)forP3–P10inmom-5singlereceptormutantandmom-5;cwn-1,mom-5;egl-20andmom-5;cwn-1;egl-20compoundmutants.(B)mom-5(blue)andlin-17(red)
mRNAcountsinP3–P10.(C)Plotofaveragelin-17mRNAversusr forP3–P10inmom-5;egl-20andmom-5;cwn-1;egl-20strains.Exponentialfitisshowninblack.
f
(D)Plotofaveragemom-5mRNAversusr forP3–P10inlin-17;cwn-1;egl-20strains.Linearfitisshowninblack.
f
cells (Figure 6A). It is intriguing that all these different ofligandandreceptorlossonPcells’division.Wefoundthat
phenotypeswereobservedinthesamemutantstrainandeven ligand affect primarily the sensing process whereby loss of
in the same mutant animal, suggesting that the values of r ligands lead to polarity reversals. Single molecule FISH
f
mayvarysignificantlyamongPcellsinthesameanimal.We experimentsonWntligandsshowthatligandsareexpressed
hypothesizedthatthedifferencesinr areduetothedifferent in a gradient. cwn-1 and egl-20 are higher in the posterior
f
expression levels of the receptors. We measured transcrip- region whereas cwn-2 is higher in the anterior region
tionallevelsof the receptorsgenes,mom-5 andlin-17, using (Harterink et al, 2011). These ligand gradients could poten-
singlemoleculeFISHinthePcellsandfoundthatanteriorP tiallyserveasthegradientsforpolarizingthePcells.Indeed,
cellsexpressedhigherlevelsofmom-5whereasposteriorcells Wnt ligands has been shown to act instructively (Goldstein
expressed higher levels of lin-17 (Figure 6B). We found a et al, 2006). But there are also cases where ligands act
positive correlation between the lin-17 count and the permissively (Whangbo et al, 2000). To determine if ligands
parameter r (Figure 6C) for both the mom-5; egl-20 and actinstructivelyorpermissively,weexpressedcwn-2poster-
f
mom-5;egl-20;cwn-1strains.Similarly,apositivecorrelation iorly using an egl-20 promoter or uniformly using a myo-3
was observed between the mom-5 mRNA level and r in the promoter in a cwn-1; cwn-2; egl-20 triple-ligand mutant
f
lin-17; egl-20; cwn-1 strain (Figure 6D). These positive (Supplementary Figure6).We found that ubiquitous expres-
correlations obtained between receptor levels and r provide sion of cwn-2 using both promoters are able to rescue the
f
quantitativesupportforourearlierconclusionthatreceptors polarityreversals,suggestingthatitistheligandlevelrather
may play an important role in amplification. Furthermore, than the gradient that is important for the sensing process.
sincedifferencesinreceptorslevelcouldexplainmostofthe However,therecentidentificationofWntinhibitor,sfrp-1,in
differences in r, it also demonstrates that the ligands’ theanteriorregionofthewormsuggeststhatligandprofileis
f
contributiontoamplificationislesssignificant. notshapedbyligandexpressionalone(Harterinketal,2011).
Anteriorexpressionofsfrp-1couldpotentiallyconvertuniform
ligandexpressionintoaligandgradient.Identificationofmore
Wnt components and quantitative measurement of ligand
Discussion
proteinprofileswillbenecessarytoresolvethisissue.
Bycombiningquantitativesinglemoleculetranscriptcounting Unlikethe ligand mutants,polarity loss is observed in the
with phenomenological modeling, we studied the effects receptor mutants. We reconcile the different phenotypes
8 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited
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RZTanetal
observed in ligand versus receptor mutants. Ligands Materials and methods
affect primarily the sensing process whereas receptors
C. elegans strains and culturing
areneededforbothsensingandamplification.Thissuggests
thatreceptorscan signalto thedownstreamproteins needed Generalmethodsforculture,manipulation,andgeneticsofC.elegans
wereasdescribedpreviously(LewisandFleming,1995).Mutations
foramplificationregardlessofwhethertheyareligand-bound
used in this study were: LGI, lin-44(n1792) (Herman and Horvitz,
whereas the function of ligand is to convey information
1994), mom-5(or57) (Thorpe et al, 1997) in mom-5; lin-17 receptor
about the directionality of polarization to the cell through strain and mom-5(gk812) for all other mom-5 strains; LGII, cwn-
the receptors. One possible molecular mechanism is that 1(ok546)(ZinovyevaandForrester,2005),mom-4(ne1539)(Takeshita
initially equal amount of receptors bind to both the anterior andSawa,2005);LGIII,lit-1(t1512)(TakeshitaandSawa,2005);LGIV,
cwn-2(ok895) (Zinovyeva and Forrester, 2005), egl-20(n585)
and posterior sides of a cells. The presence of a ligand
(Zinovyevaetal,2008);LGV,mom-2(ne874ts).Strainswerecultured
gradient would bias the amount of receptors on one side at201Cexceptforthemom-4;lit-1strain,whichwasculturedat151C
ofthecellthroughmechanismslikereductionindegradation and transferred to 251C for 7 or 9h before fixation and the Wnt
rates for ligand-bound receptors. The higher amount of quintuplemutant,whichwasgrownat151Candshiftedto251Cfor7h
beforefixation.
receptorsononesideofthecellmayleadtopositivefeedback
to bring even more receptors to the same site. This would
eventually cause the cell to become polarized and divide
asymmetrically. In the absence of ligand, positive feedback Single molecule mRNA FISH
couldstillleadtoahigheramountofreceptorsononesideof
ProbedesignandhybridizationtoperformFISHforsingletranscript
the cell due to initial stochastic differencesin the amount of measurement in C. elegans larvae was performed as previously
receptorsateachsideofthecell.Howeverinthiscase,some described(Rajetal,2008).Animalswerecollectedbywashingplates
fractionofthecellswillbepolarizedintheoppositedirection, withM9andwerefixedin4%formaldehydein1(cid:3)PBSfor45min.
Fixed animals were permeabilized in 70% ethanol overnight. All
leading to existence of divisions of both correct and reverse
probesforhybridizationwerecoupledtoeitherCy5(GEAmersham)
polarity.Whenreceptorsareabsent,therewillnotbepositive or Alexa594 (Invitrogen), depending on the desired gene com-
feedback and the cells would divide symmetrically. The binationsforimageacquisition.ImagesweretakenwithaNikonTi-E
observation that receptors cluster asymmetrically before inverted fluorescence microscope equipped with a 100(cid:3) oil-
immersion objective and a Photometrics Pixis 1024 CCD camera
division is consistent with this proposed model (Wu and
using MetaMorph software (Molecular Devices, Downington, PA,
Herman, 2007). Future work is necessary to elucidate the
USA). Three-dimensional positions of bright fluorescent spots
molecularmechanisms forthe differences in roles of ligands in each animal were detected with the aid of a custom program
andreceptors. writteninMATLAB,asdescribed(Rajetal,2008),whichwaslater
In our mom-5;wnt strains (Figure 6A), we observed loss of manually corrected for further accuracy. Nuclei were visualized
withDAPI.
polarity and polarity reversals for P cells with low and
high r, respectively. This is reminiscent of the different
f
phenotypes observed upon ligand loss in C. elegans. Loss of
ligand leads to polarity reversals for many tail blast cells, Simulation of histograms of y
including the Tcell, and loss of polarity in the EMS cell. Our Thechemicalmasterequationwassolvedtoobtaintheexactsolution
resultsuggeststhatthesedifferencesareduetolowamplifica- foreachsetofparameters.Inthesimulation,ytakesvaluesbetween0
tionstrengthintheEMSandhighamplificationstrengthinthe and901andincreasesordecreasesinstepsof11.Next,atransition
matrix, M, describingthe rates of going frombetween the different
Tcell.Itisinterestingwhysomecellshavehighamplification
valuesofyisconstructed.Sincethereare91differentvaluesthatycan
strength whereas others have low amplification strength. We
take,thetransitionmatrixisofsize91(cid:3)91.Therateofgoingfromy to
1
suggestthatlowamplificationissufficientforcorrectdivisionin y isrepresentedbyM(y þ1,y þ1)inthematrix.Furthermore,since
2 2 1
theEMSasthesingleMOM-2/ligandsourceisadjacenttothe ycanonlyincreaseordecreaseinstepsof11,onlythediagonalterms
EMS and likely to provide a steep gradient across the cell. andvaluesnexttothediagonaltermsarenon-zerointhetransition
matrix.
However, for P cells during post-embryonic development,
the gradient is shaped by many different ligands and by
many ligand-expressing cells all along the worm (Harterink
et al, 2011). Therefore, the gradient experienced by the For the simple model
P cells is likely to be shallower and more complicated to 1þg
interpret. In thiscase, it willbebeneficialforthecelltohave Mðyþ2;yþ1Þ¼ 2 rT
higher amplification is to ensure robustness. Hence, we
fory¼01–891
speculate that depending on the gradient and the complexity
otoftbhaellaingacendthsoeutrrcaedse,oceffllsbmetwayeeenxprreosbsudstifnfeesresnotfrepceoplatroirtylevaenlds Mðy;yþ1Þ¼1(cid:2)2grT
fory¼11–901
energyinvolvedinhighexpression.
Here,wehaveproposedageneralframeworkfordetermin- Mðy;yÞ¼(cid:2)ðMðy(cid:2)1;yÞþMðyþ1;yÞÞ
ingthecontributionsofproteinstosensingandamplification. fory¼21–901
This method overcomes the need for detailed knowledge
of the biochemical reactions and network topology involved Theboundaryconditionsaty¼01and901arereflecting.
in many polarizing system and allows us to extract Mð1;1Þ¼(cid:2)Mð2;1Þ
parameters that quantify the key processes of sensing and
amplification. Mð91;91Þ¼(cid:2)Mð90;91Þ
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 9
DeconvolvingtherolesofWntligandsandreceptors
RZTanetal
For the expanded model Expanded model
1þg yðtþDtÞ¼yðtÞþ1
Mðyþ2;yþ1Þ¼ 2 ðyrfþrbÞ
for
fory¼01–891 1þg
1(cid:2)g no 2 ðyrfþrbÞDt
Mðy;yþ1Þ¼ 2 ð½90(cid:2)y(cid:4)rfþrbÞ yðtþDtÞ¼yðtÞ(cid:2)1
fory¼11–901 for
Mðy;yÞ¼(cid:2)ðMðy(cid:2)1;yÞþMðyþ1;yÞÞ 1þg 1þg
fory¼21–901 2 ðyrfþrbÞDtono 2 ðyrfþrbÞDt
Sbionucnedyarcyacnonnodtittiaoknessavtaylu¼e0s1laenssdt9h0a1nar0e1raenfldecgtirnega.ter than 901, the þ1(cid:2)2gð½90(cid:2)y(cid:4)rfþrbÞDt
Mð1;1Þ¼(cid:2)Mð2;1Þ yðtþDtÞ¼yðtÞ
for
Mð91;91Þ¼(cid:2)Mð90;91Þ 1þg 1(cid:2)g
ThedistributionattimetispresentedbyP andisgeneratedbythe n4 2 ðyrfþrbÞDtþ 2 ð½90(cid:2)y(cid:4)rfþrbÞDt
t
followingequation: Theboundaryconditionsaty¼01and901arereflecting.
Ptþ1¼ðI(cid:2)MDtÞPt
Supplementary information
where I is the identity matrix. We start the simulation with P
t¼0
(y¼451)¼1asthecellsareinitiallyunpolarized.Thetotalsimulation Supplementary information is available at the Molecular Systems
time T is underdetermined and is set constant to 1 for all the Biologywebsite(www.nature.com/msb).
simulationsanddifferentmutantsanalyzed.Dtisthetimestepofthe
numerical simulation and has been chosen to be 10(cid:2)4 in our
simulation. The resulting histograms are independent of the choice Acknowledgements
ofDtaslongasDtissmallenough.
ThisworkwassupportedbyaNIHPioneeraward(1DP1OD003936)
and NIH grant R01 GM068957 to AvO and the A*STAR program,
Classification rules for correct polarity, reverse SingaporetoRZT.Several nematodestrainsusedin thisworkwere
polarity, and loss of polarity providedbytheCaenorhabditisGeneticsCenter,whichisfundedby
theNIHNationalCenterforResearchResources(NCRR).Wethank
The classification rules are y(T)4751 (correct polarity), y(T)o151 JeroenvanZonfordiscussionsonthemodel.WealsothankStefan
(reversepolarity),and151py(T)p751(lossofpolarity).Theserules Semrau and Jeroen van Zon for comments on the manuscript. We
are obtained by finding the angle that best separate the lag-2 thank Peter Reddien, Erel Levine, Susan Mango, Jeff Gore, Teije
expressionofPn.aversusPn.pbetweenWTanimalsandthemom-4; Middelkoop,ChristophEngert,DongHyunKim,ApratimSahay,and
lit-1strainat251C(Figure3AandB). ClintonHansenforgeneraldiscussions.
Authorcontributions:RZTandAvOconceivedtheproject.RZT,NJ,
andRAMperformedtheexperiments;RZTandAvOconstructedthe
Stochastic simulation of single h(t) traces computationalmodel;RZT,NJ,HCK,andAvOwrotethemanuscript.
MonteCarlosimulationwereperformedtogeneratemanysingley(t)
trajectories.Theinitialconditiony(t¼0)¼451wasusedasthecells Conflict of Interest
are initially unpolarized. For every time t, a random number n is
drawn.y(tþDt)willbeupdatedbasedonthefollowingconditions: Theauthorsdeclarethattheyhavenoconflictofinterest.
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10 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited