1 a statistically oriented asymmetric localization (soal ... · 38 soal model, we show that unc-5...
TRANSCRIPT
Astatisticallyorientedasymmetriclocalization(SOAL)modelforneuronaloutgrowth1
patterningbyCaenorhabditiselegansUNC-5(UNC5)andUNC-40(DCC)netrinreceptors2
3
GerardLimerick*,†,XiaTang*,†,WonSukLee*,†,AhmedMohamed*,AseelAl-Aamiri*,and4
WilliamG.Wadsworth*5
6
*DepartmentofPathologyandLaboratoryMedicine,RutgersRobertWoodJohnsonMedical7
School,Piscataway,NJ088548
9
†These authors contributed equally to this work 10
Genetics: Early Online, published on November 1, 2017 as 10.1534/genetics.117.300460
Copyright 2017.
2
runningtitle:neuronaloutgrowthpatterning11
12
keywords:neuronaldevelopment,axonguidance,asymmetriclocalization,Caenorhabditis13
elegans,netrinandwntsignaling14
15
correspondingauthor:16
WilliamG.Wadsworth17
DepartmentofPathologyandLaboratoryMedicine18
RutgersRobertWoodJohnsonMedicalSchool19
675HoesLaneWest20
Piscataway,NJ08854-563521
732-235-576822
3
Abstract24
Neuronsextendprocessesthatvaryinnumber,length,anddirectionofoutgrowth.25
Extracellularcueshelpdetermineoutgrowthpatterns.InCaenorhabditiselegans,neurons26
respondtotheextracellularUNC-6(netrin)cueviaUNC-40(DCC)andUNC-5(UNC5)receptors.27
PreviouslywepresentedevidencethatUNC-40asymmetriclocalizationattheplasma28
membraneisself-organizingandthatUNC-40canlocalizeandmediateoutgrowthatrandomly29
selectedsites.Hereweprovidefurtherevidenceforastatisticallyorientedasymmetric30
localization(SOAL)modelinwhichUNC-5receptoractivityaffectspatternsofaxonoutgrowth31
byregulatingUNC-40asymmetriclocalization.AccordingtotheSOALmodel,thedirectionof32
outgrowthactivityfluctuatesacrossthemembraneovertime.Randomwalkmodelingpredicts33
thatincreasingthedegreetowhichthedirectionofoutgrowthfluctuateswilldecreasethe34
outwarddisplacementofthemembrane.Bydifferentiallyaffectingthedegreetowhichthe35
directionofoutgrowthactivityfluctuatesovertime,extracellularcuescanproducedifferent36
ratesofoutgrowthalongthesurfaceandcreatepatternsofextension.Consistentwiththe37
SOALmodel,weshowthatunc-5mutationsalterUNC-40asymmetriclocalization,increasethe38
degreetowhichthedirectionofoutgrowthfluctuates,andreducetheextentofoutgrowthin39
multipledirectionsrelativetothesourceofUNC-6.Theseresultsareinconsistentwithcurrent40
modelswhichpredictthatUNC-5mediatesarepulsiveresponsetoUNC-6.Geneticinteractions41
suggestUNC-5actsthroughtheUNC-53(NAV2)cytoplasmicproteintoregulateUNC-4042
asymmetriclocalizationinresponsetoboththeUNC-6andEGL-20(wnt)extracellularcues. 43
4
Introduction44
Duringdevelopment,anintricatenetworkofneuronalconnectionsisestablished.Asprocesses45
extendfromtheneuronalcellbodies,distinctextensionpatternsemerge.Someextensions46
remainasasingleprocess,whereasothersbranchandformmultipleprocesses.Iftheybranch,47
theextensionscantravelinthesameorindifferentdirections.Extensionsvaryinlength.48
Extracellularcuesareknowntoinfluencethispatterning,buttheunderlyinglogicthatgoverns49
theformationofpatternsremainsamystery.50
51
The secreted extracellular UNC-6 (netrin) molecule and its receptors, UNC-5 (UNC5) and UNC-40 52
(DCC) are highly conserved in invertebrates and vertebrates, and are known to play key roles in cell 53
and axon migrations. In Caenorhabditis elegans, UNC-6 is produced by ventral cells in the midbody 54
and by glia cells at the nerve ring in the head (WADSWORTH et al. 1996; WADSWORTH AND 55
HEDGECOCK 1996; ASAKURA et al. 2007). It’s been observed that neurons that express the receptor 56
UNC-40 (DCC) extend axons ventrally, towards the UNC-6 sources; whereas neurons that express 57
the receptor UNC-5 (UNC5) alone or in combination with UNC-40 extend axons dorsally, away from 58
the UNC-6 sources (HEDGECOCK et al. 1990; LEUNG-HAGESTEIJN et al. 1992; CHAN et al. 1996; 59
WADSWORTH et al. 1996). 60
61
It is commonly proposed that axons are guided by attractive and repulsive mechanisms (Tessier-62
Lavigne and Goodman 1996). According to this model, an extracellular cue acts as an attractant or 63
repellant to direct neuronal outgrowth towards or away from the source of a cue. UNC-5 (UNC5) 64
has been described as a “repulsive” netrin receptor because it mediates guidance away from netrin 65
sources (Leung-Hagesteijnetal.1992;Hongetal.1999;KelemanandDickson2001;Mooreet66
al.2007). Theattractionandrepulsionmodelisdeterministic.Thatis,giventhesame67
5
conditions,theresponseoftheneuron,attractiveorrepulsive,willalwaysbethesame.This68
ideaformsthebasesoftheanalysisandinterpretationofexperimentalresults.Axonalgrowth69
conemovementtowardsorawayfromthesourceofacueisconsideredtobemediatedby70
attractiveorrepulsiveresponsestothecue.Ingeneticstudies,amutationthatdisrupts71
movementtowardsthecuesourcedenotesgenefunctionwithinanattractivepathway,72
whereasmutationsthatdisruptmovementawayfromasourcedenotesgenefunctionwithina73
repulsivepathway.Ifanaxonalgrowthconeisobservedtomovetowardsandthenawayfrom74
thesourceofacue,theresponsivenessofaneuronisthoughttoswitchfromattractiveto75
repulsive.However,itisimportanttonotethatattractionorrepulsionisnotanintrinsic76
propertyoftheinteractionbetweenthereceptorandligand.Infact,theinteractiononly77
promotesorinhibitsoutwardmovementofthemembrane.Attractionandrepulsionrefersto78
adirection,whichisanextrinsicpropertyofthecellularresponsethatvariesdependingonthe79
physicalpositionsoftheligands.Movementtowardsorawayfromacuesourceiscausedby80
attractiveandrepulsiveeffects,suchaschemoattractionandchemorepulsion,whichis81
movementthatisdirectedbychemicalgradientsofligands.Wearguethatclassifyinggene82
functionasattractiveorrepulsiveisproblematicsinceattractionandrepulsionarenotintrinsic83
propertiesofcellularmechanisms.84
85
Wehaveproposedanalternativemodelinwhichthemovementofneuronaloutgrowthisnot86
consideredintermsofattractionandrepulsion.Thismodelcomprisesthreeconcepts.The87
firstconceptisthatreceptorsalongthesurfaceofthemembranechangeposition.Thisis88
importantsincethespatialdistributionofreceptorscaninfluencethemovementthataneuron89
hasinresponsetotheextracellularligands(NGUYENetal.2014;NGUYENetal.2015).We90
hypothesizethatthespatialdistributionofUNC-40caninfluencethemannerthoughwhich91
forceisappliedtothemembraneandtherebyaffecttheoutwardmovementofthemembrane.92
6
It’sknownthatthesurfacelocalizationoftheUNC-40receptorundergoesdramaticchanges93
duringthedevelopmentoftheHSNaxon(ADLERetal.2006;XUetal.2009;KULKARNIetal.94
2013).AsHSNaxonformationbegins,UNC-40becomesasymmetricallylocalizedtotheventral95
surfaceofthecellbody,whichisnearesttheventralsourcesofthesecretedUNC-6ligand.Live96
imagingofthedevelopingleadingedgerevealsadynamicpatternofUNC-40localizationwith97
areasofconcentratedUNC-40localizationshiftingpositionsalongthesurface(KULKARNIetal.98
2013).DynamicUNC-40::GFPlocalizationpatternshavealsobeenreportedduringanchorcell99
extension(WANGetal.2014).Similartoaxonextension,theanchorcellalsosendsanextension100
throughtheextracellularmatrixandthisextensionisalsoregulatedbyUNC-40andUNC-6101
(ZIELetal.2009;HAGEDORNetal.2013).LiveimagingoftheanchorcellrevealsthatUNC-102
40::GFP“clusters”form,disassemble,andreformalongtheanchorcell’splasmamembrane103
(WANGetal.2014).104
105
Thesecondconceptisthattheasymmetriclocalizationofthereceptor,andthesubsequent106
outgrowthactivityitmediates,isstochasticallyoriented.ItwasobservedthatUNC-40can107
asymmetricallylocalizetoarandomlyselectedsurfaceiftheUNC-6ligandisnotpresentto108
provideapre-establishedasymmetriccue(XUetal.2009).Wenotedthattheself-organizing109
natureofUNC-40localizationisreminiscentofaself-organizingprocessobservedinsingle-cell110
yeast,Dictyosteliumdiscoideum,andneutrophils,wherecellmovementwilloccurinarandom111
directionifthechemotacticcueisabsentorisuniformlypresented(FRASERetal.2000;112
ARRIEUMERLOUANDMEYER2005;MORTIMERetal.2008).Theprocessthroughwhichoutgrowth113
activitybecomesasymmetricallyorganizedisthoughttoutilizepositive-andnegative-feedback114
loops(BOURNEANDWEINER2002;GRAZIANOANDWEINER2014).Suchloopsmightalsodrivethe115
asymmetriclocalizationofUNC-40(XUetal.2009;WANGetal.2014).Positiveandnegative116
feedbackareconsideredcomplementarymechanisms;positivefeedbackamplifiesthe117
7
polarizedresponsetoanextracellularcue,whilenegativefeedbacklimitstheresponseandcan118
confinethepositivefeedbacktotheleadingedge(BOURNEANDWEINER2002).The biological 119
nature of feedback loops controlling UNC-40 activity is unclear. However, they may involve the 120
differential transport of receptors and effectors to the plasma membrane surface. Imaging 121
experiments of cells in culture suggest that netrin-1 (UNC-6) regulates the distribution of DCC 122
(UNC-40) and UNC5B (UNC-5) at the plasma membrane (GOPAL et al. 2016). In these studies, 123
netrin-1 (UNC-6) was shown to stimulate translocation of DCC (UNC-40) and UNC5B (UNC-5) 124
receptors from intracellular vesicles to the plasma membrane and, further, the transported receptors 125
were shown to localize at the plasma membrane (GOPAL et al. 2016). 126
127
WearguethattheprocessthatlocalizesUNC-40toasiteontheplasmamembranepossesses128
inherentrandomness(Figure1).EvidencesuggeststhattheconformationoftheUNC-40129
moleculecontrolswhethertheprocesswillcauseUNC-40localizationtothesiteofUNC-6130
interactionortoanothersite(XUetal.2009).Weobservedthatasingleaminoacid131
substitutioninUNC-40willallowUNC-40toasymmetricallylocalizetodifferentsurfacesinthe132
absenceofUNC-6.ThebindingofUNC-6tothisUNC-40moleculecauseslocalizationtothe133
surfacenearesttheUNC-6source.However,thebindingofUNC-6withasingleaminoacid134
substitutionwillenhancetheasymmetriclocalizationtodifferentsurfaces.Asecond-siteUNC-135
6aminoacidsubstitutionwillsuppressthisenhancementandincreaseUNC-40asymmetric136
localizationatthesurfacetowardstheUNC-6source.TheseresultsindicatethatUNC-40137
conformationalchangesdifferentiallyinfluenceeachactivity.Inthecontextoffeedbackloops,138
UNC-40activityregulatesboththepositiveandnegativeloopsthatcontroltheasymmetric139
localizationofUNC-40totheplasmamembrane.Becausethesystemiscontrolledbythe140
conformationofthemolecule,randomnesswillbeintroducedinthesystembystochastic141
fluctuationsinligand-receptorbindingandbystochasticconformationalchanges.142
8
143
TheoutcomeofanUNC-40receptor’sactivityistoeithercauseanUNC-40receptortolocalize144
tothesiteofUNC-6interactionortoadifferentsite(Figure1).Thisisanimportantdiscovery145
becauseitmeansthattheasymmetriclocalizationeventsaremutuallyexclusiveand,therefore,146
thereisstatisticaldependence.Werefertothisprocessas‘statisticallyorientedasymmetric147
localization’(SOAL).ThismodelstatesthattheprobabilityofUNC-4Olocalizingandmediating148
outgrowthatthesiteofUNC-6interactionaffectstheprobabilityofUNC-40localizingand149
mediatingoutgrowthatanothersite,andviceversa.Wehavefoundthatotherextracellular150
cuescanalsoaffectUNC-40asymmetriclocalization,andthuscaninfluencetheprobabilityof151
UNC-40-mediatedoutgrowthfromdifferentsites(TANGANDWADSWORTH2014;YANGetal.152
2014).153
154
Thedevelopmentofanextensioncanbeconsideredasastochasticprocess.Atanyone155
instanceoftimeatinnumerablesitesalongtheneuron’ssurface,UNC-40interactswithUNC-6156
tomediateUNC-40asymmetriclocalizationandtheoutgrowthresponse.Atthenextinstance157
oftime,otherUNC-40receptors,includinganyjusttransportedtothesurface,mayinteract158
withUNC-6.Becausetheplasmamembraneisafluid,theforcesgeneratedbytheoutgrowth159
responsearenotalwaysactinginparallelandthedirectionofoutwardforcecanfluctuate160
(Figure2A).Itisthecollectiveimpactofalloutgrowtheventsoveraperiodoftimethatallows161
theextensiontoform.Theoutwardmovementofanextensioncouldbepreciselydescribedif162
theeffectofeachoutgrowtheventwhereknown.However,itisextremelydifficulttomeasure163
theeffectofeachsingleeventsincethereareinnumerableeventshappeningateachinstanceof164
time.WealsoarguethatthepatternofUNC-40localizationandoutgrowthacrossthesurfaceof165
themembraneevolvesovertimethrougharandomprocess.Therefore,theoutgrowthevents166
9
canonlybedescribedprobabilistically,andassuchthetimeevolutionofextensionisalso167
probabilisticinnature.168
169
Understandingtheroleageneplaysincontrollingoutgrowthmovementmightrequire170
knowledgeofitsroleinregulatingthisstochasticprocess.Todothis,weusethedirectionof171
HSNextension.Wereasonthatthecollectiveimpactofalltheoutgrowtheventsoveraperiod172
oftimecausethedevelopmentoftheHSNaxon.Thedirectionofextensionfromthecellbody173
hasaprobabilityofbeingorientatedinonedirection(KULKARNIetal.2013;TANGAND174
WADSWORTH2014;XANDWG2014;YANGetal.2014).Mathematically,thedirectionofHSN175
extensionisavariablethattakesondifferentvalues;“anterior”,“posterior”,“ventral”,and176
“dorsal”.Aprobabilityisassociatedwitheachoutcome,thuscreatingaprobability177
distribution.Thisdistributiondescribestheeffectthatalltheoutgrowtheventshadovera178
periodoftime.Duringnormaldevelopment,theprobabilityofeachUNC-40-mediated179
outgrowtheventbeingventrallyorientedisveryhighandaventralextensiondevelops.We180
haveshownthatcertaingenemutationsaffecttheprobabilitydistribution,thusrevealingthata181
geneplaysaroleinthestochasticprocess.Wecancomparewildtypeandmutantstogagethe182
degreetowhichamutationcausesthedirectionofextensiontofluctuate.Thisreflectsthe183
degreetowhichthemutationhascausedthedirectionofoutgrowthactivity,andtheoutward184
forceitcreates,tofluctuateoverthecourseofextensiondevelopment.185
186
Wearguethatunderstandingthefunctionofageneintermsofastochasticmodelofmembrane187
movementisuseful.Oftenthegoalofageneticanalysisofaxonguidanceistouncovera188
molecularmechanism.Frequently,adeterministicmodelismadewhichdescribesome189
moleculareventthatthegeneaffects.Becausethemutationaffectsaxonguidance,the190
10
moleculareventplaysaroleincausingdirectedmovement.However,thesemodelstendto191
reduceacomplexbiologicalprocesstoanisolatedcomponent.Inreality,understandinghowa192
moleculareventisabletocausedirectedmovementrequiresknowledgeofallthemanyways193
inwhichtheeventinfluences,andisinfluencedby,theothermoleculareventsofdirected194
movement.Astochasticmodelisausefultoolofexploringhowageneaffectstheoverall195
behaviorofthesystem.Tomakeananalogy,aroulettewheelcanbedescribed196
deterministically;ifeveryforceactingontheballateveryinstanceoftimeisknownthanthe197
numberonwhichtheballstopscanbepreciselydetermined.Theroleofacomponentofthe198
roulettewheelcouldbedescribedbytheeffectthatithasontheforceswhichactontheballat199
everyinstanceoftime.However,understandinghowtheeffectofthiscomponentcausesa200
particularoutcomerequireunderstandingtheeffectsofalltheothercomponents.Becausethis201
issocomplex,theoutcomeofaroulettewheelisstudiedusingastochasticmodel.Thatis,how202
doesthecomponentaffecttheprobabilityoftheballstoppingonaparticularnumber.A203
roulettewheelmustbeexactlylevelledtohaveanequalprobabilityforeachnumber.204
Removingacomponentofthewheelcancausethewheeltotiltinaparticularmanner.This205
willresultinanewoutcome,i.e.theballwillhaveahigherprobabilityofstoppingoncertain206
numbers.Althoughthisdoesnotrevealthepreciseeventthatoccursbetweenthecomponent207
andtheball,itwillrevealtheeffectthatthecomponenthasindetermininganoutcome.208
Further,bystudyingtheeffectofremovingmultiplecomponents,relationshipsthatleadto209
particularoutcomescanberevealed.210
211
Thethirdconceptofourmodelisthatneuronalmembraneoutgrowthisamasstransport212
phenomenawhichcanbedescribedasadvectionanddiffusion(Figure2).SignalingbyUNC-40213
receptorsalongasurfaceoftheneuroncanleadtocytoskeletalchangeswhichcreateforceand214
membranemovement(Figure2A).Asaresult,thereisameanflowofmembranemassinan215
11
outwarddirection(Figure2B).Thismotionisadvection,whichismasstransportbyamean216
velocityfield.Inadditiontoadvection,membranemasstransportalsooccursthroughrandom217
movement,i.e.diffusion.Becausethecellmembraneisfluid,membranemasswillmovein218
differentdirectionsasthemembraneissubjectedtoforceswhichchangeitsshape(Figure2C).219
Thedegreetowhichthemembranemassundergoesrandommovementisimportantbecause220
diffusionprocessesandadvectionprocesseshavedifferenteffectsontheextenttowhichmass221
willbedisplacedoutwardinagivenamountoftime.Therandommovementscanbe222
mathematicallydescribedusingrandomwalks.Arandomwalkisasuccessionofrandomly223
directedsteps(Figure2D).Randomwalkmodelsareusedtodescribemanydiversetypesof224
behavior,includingthemovementofaparticlethroughfluid,thesearchpatternofaforging225
animal,andthefluctuatingpriceofastock.Thebehaviorofneuronalgrowthconemovement226
duringchemotaxishasalsobeenmodeledusingrandomwalks(KATZetal.1984;BUETTNERetal.227
1994;ODDEANDBUETTNER1995;WANGetal.2003;MASKERYetal.2004).However,ratherthan228
usingarandomwalkmodeltodescribethegrossmorphologicalchangesobservedduring229
growthconemovement,inthisstudytherandomwalkisusedtomodeltherandommovement230
ofmembranemassinordertounderstandhowgeneactivityinfluencestheoutward231
displacementofthemembrane.Apropertyofrandommotionisthatthemeansquare232
displacementgrowsproportionatetothetimetraveled.Thismeansthatthemorethedirection233
ofmovementfluctuates,theshorterthedistanceoftravelinagivenamountoftime(Figure2E).234
Themodelpredictsthatifforceisappliedtothemembraneinamannerthatincreasesrandom235
movementthentheoutwarddisplacementofthemembrane’smasswilldecrease.236
237
Becauseoftheeffectrandommovementhasondisplacement,theSOALmodelmakes238
predictionsabouthowUNC-40activityaffectstherateofextension.Inadeterministicmodel,239
outgrowthactivitycausesstraight-lineoutwardmotionfromthesiteofinteraction.TheSOAL240
12
modelpredictsthattheinteractionbetweenUNC-40andUNC-6increasestheprobabilitythat241
UNC-40asymmetriclocalizationandUNC-40-mediatedoutgrowthwillbeorientedatthesiteof242
interaction.Italsodecreasestheprobabilitythatlocalizationandoutgrowthwillbeoriented243
elsewhere.Therefore,theinteractioninfluencesthespatialdistributionofUNC-40alongthe244
surfaceand,indoingso,willchangethewayforcesareappliedtothemembrane.Asthis245
processcontinuesovertime,thedirectionoftheforcesactingonthefluidmembranefluctuates.246
Thiswillaltertheadvectiveanddiffusivetransportofmembranemass.Asanexample,ifthe247
probabilityofventraloutgrowthis0.33,ofanterioroutgrowthis0.33,andposterioroutgrowth248
is0.33thentherewillbeahighdegreeofrandommovement.InteractionsbetweenUNC-40249
andUNC-6attheleadingventralsurfacecouldshifttheprobabilitiesforventraloutgrowthto250
0.8,foranterioroutgrowthto0.1,andforposterioroutgrowthto0.1.Thischangewilldecrease251
thedegreetowhichthedirectionofoutgrowthfluctuates.AsmodeledinFigure2E,thiswill252
increasedisplacement,meaningthatthemembranemassnowwillbeabletotravelfurther253
outwardsoveragivenamountoftime.Itisworthnotingthatfluctuationsinthedirectionof254
outgrowthactivitycouldoccurasveryrapidminutemovementsofmembranemass.When255
observedatthemacro-scale,thesemicro-scalefluctuationsmightnotbeseen.Instead,the256
outwardmovementofanextensionwillappearaslinear,straight-line,movement.Inthis257
paper,“fluctuation”referstovariationinthedirectionofoutgrowthactivity.“Outgrowth”258
referstothemovementofmembranemassatthemicro-scale,whereas“extension”referstothe259
movementoftheaxonthatisobservedatthemacro-scale.260
261
TheSOALmodelmakesdistinctivepredictionsaboutUNC-40-mediatedoutgrowthactivityin262
vivoandthedirectionofextension.Inadeterministicmodel,thedirectionofextensionis263
determinedbytheoutwardmovementofthemembranefromthesitewhereUNC-6andUNC-264
40interact.PositionalinformationisencodedbygradientssothatUNC-6guidesextension265
13
towardstheUNC-6source.IntheSOALmodel,UNC-6andotherextracellularcuesgovernthe266
probabilityofUNC-40asymmetriclocalization,andsubsequentUNC-40-mediatedoutgrowth,267
ateachsurfaceofthemembrane(XUetal.2009;KULKARNIetal.2013).Thedirectionof268
outgrowthisdeterminedbyadirectionalbiasthatiscreatedovertimebythecombinedeffect269
ofextracellularcues.If,forexample,theprobabilityofoutgrowthtowardsaventralUNC-6270
sourceis0.3andtheprobabilityofdorsaloutgrowthis0.3andofanterioroutgrowthis0.4,the271
directionofoutgrowthwillbeintheanteriordirection.Thatis,atanyinstanceoftimethereis272
achancethatoutgrowthmovementwillbedirectedventrallytowardstheUNC-6source,273
howeveroveralongerperiodoftimetheoutgrowthwilltravelanteriorlybecausethereis274
alwaysagreaterlikelihoodthatoutgrowthwillbeanteriorinsteadofventralordorsal.To275
reiterate,thedirectionofextensionisaproductofastochasticprocess,inwhichtheoutcome276
evolvesovertime.TheprobabilityofventraloutgrowthcreatedbytheUNC-40-mediated277
responsetoUNC-6isrequiredfortheanteriorbias.Withouttheventrallydirectedoutgrowth278
inresponsetoUNC-6,theprobabilityofventraloutgrowthwoulddecrease,shiftingthe279
directionalbias.Thus,whenconsideredasastochasticprocess,theobserveddirectional280
responsetotheinteractionsbetweenUNC-40andUNC-6isnotnecessarilyextensiontowards281
theUNC-6source.BecauseofSOAL,positionalinformationisencodedbythelocationandlevel282
oftheextracellularcuesalongthesurfaceoftheneuron.283
284
TheSOALmodelsuggestedthatUNC-40activitycouldaffectextensionmovementinwaysthat285
hadnotbeenobvious.Thefirstinsightisthatforwardmovementofanextensioncouldbe286
inhibitedasitmovestowardsasourceofacuethatpromotesoutgrowth(Figure3A).Atthe287
leadingedgeofanoutgrowth,astrongdirectionalbasisformovementtowardsanUNC-6288
sourceoccursonlyaslongastheprobabilityofUNC-40localizationatsurfacesfacingtowards289
thesourcearegreaterthantheprobabilityofUNC-40localizationatsurfacesfacingother290
14
directions.AsanextensionmovestowardsanUNC-6sourceahigherproportionoftheUNC-40291
receptorsthatflanktheleadingedgecanbecomeligated(Figure3B).BecauseoftheSOAL292
process,thiswillincreasetheprobabilityoflocalizationandoutgrowthattheflankingsites293
whiledecreasingtheprobabilityoflocalizationandoutgrowthattheleadingedge.Theresult294
willbeanincreaseinrandommovementandadecreaseintheoutwarddisplacementofthe295
membrane’smass.Paradoxically,therateofextensionwilldecreaseastheextensionmoves296
towardstheUNC-6source(Figure3C).Itisworthnotingthateveniftheprobabilityof297
outgrowthineachdirectionbecomesequal,therewillstillbeadirectionalbias.Forexample,if298
theprobabilityofoutgrowthtowardsaventralUNC-6sourceis0.33andofanterioroutgrowth299
is0.33andofposterioroutgrowthis0.33,thedirectionalbiasisventral.(Theprobabilityof300
movementinthedirectionoftheaxonshaft(backwards)islow.)301
302
Asecondinsightisthatanextensioncouldmovetowardsthesourceofacuethatinhibits303
outgrowth(Figure3A).Forexample,iftogethertheextracellularcuescreateaprobabilityfor304
ventraloutgrowthof0.7,foranterioroutgrowthof0.15,andforposterioroutgrowthof0.15,a305
directionalbiasforventraloutgrowthiscreated(Figure3B).Thiscanoccurevenifthereisa306
ventralsourceofaninhibitorycue.Theextensioncanmoveventrallytowardsthisinhibitory307
cuesource.Eventuallytheprobabilityforventraloutgrowthmightchangeto0.33,anteriorto308
0.33,andposteriorto0.33(Figure3C).Buteveninthiscase,thereisstilladirectionalbiasfor309
ventraloutgrowthandextensionwillcontinuetomovetowardsthesourceoftheinhibitory310
cue.311
312
Themodelpredictsthatmovementtowardsasourceofacuecausesthesystemtotrend313
towardsastatewheretheprobabilitiesofoutgrowthindifferentdirectionsbecomeequal.314
15
Axonsoftenchangetheirtrajectorynearthesourceofacue.Itispossiblethatthestateis315
importantbecausetheequilibriummightallowcuestobemoreeffectualatreorienting316
outgrowth(Figure4).317
318
Thethirdinsightisthatmultipleextensionsfromaneuroncouldmoveinthesamedirection319
withouthavingtofollowprepatternedextracellularpathways.Someneuronssendoutmultiple320
extensionsthatruninparalleltowardsatarget.Itiscommonlyproposedthatthesepatterns321
formbecauseextensionsfollowparallelpathwaysthatwerepreviouslyformedbyextracellular322
guidancecues.TheSOALmodelsuggeststhatmultipleUNC-40-mediatedoutgrowthscanbe323
initiatedataleadingsurfaceandthatmultipleextensionscanmaintaintheirpositionswithout324
havingtofollowprepatternedextracellularpathways.Inthismodel,aseparateextension325
beginstoformattheleadingedgebecausethedirectionalbiasatonesitebecomesgreaterthan326
thatatflankingsites.Weproposethatalongtheleadingedgetheself-organizingUNC-40327
localizationprocesscancreatemultiplesitesthathaveagreaterdirectionalbias(Figure5A).328
ThepositiveandnegativefeedbackloopsoftheSOALprocesscanallowspatialpatternsof329
outgrowthtodevelopautonomously.Oncethesesitesareestablished,outgrowthcanproceed330
fromeachsiteinthesamedirection(Figure5B).Thestrongestdirectionalbiasiscreatedwhen331
theprobabilitiesforoutgrowthareequalinthedirectionsperpendiculartothedirectionof332
extension.Theactualvalueoftheperpendicularprobabilitiesisnotcrucialforestablishinga333
directionalbias.Eventhoughthevalueoftheperpendicularprobabilitiesmayvarydepending334
onthepositionofoutgrowthalongtheperpendicularaxis,thedirectionofoutgrowthwillbe335
thesame.Ifaperpendicularequilibriumismaintained,thencuesthataffectUNC-40336
localizationandoutgrowthandwhicharedistributedalongtheperpendicularaxiswillhave337
littleeffectonthedirectionofoutgrowth.Suchanequilibriumcanbeestablishedifthe338
outgrowtheffectsofcuesdistributedalongtheperpendicularaxisbalanceouteachother.Such339
16
aconditioncouldbeestablishedbycuesthateffectoutgrowthequallyatsurfacesfacingthe340
perpendicularaxis.Evenifcuesaredistributedinagradientanequilibriumcouldexist.341
Studiesindicatethatgradientsteepness,ratherthantheconcentrationofcues,isimportantfor342
growthconeturningandguidance(BAIERANDBONHOEFFER1992;ROSOFFetal.2004;MORTIMERet343
al.2010;SLOANetal.2015).Therefore,cuesmaycreateaperpendicularequilibriumiftheyare344
distributedinashallowgradientalongtheperpendicularaxis.345
346
Afourthinsightisthatcuescandirectmovementwithoutbeinginaconcentrationgradient.347
TheSOALactivitywithinthecellinitiatesrandomwalkmovement.Aslongasanequilibrium348
alongtheperpendicularaxisexists,adirectionalbiasalongtheotheraxiscanbecreated.In349
Figure5Boutgrowthistowardsaventralcuesource,andasoutgrowthmovesupthe350
concentrationgradientofthiscuetheprobabilityofoutgrowthineachdirectionchanges.351
However,movementtowardsthesourcewouldstilloccuriftheconcentrationofextracellular352
cuesremainsconstantandtheprobabilitiesneverchange.BecauseoftheSOALprocess,a353
directionalbiascanbemaintainedalongatrackofauniformlydistributedcue.354
355
ThelastinsightisthatextracellularcuescouldaffectUNC-40localizationandoutgrowth,but356
notaffectthedirectionofoutgrowth.However,thesecuescouldhaveaneffectonthe357
morphologyandpatterningofanextension.AcandidateforsuchacueisEGL-20(wnt).The358
egl-20geneisoneofseveralWntgenesinC.elegans.Thesegenesareexpressedinaseriesof359
partiallyoverlappingdomainsalongtheanteroposterioraxisoftheanimal(SAWAAND360
KORSWAGEN2013).EGL-20isexpressedincellsposteriortoHSN(WHANGBOANDKENYON1999;361
PANetal.2006;HARTERINKetal.2011).ThesourcesofUNC-6andEGL-20areroughly362
perpendiculartoeachother.WehaveobservedthatlossofEGL-20functioncausesUNC-40363
17
asymmetricallocalizationtoorienttorandomlyselectedsurfacesofHSNandcausestheaxonto364
initiallyextendfromtheHSNcellbodyindifferentdirections(KULKARNIetal.2013;TANGAND365
WADSWORTH2014).UNC-6andEGL-20signalingcouldbothimpingeonthefeedbackloopsthat366
regulateUNC-40SOAL.Indoingso,thesecueswouldacttogethertoinfluencethepatternof367
extension.Inthispaper,weprovidefurthergeneticevidencethatthedownstreamsignalsfrom368
bothcuesconvergetoregulatetheUNC-40SOALprocess.369
370
WesuggestthatUNC-5playsanimportantroleincoordinatingtheUNC-40SOALprocesswith371
non-UNC-40-mediatedresponsesthataffectoutgrowth.Previouslywereportedthatlossof372
UNC-5causesUNC-40asymmetricallocalizationtoorienttorandomlyselectedsurfacesofHSN,373
causingtheaxontoinitiallyextendindifferentdirections(KULKARNIetal.2013).Thissuggests374
thatUNC-5functionstoincreasetheprobabilityofUNC-40asymmetriclocalizationbeing375
orientedtothesiteofUNC-6andUNC-40interaction.Thatis,UNC-5promotesstraight-line376
motionbyinhibitingthedegreetowhichthedirectionofUNC-40-mediatedoutgrowth377
fluctuates.UNC-5hasotherfunctionsaswell.UNC-5isprimarilyknownforitsrolein378
mediatingmovementawayfromUNC-6sources.Forexample,UNC-5isrequiredforthedorsal379
migrationofDAandDBmotorneuronaxonsawayfromventralUNC-6sources(HEDGECOCKet380
al.1990).DAandDBguidanceutilizesbothUNC-40-dependentandUNC-40-independent381
pathways,althoughguidanceissignificantlylessdisruptedbylossofUNC-40thanbylossof382
UNC-5(HEDGECOCKetal.1990;MACNEILetal.2009).WehypothesizethatUNC-5increasesthe383
probabilityofnon-UNC-40-mediatedoutgrowthbeingorientedtowardssiteswherethereare384
notinteractionsbetweenUNC-5andUNC-6.Thisincreasestheprobabilityofoutgrowth385
movementindirectionsnottowardsUNC-6sources.Finally,wepredictthatUNC-5function386
canalsoincreasetheprobabilitythatnon-UNC-40-mediatedoutgrowthwillorienttothesiteof387
interactionbetweennon-UNC-40receptorsandnon-UNC-6extracellularcues.Evidencefor388
18
thiscomesfromtheobservationthatinrpm-1mutantstheoverextensionofthePLMaxoncan389
besuppressedbylossofUNC-5,butnotbythelossofUNC-40orUNC-6(LIetal.2008).In390
summary,webelieveUNC-5can:1)increasetheprobabilityofUNC-40-mediatedoutgrowthat391
thesitesofUNC-6andUNC-40interactions;2)decreasetheprobabilityofUNC-40-mediated392
outgrowthatsiteswhereUNC-6isnotpresent;3)decreasetheprobabilityofnon-UNC-40-393
mediatedoutgrowthatthesiteofUNC-5andUNC-6interactions;and4)increasethe394
probabilityofnon-UNC-40-mediatedoutgrowthatsiteswheretherearenoUNC-6interactions.395
Thesefunctionscanbeconsideredintermsofthepositiveandnegativefeedbackloopsofthe396
SOALmodel(Figure6),whereUNC-5helpsregulatedthefeedbackloopsassociatedwithUNC-397
40activity.398
399
Becauseoftheseideas,wereasonedthatUNC-5activitycouldaffectextensionmovementin400
waysthathadnotbeenobvioustous.First,UNC-5mightaffectthepatterningofextensionthat401
travelstowardsanUNC-6source.Asdiscussedabove,previousevidencesuggestsUNC-5402
regulatestheasymmetriclocalizationofUNC-40.UNC-5interactionswithUNC-6andUNC-40403
couldinfluencethefeedbackloops(Figures1and6).Byregulatingthedegreetowhichthe404
directionofUNC-40-mediatedoutgrowthfluctuates,UNC-5couldaffectrandommovementand405
theoutwarddisplacementofmembranemass.Thiscouldaffecttherateofextensiontowards406
anUNC-6sourceorwhetherextensioncanoccur.Incaseswheremultipleextensionsform407
fromasurface,theeffectUNC-5hasontheloopscouldinfluencewhethersiteswitha408
predominatedirectionalbiascanbeestablished.409
410
Second,UNC-5couldplayaroleindeterminingwhetheranextensionchangesdirection.As411
discussedearlier,iftheUNC-40receptorsbecomesaturatednearanUNC-6sourcethenthe412
19
probabilityofUNC-40-mediatedoutgrowthtowardsthesourceandalongtheperpendicular413
axistendstobecomeequal.Atthispoint,evenasmallincreaseintheprobabilityofnon-UNC-414
40-mediatedoutgrowthtothesiteofnon-UNC-6andnon-UNC-40interactionscouldalterthe415
directionalbias(Figure4).AchangeinUNC-5activitycouldhelppromoteashiftfroma416
directionalbiasdeterminedbyUNC-40andUNC-6interactions,toonedeterminedbynon-417
UNC-40andnon-UNC-6interaction.418
419
BecauseofthepredictionsthattheUNC-40SOALmodelmakes,wedecidedtoreexaminethe420
unc-5loss-of-functionphenotypesandtoinvestigategeneticinteractionsamongunc-5,unc-6,421
unc-40andegl-20thatregulatedtheasymmetriclocalizationofUNC-40.Wefindevidencethat422
UNC-5regulatesthelengthandnumberofprocessesthatextendtowardsanUNC-6sourceand423
thatUNC-5helpscontroltheabilityofaxonstoextendindifferentdirections.Inaddition,we424
findgeneticinteractionsthatsuggestUNC-5,togetherwithUNC-53(NAV2),functionsto425
regulateUNC-40SOALinresponsetotheUNC-6andEGL-20(wnt)extracellularcues.Inthe426
resultsectionofthispaperwedescribephenotypescausedbymutations;andinthediscussion427
sectionwedescribehowthesephenotypescouldbepredictedbytheSOALmodel.Wesuggest428
thattheSOALmodelisusefulforunderstandinghowgenesregulatethepatterningofaxon429
extensions.430
431
20
MaterialsandMethods432
Strains433
Strainswerehandledat20℃usingstandardmethods(Brenner,1974)unlessstated434
otherwise.ABristolstrainN2wasusedaswildtype.Thefollowingalleleswereused:LGI,unc-435
40(e1430),unc-40(ur304),zdIs5[mec-4::GFP];LGII,unc-53(n152);LGIV,unc-5(e152),unc-436
5(e53),unc-5(ev480),unc-5(ev585),egl-20(n585),kyIs262[unc-86::myr-GFP;odr-1::dsRed];LGIV,437
madd-2(ky592),madd-2(tr103);LGX,mig-15(rh148),unc-6(ev400),sax-3(ky123),sax-3(ky200).438
Transgenesmaintainedasextrachromosomalarraysincluded:kyEx1212[unc-86::unc-40-439
GFP;odr-1::dsRed].440
441
Analysisofaxonoutgrowthandcellbodyposition442
HSNneuronswerevisualizedusingexpressionofthetransgenekyIs262[unc-86::myr-GFP].The443
mechanosensoryneurons,AVM,ALM,andPLM,werevisualizedusingtheexpressionofthe444
transgenezdIs5[Pmec-4::GFP].Synchronizedwormswereobtainedbyallowingeggstohatch445
overnightinM9bufferwithoutfood.Thelarvalstagewasdeterminedbyusingdifferential446
interferencecontrast(DIC)microscopytoexaminethegonadcellnumberandthegonadsize.447
Stagedlarvaeweremountedona5%agarosepadwith10mMlevamisolebuffer.Imageswere448
takenusingepifluorescentmicroscopywithaZeiss63Xwaterimmersionobjective.449
450
ThenumberofprocessesduringearlyL1larvalstagewasscoredbycountingthenumberof451
processesthatextendedforadistancegreaterthanthelengthofonecellbody.Wereport452
instancesinwhichtherewerenosuchprocesses,oneprocessormorethanoneprocesses.In453
theL2larvalstage,asingleearlyprocesswasscorediftherewasonlyonemajorextension454
fromtheventralleadingedge.TheHSNcellbodyinL2stagelarvaewasscoredasdorsalifthe455
21
cellbodyhadfailedtomigrateventrallyandwasnotpositionednearthePLMaxon.InL4stage456
larvae,amultipleventralprocessesphenotypewasscoredifmorethanonemajorextension457
protrudedfromtheventralsideofcellbody.458
459
Extensionintothenerveringwasscoredasdefectiveiftheaxondidnotextendfurtherthan460
approximatelyhalfthewidthofthenervering.Anteriorextensionwasscoredasdefectiveif461
theaxondidnotextendfurtheranteriorlythanthenervering.PLMaxonsarescoredasover-462
extendingiftheyextendedfurtheranteriorthanthepositionoftheALMcellbody.463
464
AnalysisofthedirectionofHSNoutgrowth465
HSNwasvisualizedusingthetransgenekyIs262[unc-86::myr-GFP].L4stagelarvaewere466
mountedona5%agarosepadwith10mMlevamisolebuffer.Ananteriorprotrusionwas467
scorediftheaxonextendedfromtheanteriorsideofthecellbodyforadistancegreaterthan468
thelengthofthreecellbodies.Adorsalorposteriorprotrusionwasscorediftheaxonextended469
dorsallyorposteriorlyforadistancegreaterthantwocellbodylengths.HSNwasconsidered470
multipolarifmorethanoneprocessextendedalengthgreaterthanonecellbody.Imageswere471
takenusingepifluorescentmicroscopywithaZeiss40Xobjective.472
473
AnalysisoftheUNC-40::GFPlocalizationinL2stageanimal474
ForanalysisofUNC-40::GFPlocalization,L2stagelarvaewiththetransgenicmarker475
kyEx1212[unc-86::unc-40::GFP;odr-1::dsRed]weremountedona5%agarosepadwith10mM476
levamisolebuffer.Stagingwasdeterminedbyexaminingthegonadcellnumberandthegonad477
sizeunderdifferentialinterferencecontrast(DIC)microscopy.Imagesweretakenusing478
epifluorescentmicroscopywithaZeiss63Xwaterimmersionobjective.TheUNC-40::GFP479
22
localizationwasdeterminedbymeasuringtheaverageintensityunderlinesdrawnalongthe480
dorsalandventraledgesofeachHSNcellbodybyusingImageJsoftware.Foranalysisofthe481
anterior–posteriororientationofUNC-40::GFP,thedorsalsegmentwasgeometricallydivided482
intothreeequallengths(dorsalanterior,dorsalcentralanddorsalposteriorsegments).The483
line-scanintensityplotsofeachofthesesegmentswererecorded.ANOVAtestwasusedto484
determineifthereisasignificantdifferencebetweenintensitiesofthethreesegments.The485
dorsaldistributionwasconsidereduniformifp³0.05andwasconsideredasymmetricalif486
p£0.05.Withinanasymmetricpopulation,thehighestpercentintensitywasconsideredto487
localizeUNC-40::GFPtoeitheranterior,posteriororcentraldomainofthedorsalsurface.488
489
Computations490
Aprogramtosimulateatwo-dimensionallatticerandomwalkbasedontheprobabilityof491
dorsal,ventral,anterior,andposterioroutgrowthforamutant(Table1)wascreatedusing492
MATLAB.(Thedirectionsoftheaxonsfrommultipolarneuronswerenotscored.Theseaxons493
appeartobehaveinthesamemannerastheaxonsfrommonopolarneurons,butthishasnot494
yetbeentested.)Theprobabilityofdorsal,ventral,anterior,orposterioroutgrowthwas495
assignedforthedirectionofeachstepofarandomwalkmovingup,down,leftorright,496
respectively(Figure9).Eachvariableisconsideredindependentandidenticallydistributed.497
Simulationsof500equalsizesteps(size=1)wereplottedfor50tracks(Figure1B,5Band6B498
inserts).AGaussiandistributionforthefinalpositionsofthetrackswasgeneratedusing499
Matlab’srandomfunction(Figure6).500
501
Themeansquareddisplacement(MSD)isusedtoprovideaquantitativecharacteristicofthe502
23
motionthatwouldbecreatedbytheoutgrowthactivityundergoingtherandomwalk.Using503
therandomwalksgeneratedforamutanttheMSDcanbecalculated:504
𝑚𝑠𝑑 𝜏 =< [𝑟 𝑡 +τ − r 𝑡 ]/ >505
Here,r(t)isthepositionattimetandτisthelagtimebetweentwopositionsusedtocalculate506
thedisplacement,Δr(τ)=r(t+τ)-r(t).Thetime-averageovertandtheensemble-averageover507
the50trajectorieswerecalculated.ThisyieldstheMSDasafunctionofthelagtime.A508
coefficientgivingtherelativerateofdiffusionwasderivedfromalinearfitofthecurve.The509
firsttwolagtimepointswerenotconsidered,asthepathsoftenapproximateastraightlineat510
shortintervals.511
DataAvailability512
AllstrainsnotprovidedbytheCaenorhabditisGeneticsCenterareavailableuponrequest.The513
authorsstatethatalldatanecessaryforconfirmingtheconclusionspresentedinthearticleare514
representedfullywithinthearticle.515
516
Results517
UNC-5regulatesthepatternofoutgrowthfromtheHSNneuron518
ToinvestigatewhetherUNC-5activitycanregulatethelengthornumberofprocessesthata519
neuroncandevelopwhenoutgrowthistowardsanUNC-6source,weexaminedthe520
developmentoftheHSNaxoninunc-5mutations.TheHSNneuronsendsasingleaxontothe521
ventralnervecord,whichisasourceoftheUNC-6cue(WADSWORTHetal.1996;ADLERetal.522
2006;ASAKURAetal.2007).Axonformationisdynamic(ADLERetal.2006).Shortlyafter523
24
hatching,HSNextendsshortneuritesindifferentdirections.Theseneurites,whichdynamically524
extendandretractfilopodia,becomerestrictedtotheventralsideoftheneuronwherea525
leadingedgeforms.Multipleneuritesextendfromthissurfaceuntilonedevelopsintoasingle526
axonextendingtotheventralnervecord.Measurementsofgrowthconesize,maximallength,527
anddurationofgrowthconefilopodiaindicatethatUNC-6,UNC-40,andUNC-5controlthe528
dynamicsofprotrusion(NORRISANDLUNDQUIST2011).529
530
We observe that in unc-5 mutants, the patterns of extension are altered. In wild-type animals at the 531
L1 stage of development most HSN neurons extends more than one short neurite, however in unc-532
5(e53) mutants nearly half the neurons do not extend a process (Figures 7A and 7B). During the L2 533
stage in wild-type animals a prominent ventral leading edge forms and the cell body undergoes a 534
short ventral migration that is completed by the L3 stage. By comparison, in unc-5 mutants the cell 535
body may fail to migrate and instead a single large ventral process may form early during the L2 536
stage (Figures 7A, 7C and 7E). It may be that the ventral migration of the HSN cell body requires the 537
development of a large leading edge with multiple extensions. Together the observations indicate 538
that loss of unc-5 function affects the patterning of outgrowth, i.e. the timing, length, and number of 539
extensions that form. Loss of unc-5 function does not prevent movement, in fact, a single large 540
ventral extension can form in the mutant at a time that is even earlier than when a single ventral 541
extension can be observed in wildtype. The earlier appearance of a single ventral extension in unc-5 542
mutants appears to be the result of a difference in morphology, rather than of developmental timing. 543
The failure of the HSN cell body to migrate ventrally and the different pattern of outgrowth at the 544
leading edge causes an earlier discernable single extension. 545
546
25
Wetestedfourdifferentunc-5allelesintheseexperiments.Theunc-5(e53)alleleisaputative547
molecularnullallele,unc-5(ev480)ispredictedtotruncateUNC-5afterthecytoplasmicZU-5548
domainandbeforetheDeathDomain,unc-5(e152)ispredictedtotruncateUNC-5beforethe549
ZU-5domainandDeathDomain,andunc-5(ev585)isamissenseallelethataffectsapredicted550
disulfidebondintheextracellularIg(C)domain(KILLEENetal.2002).Althoughboththeunc-551
5(ev480)andunc-5(e152)arepredictedtocauseprematureterminationofproteintranslation552
inthecytodomain,theunc-5(e152)productretainsthesignalingactivitythatpreventsthese553
phenotypes.Basedonotherphenotypes,previousstudiesreportedthattheunc-5(e152)allele554
retainsUNC-40-dependentsignalingfunctions(MERZetal.2001;KILLEENetal.2002).555
556
UNC-5isrequiredfortheinductionofmultipleHSNaxonsbyUNC-6∆Candamig-15557
mutation558
TheresultsabovesuggestthatUNC-5activitycanregulatethenumberofHSNextensionsthat559
form.Tofurthertestthishypothesis,wecheckedwhetherlossofUNC-5functioncansuppress560
thedevelopmentofadditionalprocessesthatcanbeinduced.Previouslywereportedthat561
expressionoftheN-terminalfragmentofUNC-6,UNC-6∆C,inducesexcessivebranchingof562
ventralnervecordmotorneuronsandthatlossofUNC-5functioncansuppressthisbranching563
(LIMetal.1999).WenowreportthatHSNdevelopsanextraprocessinresponsetoUNC-6∆C564
andthatlossofUNC-5functionsuppressesthedevelopmentofthisextraprocess(Figures7D565
and7F).566
567
To investigate whether this UNC-5 activity might involve known effectors of asymmetric neuronal 568
outgrowth, we tested for genetic interactions between unc-5 and both mig-10 and mig-15. MIG-10 569
(lamellipodin) is a cytoplasmic adaptor protein that can act cell-autonomously to promote UNC-40-570
26
mediated asymmetric outgrowth (ADLER et al. 2006; CHANG et al. 2006; QUINN et al. 2006; QUINN 571
et al. 2008; MCSHEA et al. 2013). MIG-15 (NIK kinase) is a cytoplasmic protein and evidence 572
indicates that mig-15 functions cell-autonomously to mediate a response to UNC-6 (POINAT et al. 573
2002; TEULIÈRE et al. 2011). It’s proposed that mig-15 acts with unc-5 to polarize the growth cone’s 574
response and that it controls the asymmetric localization of MIG-10 and UNC-40 (TEULIÈRE et al. 575
2011; YANG et al. 2014). We previously noted that HSN neurons often become bipolar in mig-15 576
mutants and frequently UNC-40::GFP is localized to multiple surfaces in a single neuron, suggesting 577
that loss of MIG-15 enhances the ability of UNC-40::GFP to cluster (YANG et al. 2014). In our 578
experiments we used the mig-10 (ct141) loss-of-function allele (MANSER AND WOOD 1990; MANSER 579
et al. 1997) and the mig-15(rh148) allele, which causes a missense mutation in the ATP-binding 580
pocket of the kinase domain and is a weak allele of mig-15 (SHAKIR et al. 2006; CHAPMAN et al. 581
2008).582
583
WefindthattheextraprocessesinducedbyUNC-6∆Cexpressionaresuppressedbymig-584
10(ct141)(Figurs7F).Wealsofindthatthemig-15mutationcausesextraHSNprocessesand585
thatthelossofUNC-5functionsuppressestheseextraHSNprocesses(Figures7Fand7G).586
TheseresultssupportthehypothesisthattheabilityofUNC-5toregulatethedevelopmentof587
multipleprotrusionsinvolvesthemolecularmachinerythatcontrolsUNC-40-mediated588
asymmetricneuronaloutgrowth.589
590
UNC-5isrequiredforPLMoverextension591
The SOAL model predicts that the ability of UNC-5 to regulate the length and number of neural 592
protrusions is independent of the direction of outgrowth. HSN sends a single axon ventrally, while 593
PLM sends an axon anteriorly from a posteriorly positioned cell body. The HSN axon travels 594
27
towards UNC-6 sources, whereas the PLM axon pathway is perpendicular to UNC-6 sources. To 595
investigate whether UNC-5 activity can regulate the length or number of processes that develop 596
perpendicular to UNC-6 sources we examined the development of the PLM axon. We also chose 597
PLM because UNC-5wasalreadyknowntoaffectthelengthofthePLMaxon(LIetal.2008).598
599
GiventhatUNC-5activityisinvolvedintheoverextensionofthePLMaxon,andthatthemig-15600
mutationaffectsHSNoutgrowthinanUNC-40dependentfashion,wedecidedtotestwhether601
PLMoverextensionmightbeinducedbythemig-15mutationinanUNC-40-dependentfashion.602
TheHSNresultssuggestthatalteringmig-15functioncreatesasensitizedgeneticbackground.603
Thatis,theunc-5(ev480)mutationsuppressesHSNoutgrowthextensioninboththewild-type604
andmig-15(rh148)backgrounds,butthemig-15mutationcreatesastrongerpatterning605
phenotype.Thisideaissupportedbytheevidencethatthemig-15mutationenhancesthe606
abilityofUNC-40tolocalizeatsurfaces(YANGetal.2014).607
608
Wefindthatinmig-15(rh148)mutantsthePLMaxonoftenfailstoterminateatitsnormal609
positionandinsteadextendsbeyondtheALMcellbody.Thisoverextensionissuppressedin610
unc-5(e53);mig-15(rh148)andunc-40(e1430);mig-15(rh148)mutants(Figures8Aand8B).611
TheresultsareconsistentwiththeideathatUNC-5isrequiredfortheUNC-40-mediated612
outgrowthactivitythatcausesoverextensioninmig-15(rh148)mutants.613
614
UNC-5isrequiredforALMandAVMbranchingandextension615
WealsoinvestigatedtheeffectofUNC-5activityonpatterningwheresourcesofUNC-6and616
othercuesareinamorecomplexarrangement.Specifically,weexaminedwhetherUNC-5plays617
aroleintheoutgrowthofAVMandALMprocessesatthenervering.Duringlarval618
28
development,processesfromtheAVMneuronandthetwoALMneurons(oneoneachsideof619
theanimal)migrateanteriorlytothenerveringatdorsalandventralpositionsrespectively620
(Figure8C).At the nerve ring each axon branches; one branch extends further anteriorly and the 621
other extends into the nerve ring. Evidence suggests that at the midbody of the animal the 622
positioning of these axons along the dorsal-ventral axis requires UNC-6, UNC-40, and UNC-5 623
activity. In unc-6, unc-40, and unc-5 null mutants, or when the UNC-6 expression pattern is altered, 624
the longitudinal nerves are mispositioned (REN et al. 1999). Glia cells and neurons at the nerve ring 625
are sources of UNC-6 (WADSWORTH et al. 1996). The guidance of some axons in the nerve ring are 626
disrupted in unc-6 and unc-40 mutants (HAOetal.2001;YOSHIMURAetal.2008).Theprecise627
spatialandtemporalarrangementoftheUNC-6cueinrelationshiptothepositionofthe628
migratinggrowthconesisnotfullyunderstood.Nevertheless,theanteriorlymigratinggrowth629
conesappeartousetheUNC-6cuefromtheventralsourcestohelpmaintainthecorrectdorsal-630
ventralposition,evenwhilemovingtowardsthenervering,whichisanewsourceofUNC-6631
thatisperpendiculartotheventralsource.Atthenerveringtheaxonsbranch.Oneprocess632
continuesanteriorly,movingpastthenewUNC-6source,whereastheotherprojectsataright633
angleandmovesparalleltothenewsource.634
635
Wefindgeneticinteractionsinvolvingunc-5,unc-40,andmig-15thataffectoutgrowth636
patterningoftheALMandAVMextensionsatthenervering(Figures8C,8D,and8E).Inmig-637
15(rh148);unc-5(e53)mutants,theAVMaxonoftenfailstoextendanteriorlyfromthebranch638
pointandonlyextendsintothenervering,oritfailstoextendintothenerveringandonly639
extendsanteriorly,oritfailstodobothandterminatesatthispoint.Inunc-40(e1430)mutants,640
theaxonoftenfailstobranchintothenervering,althoughitextendsanteriorly.Incomparison,641
inunc-40(e1430);mig-15(rh148)mutantsmoreaxonsextendintothenervering.Theseresults642
29
suggestthatUNC-5(andMIG-15)helpsregulateUNC-40-mediatedoutgrowthtopatternthe643
outgrowthatthenervering.644
645
Interactionsbetweenunc-5andothergenesaffectaprobabilitydistributionforthe646
directionofextension647
Wehypothesizethatthereareinteractionsbetweenunc-5andothergenesthatcontrolthe648
degreetowhichthedirectionofoutgrowthfluctuates.Probabilitydistributionsforthe649
directionofextensionareusedtostudyhowgenesaffectthefluctuationofoutgrowthactivity.650
Bycomparingthedistributionscreatedfromwild-typeandmutantanimals,therelativeeffect651
thatgeneshaveonthefluctuationcanbedetermined.Toaccomplishthis,thedirectionthatthe652
HSNaxoninitiallyextendsfromthecellbodyisscored(Figure9A). 653
654
Usingthisassay,weexaminedgeneticinteractionsbetweenunc-5andfourothergenes;elg-20,655
sax-3,madd-2,orunc-6.Wehavechosentheseparticulargenesbecausepreviousobservations656
suggestinteractions.1)EGL-20(Wnt)isasecretedcueexpressedfromposteriorsources(PAN657
etal.2006)anditaffectstowhichsurfaceoftheHSNneurontheUNC-40receptorlocalizesand658
mediatesoutgrowth(KULKARNIetal.2013).Basedonadirectionalphenotype,asynergistic659
interactionbetweenunc-5andegl-20hasbeenobserved.Ineitherunc-5oregl-20mutantsthe660
ventralextensionofAVMandPVMaxonsisonlyslightlyimpaired,whereasinthedouble661
mutantsthereismuchgreaterpenetrance(LEVY-STRUMPFANDCULOTTI2014).2)SAX-3(Robo)is662
areceptorthatregulatesaxonguidanceandisrequiredfortheasymmetriclocalizationofUNC-663
40inHSN(TANGANDWADSWORTH2014).Basedonadirectionalphenotype,SAX-3andUNC-40664
appeartoactinparalleltoguidetheHSNtowardstheventralnervecord(XUetal.2015).3)665
MADD-2isacytoplasmicproteinofthetripartitemotif(TRIM)familythatpotentiatesUNC-40666
30
activityinresponsetoUNC-6(ALEXANDERetal.2009;ALEXANDERetal.2010;HAOetal.2010;667
MORIKAWAetal.2011;SONGetal.2011;WANGetal.2014).MADD-2::GFPandF-actincolocalize668
withUNC-40::GFPclustersintheanchorcell(WANGetal.2014).4)Ofcourse,UNC-6isanUNC-669
5ligand.DCC(UNC-40)andUNC5(UNC-5)arethoughttoactindependentlyorinacomplexto670
mediateresponsestonetrin(UNC-6)(COLAVITAANDCULOTTI1998;HONGetal.1999;MACNEILet671
al.2009;LAIWINGSUNetal.2011). 672
673
Inatestforinteractionwithegl-20,wefindthatincomparisontounc-5(e53)oregl-20(n585)674
mutants,theunc-5(e53);egl-20(n585)doublemutanthavealowerprobabilityforventral675
outgrowthandhigherprobabilityforoutgrowthinotherdirections(Table1).Thissuggests676
thatunc-5andegl-20mayactinparalleltoachievethehighestprobabilityforHSNventral677
outgrowth,i.e.theyacttopreventUNC-40-mediatedoutgrowthfromfluctuatinginother678
directions.679
680
Inatestforinteractionwithsax-3,wefindthattheprobabilityofoutgrowthineachdirectionin681
unc-5(e53);sax-3(ky200) mutantsissimilartotheprobabilitiesinsax-3(ky200)orsax-3(ky123)682
mutants(Table1).Giventheresultswithunc-5andegl-20,wefurthertestedtheprobabilityof683
outgrowthineachdirectioninegl-20(n585);sax-3(ky123) mutants.Wefindthatitissimilarto684
theprobabilitiesinsax-3(ky200)orsax-3(ky123)mutants(Table1).Thesax-3(ky123)allele685
resultsinadeletionofthesignalsequenceandfirstexonofthegene,whereassax-3(ky200)686
containsamissensemutationwhichisthoughttocauseproteinmisfoldingandmislocalization687
attherestrictivetemperature(25°C)(ZALLENetal.1998;WANGetal.2013).Theegl-688
20(n585);sax-3(ky123) mutants do not grow well and so it is easier to use the temperature sensitive 689
31
sax-3 allele. Together,theresultssuggestthatsax-3mayberequiredforboththeunc-5-andthe690
egl-20-mediatedactivitiesthatallowthehighestprobabilityforHSNventraloutgrowth.691
692
In a test for interaction with madd-2, we find that the probability of outgrowth in each direction in 693
unc-5(e53);madd-2(tr103) mutants is similar to the probabilities in madd-2(tr103) mutants (Table 1). 694
There is a higher probability for anterior HSN outgrowth, similar to what is observed in unc-695
40(e1430) mutants. Theseresultssuggestthatmadd-2mightberequiredfortheunc-40696
outgrowthactivity.Theprobabilityofoutgrowthineachdirectioninmadd-2(tr103);sax-697
3(ky123) mutantsissimilartotheprobabilitiesinsax-3(ky200)orsax-3(ky123)mutants(Table698
1).Themadd-2(tr103)alleleappearstoactasageneticnull(ALEXANDERetal.2010).699
700
Inatestforinteractionwithunc-6,wefindthattheprobabilityofoutgrowthineachdirection701
inunc-5(e53);unc-6(ev400) and unc-40(e1430);unc-5(e53) mutantsissimilartotheprobabilities702
inunc-6(ev400)mutantsinsofarasthereisalowerprobabilityforventraloutgrowthanda703
higherprobabilityforanterioroutgrowth(Table1).However,theprobabilitiesineach704
directionareclosertothoseobtainedfromtheunc-40(e1430)mutantsbecausetheprobability705
ofanterioroutgrowthislowerinthesemutantsthaninunc-6mutants.ThissuggestthatUNC-5706
andUNC-40mighthelpincreasetheprobabilityofanterioroutgrowthintheabsenceofUNC-6.707
708
unc-5 is a member of a class of genes that has a similar effect on the spatial extent of movement709
Theresultsaboveshowthatunc-5anditsinteractionswithothergenesaffectthedegreeto710
whichthedirectionofoutgrowthfluctuates.Thedegreeoffluctuationdiffersdependingonthe711
genesinvolved.Apropertyofrandommovementisthatthemorethedirectionofmovement712
fluctuates,theshorterthedistanceoftravelisinagivenamountoftime(Figure2E).Todepict713
32
howunc-5andothergenesdifferentiallyregulatethespatialextentofmovement,weuse714
randomwalkmodeling.Randomwalksdescribemovementthatoccursasaseriesofstepsin715
whichtheanglesandthedistancesbetweeneachstepisdecidedaccordingtosomeprobability716
distribution.Byusingtheprobabilitydistributionobtainedfromamutantforeachstepofa717
randomwalk,andbykeepingthedistanceofeachstepequal,arandomwalkcanbe718
constructed(Figure9A).Ineffect,thismethodappliestheprobabilitydistributiontodiscrete719
particleshavingidealizedrandomwalkmovementonalattice.Byplottingrandomwalks720
derivedfromwild-typeanimalsanddifferentmutants,therelativeeffectthatmutationshave721
onrandomwalkmovementcanbevisualized.Forexample,Figure9Bshows50tracksof500722
stepsforwildtypeandtwomutants(mutantAisunc-5(e53)andmutantBisegl-20(n585);sax-723
3(ky123)).Thisrevealstheeffectthatamutationhasonthedisplacementofmovement.After724
500stepsthedisplacementfromtheorigin(0,0)isonaveragelessformutantAthanfor725
wildtype,andlessformutantBthanforwildtypeormutantA.726
727
Therandomwalkmodelsshowtherelativeeffectthatamutationhasonapropertyof728
outgrowthmovement.Itisworthnotingthatthisisnotmodelingtheactualtrajectoryof729
migratingaxons.Asdiscussedintheintroduction,neuronaloutgrowthisessentiallyamass730
transportprocessinwhichmass(themolecularspeciesofthemembrane)issustainedatthe731
leadingedgeandmovesoutward.Ourassaycomparestheeffectthatdifferentmutations732
wouldhaveonthemovementofmassattheleadingedgeofanextensioniftheconditionsofthe733
systemwerekeptconstant.Ofcourse,invivotheconditionsarenotconstant.Forone,asan734
extensionmovesitwillencounternewenvironmentswherethecuesmaybeneworatdifferent735
concentrations,allofwhichaffecttheprobabilitydistribution.Theactualpatternsof736
outgrowthobservedaretheresultofalltheprobabilitiesforoutgrowththatoccurateach737
33
instanceoftime.Ithasrecentlybeensuggestedthatourdescriptionmightbemoreaccurately738
describedasneuro-percolation,asuperpositionofrandom-walks(AIELLO2016).739
740
Ourrandomwalkanalysiscomparestheeffectthatdifferentmutationshaveontheproperties741
ofmovement.Inwild-typeanimals,thereisahighprobabilityforoutgrowthintheventral742
direction.Theanalysisshowsthatconditionsinwildtypecreatenearlystraight-linemovement,743
i.e.ifthesamerandomwalkisrepeatedlydoneforthesamenumberofsteps,startingatthe744
sameorigin,thefinalpositionofthewalkalongthexaxisdoesnotvaryagreatamount.In745
comparison,wefindthatamutationcancreaterandomwalkmovementinwhichthefinal746
positionismorevaried.Thisvariationoccursbecausethemutationincreasestheprobabilityof747
outgrowthinotherdirections.Foreachmutation,wesimulate50randomwalksof500steps748
andderivethemeanandstandarddeviationofthefinalpositionalongtheX-axis.Tocompare749
strains,weplotthenormaldistribution,settingthemeanatthesamevalueforeach.The750
differencebetweenthecurveforamutantandwildtypeshowsthedegreetowhichthe751
mutationcausedthedirectionofoutgrowthtofluctuate(Figure9C).752
753
Theresultsrevealfourdifferentdistributionpatterns(Figure10).Thefirstclassisthewild-754
typedistribution,whichhasthedistributioncurvewiththehighestpeak.Thesecondclass755
comprisesunc-5,egl-20,unc-53,andunc-6inwhichthedistributioncurveisflatterthanthe756
wild-typecurve.Weincludedunc-53becauseourpreviousstudyshowedthatithasgenetic757
interactionswithunc-5andunc-6(KULKARNIetal.2013).Theunc-53geneencodesa758
cytoskeletalregulatorrelatedtothemammalianNAVproteinsandunc-53mutationscause759
guidancedefects(MAESetal.2002;STRINGHAMetal.2002;STRINGHAMANDSCHMIDT2009).The760
thirdclasshasadistributioncurvewhichisflatterthanthesecondandcomprisessax-3,mig-15,761
34
andseveraldoublemutationcombinations(Figure10).Thefourthclasshastheflattest762
distributioncurveandcomprisesegl-20;sax-3,unc-40;sax-3,andunc-53;sax-3;unc-6.Thisclass763
indicatesthegreatestdegreeoffluctuation.Theabilitytocausethedirectionofmovementto764
fluctuateisnotassociatedwithaspecificdirectionofHSNmovement.Forexample,unc-5;sax-3,765
unc-53;unc-6,unc-40;egl-20,andmadd-2;sax-3eachshowawidelydispersedpattern,butthe766
directionisventral,dorsal,anterior,andposterior,respectively(Figure10).767
768
Thedistributionpatternsindicatethatgeneshavedifferenteffectsontheextentthatoutgrowth769
movementcantravelthroughtheenvironment.Meansquareddisplacement(MSD)isa770
measureofthespatialextentofrandommotion.TheMSDcanbecalculatedfromtherandom771
walkdata.PlottingMSDasafunctionofthetimeintervalshowshowmuchanobjectdisplaces,772
onaverage,inagivenintervaloftime,squared(Figure11A).Fornormalmoleculardiffusion,773
theslopeoftheMSDcurveisdirectlyrelatedtothediffusioncoefficient.Incellmigration774
modelsthisvalueisreferredtoastherandommotilitycoefficient.Coefficientsare775
experimentallydetermined;theydescribehowlongittakesaparticularsubstancetomove776
throughaparticularmedium.Wedeterminethisvalueinordertonumericallyandgraphically777
comparehowmutationscanalterdisplacementrelativetowildtype(Figure11B).Thefour778
classesofgenesareapparentbycomparingtheheightofthebarsinFigure11B.Resultsforthe779
unc-40mutationarealsoshow.Therandomwalkpatternispublished(TANGANDWADSWORTH780
2014).781
782
Theresultsofthismodelingsuggestthattheactivitiesofcertaingenes,andcombinationsof783
genes,havedistincteffectsontherateofoutgrowthmovement.Intheory,thesedifferences784
couldbeanimportantmeansbywhichgenescausedifferentoutgrowthpatterns.785
35
786
UNC-40receptorclusteringiscoupledtotheSOALprocess787
WeinvestigatedtherelationshipbetweenUNC-40::GFPlocalizationandoutgrowthmovement.788
BeginningintheearlyL2stage,UNC-40::GFPbecomeslocalizedtotheventralsideofHSNin789
wildtype(ADLERetal.2006;KULKARNIetal.2013).Reflectingthedynamicmorphological790
changesthatoccurastheHSNaxonforms,thesiteofasymmetricUNC-40::GFPlocalization791
alternatesintheneuritesandalongtheventralsurfaceoftheneuron(KULKARNIetal.2013).792
DynamicUNC-40::GFPlocalizationpatternshavealsobeenreportedfortheanchorcell,in793
whichUNC-40andUNC-6arealsokeyregulatorsofextension(ZIELetal.2009;HAGEDORNetal.794
2013).LiveimagingoftheanchorcellrevealsthatUNC-40::GFP“clusters”form,disassemble,795
andreformalongthemembrane(WANGetal.2014).However,liveimagingcan’tdirectly796
ascertainwhetherthepositionofaclusterisrandomlydeterminedsinceamovementevent797
cannotberepeatedlyobservedtodetermineaprobabilitydistribution.Mathematicalmodeling798
ofclustermovementasastochasticprocesshasnotbeendone.799
800
TheUNC-40::GFPclusteringphenomenaraisesquestionsabouttherelationshipbetween801
robustUNC-40clustering(i.e.,sitesofdistinctUNC-40localizationobservablebyUNC-40::GFP)802
andUNC-40-mediatedoutgrowthactivity.TwomodelsarepresentedinFigure12.Inthefirst803
model,theoutputoftheSOALprocessisreceptorclustering(Figure12A).Afteracluster804
becomesstabilizedatasite,themachineryrequiredforoutgrowthisrecruitedandoutgrowth805
occurs.Inourmodel,theSOALprocessandUNC-40-mediatedoutgrowthactivityarecoupled806
andarepartofthesamestochasticprocessthatoccursatthemicro-scale(Figure12B).UNC-807
40::GFPclusteringisamacro-scaleeventwhichcanbeobserved.Itisaconsequenceofthe808
micro-scaleevents.809
36
810
Themodelsmakespecificpredictionsthatcanbetested.Inthefirstmodel,UNC-40-mediated811
outgrowthwillnothappenifUNC-40doesnotcluster.Inourmodel,thelossofUNC-40812
clusteringdoesnotleadtoalossofUNC-40-mediatedoutgrowth.Inthesax-3mutantthereisa813
largefluctuationinthedirectionofoutgrowth;itisinthethirdclassofmutants(Figures10and814
11).Wepreviouslyreportedthatsax-3isrequiredforrobustUNC-40::GFPasymmetric815
localization;insax-3mutantsUNC-40::GFPremainsuniformlydispersedaroundtheperiphery816
ofHSN((TANGANDWADSWORTH2014)andFigure13).Whereasinthesax-3mutantthereisa817
ventralbiasforoutgrowth,intheunc-40;sax-3mutantthereisnot(Figure10).Thissuggests818
thatinthesax-3mutantthereisUNC-40-mediatedoutgrowthactivitythathelpscreatea819
ventralbias.ThisisconsistentwithourmodelbecauseUNC-40-mediatedoutgrowthactivityis820
occurringevenwhenrobustUNC-40::GFPisnotobserved.821
822
Wehypothesizethataconsequenceofthemicro-scaleSOALprocessovertimeismacro-scale823
UNC-40clustering.Ifso,thenunc-5activityshouldaffectUNC-40::GFPclusteringbecauseit824
affectsthedegreetowhichthedirectionofUNC-40receptorlocalizationfluctuates.However,825
eventhoughthereisahigherprobabilitythatlocalizationoccursatsurfacesotherthanatthe826
ventralsurface,weobserverobustasymmetricallylocalizedUNC-40::GFPclusteringinunc-827
5(e53)mutants(KULKARNIetal.2013).Wespeculatethatunc-5(e53),aswellasothergene828
mutations,donotcausethedirectionofUNC-40localizationtofluctuateenoughtoprevent829
observableUNC-40::GFPclustering.WethereforedecidedtoexamineUNC-40::GFPclustering830
indoublemutantstodeterminewhethertheabilitytoobserveUNC-40::GFPclusteringis831
correlatedwiththedegreeoffluctuation.832
833
37
Wemadedoublemutantcombinationsbetweenunc-5,andegl-20orunc-53.Inegl-20andunc-834
53singlemutantsthereisfluctuationinthedirectionofoutgrowth(Figures10and11)and835
robustasymmetricalUNC-40::GFPlocalization(Figure13,unc-53resultswerepreviously836
reported(KULKARNIetal.2013)).Incomparisontothesinglemutants,thedoublemutantsall837
showanincreaseinthedegreetowhichthedirectionofoutgrowthfluctuates(Figures10and838
11).Further,incontrasttothesinglemutants,UNC-40::GFPremainsuniformlydispersed839
aroundtheperipheryofHSNinthedoublemutants(Figure13).Theresultssuggesta840
correlationbetweenincreasedfluctuationofUNC-40-mediatedoutgrowthactivityandthe841
abilitytodetectUNC-40::GFPclustering.Thisisconsistentwithourmodel(Figure12B).We842
alsoobservethatinmadd-2(tr103)mutantsthedirectionofoutgrowthfluctuates(Table1),but843
unlikeegl-20andunc-53singlemutants,thereisnotrobustasymmetricalUNC-40::GFP844
localizationandUNC-40::GFPremainsuniformlydispersed(Figure13).Thedoublemutants,845
unc-5;madd-2,aresimilartothesinglemadd-2mutant.Similarresultsareobservedwithsax-3846
andunc-5;sax-3mutants(Figure13).Wehypothesizethatinthemadd-2andsax-3mutations847
thedegreetowhichthedirectionofUNC-40localizationfluctuatesissogreatthattheunc-5848
mutationmakesnodifferenceontheUNC-40::GFPclusteringphenotype.849
850
Discussion 851
Wehaveproposedamodelofneuronaloutgrowthmovementthatisbasedonstatistically852
orientedasymmetriclocalization(SOAL).ThismodelstatesthattheprobabilityofUNC-4O853
localizingandmediatingoutgrowthatonesiteaffectstheprobabilityoflocalizationand854
outgrowthatothersitesaswell.Byregulatingthisprocess,genescontrolthedegreetowhich855
thedirectionofoutgrowthfluctuatesand,consequently,theoutwardmovementoftheplasma856
membrane.UNC-5isareceptorforUNC-6andcanformacomplexwithUNC-40.UNC-5is857
commonlyproposedtodirectoutgrowthbymediatingarepulsiveresponsetoUNC-6.In858
38
contrast,ourmodelisnotbasedontheconceptofrepulsionanditpredictsthatUNC-5can859
controltherateofoutwardmovementthatisdirectedtowards,awayfrom,orperpendicularto860
UNC-6sources.Wereportthatunc-5loss-of-functionmutationsaffectthedevelopmentof861
multipleneuritesthatdevelopfromHSNandextendtowardsUNC-6sources.Theyalso862
suppressthedevelopmentofextraHSNprocesseswhichareinducedbyamig-15mutationor863
byexpressionoftheN-terminalfragmentofUNC-6andwhichextendtowardsUNC-6sources.864
Wealsoobservethatunc-5mutationssuppresstheanterioroverextensionofthePLMaxonthat865
occursinthemig-15mutant.ThisaxonextendsperpendiculartoUNC-6sources.Finally,unc-5866
loss-of-functionmutationsaffectthebranchingandextensionofALMandAVMaxonsatthe867
nerveringwherethesourcesofUNC-6areinamorecomplexarrangement.Belowwediscuss868
howtheSOALmodelcanbeusedtointerpretunc-5mutantphenotypes.Wearguethatineach869
case,phenotypescanbeexplainedbytheabilityofUNC-5toaffectUNC-40asymmetric870
localization,whichinturncontrolsthedegreetowhichthedirectionofoutgrowthactivity871
fluctuatesandtheextentofoutwardmovement.Ourmodelalsosuggestsgenesthatwere872
previouslyclassifiedasregulatingattractionorrepulsionmightactwithunc-5toregulate873
neuronaloutgrowthbycontrollingthedegreetowhichthedirectionofUNC-40-mediated874
outgrowthfluctuates.WeshowthatUNC-5actstogetherwiththecytoplasmicproteinUNC-53875
toregulateUNC-40asymmetriclocalizationinresponsetotheUNC-6andEGL-20extracellular876
cues.877
878
PLMextensionphenotype:Wehypothesizethatcue(s)presentaroundthePLMcellbody879
createastrongbiasforanterioroutgrowthactivity(Figure14A).TheseincludeUNC-6and880
othercuesthatflankthelongitudinalpathwayandcauseanequalprobabilityofoutgrowthin881
thedorsalandventraldirections.UNC-40SOALactivityactstosuppressnonUNC-40SOAL882
activity(Figure6).Astheextensionmovestowardsmoreanteriorpositions(Figure14A,883
39
positions2and3),itencountershigherlevelsofacue(s)thatpromotesoutgrowththrough884
nonUNC-40receptors.Asaresult,theprobabilityofnonUNC-40SOALactivityatthedorsaland885
ventralsurfacesoftheleadingedgeincreases.Becausetheasymmetriclocalizationofa886
receptorisstatisticallydependent,theprobabilityofnonUNC-40SOALactivityattheanterior887
surfaceoftheleadingedgemustdecreaseasthelocalizationelsewhereincreases.Whilethis888
effectdoesnotnecessarilychangetheanteriorbiasforoutgrowth,itdoessignificantly889
increasesthedegreetowhichthedirectionofnonUNC-40outgrowthactivityfluctuates,which890
consequentlydecreasestheextentofoutwardmovement(Figure14C).Thiseffectstalls891
forwardmovement.892
893
WehypothesizethatmutationsaffectthedegreetowhichthedirectionofnonUNC-40894
outgrowthactivityfluctuatesatposition3(Figure15).MIG-15appearstopromotenonUNC-40895
SOALactivity,whereasUNC-5promotesUNC-40SOALactivity.Becauseeachactivitycan896
suppresstheother,differentdomainsofnonUNC-40andUNC-40SOALactivitycanbe897
establishedalongthesurfaceoftheleadingedge.Astheextensionmovestowardsposition3,898
thereishighernonUNC-40activityatthemoreanteriorsurfaceandhigherUNC-40activityat899
thedorsalandventralsurfaces.BysuppressingnonUNC-40activity,themig-15mutation900
increases,relativetowildtype,theUNC-40activityatthedorsalandventralsurfacesatposition901
3.ThisUNC-40activitydecreasestheprobabilityofnonUNC-40activityatthesesurfacesand902
increasestheprobabilityofnonUNC-40activityattheanteriorsurface.Byreducingthedegree903
towhichnonUNC-40outgrowthfluctuates,agreateranteriordirectionalbiasiscreatedinthe904
mig-15mutants.Thisresultsinoverextension.Theunc-5mutationrepressestheUNC-40905
activityatthedorsalandventralsurfaces,increasingthedegreetowhichthedirectionofthe906
nonUNC-40outgrowthactivityfluctuates.Thissuppressestheoverextensioncausebythemig-907
15mutation.908
40
909
AVMnerveringbranchingandextensionphenotype:SimilartowhatisproposedforPLMat910
position3inFigure14,allthesurfacesoftheleadingedgeofAVMbecomeexposedtohigh911
levelsofacue(s)(Figure16A,position1).Thedegreetowhichthedirectionofoutgrowth912
activityfluctuatesgreatlyincreasesandoutwardmovementstalls.ForAVM,thisoccursatthe913
nervering,whichisasourceofUNC-6.However,forAVMtherearecuesatthenervering914
whicharearrangedperpendiculartooneanother.WeproposethatthehighlevelofUNC-6at915
allsurfacesallowsUNC-40SOALactivitytobecomemoreuniformlydistributedalongall916
surfacesoftheleadingedge(Figure16B)andcreatesastate where the probabilities of outgrowth 917
in every direction become equal. Both anterior and dorsal outward movement stalls (Figure 16C). 918
This state allows any new cues encountered to effectively create a directional bias (Figure 4). UNC-6919
andothercuesarearrangedalongthenervering,whereasnonUNC-6cuesarearranged920
anteriorofthenervering.Assomeoutgrowthventuresanteriorlyanddorsally,thesecues921
stimulatethedevelopmentof nonUNC-40 and UNC-40 SOAL activity domains (Figure 16B, 922
position 2). Even slight outward movement in the anterior or dorsal directions may reinforce 923
movement in that direction if cues arranged along the axis perpendicular to the direction bias 924
suppress the UNC-40 or nonUNC-40 SOAL activity along the surfaces perpendicular to the 925
directional bias (as depicted in Figure 14B, position 1).926
927
WehypothesizethatmutationsaffectthedegreetowhichthedirectionofUNC-40andnonUNC-928
40outgrowthactivityfluctuatesatposition2(Figure17).Inunc-40mutants,thelackofdorsal929
UNC-40activityallowsthedirectionofnonUNC-40outgrowthtofluctuatemore.However,the930
anteriorcuesincreasetheprobabilityofanteriorlydirectednonUNC-40outgrowthand,931
thereby,decreasetheprobabilityofdorsallydirectedactivity.Thissuppressesdorsal932
extension,whilestillallowinganteriorextension.LossofMIG-15activityintheunc-40mutant933
41
backgroundsuppressesthenonUNC-40SOAL.Incomparisontothesingleunc-40mutant,in934
unc-40;mig-15mutantstheprobabilityofanterioroutgrowthinresponsetotheanteriorcuesis935
lower.Consequently,theprobabilityofdorsalnonUNC-40outgrowthishigher.Wespeculate936
thatthisallowssomedorsalextension.Inunc-5mutants,UNC-40SOALactivityisreduced,but937
theactivityisstillsufficienttoallowdorsalextension.LossofbothUNC-5andMIG-15function938
mostseverelyhamperstheabilitytodirectthereceptorsspecificallytoonesurface.Theunc-939
5;mig-15mutantshavethemostabnormaloutgrowthpatterns.940
941
HSNextensionphenotypes:Wehypothesizethatthereishighprobabilityforventrally942
directedoutgrowthfromtheHSNcellbodybecauseofthestrongoutgrowth-promotingeffect943
oftheUNC-40-mediatedresponsetotheUNC-6cue,whichisinahigherconcentrationventral944
ofthecellbody(Figure18A).WehypothesizethatthesameprocesstakesplaceintheHSN945
neuronasinthePLMneuron,exceptthemovementistowardstheUNC-6source.Wedepictin946
Figure8Bthatatposition1thereissomenonUNC-40SOALactivityattheventralsurfaceofthe947
leadingedge.Byposition2,higherlevelsofUNC-6increaseUNC-40SOALandsuppressventral948
nonUNC-40SOALactivity.Atpositon3,UNC-6ispresentathighlevelsalongallsurfacesand949
thedirectionofUNC-40outgrowthgreatlyfluctuates.Possibly,thedegreetowhichthe950
directionofUNC-40andnonUNC-40outgrowthactivityfluctuatesisgreateratposition1,than951
atposition2(Figure18C).However,atposition3thefluctuationisgreatest.952
953
WehypothesizethattheinterplaybetweenUNC-40andnonUNC-40SOALactivityallows954
multipleextensionstodevelopinthesamedirection.Infact,UNC-40, UNC-5, MIG-15, and 955
UNC-6 (netrin) activities may function as a type of reaction-diffusion system (TURING 1952; GIERER 956
AND MEINHARDT 1972; MEINHARDT AND GIERER 2000; KONDO AND MIURA 2010; GOEHRING AND 957
42
GRILL 2013). Along the ventral surface there is a competition between UNC-40 receptors to direct 958
further UNC-40 localization to that site and to inhibit flanking receptors from doing the same. 959
Overtime, the SOAL activity that began at one site predominates, leading to an area of higher 960
outgrowth activity (Figure 19). We speculate that by helping to suppress UNC-40 SOAL activity, 961
nonUNC-40 activity increases the threshold by which the SOAL activity at one site can begin to 962
predominate. The mig-15 mutation suppresses the nonUNC-40 SOAL activity and decreases the 963
threshold. This may allow more sites along the membrane where UNC-40 SOAL activity can 964
predominate. The sites do not overlap because of the long-range negative feedback that inhibits 965
neighboring UNC-40 activity. The unc-5 mutation suppresses UNC-40 SOAL activity, both the 966
positive and negative feedback loops. This retards the ability to enhance and localize the process to 967
one area of the surface. This causes greater fluctuation in the direction of outgrowth activity across 968
the entire ventral surface of the neuron. As a result, the rate of initial outgrowth is even less than that 969
which occurs in wildtype and the area of outward growth is broader. 970
971
AgeneticpathwayforUNC-40asymmetriclocalization972
We present a genetic pathway for the asymmetrical localization of UNC-40 based on the phenotype 973
of robust UNC-40::GFP clustering in HSN. Afullunderstandingofthemolecularmechanisms974
underlyingtheSOALprocessisanimportantlong-termgoal.SincewebelievethatUNC-975
40::GFPclusteringisareadoutofthatprocess,constructinggeneticpathwaysfortheclustering976
ofUNC-40::GFPisasteptowardthisgoal.WewishtoknowhowUNC-5mediatessignaling977
withinHSNthatcontrolstheUNC-40asymmetriclocalizationprocess.However,arolefor978
UNC-5inHSNisparadoxicalgiventhewidespreadideathatUNC-5mediatesarepulsive979
responsetoUNC-6andthatHSNoutgrowthistowardsthesourceofUNC-6.Allthesame,we980
suggestacell-autonomousroleforUNC-5inHSNisthemostparsimoniousmodel.First,UNC-5981
isanUNC-6receptorthatcanmediateneuronalresponseswhenincomplexwithUNC-40982
43
(HONGetal.1999;GEISBRECHTetal.2003;KRUGERetal.2004;FINCIetal.2014).Wepreviously983
showedthatUNC-40conformationalchangesregulateHSNasymmetriclocalizationinHSN(XU984
etal.2009)andwenowshowthatUNC-5regulatesUNC-40asymmetriclocalizationinHSN.It985
isthereforeplausiblethatUNC-5affectsUNC-40conformationalchangesthatregulateUNC-40986
asymmetriclocalization.Second,UNC-5canalterthenumbertoHSNoutgrowthsinresponse987
toUNC-6andtotheUNC-6∆Cligand.DirectionalguidancebyUNC-6andUNC-6∆Cisgenerally988
normalinanunc-5mutant,suggestingthattheabilityofUNC-5toregulatethenumberof989
outgrowthsisnotduetoanalterationintheextracellulardistributionofitsUNC-6ligand.990
Further,theUNC-6∆Cligandandthemig-15mutationcreatethesameoutgrowthphenotype,991
whichcanbesuppressedbylossofUNC-5function,andwehaveshownthatMIG-15actscell992
autonomouslyinHSNtoregulateUNC-40asymmetriclocalization(YANGetal.2014).Further,993
wehaveshownthattheUNC-5-mediatedresponsethatregulatesUNC-40asymmetric994
localizationalsodependsonUNC-53(NAV2)(KULKARNIetal.2013),acytoplasmicproteinthat995
functionscell-autonomouslyforcellmigrationandaxonguidance(STRINGHAMetal.2002).996
Together,theseobservationsstronglysuggestthatUNC-5directlyregulatessignalingwithin997
HSN.Third,aroleforUNC-5intheguidanceofAVMandPVMaxonstowardsUNC-6sources998
hasalsobeensuggested.Asynergisticinteractionbetweenunc-5andegl-20isobserved;in999
eitherunc-5oregl-20mutantstheventralextensionofAVMandPVMaxonsisonlyslightly1000
impaired,whereasinthedoublemutantsthereisamuchgreaterpenetrance(LEVY-STRUMPFAND1001
CULOTTI2014).Theexpressionofanunc-5transgeneinAVMandPVMcanrescuetheAVMand1002
PVMaxonguidancedefectsoftheunc-5;egl-20doublemutant(LEVY-STRUMPFANDCULOTTI2014).1003
WenotethatforHSN,transgenicrescueusingunc-5constructshavenotbeensuccessfulandin1004
wild-typeanimalsUNC-5expressioninHSNhasnotbeenreported.Aswell,expressionhasnot1005
beenreportedinAVM,PVM,andPLMwild-typeneurons.Wesuspecttheremaybetechnical1006
difficultiesorthatUNC-5expressionmightbelowinthesecells.UNC-5isdetectedinPLMin1007
44
rpm-1mutants,whichisconsistentwithevidencethatUNC-5activityisrequiredforPLM1008
overextensioninthesemutants(LIetal.2008).1009
1010
To construct geneticpathways,weusethereadoutofwhetherUNC-40::GFPisclearlyand1011
consistentlylocalizedtoanysideoftheHSNneuronindifferentmutants(Figure13).A1012
summaryoftheresultsispresented(Figure20A).UNC-6isrequiredforrobustasymmetric1013
UNC-40localization;intheabsenceofUNC-6functionUNC-40remainsuniformlydistributed1014
alongthesurfaceoftheplasmamembrane.ThelossofbothUNC-53andUNC-5functionalso1015
resultsinauniformdistribution,howeverlossofeitheronealonedoesnot.Thissuggeststhat1016
UNC-53andUNC-5pathwaysactredundantlydownstreamofUNC-6(Figure20B).Moreover,1017
weobservethereisrobustasymmetricUNC-40localizationwhenthereisalossofUNC-61018
activityinadditiontothelossofUNC-53andUNC-5.Thissuggestsathirdpathwaythatis1019
suppressedbyUNC-6whenUNC-53andUNC-5activityaremissing.LossofbothUNC-5and1020
UNC-6doesnotallowUNC-40localization,whereaslossofbothUNC-53andUNC-6does,1021
thereforeUNC-53,ratherthanUNC-5,actswithUNC-6tosuppressthethirdpathway.1022
1023
UNC-40becomeslocalizedwhenEGL-20activityislost.Aswell,UNC-40becomeslocalized1024
whenbothEGL-20andUNC-53activitiesarelost.ThisisconsistentwithUNC-6promoting1025
UNC-40localizationviatheUNC-5pathway.LossofEGL-20andUNC-5preventsUNC-401026
localization.Intheseanimals,theUNC-5pathwayisabsentandUNC-6ispresenttoblockthe1027
thirdpathway,thereforetheUNC-53pathwaythatleadstoUNC-40localizationmustrequire1028
EGL-20,aswellasUNC-6.1029
1030
45
LossofUNC-6activityorlossofbothUNC-6andEGL-20activitypreventslocalization,whereas1031
lossofonlyEGL-20doesnot.Toexplainthis,weproposethatwhenUNC-6islost,thethird1032
pathway,whichwouldotherwisebeactivatedbythelossofUNC-6,remainssuppressed1033
becauseEGL-20activitypromotessuppressionviaUNC-53activity.Thissuppressionalso1034
explainswhylossofUNC-6andUNC-5activitydoesnotcauselocalization.1035
1036
ThegeneticpathwaysareconsistentwiththemodelsproposedinFigures1and6.Inthe1037
models,positivefeedbackloopsamplifythepolarizedresponsestoextracellularcues,whereas1038
negativefeedbacklimitstheresponsesandconfinesthepositivefeedbacktothesitesof1039
interaction.WehypothesizethattheUNC-5andUNC-53geneticpathwaysshownatthetop1040
andbottomofFigure20BcorrespondtothepositivefeedbackloopsdepictedinFigures1and61041
bythearrows.The“?”geneticpathwaycorrespondstoUNC-40asymmetriclocalizationand1042
outgrowthactivityintheabsenceofUNC-6.TheUNC-53geneticpathwaysinFigure20Bthat1043
blockthe“?”pathwaycorrespondstothenegativefeedbackloops(lines)inFigures1and61044
whichpreventUNC-40asymmetriclocalizationandoutgrowthintheabsenceofUNC-6.Lossof1045
bothUNC-6andEGL-20preventsrobustasymmetricUNC-40localizationbecausebothUNC-6-1046
andEGL-20-mediatedpositivefeedbackloopsaredisrupted.Apositivefeedbackloopmaybe1047
necessarytoestablishanegativefeedbackloop.Therefore,the“?”pathwayisnotactivewhen1048
bothUNC-6andEGL-20areabsent.1049
1050
ModelforhowmultiplereceptorSOALactivitiesdeterminethedirectionand1051
displacementofmembranemovement1052
WehypothesizethatUNC-5activityregulatestheSOALactivitiesofboththeUNC-40and1053
nonUNC-40receptors.UNC-5functionswithUNC-40toincreasetheprobabilityofUNC-401054
46
localizingandmediatingoutgrowthatsiteswhereUNC-6interactswithUNC-40(Figure21A,1055
1).IfUNC-5activityisreducedorlost,UNC-40stillmediatesoutgrowth,butthereisahigher1056
probabilityoflocalizationandoutgrowthatsiteswhereUNC-40doesnotinteractwithUNC-61057
(Figure21A,2).Ineithercase,outgrowthoccursinthesamedirection.However,theeffecton1058
membranedisplacementisdifferent(Figure21B,1and2).IntheabsenceofUNC-40,UNC-51059
canmediateanoutgrowthresponsetoUNC-6.WehypothesizethatinresponsetoUNC-6,UNC-1060
5inhibitsoutgrowthactivity.ThisinhibitionlowerstheprobabilityofnonUNC-40receptors1061
localizingandmediatingoutgrowthatthesitesofUNC-5andUNC-6interactionand,1062
consequently,increasestheprobabilityofnonUNC-40-mediatedoutgrowthatsiteswithout1063
UNC-6(Figure21A,3).ByaffectingtheprobabilitiesofnonUNC-40localization,UNC-5activity1064
influencesthedegreetowhichthedirectionofnonUNC-40-mediatedoutgrowthfluctuates1065
(Figure21A,4).And,therefore,thelevelofUNC-5activityaffectsmembranedisplacement1066
producedbynonUNC-40outgrowthactivity(Figure21B,3and4).TheSOAL activities of these 1067
receptors is proposed to occur dynamically and concurrently across the membrane at the micro-scale 1068
(Figures 1 and 2). This model predicts that the rate of outgrowth and the net directional bias are 1069
regulated by the relative activities of the UNC-5, UNC-40, and the nonUNC-40 receptors. 1070
1071
For the initial outgrowth of HSN, we propose that multiple receptor SOAL activities determine the 1072
direction and displacement of membrane movement. Figure 22 shows an overlay of the random walk 1073
analyses derived from different mutants that have lost receptor function (bottom schematic). This 1074
provides a picture of the relative effects that these receptors have on the directional bias and 1075
displacement of membrane movement during the initial outgrowth from the HSN cell body. To 1076
explain the different patterns, we propose that the receptor SOAL activities act in concert with each 1077
other and are interdependent (Figure 22, top schematics). In wildtype, the UNC-40 response to 1078
UNC-6 at the ventral surface dominates (Figure 22, 1). However, UNC-5 and SAX-3 activities 1079
47
modify this response by regulating the degreetowhichthedirectionofUNC-40-mediated1080
outgrowthfluctuates.WhereasUNC-5mayinteractdirectlywithUNC-40toregulatetheUNC-1081
40responsetoUNC-6,SAX-3mightinhibitdorsaloutgrowthactivityinresponsetotheSLT-11082
extracellularcue,whichisexpressedbythedorsalbodywallmusclesduringHSNaxon1083
development(HAOetal.2001).ThisinhibitionlowerstheprobabilityofUNC-40receptors1084
localizingandmediatingoutgrowthatmoredorsalsitesand,consequently,increasesthe1085
probabilityofUNC-40-mediatedoutgrowthatventralsites(Figure22,4).Byincreasingthe1086
degreetowhichthedirectionofUNC-40-mediatedoutgrowthfluctuates,bothUNC-5andSAX-31087
regulatemembranedisplacement,howevertheyhavelessinfluenceontheinitialventral1088
directionalbias,whichisprimarilycreatedbytheUNC-40responsetoUNC-6.1089
1090
LossofUNC-40orofbothUNC-40andUNC-5causesananteriordirectionalbias(Figure22).1091
WehypothesizethatthisbiasiscreatedbynonUNC-40receptorsusingthesameprocess1092
throughwhichUNC-5candirectoutgrowthawayfromthesitesofUNC-6interaction.We1093
speculatethatanextracellularcuefromtheposteriortailregionoftheanimalinteractswitha1094
receptorthatinhibitsoutgrowth.ThisincreasestheprobabilityofanonUNC-40receptorto1095
localizeandmediateoutgrowthatsitesthatarenotsuppressed(Figure22,5).Asdiscussed1096
earlier,EGL-20isacandidateforsuchanextracellularcue.1097
1098
WeobservethatlossofUNC-40andSAX-3causesdorsaloutgrowth.ThissuggeststhatSAX-3,1099
inadditiontoinhibitingUNC-40localization,alsoinhibitsthenonUNC-40outgrowthactivity1100
(Figure22,2).IntheabsenceofSAX-3inhibition,UNC-5activitycanorientthenonUNC-401101
outgrowthactivityawayfromtheventralsitesofUNC-6interaction(Figure22,6).LossofSAX-1102
3alsoaffecttheorientationofoutgrowthactivityinthesinglesax-3mutant.Thebiastowards1103
48
thesitesofUNC-6interactionthatisinducedalongtheventralmembranebyUNC-40activity1104
(Figure22,1)maybeshiftedposteriorlyduetothelossoftheinhibitionofUNC-5activityby1105
SAX-3(Figure 22, 3).UNC-5inhibitsnonUNC-40outgrowthactivity(Figure22,6),which1106
contributestoanteriorlydirectedbias.Similarly,lossofonlyUNC-5activitycouldshiftthe1107
biasanteriorlysincethelossofUNC-5activitythatinhibitsnonUNC-40outgrowthactivity1108
wouldallowsagreateranteriorbiasduetoincreasednonUNC-40outgrowthactivity.This1109
effectmaybelostintheunc-5;sax-3doublemutantbecausethelossofUNC-40inhibitionby1110
SAX-3wouldallowgreaterinhibitionofnonUNC-40activitybyUNC-40.1111
1112
Atheoryofoutgrowthpatterning1113
Thispaperdescribesatheoryofoutgrowthpatterning.Thetheoryisbasedontheunderlying1114
principlesdescribedintheIntroduction.Clearly,thetheoryneedstobefurthertestedand1115
refined.Forexample,inordertoexplainpatternsofoutgrowthcausedbysomemutations,we1116
invokedmolecularactivitiesandstatesforwhichthereisverylittleexperimentalevidence.1117
Nevertheless,thetheorymayproveusefulpreciselybecauseitpresentsnewideasthatcanbe1118
experimentallytested.Indeed,wereexaminedunc-5mutantstolookforphenotypespredicted1119
bythetheory.Itishopedthateventuallythistheorycouldleadtoamoreunifyingframework1120
forexplainingthedevelopmentofoutgrowthpatterns.1121
1122
Acknowledgments1123
WethankCaenorhabditisGeneticsCenter,J.Culotti,andC.Bargmannforstrains;wethank1124
MarthaSotoandmembersoftheSotolaboratoryforsupportandhelpfuldiscussions;wethank1125
MarthaSoto,PeterYurchenco,BhumiPatelandLeelyRezvaniforcommentsonthemanuscript.1126
Wealsothanktheeditorsandreviewersofthejournalfortheirinsightfulcommentsand1127
49
suggestions.ThisworkwassupportedbygrantsNS033156andNS061805fromtheNational1128
InstitutesofHealth,NationalInstituteofNeurologicalDisordersandStrokeandgrant07-3060-1129
SCR-E-0fromtheNewJerseyCommissiononSpinalCordtoWGW.Thisworkwasalso1130
supportedbygrantDFHS13PPCO28fromtheNewJerseyCommissiononCancerResearchto1131
AM. 1132
50
Table1133
1134
1135Table1.DirectionofAxonFormationfromtheHSNCellBody
directionofaxonprotrusion
dorsal ventral anterior posterior multipolar
% % % % % n reference
wildtype 0 96+2 3+2 0 1+1 221 (KULKARNIetal.2013)
unc-6(ev400) 2+2 3+2 81+2 8+2 6+1 218 (KULKARNIetal.2013)
unc-40(e1430) 2+1 6+2 67+2 19+1 6+1 183 (KULKARNIetal.2013)
unc-5(e53) 0 75+3 19+2 1+1 5+1 245 (YANGetal.2014)
unc-53(n152) 0 67+3 22+2 5+1 6+1 238 (KULKARNIetal.2013)
sax-3(ky123) 2+1 31+1 21+1 37+2 9+2 232 (TANGANDWADSWORTH2014)
sax-3(ky200)* 2±1 32±1 19±2 42±3 5±2 198 (TANGANDWADSWORTH2014)
unc-5(e53);sax-3(ky200) 2±1 40+3 24±2 28±2 6±1 120
unc-5(e53);unc-6(ev400) 4±2 5±3 59±4 22±4 9±1 201
unc-5(e53);egl-20(n585) 3±1 28±4 22±4 35±5 11±2 114
unc-53(n152);unc-5(e53) 0 19+1 62+2 17+1 3+1 224 (KULKARNIetal.2013)
unc-53(n152);unc-6(ev400) 24+2 0 19+2 22+2 34+3 144 (KULKARNIetal.2013)
unc-53(n152);sax-3(ky123) 1±1 47±3 24±2 23±5 6±3 207 (TANGANDWADSWORTH2014)
unc-40(e1430);unc-5(e53) 5+1 6+1 55+2 19+2 14+1 196 (KULKARNIetal.2013)
unc-40(e1430);sax-3(ky200)* 14±3 2±1 40±2 35±3 9±4 191 (TANGANDWADSWORTH2014)
sax-3(ky200)*;unc-6(ev400) 8±1 8±2 49±3 20±5 14±2 211 (TANGANDWADSWORTH2014)
unc-53(n152);unc-5(e53);unc-6(ev400) 23+2 0 34+2 15+2 28+2 148 (KULKARNIetal.2013)
unc-53(n152);sax-3(ky200)*;unc-6(ev400) 11±2 2±1 33±4 30±3 25±5 189
egl-20(n585) 0 64±2 21±2 7±1 8±1 304 (TANGANDWADSWORTH2014)
egl-20(n585);unc-6(ev400) 18±2 0 43±2 15±2 24±2 205 (TANGANDWADSWORTH2014)
unc-40(e1430);egl-20(n585) 6±2 17±2 45±5 15±2 16±2 173 (TANGANDWADSWORTH2014)
egl-20(n585);sax-3(ky123) 1±1 12±2 39±2 39±1 8±3 177 (TANGANDWADSWORTH2014)
madd-2(tr103) 0 19±2 55±5 17±4 8±2 179
madd-2(ky592) 0 52±2 43±2 5±1 0 95
unc-5(e53);madd-2(tr103) 3±1 15±2 52±4 17±4 13±1 197
madd-2(tr103);sax-3(ky123) 2 24±3 19±4 47±1 7±2 171
unc-53(n152);madd-2(tr103) 1±1 15±2 43±2 17±1 24±4 148
mig-15(rh326) 2±1 15±1 24±3 11±3 48±8 131 (YANGetal.2014)
Numbersrepresentpercentagevalue+SEM.*Animalsgrownatthesax-3(ky200)restrictivetemperature(25°C).
1136
51
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Ren, X. C., S. Kim, E. Fox, E. M. Hedgecock and W. G. Wadsworth, 1999 Role of netrin UNC-6 in 1276patterning the longitudinal nerves of Caenorhabditis elegans. J Neurobiol 39: 107-118. 1277
Rosoff, W. J., J. S. Urbach, M. A. Esrick, R. G. McAllister, L. J. Richards et al., 2004 A new 1278chemotaxis assay shows the extreme sensitivity of axons to molecular gradients. Nat Neurosci 7: 1279678-682. 1280
Sawa, H., and H. C. Korswagen, 2013 Wnt signaling in C. elegans. WormBook: 1-30. 1281
Shakir, M. A., J. S. Gill and E. A. Lundquist, 2006 Interactions of UNC-34 Enabled with Rac 1282GTPases and the NIK kinase MIG-15 in Caenorhabditis elegans axon pathfinding and neuronal 1283migration. Genetics 172: 893-913. 1284
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Sloan, T. F., M. A. Qasaimeh, D. Juncker, P. T. Yam and F. Charron, 2015 Integration of shallow 1285gradients of Shh and Netrin-1 guides commissural axons. PLoS Biol 13: e1002119. 1286
Song, S., Q. Ge, J. Wang, H. Chen, S. Tang et al., 2011 TRIM-9 functions in the UNC-6/UNC-40 1287pathway to regulate ventral guidance. Journal of genetics and genomics = Yi chuan xue bao 38: 1-11. 1288
Stringham, E., N. Pujol, J. Vandekerckhove and T. Bogaert, 2002 unc-53 controls longitudinal 1289migration in C. elegans. Development 129: 3367-3379. 1290
Stringham, E. G., and K. L. Schmidt, 2009 Navigating the cell: UNC-53 and the navigators, a family 1291of cytoskeletal regulators with multiple roles in cell migration, outgrowth and trafficking. Cell 1292adhesion & migration 3: 342-346. 1293
Tang, X., and W. G. Wadsworth, 2014 SAX-3 (Robo) and UNC-40 (DCC) Regulate a Directional 1294Bias for Axon Guidance in Response to Multiple Extracellular Cues. PLoS One 9: e110031. 1295
Tessier-Lavigne, M., and C. S. Goodman, 1996 The molecular biology of axon guidance. Science 1296274: 1123-1133. 1297
Teulière, J., C. Gally, G. Garriga, M. Labouesse and E. Georges-Labouesse, 2011 MIG-15 and ERM-12981 promote growth cone directional migration in parallel to UNC-116 and WVE-1. Development 138: 12994475-4485. 1300
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Figure1.Statisticallyorientedasymmetriclocalization(SOAL).Atsitesalongtheplasma1335
membrane,UNC-40interactswiththeUNC-6extracellularcue.Aself-organizingprocessis1336
triggeredthatutilizespositive-andnegative-feedbackloops.Positivefeedback(yellowarrows)1337
amplifiesthepolarizedresponsetoanextracellularcue,whilenegativefeedback(yellowlines)1338
limitstheresponseandcanconfinethepositivefeedbacktothesiteofUNC-40andUNC-61339
interaction.TheoutcomeofanUNC-40receptor’sactivityistoeithercauseanUNC-40receptor1340
tolocalizeandmediateoutgrowthatthesiteofUNC-6interactionoratadifferentsite.1341
Randomnessisconsideredinherentinthisprocessandeachlocalizationeventismutually1342
exclusive.ThestatisticaldependencemeansthattheprobabilityofUNC-4Olocalizingand1343
mediatingoutgrowthatthesiteofUNC-6interactionaffectstheprobabilityofUNC-401344
localizingandmediatingoutgrowthatanothersite,andviceversa.Astimepasses,thisprocess1345
causesrandomlydirectedoutgrowthactivity(force)thatdrivestheoutwardmovementofthe1346
membrane. 1347
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Figure2.Modelforoutgrowthmovement.(A)Theoutwardmovementoftheneuronal1352
membraneisdepictedasamasstransportphenomena.Thecellmembraneisfluidand1353
membranemasswillmoveindifferentdirectionsasthemembraneissubjectedtoforces1354
(arrows)whichchangeitsshape.Receptorsmediatecellularresponseswhichcreatesthe1355
outwardforce.Theforcecausesmovementofthelipidsandproteinsoftheplasmamembrane.1356
Aunitofthismassisshownwithinabox.Membranemassisrepresentedbyaboxin1357
subsequentschematicdiagrams.(B)Themeanflowofmembranemass(box)canbedescribed1358
asadvectionanddiffusion.Theprobabilitydensityfunctionofthepositionofmassasa1359
functionofspaceandtimeisdescribedmathematicallybyanadvection-diffusionequation.1360
Masstransportbyameanvelocityfieldisadvection.BecauseoftheSOALprocessandthefluid1361
natureofthemembrane,masstransportalsooccursthroughrandommovement,whichis1362
diffusion.(C)Duringoutwardmovementoftheleadingedge(times1-4),membranemolecules1363
moveinthedirectionofadvectionaswellasrandomlyinotherdirections.(D)Thepaththat1364
themembranemoleculestakeduringoutgrowthcanbedescribedasarandomwalk,whichisa1365
successionofrandomlydirectedsteps.Depictedarethepositionofmassaftereachstepofa1366
successionoffourstepsasshowninC.Eachstepcorrespondstoatimepoint.(E)Fortwo1367
examples,50simulatedrandomwalksof500stepswereplottedfromanorigin(0,0).Foreach1368
steptheprobabilityofmovingtotheright,left,ordownisgivenbelowtheplots.Theplots1369
illustratethatincreasingthedegreetowhichthedirectionofmovementfluctuates,decreases1370
theoutwarddistancethatmasscantravel.WepredictthattheSOALprocessinfluencesthe1371
degreeofrandommembranemovementand,consequently,theoutwarddisplacementofthe1372
membrane.1373
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Figure3.Modelforoutgrowthmovementtowardsextracellularcuesthatpromoteor1383
inhibitoutgrowthactivity.(A)Schematicdiagramoftheoutgrowthofaneuronthroughan1384
environmentofmultipleextracellularcues.Thesecuesmaybemoleculespresentatthe1385
surfacesofsurroundingcellsandextracellularmatrix,ortheymaybephysicalinteractionsthat1386
influenceoutgrowthactivity.Theextracellularcuesarerepresentedascolorgradientsofblue,1387
orange,andred.Theneuron’sresponsetocuesarrangedalongtheanterior/posterioraxis1388
(orangeandred),createanequalprobabilityforUNC-40asymmetriclocalizationand1389
outgrowthintheanteriorandposteriordirections.Theextensiontransversesthreedifferent1390
positions(1-3)asitdevelopstowardsaventralsourceofacue(blue).(B)TheSOALprocessis1391
illustratedasinFigure1forthethreepositionsshowninA.Shownarescenariosfor1392
movementtowardsacue(A,blue)thatpromotesoutgrowth(blue+)orthatinhibitsoutgrowth1393
(blue-).Thecuesacttoincrease(promote)anddecrease(inhibit)theprobabilityofoutgrowth1394
fromasurface.Atpositions1and2cuesalongtheanterior/posterioraxis(orange-andred-)1395
preventoutgrowthintheanteriororposteriordirections.Atposition3,thecuefromthe1396
ventralsourcepredominates.(C)RandomwalkmodelingasdescribedinFigure2E.Ateach1397
position(A,1-3),cuesaltertheprobabilitydistributionforthedirectionoflocalizationand1398
outgrowth.Beloweachplotistheprobabilitydistributionusedtocreatetherandomwalk(see1399
MaterialsandMethods).Probabilitydistributionswereselectedtorepresenthowdifferent1400
levelsoftheventralcuemightchangetheprobabilitydistributionateachposition.Theplots1401
illustratetheprobabilitydensityfunctionofthepositionofmassasafunctionofspaceandtime1402
ifmovementoccurredaccordingtothatprobabilitydistribution.Forbothscenarios,anequal1403
probabilityofanteriorandposterioroutgrowthcanallowaventraldirectionalbiasatposition1404
1.Movementtowardsapromotingcuesourcecanallowagreaterprobabilityforventral1405
outgrowthand,correspondingly,alowerprobabilityforanteriorandposterioroutgrowth1406
(position2).Movementtowardsaninhibitingcuesourcecanallowalowerprobabilityfor1407
62
ventraloutgrowthand,correspondingly,agreaterprobabilityforanteriorandposterior1408
outgrowth(position2’).Theventraldirectionalbiasismaintained.Ineitherscenario,anequal1409
probabilityforoutgrowthinalldirectionsmayoccurasthereceptorsbecomesaturated1410
becauseofthehighlevelofthecuefromtheventralsource(position3).Themodelingpredicts1411
thatinbothscenarioschanginglevelsoftheventralcuewillnotalterthedirectionofoutward1412
movement,althoughitmayaltertheoutwarddisplacementofthemembrane’smass.Seetext1413
fordetails.1414
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Figure4.Modelforoutgrowthmovementthatchangesdirection.(A)Schematicdiagram1422
oftheoutgrowthofaneuronthroughanenvironmentofmultipleextracellularcuesas1423
describedinFigure3A.Positions1’-3’representthepositionafterachangefromventralto1424
anterioroutgrowth.(B)Ateachposition(A,1-3),theprobabilitydistributionforthedirection1425
oflocalizationandoutgrowthisgivenasinFigure3C.Inorderforthedirectionofoutgrowthto1426
shiftanteriorlyateachposition,theprobabilitydistributionmustshifttocreateabiasfor1427
anteriorlydirectedoutgrowth.Thisisdepictedbytheprobabilitydistributionof0.4anterior,1428
0.3dorsal,and0.3ventralforpositions1’-3’.Numbersinredindicatethedegreetowhichthe1429
probabilitiesmustchangebetweenthepositions.Themodelpredictsthatasthesystemtrends1430
towardsastatewheretheprobabilitiesofoutgrowthindifferentdirectionsbecomeequal,cues1431
thatcouldshiftthedirectionbiasbecomemoreeffectual.1432
1433
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64
Figure5.Modelforthedevelopmentofmultipleoutgrowthsthatextendinthesame1436
direction.(A)TheSOALprocessisillustratedforsitesalongasurfaceofaneuronasinFigure1437
1.ThepositiveandnegativefeedbackloopsoftheSOALprocessallowspatialpatternsof1438
outgrowthtodevelopautonomously.Thenumberofsiteswhereastrongdirectionalbiasis1439
ultimatelycreatedisdictatedbytherelativeeffectivenessofthepositiveandnegativefeedback1440
loops.(B)Schematicdiagramoftheoutgrowthofaneuronthroughanenvironmentofmultiple1441
extracellularcuesasdescribedinFigure3A.Theflowofmembranemass(box)atdifferent1442
sitesdependsontheprobabilitydistributionforthedirectionofoutgrowthcreatedatregions1443
alongthesurface.RandomwalkmodelingasdescribedinFigure2Eisshownbelowthe1444
schematicdiagram.AttimeX,twositeswhichhaveagreaterdirectionalbias(2and4)are1445
establishedbytheSOALprocessasdepictedinA.Cuesmaynotbepresentinsteepgradients1446
alongtheaxisperpendiculartothedirectionofextension.Theresponsetothesecuescreates1447
probabilitiesforoutgrowththatareequalintheperpendiculardirections.Thegreatest1448
directionalbiasiscreatedwhenthereisanequilibriumfortheprobabilityofoutgrowthin1449
perpendiculardirections.Becausecuelevelsmayvarygraduallyalongtheperpendicularaxis,1450
thestrengthofthedirectionalbiasatsitesmaydiffer,howeverthebiaswillbeorientedinthe1451
samedirection.Attimex+1,positions2and4haveproceededfurtheroutwardbecauseof1452
greatermembranedisplacement.Thiseffectismagnifiedbyincreasinglevelsoftheoutgrowth1453
promotingcue(blue).Thisactivitytogether,whenaveragedovertimeacrossasurface,is1454
predictedtocausethedynamicdevelopmentofmultipleextensions.1455
1456
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Figure6.ModelforthecontrolofoutgrowthactivitybySOAL.Schematicdiagramofthe1475
controlofUNC-40-andnonUNC-40-mediatedactivity.Neuronalsurfacesoftheneuronare1476
subjectedtodifferentlevelsofUNC-6(blue)aswellasnonUNC-6extracellularcues(orange).1477
TheSOALprocessregulatesbothUNC-40andnonUNC-40-mediatedactivity.Positivefeedback1478
(arrows)amplifiesthepolarizedresponsetoanextracellularcue,whilenegativefeedback1479
(lines)limitstheresponseandcanconfinethepositivefeedbacktothesiteofligand1480
interaction.Thelong-rangenegativefeedbackmediatedbyUNC-40inhibitsUNC-40activity,as1481
wellasnonUNC-40activity.Similarly,long-rangenegativefeedbackmediatedbynonUNC-401482
activityinhibitsnonUNC-40activity,aswellasUNC-40activity.1483
1484
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Figure7.UNC-5regulatesthepatterningofoutgrowthextensionsfromHSN.(A)1494
PhotomicrographsofHSNattheL1,L2,andadultstagesinwildtypeandunc-5(e53)mutants.1495
InL1andL2animalsneuriteextensions(arrows)areoftenobservedinwild-typeanimalsbut1496
aremorerareinunc-5mutants.Theshortventralmigrationofthecellbodythatoccursin1497
wild-typeanimalsometimesfailsinunc-5mutants,leavingthecellbodyfartherfromthePLM1498
axon(arrowhead)withasinglelongerventralextension.Thepositionofthecellbodyremains1499
dorsal.Scalebar:10μm.(B)ThepercentageofHSNneuronwith0,1,ormorethan1neurite1500
extensionattheL1stage.Inunc-5mutantsnearlyhalfoftheneuronsdonotextendaprocess.1501
Errorbarsindicatedthestandarderrormean;nvaluesareindicatedaboveeachcolumn.1502
Significantdifferences(two-tailedt-test),*P<0.001.(C)ThepercentageofHSNneuronswitha1503
singlelongextensionattheL2stage.Severalunc-5allelesweretestedasdescribedinthetext.1504
Inmutantswithloss-of-functionthereismoreoftenasingleextensionfromthecellbodyand1505
thecellbodyisdorsallymispositioned.(D)PhotomicrographsofHSNattheearlyL4,lateL4,1506
andadultstagesinwildtypeandinanimalsexpressingUNC-6∆C.TheexpressionofUNC-6∆C1507
inducesmultipleprocesses,mostoftentwomajorextensions,thatareguidedventrally.(E)The1508
percentageofHSNneuronswithacellbodymispositioneddorsallyattheL2stage.Inloss-of-1509
functionmutantsthecellbodyoftenfailstoundertakeashortventralmigrationduringtheL21510
stage.Themigrationisnotdelayed,butratheritremainsdorsal.(F)ThepercentageofHSN1511
neuronswithmultipleventralextensionsattheL4stage.Theadditionalprocessesinducedby1512
UNC-6∆Ccanbesuppressedbyunc-5andmig-10mutations.Additionalprocessesinducedby1513
mig-15(rh148)canalsobesuppressedbytheunc-5mutation.(G)PhotomicrographsofHSNat1514
adultstagesinamig-15mutant.SimilartoUNC-6∆Cexpression,mig-15mutationscanalso1515
causeadditionalprocessesthatareguidedventrally(YANGetal.2014).1516
1517
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1518
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Figure8.UNC-5regulatesthepatterningofextensionfromALM,AVM,andPLM.(A)1520
PhotomicrographsoftheALM,AVM,andPLMneuronsattheL4stageinwild-typeanimalsand1521
mig-15mutants.Inwildtype(top)asinglePLMaxontravelsanteriorlyfromtheposteriorcell1522
body(notshown).Nearthevulva(arrow)theaxonbranches;onebranchextendstothe1523
ventralnervechordandanotherextendsanteriorly.Theanteriorextensionterminatesbefore1524
reachingtheareaoftheALMcellbody.Inmig-15mutantsthePLMcanextendanteriorlypast1525
theALMcellbody(bottom).(B)ThepercentageofPLMneuronswherethePLMneuron1526
extendanteriorlypasttheALMcellbody.Theanteriorextensionoftenover-extendsinmig-151527
mutants.Lossofunc-5orunc-40functioncansuppressthisphenotype.(C)Photomicrographs1528
oftheALMandAVMneuronsattheL4stageinwild-typeanimalsandmutantsshowing1529
differentpatternsofoutgrowthextension.Inwildtype(top)asingleaxontravelsanteriorlyto1530
thenervering(arrowheads).Atthenerveringtheaxonbranches;onebranchextendsfurther1531
anteriorlyandtheotherextendsintothenervering.Inmutants,oneorbothaxonsmayonly1532
extendanteriorlyandwillnotextendintothenervering(secondfromtop).Oroneorboth1533
axonswillonlyextendintothenerveringandwillnotextendanteriorly(thirdfromtop).Or1534
oneorbothaxonswillfailtoextendintoeitherthenerveringoranteriorly(bottom).Scalebar:1535
20μm.(D)ThepercentageofAVMneuronswheretheAVMneuronfailedtoextendintothe1536
nervering.Theneuronoftenfailstoextendintheunc-40andmig-15;unc-5mutants,whereasit1537
doesextendinthemig-15,unc-5,andmig-15;unc-40mutants.Errorbarsindicatedthestandard1538
errormean;nvaluesareindicatedaboveeachcolumn.Significantdifferences(two-tailedt-1539
test),*P<0.001.(E)ThepercentageofAVMneuronswheretheAVMneuronfailedtoextend1540
anteriorly,pastthenervering.Theneuronoftenfailstoextendanteriorlyinthemig-15;unc-51541
mutants,whereasitdoesextendinthemig-15,unc-5,unc-40,andunc-40;mig-15mutants.There1542
isasignificantdifferencebetweentheunc-40andunc-40;mig-15mutants.1543
15441545
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1546 1547
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Figure9.Assaytomeasuretheeffectsamutationhasonmovement.(A)Thedirectionof1548
outgrowthextensionfromtheHSNcellbodycanvaryandwhethertheaxondevelopedinthe1549
dorsal,anterior,posterior,orventraldirectioninL4stageanimalsisscored(leftpanel).This1550
createsaprobabilitydistributioninwhichthedirection(X)isarandomvariable(centerpanel).1551
Asimplerandomwalkisgeneratedbyusingthesameprobabilitydistributionforasuccession1552
ofstepswithanequaltimeinterval(rightpanel).(B)Forwildtypeandtwomutants,501553
simulatedrandomwalksof500stepswereplottedfromanorigin(0,0).Theresultsgraphically1554
indicatethedirectionalbiasformovement.ForrandomwalkmovementcreatedinmutantA1555
(red,resultsfromunc-5(e53)),thedirectionalbiasisshiftedanteriorly(left)relativeto1556
wildtype.Theresultsalsographicallyshowthedisplacementofmovement.Forrandomwalk1557
movementcreatedinmutantB(blue,resultsfromegl-20(n585);sax-3(ky123)),theaverageof1558
thefinalposition(displacement)fromtheoriginisamuchshorterdistancethanwildtype.(C)1559
Plotsofthenormaldistributionofthefinalpositionalongthexaxisoftherandomwalktracks1560
showninB.Themeanpositionforeachissetat0.Theplotsgraphicallyillustratehowrandom1561
walksconstructedfromtheprobabilitydistributionforthedirectionofoutgrowthextensions1562
canrevealadiffusionprocess.1563
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Figure10.Mutationshavedifferenteffectsonmovement.Examplesofrandomwalk1567
analysesusingthedirectionofaxondevelopmentfromtheHSNneuronindifferentmutants1568
(Table1).ThegraphswerecreatedasdescribedinthefigurelegendofFigure9.Foreach1569
panel,plotsareshownforthenormaldistributionofthefinalpositionalongthexaxisforthe1570
randomwalktracksplottedintheinserts.Theinsertsdepicttherandomwalkmovementthat1571
wouldbeproducedbytheprobabilitydistributionforthedirectionofoutgrowthinthemutant.1572
Plotsderivedfromthesamedataarecoloredalike.Eachpaneldepictstheanalysesoffour1573
differentmutantsandwildtype.Threedifferentdistributionpatternsareobserved:(1)the1574
wild-typedistribution,whichhasthedistributioncurvewiththehighestpeak;(2)theunc-5,1575
egl-20,unc-53,andunc-6(notshown)distribution,whichisflatterthanthewild-typecurve;(3)1576
themadd-2,sax-3,mig-15,anddoublecombinations,whichhavetheflattestdistributioncurve.1577
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Figure11.Mutationsalterthespatialextentofmovement.(A)Plottedarethemean1581
squareddisplacement(MSD)curvesasafunctionoftimeinterval(dt).Thevaluesarein1582
arbitraryunits,sincethetimescalewasarbitrarilysetat1.Thecurvesshowtheextentthat1583
differentmutationscanaltertheMSDrelativetowildtypeandtheMSDcausedbyanunbiased1584
randomwalk.Foreachtimeinterval,meanands.e.m.areplotted.(B)FromtheslopeofMSD1585
curvesacoefficientcanbederivedthatgivestherelativerateofdiffusion.Coloredbars1586
correspondtothelike-coloredcurvesgiveninpanelA.Thecoefficientsforunc-5,egl-20,unc-1587
53,andunc-6formaclassthatisdistinctfromthatderivedfromwildtypeandfromthedouble1588
mutants.1589
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1591 1592
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Figure12.ModelsfortherelationshipbetweenUNC-40-mediatedoutgrowthactivityand1593
UNC-40receptorclustering.(A)TheSOALprocessisillustratedasinFigure1.Inthismodel,1594
theself-organizingUNC-40SOALprocesscausesobservableUNC-40receptorclustering.UNC-1595
6stabilizesreceptorclusteringatasiteandtheoutgrowthmachineryisthenrecruitedtocause1596
outgrowthatthesite.Althoughtheinitialdirectionofasymmetricreceptorlocalizationis1597
determinedstochastically,thedirectionofoutgrowthisdeterminedbythesiteofstabilization.1598
(B)Inthismodel,theself-organizingUNC-40SOALprocessiscoupledtotheoutgrowth1599
machinery.Thedirectionofbothasymmetricreceptorlocalizationandoutgrowthactivityare1600
stochasticallydetermined.Observablereceptorclusteringarisesastheresultoftheprocess1601
becausereceptorlocalizationcanbecomesuccessivelyconcentratedtoasmallerareaover1602
time.Clusterformationisanobservablephenomenonoftheprocess,notaprerequisitefor1603
outgrowthactivity.Thismodelpostulatesinnumerablefluctuatingsitesthatgenerateforcein1604
variousdirectionsalongthemembrane.1605
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Figure13.MutationsaffectasymmetricintracellularUNC-40::GFPlocalization.(A)Graph1610
indicatingthedorsal-ventrallocalizationofUNC-40::GFPinHSN.Thegraphshowstheaverage1611
ratioofdorsal-to-ventralintensityfromlinescanintensityplotsoftheUNC-40::GFPsignal1612
aroundtheperipheryoftheHSNcell.UNC-40::GFPisventrallylocalizedinwildtype,butthe1613
ratioisdifferentinthemutants.Errorbarsrepresentstandarderrorofmean.Belowisa1614
graphicrepresentationofthepossibleUNC-40localizationpatternswhentheintensityratiois1615
≥1oris<1.(B)Graphindicatingtheanterior-posteriorlocalizationofUNC-40::GFP.To1616
determineorientation,line-scanintensityplotsoftheUNC-40::GFPsignalacrossthedorsal1617
peripheryoftheHSNcellweretaken,thedorsalsurfacewasgeometricallydividedintothree1618
equalsegments,andthetotalintensityofeachwasrecorded.Thepercentintensitywas1619
calculatedforeachsegmentandANOVAwasusedtodetermineifthereisasignificant1620
differencebetweenthethreesegments(seeMaterialandMethods).Thegraphshowsthe1621
percentofanimalsthathadsignificantlocalizationintheindicatedsegmentsorthathad1622
uniformdistribution.Whereasintheunc-5andegl-20mutantsthereisabiasforanterioror1623
posteriorlocalization,thereisauniformdistributioninunc-5;egl-20doublemutants.Uniform1624
distributionisalsoobservedinstrongloss-of-functionsax-3andmadd-2mutants.(*)Animals1625
grownatthesax-3(ky200)restrictivetemperature(25°C).Beloweachgraphisa1626
representationofthepossibleUNC-40localizationpatterns.TheorientationofUNC-401627
localizationiscolor-codedasinB.1628
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Figure14.ModelfortheoutgrowthmovementofPLM.Schematicdiagramsofthe1632
anteriorlydirectedoutgrowthofPLM.ThefeaturesoftheschematicarepresentedinFigure3.1633
(A)Anextensionencountersdifferentlevelsofextracellularcuesateachofthreepositions(1-1634
3).Cuesdorsalandventralofthepathwaymaintainanequalprobabilityofoutgrowthinboth1635
directions.Theextensionencountersincreasinglevelsofanextracellularcue(s)asitmoves1636
towardsposition3.Atposition3,acue(s)preventfurtheranteriorextensioninwildtype.(B)1637
TableshowingforeachofthepositionsdepictedinAthepositivefeedback(arrows)and1638
negativefeedback(lines)associatedwithSOALactivity(seeFigure6)andthepredictedeffect1639
theSOALactivityhasonoutgrowthactivity.Atposition1,strongUNC-40activityalongthe1640
dorsalandventral(notshown)facingsurfacesoftheleadingedgeinhibitnonUNC-40activity.1641
BecauseoftheSOALprocess,thisinhibitionincreasednonUNC-40activityattheanterior1642
surfaceoftheleadingedge.Atpositions2and3,increasinglevelsofthenonUNC-40activityat1643
thedorsalandventralsurfacesinhibitUNC-40activity.TheincreaseinnonUNC-40activityat1644
thedorsalandventralsurfacescauseadecreaseinnonUNC-40activityattheanteriorsurface.1645
Asaresult,thedegreetowhichthedirectionofnonUNC-40-mediatedoutgrowthactivity1646
fluctuatesisgreatestatposition3.(C)ForeachpositioninA,randomwalkmodelingisshown1647
asdescribedinFigure2E.Theresponsetotheextracellularcuesprogressivelyincreasesthe1648
degreetowhichthedirectionofoutgrowthactivityfluctuates.Byposition3,thedegreeof1649
fluctuationcausesamuchlowerdisplacementofmembranemass.Thelowrateofoutward1650
movementcausesextensiontostall.1651
1652
82
1653
1654
83
Figure15.ModelfortheeffectsthatmutationshaveontheoutgrowthmovementofPLM.1655
TableshowingtheeffectsofdifferentmutationsontheoutgrowthofPLMatposition3,Figure1656
14.PLMoutgrowthstallsinwildtype,unc-40,andunc-5;mig-15mutantsatposition3,but1657
overextendsinmig-15mutants.Inthismodel,themig-15mutationrepressestheabilityof1658
nonUNC-40SOALactivitytosuppressUNC-40activityatthedorsalandventralsurfaces.1659
IncreasedUNC-40SOALactivitysuppressesnonUNC-40SOALactivityatthesesurfaces.1660
Becauseofthestatisticaldependenceofthelocalizationprocess,decreasingnonUNC-40SOAL1661
activityatthedorsalandventralsurfacesincreasesnonUNC-40SOALactivityattheanterior1662
surface.Ascomparedtowildtype,thedegreetowhichthedirectionofnonUNC-40outgrowth1663
activityfluctuatesislessand,therefore,outwarddisplacementisgreater.Thisallowfurther1664
anterioroutgrowthatposition3.LossofUNC-5functioninthemig-15mutantdecreasesthe1665
abilityofUNC-40SOALactivitytosuppressesnonUNC-40SOALactivityatthedorsaland1666
ventralsurfaces,therebyincreasingthedegreetowhichthedirectionofnonUNC-40outgrowth1667
activityfluctuates.Thisreducesoutwarddisplacementandsuppressestheoverextension1668
phenotype.1669
1670
1671
84
1672 1673
85
Figure16.ModelfortheoutgrowthmovementofAVMatthenervering.Schematic1674
diagramsoftheoutgrowthofAVMatthenervering.Thefeaturesoftheschematicare1675
describedinFigure3.(A)Atposition1,allsurfacesexperiencehighlevelsofUNC-6.At1676
position2,theextensionencountersnewcue(s)attheanteriorsurface.(B)Tableshowingfor1677
eachofthepositionsdepictedinAthepositivefeedback(arrows)andnegativefeedback(lines)1678
associatedwithSOALactivity(seeFigure6)andthepredictedeffectthattheSOALprocesshas1679
onoutgrowthactivity.Atposition1,strongUNC-40SOALactivityalonganterioranddorsal1680
facingsurfacesoftheleadingedgeinhibitnonUNC-40SOALactivity.ThereisstrongUNC-401681
mediatedoutgrowthfromallsurfaces.Atposition2,nonUNC-40SOALactivityattheanterior1682
surfaceinhibitsUNC-40SOALactivity,whereasUNC-40SOALactivityatthedorsalsurface1683
inhibitsnonUNC-40SOALactivity.Asaresult,UNC-40outgrowthactivityislimitedtothe1684
dorsalsurfaceandnonUNC-40outgrowthactivityislimitedtotheanteriorsurface.(C)1685
RandomwalkmodelingisshownasdescribedinFigure2E.Becauseofthelargedegreeto1686
whichthedirectionofoutgrowthfluctuates,outwardmovementstalls.Thisallowscuesthat1687
arearrangeddorsalandanteriortotheprojectiontoeffectivelycreateabiasforoutgrowthin1688
therespectivedirection(seeFigure4).AdorsaldirectionalbiaswilldevelopbecauseUNC-401689
andotherreceptorsmediatesanoutgrowthresponsetoUNC-6andothercuesalongthenerve1690
ring.AnanteriordirectionalbiaswilldevelopbecausenonUNC-40mediatesanoutgrowth1691
responsetocuesalongananteriorpathway.1692
1693
1694
86
1695
1696
1697
87
Figure17.ModelfortheeffectsthatmutationshaveontheoutgrowthmovementofAVM1698
atthenervering.TableshowingtheeffectsofdifferentmutationsontheoutgrowthofAVMat1699
position2,Figure16.Whereasinwildtype,UNC-40SOALactivitysuppressesnonUNC-40SOAL1700
activityatthedorsalsurface,inunc-40mutantsthereisnosuppressionandnonUNC-40activity1701
mayoccur.However,nonUNC-40activityisgreaterattheanteriorsurfacebecauseofthe1702
responsetoanteriorcuesandthisdepressesnonUNC-40activityatthedorsalsurfacebecause1703
oftheSOALprocess.Asaresult,thereisoftenanteriorextensionfromthenerveringareabut1704
nodorsalextensionintothenervering.Inunc-5mutants,UNC-40SOALactivityisreducedbut1705
itisstilldorsallyoriented.Thisallowsdorsalextensioninthemutants.Inmig-15mutants,1706
nonUNC-40SOALactivityisrepressed.ThisresultsinlowernonUNC-40activityattheanterior1707
surface.However,anteriorextensionstilloccur,asdoesdorsalextensionbecauseofUNC-401708
activity.LossofUNC-40inthemig-10backgroundallowsextensioninbothdirections.In1709
comparisontothesingleunc-40mutant,thereducednonUNC-40SOALactivityatanterior1710
surfaceinthedoubleunc-40;mig-15mutantdoesn’tdepressdorsalnonUNC-40outgrowth1711
activityasmuch,allowingmoreextensionintothenervering.LossofUNC-5inthemig-101712
backgroundcausesthemostabnormaloutgrowthmorphologies,presumablybecausethe1713
repressionofbothUNC-40andnonUNC-40SOALactivitiesdoesnotallowUNC-40and1714
nonUNC-40outgrowthactivitiestobewellsortedtodifferentsurfaces.1715
1716
1717
88
1718
1719
1720
89
Figure18.ModelfortheoutgrowthmovementofHSN.Schematicdiagramsoftheventral1721
outgrowthofHSN.ThefeaturesoftheschematicaredescribedinFigure3.(A)Astheleading1722
edgeoftheextensionmovesventrallyitencountershigherlevelsofUNC-6.Atposition3,all1723
surfacesexperiencehighlevelsofUNC-6.Cuesanteriorandposteriorofthepathwaymaintain1724
anequalprobabilityofoutgrowthinbothdirections.(B)Tableshowingforeachofthe1725
positionsdepictedinAthepositivefeedback(arrows)andnegativefeedback(lines)associated1726
withSOALactivity(seeFigure6)andthepredictedeffectthattheSOALprocesshason1727
outgrowthactivity.Atposition1,strongUNC-40SOALactivityalongtheventralfacingsurfaces1728
oftheleadingedgeinhibitnonUNC-40SOALactivity.BecauseoftheSOALprocess,this1729
inhibitionincreasednonUNC-40activityattheanteriorandposterior(notshown)surfacesof1730
theleadingedge.NonUNC-40SOALactivityalongtheanteriorandposteriorsurfacessuppress1731
UNC-40SOALactivityatthesesurfaces.Atpositions2and3,increasinglevelsoftheUNC-401732
SOALactivityattheanteriorandposteriorsurfacesinhibitnonUNC-40SOALactivity.The1733
increaseinUNC-40activityattheanteriorandposteriorsurfacescauseadecreaseinnonUNC-1734
40SOALactivity.Asaresult,thedegreetowhichthedirectionofUNC-40-mediatedoutgrowth1735
activityfluctuatesisgreatestatposition3.(C)ForeachpositioninA,randomwalkmodelingis1736
shownasdescribedinFigure2E.Atfirst,theresponsetotheextracellularcuesmay1737
progressivelydecreasesthedegreetowhichthedirectionofUNC-40andnonUNC-401738
outgrowthactivityfluctuates.However,asUNC-40SOALactivitypredominatesatallsurfaces,1739
thedegreebywhichthedirectionofUNC-40outgrowthfluctuatesincreases.Byposition3,the1740
degreeoffluctuationcausesamuchlowerdisplacementofmembranemass.1741
1742
90
1743
1744
1745
91
Figure19.ModelfortheeffectsthatmutationshaveontheoutgrowthmovementofHSN.1746
TableshowingtheeffectsofdifferentmutationsontheoutgrowthofHSNatposition1,Figure1747
18.Mutationscanaltertherateofoutgrowthandthenumberofextensions.Inthismodel,the1748
relativelevelsofUNC-40andnonUNC-40SOALactivitycontrolsthispatterning.Inwildtype,1749
theabilityofUNC-40SOALactivitytopredominateatonesitealongthemembraneisenhanced1750
bynonUNC-40SOALactivity,whichmayincreasethethresholdatwhichUNC-40positive1751
feedbackbecomeseffective.Overtime,theareawhereUNC-40SOALpredominatescauses1752
greaterUNC-40outgrowthactivity.Asoutwardmovementoccurs,higherlevelsofUNC-6are1753
encountered.Thisenhancesandlocalizestheprocesstothatarea.Inmig-15mutantsthe1754
suppressionofnonUNC-40SOALactivityreducesthethresholdatwhichUNC-40SOALactivity1755
maypredominateatasite.ThisallowsmultiplesitesalongthemembranewhereUNC-40SOAL1756
activitymaypredominate.MultipleextensionsmaydevelopasshowninFigure5.LossofUNC-1757
5,whichsuppressesUNC-40SOALactivity,retardstheabilitytoenhanceandlocalizethe1758
process.Thiscausesgreaterfluctuationinthedirectionofoutgrowthactivityacrosstheentire1759
ventralsurfaceoftheneuron,whichuniformlydecreasesthedisplacementofmembrane.1760
1761
1762
92
1763
1764
1765
93
Figure20.Geneticpathwaysforself-organizingUNC-40asymmetriclocalization.(A)1766
TablesummarizingtheresultsofexperimentspreviouslyreportedanddescribedinFigure131767
ofthispaper.(B)ThegeneticdatasupportamodelwherebytheUNC-6andEGL-201768
extracellularcuesregulateatleastthreepathwaysleadingtorobustasymmetricUNC-401769
localization.RobustasymmetricUNC-40localizationreferstotheabilitytoobserveUNC-1770
40::GFPclusteringatthesurfaceoftheneuron.Arrowsrepresentactivation;barsrepresent1771
repression.Seetextforthelogicusedtoconstructthepathways.1772
1773
94
1774
1775
95
Figure21.ModelforHSNmembranemovementmediatedbyUNC-5activity.(A)1776
SchematicdiagramsofSOALactivitiesmediatedbyUNC-5,UNC-40,andanunknownnonUNC-1777
40receptor.ReceptorSOALactivityoccursdynamicallyalongthemembraneatthemicro-scale1778
(Figures1and2)andcanovertimecreateanetdirectionalbiasforoutgrowth(greenarrow).1779
UNC-5functionstogetherwithUNC-40toenhanceUNC-40SOALactivityandUNC-40-mediated1780
outgrowthatthesiteofUNC-6interaction(1).IfUNC-5activityisreducedorlost,the1781
probabilityofUNC-40SOALactivityatsiteswhereUNC-40isnotUNC-6-ligatedincreasesand1782
thisincreasesthedegreetowhichthedirectionofUNC-40-mediatedoutgrowthfluctuatesover1783
time(2).IntheabsenceofUNC-40,UNC-5inhibitsoutgrowthactivityatthesitesofUNC-61784
interaction.UNC-5SOALactivityatthesiteofUNC-6interactionpreventsnonUNC-40SOAL1785
activityandnonUNC-40-mediatedoutgrowthatthislocation,increasingtheprobabilityof1786
nonUNC-40SOALactivityandnonUNC-40-mediatedoutgrowthatotherlocations.Overtime,1787
thiscreatesadirectionalbiasawayfromthesiteswhereUNC-6interactswithUNC-5(3).If1788
UNC-5activityisreduced,theinhibitionofnonUNC-40-mediatedoutgrowthatsiteswhere1789
UNC-6interactswithUNC-5decreases.Thisincreasesthedegreetowhichthedirectionof1790
nonUNC-40-mediatedoutgrowthfluctuatesovertime(4).(B)Randomwalkmodelingas1791
describedinFigure2EisshownforeachofthedepictionsshowninA.Thedirectionalbiasthat1792
evolvesovertimedirectstheflowofmembranemass(box).Thedisplacementofmembrane1793
massdependsontheprobabilitydistributionforthedirectionofoutgrowth.Displacement1794
towardstheUNC-6sourceisgreatestwhenUNC-40andUNC-5activitiesdecreasethedegreeto1795
whichthedirectionofoutgrowthfluctuates(1),whereasdisplacementdecreasesasUNC-51796
activityisreducedandthedegreetowhichthedirectionofUNC-40-mediatedoutgrowth1797
fluctuatesincreases(2).IntheabsenceofUNC-40,UNC-5helpsincreasenonUNC-40-mediated1798
membranedisplacementatsiteswherethereislessUNC-5andUNC-6interaction(3).Ifthe1799
strengthofUNC-5inhibitiondecreasesatthesitesofUNC-5andUNC-6interaction,thenthe1800
96
degreetowhichthedirectionofnonUNC-40-mediatedoutgrowthfluctuateswillincrease,1801
therebydecreasingmembranedisplacement(4).1802
1803
1804
1805
1806
97
Figure22.ModelfortheoverridinglogicofhowmultiplereceptorSOALactivitiesdirect1807
theinitialoutgrowthofHSN.SchematicdiagramsasdescribedinFigure22fortheSOAL1808
activitiesmediatedbyUNC-5,UNC-40,SAX-3,anEGL-20receptor,andanunknownnonUNC-401809
receptor(top).Asdescribedbeloweachdiagram,theactivitiescanoccurinconcertwitheach1810
otherandareinterdependent.Randomwalkanalysesusingthedirectionofaxondevelopment1811
fromtheHSNneuronindifferentmutantsareshownasdescribedinFigure10(bottom).The1812
graphswerecreatedasdescribedinthefigurelegendofFigure9.Thegraphsindicatethe1813
relativeeffectsthatthemutationshaveonthedirectionalbiasanddisplacementofmovement1814
duringtheinitialoutgrowthfromHSN.Linesconnectingtherandomwalkanalysisofamutant1815
toSOALactivitiesdepictthelogicunderlyingthedirectionalbias.Forexample,inunc-40(-1816
);sax-3(-)thereisadorsaldirectionalbias(randomwalkanalysisingreen).Asdescribedin1817
Figure21,UNC-5SOALactivitycanorientnonUNC-40-mediatedoutgrowthdorsallyinthe1818
absenceofUNC-40(greenconnectingline).However,thisrequiresthelossofdorsalSAX-31819
activity,whichwouldotherwiseinhibitUNC-5andnonUNC-40activity(greenconnectinglines1820
withX).Seetextforfurtherdetailsaboutthelogicunderlyingeachmutant.1821
1822
98
1823
1824