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

william.wadsworth@rwjms.rutgers.edu 23

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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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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

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1824