Stochastic Interaction between Neural Activity and Molecular Cues in the Formation of Topographic

18 Pages·2015·6.07 MB·English

by  Melinda T. Owens

Article
Stochastic Interaction between Neural Activity and
Molecular Cues in the Formation of Topographic
Maps
Highlights Authors
d HeterozygousIslet2-EphA3knockinmicedisplayvariationin MelindaT.Owens,DavidA.Feldheim,
visualmaporganization MichaelP.Stryker,JasonW.Triplett
d Variationwasfoundbetweenmice,betweenhemispheres, Correspondence
andwithinasinglemap
[email protected]
d Variationinmaporganizationisreflectedbothfunctionally
In Brief
andanatomically
Inthisstudy,Owensetal.demonstrate
d Properlycorrelatedspontaneousactivityisrequiredformap variabilityintopographicmap
organizationvariation organizationinamousemodelinwhich
molecular-andactivity-dependentforces
arerenderednearlyequalinbalance.
Thesefindingssuggestaninherent
stochasticityinestablishmentof
topography.
Owensetal.,2015,Neuron87,1261–1273
September23,2015ª2015ElsevierInc.
http://dx.doi.org/10.1016/j.neuron.2015.08.030
Neuron
Article
Stochastic Interaction between Neural
Activity and Molecular Cues
in the Formation of Topographic Maps
MelindaT.Owens,1DavidA.Feldheim,2MichaelP.Stryker,1andJasonW.Triplett2,3,*
1CenterforIntegrativeNeuroscienceandDepartmentsofPhysiologyandBioengineering&TherapeuticSciences,UniversityofCalifornia,
SanFrancisco,SanFrancisco,CA94143,USA
2Molecular,Cell&DevelopmentalBiology,UniversityofCalifornia,SantaCruz,SantaCruz,CA95064,USA
3CenterforNeuroscienceResearch,Children’sNationalHealthSystem,Washington,DC20010,USA
*Correspondence:[email protected]
http://dx.doi.org/10.1016/j.neuron.2015.08.030
SUMMARY rin-As,areexpressedincountergradientsalongthetemporal-
nasal (T-N) axis of the retina and the anterior-posterior (A-P)
Topographic maps in visual processing areas main- axisoftheSC.InteractionsbetweeninnervatingRGCsandcol-
tain the spatial order of the visual world. Molecular licularcellsresultsintemporalRGCsterminatinganteriorly,while
cues and neuronal activity both play critical roles in nasal RGCs terminate posteriorly, in the SC (Triplett, 2014).
mapformation,buttheirinteractionremainsunclear. DisruptionofEphA/ephrin-Asignalingresultsintopographicer-
Here, we demonstrate that when molecular- and rorsalongtheazimuthaxisintheSC,dorsallateralgeniculate
nucleus (dLGN), and primary visual cortex (V1) that manifest
activity-dependentcuesarerenderednearlyequalin
anatomicallyasectopicterminationzones(TZs)andfunctionally
force,theydrivetopographicmappingstochastically.
astopographicallyincorrectreceptivefields(Brownetal.,2000;
The functional and anatomical representation of
Cang et al.,2005a, 2008b; Feldheim et al.,2000; Frise´net al.,
azimuth in the superior colliculus of heterozygous
1998;Pfeiffenbergeretal.,2006;Triplettetal.,2009).
Islet2-EphA3 knockin (Isl2EphA3/+) mice is variable:
In addition to molecular cues, correlated neuronal activity
maps may be single, duplicated, or a combination playsacriticalroleinmapformation.Duringdevelopment,spon-
of the two. This heterogeneity is not due to genetic taneouswavesofactivitypropagateacrosstheretinaandinitiate
differences, since map organizations in individual corresponding waves in retinorecipient nuclei (Ackman et al.,
mutantanimalsoftendifferbetweencolliculi.Disrup- 2012;Meisteretal.,1991).Disruptionofthesewavesresultsin
tionofspontaneouswavesofretinalactivityresulted errorsintopography,suchthattheTZsofRGCsintheSCare
in uniform map organization in Isl2EphA3/+ mice, foundinapproximatelythecorrecttopographiclocationbutfail
to refine to establish a discrete map (Chandrasekaran et al.,
demonstrating that correlated spontaneous activity
2005;McLaughlinetal.,2003).Functionally,thisisreflectedas
is required for map heterogeneity. Computational
anincreaseinthenumberofRGCsynapticinputstocollicular
modelingreplicatesthisheterogeneity,revealingthat
cellsandincreasesinthereceptivefieldsizesoftheseneurons
molecular- and activity-dependent forces interact
(Cangetal.,2008a;Chandrasekaranetal.,2005).Interestingly,
simultaneouslyandstochasticallyduringtopographic
anatomical and functional perturbations in the absence of
mapformation. spontaneous activity are observed specifically in the azimuth
domain, which has been attributed to the unique spatiotem-
poral properties of retinal waves (Stafford et al., 2009). Similar
INTRODUCTION changes are also observed in the dLGN and V1, suggesting
a common role for spontaneous activity in topographic map
In the visual system, the spatial relationships of objects in the formation throughout the visual system (Cang et al., 2005b;
worldarefaithfullyrelayedthroughouthigherprocessingcenters Grubbetal.,2003).Together,molecular-andactivity-dependent
throughtheestablishmentoftopographicmaps(CangandFeld- forces play the dominant roles in topographic mapping along
heim,2013).Theretina’sprojectiontothesuperiorcolliculus(SC) theazimuthaxis,asdisruptionofbothforcessimultaneouslyre-
hasservedasamodeltounderstandthemolecularandactivity- sults in a nearly complete loss of topography in the SC (Cang
dependentforcesthatdrivemapformationfordecades(Gaze, etal.,2008b;Pfeiffenbergeretal.,2006).However,therelative
1981). Retinal ganglion cells (RGCs) project to the SC during strengthofeachoftheseforcesremainsunclear.
earlypost-natal lifeandarerefinedtoafinaltopographicmap Basedoninvivostudiesingeneticallymodifiedmice,several
by the end of the first post-natal week (McLaughlin et al., computationalmodelshavebeendevelopedtoexplaintherole
2003).Graded molecularcuesplayaroleintheestablishment ofmolecular-andactivity-dependentforcesintheestablishment
of retinocollicular topography along the azimuth axis. Specif- of topography. The relative signaling model argues that local
ically,EphAreceptortyrosinekinasesandtheirligands,theeph- comparisonsinEphAsignalingstrengthbyRGCsresultsinan
Neuron87,1261–1273,September23,2015ª2015ElsevierInc. 1261
ordered distribution of terminals in the SC (Reber et al., 2004; varies depending on their location along the T-N axis of the
Bevinsetal.,2011).Suchamodelissupportedbyexperiments retina.Forinstance,innasalretina,expressionofendogenous
inwhichthelevelofEphAreceptorsignalingwasalteredinasub- EphAs is low, so Isl2+, EphA3-overexpressing RGCs should
setofRGCs,resultingintheformationofabifurcatedmapinthe have distinct EphA signaling strengths from Isl2(cid:2) RGCs. In
SC(Brownetal.,2000).Asecond,permissivearborizationmodel contrast, RGCs in the temporal retina express high levels of
positsthatmapdevelopmentproceedsinastep-wisefashion, endogenousEphAs,suchthatthedifferenceinEphAsignaling
in which molecular forces establish broad zones for potential strengthisminimalbetweenIsl2+andIsl2(cid:2)RGCs.Thus,onepre-
synapseformation,whilelateractivity-dependentandcompeti- dictionofthispatternofEphAexpressionwouldbethatIsl2+and
tive forces dictate final map organization (Grimbert and Cang, Isl2(cid:2)RGCsfromthenasalretinawouldprojecttotwodistinctre-
2012).Thismodelissupportedbyaccumulatingevidenceofa gionsoftheSC,whilethosefromthetemporalretinawouldproj-
roleforEphA/ephrin-Areversesignaling(Limetal.,2008;Rashid ect to a similar region in the anterior SC. Indeed, anatomical
etal.,2005;Yatesetal.,2001),axonalcompetition(Triplettetal., tracingexperimentsinIsl2EphA3/+micesupportedthishypothe-
2011),andinteraxonalsignaling(SuetterlinandDrescher,2014) sis(Brownetal.,2000).Thesedataalsopredictthattheazimuth
inretinocollicularmapformation.Finally,stochasticmodelspro- representationalongtheA-PaxisoftheSCwouldbesplitinto
posethatRGCsexchangesynapsesintheSCtooptimizeadhe- twoincompletemapsofspace,whereintheanteriorofapproxi-
sion,drivenbyacombinationofmolecularforces,competition, matelytwo-thirdsofthemapwouldhaveafullrepresentationof
and activity (Koulakov and Tsigankov, 2004; Tsigankov and centralvisualspaceandapartialrepresentationoftheperiphery,
Koulakov,2006,2010).Whilethismodelreplicatestopographic whiletheposteriorone-thirdwouldhaveapartialrepresentation
organizations found in control and mutant mice in vivo, clear oftheperiphery.However,thefunctionalorganizationinthatSC
empiricaldatasupportingstochasticityremainselusive. inIsl2EphA3/+micehasnotbeeninvestigated.
Here, we demonstrate an activity-dependent, stochastic To determine the functional topographic organization of the
mechanismfortheestablishmentofretinocolliculartopography. SCinadultIsl2EphA3/+mice,weperformedintrinsicsignaloptical
Utilizing intrinsic signal optical imaging in heterozygous Islet2- imaging,asdescribedpreviously(KalatskyandStryker,2003).
EphA3knockinmice(Isl2EphA3/+),weshowthatmaporganization This technique allows the observation of either the azimuth or
exhibitstremendousheterogeneitybothamongIsl2EphA3/+indi- elevationrepresentationofspaceatapopulationlevelinalarge
viduals and even within single animals. Map heterogeneity is portionoftheSCatonce.Indeed,inWTmice,asingleazimuth
alsoexhibitedanatomically,asassayedbyanterogradetracing representationandsingleelevationrepresentationareobserved
ofRGCsandanalysisofIsl2+RGCprojectionpatterns.Neural intheSCcontralateraltothestimulatedeye(Figures1Dand1E).
activityisrequiredforthemanifestationofheterogeneityinmap InadulthomozygousIsl2EphA3/EphA3mice,theazimuthrepresen-
organization,sincedisruptionofspontaneousretinalwavesre- tationintheSCisduplicated,whiletheelevationrepresentation
sulted in only a single type of map. Heterogeneity akin to that remainssingular,consistentwithourpreviousfindings(Figures
observed in the Isl2EphA3/+ was replicated by a computational 1F and 1G) (Triplett et al., 2009). Interestingly, while heterozy-
model when the EphA signaling factor was set appropriately. gous Isl2EphA3/+ animals had functional maps of similar size
Smallvariationsinthisfactorresultedinconsistentmaporganiza- and strength to WT and Isl2EphA3/EphA3 mice (Figures S1A–
tions,mimickingtheconsistencyfoundinwild-type(WT)andho- S1C),weobservedheterogeneityintheorganizationofazimuth
mozygousIsl2EphA3/EphA3animals.Takentogether,theseresults representations(Figures1H–1O,n=16).Theserepresentations
suggestthatactivity-dependentandmolecularforcesarenearly fellintothreequalitativecategories:(1)single(Figure1H),similar
equalinbalanceduringtheestablishmentoftopographyandthat tothoseofWTanimals,(2)doubled(Figure1J),similartothose
localtopographycanbedrivenbyeitherinastochasticmanner. seen in Isl2EphA3/EphA3 mice, and (3) partially doubled and
partiallysingle(Figure1L),hereafterreferredtoasmixed-type.
RESULTS Importantly,thedifferencesobservedwerenotduetovariability
inresponsiveness,aseachofthetypesoccupiedsimilarareasof
HeterogeneityofMapOrganizationinIsl2EphA3/+Mice theSC(FigureS1D).
One of the most elegant investigations of the role of EphA To quantitatively categorize azimuth map organizations in
signalingintopographicmapformationinvolvedthegeneration Isl2EphA3/+mice,weplottedtheazimuthphaseasafunctionof
oftheIslet2-EphA3knockinmouseline(Isl2EphA3)(Brownetal., positionalongtheA-Paxisatthreedifferentisoelevationpoints
2000). Inthesemice, anEphA3cDNAwas insertedinto the30 inthemap(Figure1N).Wethendeterminedtwoindicestobetter
UTR of the Islet2 locus. This manipulation produced a salt describetherelationshipsbetweentheazimuthrepresentations
andpepperarrangementoftwopopulationsofRGCs:(1)Isl2(cid:2) at these distinct elevations (see Experimental Procedures).
RGCs that express endogenous levels of EphA receptors and Briefly, wefirstgenerated a‘‘linear fitindex,’’ whichdescribes
(2)Isl2+RGCsthatexpressendogenousEphAsandexogenous thegoodnessoffittoalinearregressionfortheazimuthphase
EphA3. In homozygous Isl2EphA3/EphA3 mice, the difference in plotateachelevationmeasured.Next,wedeterminedan‘‘intra-
total EphA signaling between Isl2(cid:2) and Isl2+ RGCs is large, mapcorrelationindex,’’whichdescribesthefidelityofmaporga-
resultinginthesegregationofthesetwopopulationsintheSC nizationbetweeneachazimuthphaseplotwithinasinglemap.
and the formation of two coherent anatomical and functional Byplottingthelinearfitindexasafunctionoftheintramapcor-
mapsofspace(Brownetal.,2000;Triplettetal.,2009).Inhetero- relation index, we found that individual maps fell into distinct
zygous Isl2EphA3/+ mice, however, the difference in EphA sig- clusters, corresponding to single maps of Isl2+/+ mice, double
naling strength between populations of Isl2+ and Isl2(cid:2) RGCs maps of Isl2EphA3/EphA3 mice, and mixed maps of Isl2EphA3/+
1262 Neuron87,1261–1273,September23,2015ª2015ElsevierInc.
Figure1. HeterogeneityintheFunctionalAzimuthRepresentationintheSCofIsl2EphA3/+Mice
(A–C)Schematicsofintrinsicsignalopticalimagingparadigm.Driftingvertical(azimuth,B)andhorizontal(elevation,C)arepresentedonascreenplaced25cm
fromananesthetizedmouse.RegionsoftheSCrespondingtodifferentregionsofthevisualfieldarepseudo-coloredasindicated.
(DandE)Azimuth(D)andelevation(E)representationsinawild-typeSCrevealasinglecoherentmapineachcase(n=4).
(FandG)ImagingofSCresponsesinanIsl2EphA3/EphA3mouserevealacompleteduplicationofazimuth(F)andadiscontinuityattheborderofthesemapsinthe
elevationrepresentation(G)(n=5).
(H–M)ImagingofSCresponsesinanIsl2EphA3/+revealsavarietyoforganizationsintheazimuthrepresentations:single(HandI),double(JandK),andmixed-type
(LandM)(n=16).
(N)Phaseplotsoftheazimuthrepresentationalongtheanterior-posterioraxisoftheSCatthreeisoelevationpointsfromIsl2EphA3/+miceexhibitingasinglemap
organization(toprow),doubleorganization(middlerow),andmixedorganization(bottomrow).Bluedashedlinesrepresentthebestlinearfitforeachphaseplot.
(O)Maporganizationsplottedbytwoquantitativeindices.Isl2+/+maps(blackdots)fallwithintheregiondeterminedtobesingle,Isl2EphA3/EphA3maps(reddots)
fallwithinthedoublezone,andIsl2EphA3/+maps(greendots)aredistributedacrosssingle,double,andmixedregionsoftheplot.Scalebar,0.5mm;A,anterior;
L,lateral.
that fell between the single and double clusters (Figure 1O). the maps of space to be coherent (Figure 1G; Triplett et al.,
Basedonthisanalysis,wefoundthat25.0%(4/16)ofIsl2EphA3/+ 2009). This discontinuity is present only in the mice that have
mapsweresingle,18.8%(3/16)weredouble,and56.3%(9/16) doubled or partially doubled maps of azimuth and is absent
weremixedtype. in the Isl2EphA3/+ mice with single maps (Figure 1M). Taken
Althoughthemapsofazimuthdisplaythemostobviousdiffer- together,thesedatademonstrateheterogeneityintheorganiza-
ences,theelevationmapsdifferaswell.InIsl2EphA3/EphA3mice, tionofmapsintheIsl2EphA3/+SCandsuggestastochasticpro-
the elevation maps display a discontinuity that allows each of cessmayunderliemapformation.
Neuron87,1261–1273,September23,2015ª2015ElsevierInc. 1263
Figure 2. Bilateral Heterogeneity of Azi-
muthRepresentationinOpposingCollicular
HemispheresofIsl2EphA3/+Mice
(A) Schematics of imaging paradigm to evaluate
azimuthandelevationrepresentationsineachSC
hemisphereofasinglemouse.
(BandC)Azimuthandelevationrepresentations
intheleftandrightSCoftwodifferentIsl2EphA3/+
micerevealsheterogeneitybetweenhemispheres
(n=7).
(D)MaporganizationsofIsl2EphA3/+miceinwhich
bothSCswereimagedplottedbytwoquantitative
indices.Eachpairofcoloreddotsrepresentsthe
twoSCsofanindividualIsl2EphA3/+mouse.Scale
bar,0.5mm;A,anterior;L,lateral;M,medial.
imuth representation was singular in the
right hemisphere but mixed type in the
lefthemisphere.Thesedatasuggestthat
heterogeneity in map organization is not
due to subtle changes in EphA3 expres-
sion level due to genetic background.
Despite this, the possibility remains that
subtle differences in EphA3 expression
from the Isl2 locus between eyes may
cause the heterogeneity observed be-
tweencolliculiofthesameanimal.How-
ever, our observations that different
regions of a single SC are organized
differently in a substantial portion of
Isl2EphA3/+micesuggeststhatgeneticdif-
ferencesplayaminimalroleinthehetero-
geneityobserved.
HeterogeneityofMapOrganization
inIsl2EphA3/+MiceIsNotdueto
SuppressionofVisualResponses
Anotherpossibleexplanationforthehet-
erogeneity observed in individual func-
tional maps is that some of the retinal
inputs into the SC are being functionally
suppressed.Visualmapsinprimaryvisual
cortexareabletosuppressaberrantinput
HeterogeneityofMapOrganizationinIsl2EphA3/+MiceIs fromthelateralgeniculatenucleusinthe‘‘Midwestern’’varietyof
NotduetoGeneticVariation Siamesecat(KaasandGuillery,1973),buttheextenttowhich
One potential source of heterogeneity in map organization mapsinSCcansuppressretinalinputisunknown.Toaddress
observed in Isl2EphA3/+ mice could be differences in genetic thepossibilityoffunctionalsuppression,weimagedtheSCsof
backgroundbetweenmice.Ifthiswerethecase,thentheorga- Isl2EphA3/+micewhileshowingthemspatiallyrestrictedstimuli.
nizationofthevisualmapshouldbethesameinbothcolliculiof These stimuli would only excite a small part of the retina at
anindividualmouse.Todeterminewhetherthiswerethecase, once, potentially activating ectopic termination sites that are
weimagedthecolliculiofbothhemispheresinseveralIsl2EphA3/+ normally suppressed when full-field stimuli are presented. We
mice. Strikingly, we often found different azimuth representa- focused on Isl2EphA3/+ mice with mixed-type maps, since we
tionsintherightandleftSCsinIsl2EphA3/+miceinwhichbothcol- would be able to compare in the same SC areas of activation
liculiwereimaged(Figures2Band2C).Indeed,wefoundthatin thatgiveadoubledmapandareasofactivationthatgiveasingle
fiveofsevenmice,theorganizationofmapsintheleftandright map.Isl2EphA3/+micewereshownaseriesofstimuliconsisting
SCfellintodistinctcategorieswhenplottingthelinearfitindexas ofshortbarsthatsubtendedonly5(cid:3) ofvisualangleinazimuth
a function of the intramap correlation index (Figure 2D). For (Figure3B).TheareasinSCthateachbaractivatedwerecom-
example,Figure2CdepictsanIsl2EphA3/+animalinwhichtheaz- bined, and this map was compared to the map derived from
1264 Neuron87,1261–1273,September23,2015ª2015ElsevierInc.
Figure3. LackofFunctionalSuppressionin
theSCofIsl2EphA3/+Mice
(A and B) Schematics of full-field (A) and
spatially restricted (B) stimuli used to determine
whethersubsetsofSCregionsmaybefunctionally
suppressed.
(C–F)AzimuthrepresentationsfromtheSCoftwo
Isl2EphA3/+micederivedfromtheuseoffull-field
stimulus(CandE)orspatiallyrestrictedstimuli(D
andF).
observed the greatest degree of hetero-
geneity. In some colliculi, Isl2-GFP+
RGCsappearedtobeevenlydistributed
over the posterior SC (Figure 4A, right
hemisphere), while in others, large re-
gions appeared devoid of Isl2-GFP+
RGC innervation (Figure 4A, left hemi-
sphere, and Figure 4C). In several in-
stances we observed dense islands of
Isl2-GFP+ innervation (Figures 4A, 4A0
and 4A00, arrows), suggesting that clus-
teringoftheseterminalsoccursinasto-
chastic manner. To quantitatively asses
theheterogeneityofIsl2-GFP+RGCspro-
jectionsintheSCofIsl2EphA3/+mice,we
comparedtheintensityofGFP+terminals
alongtheA-Paxisatthreepositionsalong
theM-Laxis(Figures4Cand4D,bottom
row). As a control, we measured the in-
tensity along the same M-L positions of
all RGC terminals, which were labeled
conventionalfull-fieldstimuli(Figures3C–3F).Ineverycase(n= by intraocular injection of fluorescently tagged Cholera Toxin
4),themapobtainedfromspatiallyrestrictedstimulimatchedthe subunitB(Figures4Band4D,toprow).Plottingfluorescencein-
mapsobtainedwithfull-fieldstimulationverywell.Theseresults tensityasafunctionofthepositionalongtheA-Paxis,wefound
confirmthereliabilityofourimagingmethodanddonotsupport thatthedistributionofallRGCswassimilarateachM-Lposition
functionalsuppressionasthesourceofheterogeneityobserved acrosscolliculi(Figure4D,toprow).Incontrastthedistributionof
inIsl2EphA3/+mice. Isl2-GFP+terminalsshowedmorevariability(Figure4D,bottom
row).Toquantifythis,wecalculatedthepairwisecorrelationco-
FunctionalHeterogeneityofMapOrganizationin efficients between intensity plots for both Isl2-GFP+ and all
Isl2EphA3/+MiceReflectsAnatomicalHeterogeneity RGCs for each SC and determined the average to generate a
Anotherpossibleinterpretationofthesedataisthatthehetero- correlation index (n = 9 SCs for all RGCs and n = 12 SCs for
geneityintheorganizationofintrinsicopticalsignalmapsreflects Isl2-GFP+RGCs).WefoundthatateachM-Lposition,thecorre-
alterations in collicular neuron functionality rather than altered lation index of Isl2-GFP+ RGC projections was significantly
projectionpatternsofRGCs.Asaninitialtestofthispossibility, reducedcomparedtothatofallRGCs(Figure4E).Thesedata
weexaminedtheprojectionpatternsofIsl2+RGCsusingatrans- demonstrate heterogeneity in the projection patterns of Isl2-
genicmouseinwhichGFPisexpressedinthesoma,dendrites, GFP+RGCsubtypesinIsl2EphA3/+mice.
andaxons(Triplett etal.,2014).Consistentwithourfunctional Tofurtheranalyzepossiblevariationintheanatomicalorgani-
data, we observed heterogeneity in the organization of Isl2- zationinIsl2EphA3/+mice,wetracedRGCprojectionsbyfocalin-
GFP+RGC projections inthe SCof Isl2EphA3/+mice(Figure 4). jectionofDiIintothenasalretina,sincetheposteriorSCiswhere
As expected, we found the densest Isl2-GFP+ innervation in theobservedheterogeneityisexpressedfunctionally.Incontrast
theanteriorSCandareadilyobservable‘‘boundary,’’presum- topreviousreports(Bevinsetal.,2011;Brownetal.,2000;Reber
ably at the border of a duplicated map (Figure 4A, dotted line etal.,2004),wefoundthatlabelednasalaxonsinIsl2EphA3/+mice
in Figures 4A0 and 4A00). Interestingly, the shape and precise exhibitedvariabilityintheorganizationoftheirterminations(Fig-
locationofthis‘‘boundary’’variedbetweencolliculiofdifferent ure5).Consistentwithpreviousstudies,wefoundthatasingle
mice and between collicular hemispheres of the same mouse injectioninnasalretinaofadultIsl2EphA3/+miceresultedintwo
(Figure 4A0 versus 4A00). Posterior to the ‘‘boundary,’’ we termination zones (TZs) in the SC (55.6%, 10/18) (Figures 5A
Neuron87,1261–1273,September23,2015ª2015ElsevierInc. 1265
Figure 4. Heterogeneity in the Projection
PatternsofIsl2+RGCsinIsl2EphA3/+Mice
(A–A00)DorsalviewsofIsl2-GFPprojectionstothe
SC(whitedashedregions)inwholemountofan
adultIsl2EphA3/+micerevealdistinctorganizations
(A).Enlargedviewsofregionsofinterest(A0 and
A00) indicated in (A). Dashed lines indicate the
‘‘border’’ between regions of high and low Isl2-
GFP+RGCinnervation.Arrowsindicateclustersof
Isl2-GFP+RGCterminals.
(B and C) Dorsal views of the projections of all
RGCs(B)andIsl2-GFP+RGCs(C)totheleftSCof
an adult Isl2EphA3/+ mouse. Dashed purple and
greenlinesarelocatedatthe25th,50th,and75th
percentileofthemedial-lateralaxisoftheSC.
(D)Plotsofthefluorescenceintensitysignalofall
RGCs(toprow)andIsl2-GFP+RGCs(bottomrow)
fromthreerepresentativeIsl2EphA3/+SCs.Intensity
wasplottedasafunctionofpositionalongtheA-P
axis at three different parasagittal planes of the
M-Laxis,indicatedbydashedlinesin(B)and(C).
(E) Quantification of the average correlation
indices at each parasagittal plane for all RGCs
(blackbars,n=8)andIsl2-GFPRGCs(graybars,
n=11).Dataarepresentedasaverage±SEM.
Scalebar,0.5mm;L,lateral;P,posterior;OT,optic
tract;M,medial;A,anterior;**p<0.01versusAll
RGCs;***p<0.001versusAllRGCs.
force that would drive map organization
to a duplicated state in the Isl2EphA3/+
SC; thus, a counter-balancing force of
equalmagnitudemustexistinthedevel-
oping SC to drive map organization
to the single and mixed-type states.
One possible counter-balancing force is
correlated spontaneous retinal waves
and5G);however,inasubstantialproportionofcases,asingle during early post-natal development, which have been shown
injection in nasal retina resulted in one TZ (33.3%, 6/18) or a toplayacriticalroleintopographicmapping,actingtocluster
‘‘smeared’’ TZ (11.1%, 2/18) (Figures 5A–5C). In addition to axonalterminalsofneighboringRGCsandrefinethereceptive
examining the TZ pattern of labeled RGCs in these mice, we fields of individual collicular neurons (Chandrasekaran et al.,
alsoperformedintrinsicsignalopticalimagingintheSCofthe 2005;McLaughlinetal.,2003).Wehypothesizedthatthecorre-
samemouseinordertomakedirectcomparisonsofanatomical lated activity generated by spontaneous waves provides a
andfunctionalorganizations.Asexpected,functionalmaporga- counter-balancing force strong enough to overcome the eph-
nizations reflected anatomical organizations on the whole. rin-A/EphAmolecularforceintheIsl2EphA3/+SC.Totestthispos-
Indeed, a c2 test in which single maps were assigned an ex- sibility,weimagedtheSCsofmiceinwhichthenormalpatternof
pectedvalueof1TZ,doublemaps2TZs,andmixedmap1.5 spontaneousretinalwavesweredisrupted.Inmicelackingthe
TZs, the probability of observing the expected number of TZs b2subunitofthenicotinicacetylcholinereceptor(b2(cid:2)/(cid:2)),retinal
isveryhigh(c2 =0.963,c2 =0.987,c2 =0.975). waves have altered spatiotemporal properties, resulting in
single double mixed
These data suggest that the anatomical organization of nasal abnormal topographic refinement in the SC (Chandrasekaran
RGC inputs in the SC of Isl2EphA3/+ mice are heterogeneously etal.,2005;McLaughlinetal.,2003;Staffordetal.,2009).We
organizedinasimilarmannertothatobservedforthefunctional crossedIsl2EphA3/+miceintotheb2(cid:2)/(cid:2)backgroundtodetermine
representation. theroleofspontaneousretinalwavesinthegenerationofhetero-
geneity in topographic organization. While we found that both
SpontaneousRetinalActivityRequiredfor the azimuth and elevation representations of Isl2EphA3/+/b2(cid:2)/(cid:2)
Heterogeneity mice hadsignificantly decreased peak amplitudes incompari-
Ourfindings thusfarsuggestthatEphAsignaling in Isl2EphA3/+ son to those of Isl2EphA3/+/b2+/(cid:2) littermates (Figure S2), we
miceisatalevelthatproducesinstabilityandheterogeneityin wereabletoobtaininterpretablemaps(Figure6).Insupportof
maporganizationintheposteriorSC.Severallinesofevidence ourhypothesis,wefoundthatinIsl2EphA3/+/b2(cid:2)/(cid:2)mice,retino-
suggest that ephrin-A/EphA molecular interactions provide a collicular maps were similar across SCs, all resembling single
1266 Neuron87,1261–1273,September23,2015ª2015ElsevierInc.
Figure 5. Correlation of Anatomical and
FunctionalMapOrganizationsinIsl2EphA3/+
Mice
(A–C)DorsalviewsoftheSCsofIsl2EphA3/+micein
whichthenasalretinawasfocallylabeledwithDiI
revealsone(A),two(B),orasmeared(C)termi-
nationzone(TZ)(n=18).
(D–F)Correspondingfunctionalrepresentationsof
azimuthtotheIsl2EphA3/+micelabeledin(A)–(C).
(G) Map organizations of traced and imaged
Isl2EphA3/+SCsplottedbytwoquantitativeindices.
Axonlabelingresultinginone(blackcircles),two
(red circles), or smeared (green circles) TZs is
indicated.Scalebar,0.5mm;A,anterior;L,lateral.
studies have revealed this possibility.
Indeed,previouscomputationalmodeling
ofSCdevelopmenthasbeenusedtovali-
date the results of anatomical tracing in
Isl2EphA3/EphA3andIsl2EphA3/+mice(Bev-
ins et al., 2011; Grimbert and Cang,
2012;KoulakovandTsigankov,2004;Tsi-
gankov and Koulakov, 2010). Here, we
modifyapreviouslydescribedmathemat-
ical model to replicate in silico the vari-
abilityweobservedinvivo.Inourmodel,
weassumethatallRGCsinitiallyproject
to the posterior-most SC, regardless of
their cell body location along the T-N
axisoftheretina,aspreviouslydescribed
(SimonandO’Leary,1992).Indeed,thisis
necessary for a stochastic resolution to
the push and pull forces of activity and
molecules we observe in Isl2EphA3/+
mice. However, recent models have
suggested that in the Isl2EphA3/+ and
Isl2EphA3/EphA3 mouse models, Isl2+
RGCsareunabletoprojecttotheposte-
rior-mostSCduetothehighexpression
level of EphA receptors (Grimbert and
Cang, 2012). To resolve this issue, we
mapsbothqualitativelyandquantitatively(Figures6B,6E,and examinedIsl2-GFP+RGCprojectionpatternsduringthedevel-
6F).Thissurprisingresultmaybeexplainedbytheknownalter- opment of retinocollicular topography. In contrast to previous
ationsinspatiotemporalpropertiesofwavesintheb2(cid:2)/(cid:2)mouse models, we find Isl2-GFP+ fibers in the posterior-most SC at
(Stafford et al., 2009; see Discussion). Importantly, Isl2EphA3/+/ earlydevelopmentalages(post-natalday2and4[P2andP4])
b2+/(cid:2) littermates exhibited map heterogeneity, as 50.0% (2/4) inIsl2EphA3/+mice(FiguresS3AandS3B).Indeed,evenatages
hadsinglemapsand50.0%(2/4)hadmixed-typemaps(Figures inwhichrefinementhasbegunandIsl2-GFP+fibersshowacon-
6Aand6F).Takentogether,thesedatasuggestthatcorrelated centrationintheanteriorSC(P6andP8),asubsetoffiberscan
spontaneousretinalactivityactsasacounterbalancetomolec- be found in the posterior SC (Figures S3C and S3D). Taken
ularforcestoinfluencethelocalorganizationoftheretinocollic- together with our modeling results, these data suggest that
ularmap. Isl2+andIsl2(cid:2)RGCaxonsareintermingledduringdevelopment
ofretinocolliculartopographyinIsl2EphA3/+mice,allowingfora
InSilicoModelPredictsMapHeterogeneityofMap competition between molecular and activity-dependent forces
OrganizationinIsl2EphA3/+Mice thatresolvesitselfinastochasticmanner.
Thepresenceofmixed-typemapsandheterogeneityobserved Tobetterdescribethestochasticnatureoftopographicmap
in Isl2EphA3/+ mice suggests a stochastic process in map for- formation,wemodifiedthemodelproposedbyTsigankovand
mationdrivenbyinteractionsbetweenmolecular-andactivity- Koulakov, in which map formation depends on graded chem-
dependentforces.However,neitherexperimentalnormodeling ical cues and activity-dependent refinement (Tsigankov and
Neuron87,1261–1273,September23,2015ª2015ElsevierInc. 1267
Koulakov,2006,2010).TheSCisrepresentedbya100by100
matrix to simulate the termination sites for RGC axons (Fig-
ure7A).ThechemicalcuesalongtheN-Taxisofthemapsimu-
latethegradedexpressionofEphAandephrin-Ainbothretina
andSC(seeExperimentalProceduresfordetaileddescriptions).
The exogenous EphA3 in the retinas of Isl2EphA3/EphA3 and
Isl2EphA3/+ mice is simulated by adding a fixed factor, DR, to
the‘‘chemicalcue’’profileofeveryotherRGC;theDRusedfor
modelingIsl2EphA3/EphA3miceistwiceasmuchtheoneusedto
model Isl2EphA3/+ mice to represent the effect of possessing
two Isl2-EphA3 alleles as opposed to one. Initially, the map is
random, but it undergoes a series of optimization steps. At
each step, two randomly chosen RGCs are exchanged with
theprobabilityp=1/[1+exp(4*DE)],whereDE=DE +DE
chem act
isthechangeinadhesiveenergyduetotheexchange.Ingeneral,
DE is minimized when the RGC expressing the highest
chem
amountsofreceptorprojecttoplacesintheSCexpressingthe
lowest amounts of ligand and vice versa, which makes sense
giventherepulsivenatureoftheinteractionbetweentheEphAs
andephrin-As.DE isminimizedwhenRGCsthatarecloseto
act
eachotherintheretinaprojectclosetoeachotherintheSC.Af-
ter107steps,orderlyandorganizedtopographicmapsappear.
WhenDRissettozero,simulatingmapformationinWTanimals,
themapsarealwayssingle(Figure7B).WhenDRissettoahigh
number (0.70), representing conditions in the Isl2EphA3/EphA3
mouse,themapsarealwaysdoubled(Figure7C).However,at
the intermediate value of DR = 0.35, different simulation runs
give maps of divergent structures, reminiscent of the maps
seen in Isl2EphA3/+ mice (Figure 7D). Some runs give rise to
mapsthatarealmostentirelysingle,ordoubled,andthemajority
ofmapsaremixed.
Previous studies of topographic map formation hint that
changes in the sum of EphA in the retina results in alterations
ofretinocollicular maporganization (Bevinsetal.,2011;Reber
etal.,2004).Todeterminethesensitivityofouroptimalitymodel,
wevariedthevalueofDRaroundtheintermediatevaluethatre-
sultedinheterogenousoutcomes.Wefoundthatincreasingor
decreasingthevalueofDRby±0.05(±16.6%)eliminatedhet-
erogeneity and consistently resulted in fully doubled or single
maps, respectively (Figure 7E). These data indicate that the
in silico model utilized here is able to replicate key aspects of
mapformation,includingtheheterogeneityobservedinvivoin
Isl2EphA3/+ mice. Further, the sensitivity of map organization to
smallchangesinDRtakentogetherwithourfindingthatsponta-
neousretinalactivityisrequiredforheterogeneityprovidestrong
supportthatmolecular-andactivity-dependentforcesarenearly
Figure6. DisruptionofRetinalWavesEliminatesHeterogeneityin equallyinbalanceduringtheformationoftopographicmaps.
theAzimuthRepresentationintheSCofIsl2EphA3/+Mice
(A and B) Intrinsic signal optical imaging of the azimuth representation in DISCUSSION
Isl2EphA3/+/b2+/(cid:2)(n=4)(A)andIsl2EphA3/+/b2(cid:2)/(cid:2)(n=4)(B).
(CandD)Intrinsicsignalopticalimagingoftheelevationrepresentationin
Theretinocollicularprojectionhasservedasamodeltounder-
Isl2EphA3/+/b2+/(cid:2)(C)andIsl2EphA3/+/b2(cid:2)/(cid:2)(D).
stand the mechanisms by which topographic projections be-
(E)Phaseplotsoftheazimuthrepresentationalongtheanterior-posterioraxis
oftheSCatthreeisoelevationpointsfromanIsl2EphA3/+/b2(cid:2)/(cid:2)SC. tween brain regions are established. Important roles for both
(F)MaporganizationsofIsl2EphA3/+/b2+/(cid:2)(darkbluedots)andIsl2EphA3/+/b2(cid:2)/(cid:2) molecular cues and activity-dependent forces have been well
(lightbluedots)SCsplottedbytwoquantitativeindices.Scalebar,0.5mm;A, established,yethowtheseforcesinteracttomediatemapfor-
anterior;L,lateral. mation remains unresolved. Here we demonstrate that local
topographic map formation proceeds stochastically, driven by
equally balanced molecular- and activity-dependent forces.
1268 Neuron87,1261–1273,September23,2015ª2015ElsevierInc.
Figure7. ReplicationofHeterogeneityina
Mathematical Model of Retinocollicular
Mapping
(A)Representationsoftheretinaasa1003100
matrix,withcorrespondingcolor-codingbasedon
positionalongtheD-VandT-Naxes.
(BandC)Resultsofsimulationsofthemodelrun
with thevalueforexogenous EphA3expression
(DR) set to 0.00 (for wild-type; B) or 0.70 (for
Isl2EphA3/EphA3; C) reveal predicted organizations
of projections along the A-P and L-M axes of
theSC.
(D) Representative examples of three distinct
simulationsofthemodelwhenDRwassetto0.35
(forIsl2EphA3/+mice)revealsaheterogeneityinthe
organizationofinputsalongtheA-Paxis.
(E) Minor changes in DR around 0.35 yielded
consistent map organizations that were singular
(0.30) or doubled (0.40). D, dorsal; V, ventral;
T, temporal; N, nasal; A, anterior; P, posterior;
L,lateral;M,medial.
RGCs, there was a single TZ in the SC,
whereas previous studies reported that
all nasal tracings resulted in two TZs.
Such a discrepancy may be due to the
small number of tracings carried out in
previous studies; only 5 were done in
thenasalretina(definedas%40%ofthe
Thesefindingsnotonlyresolvetheissueoftherelativerolesof N-Taxis)(Brownetal.,2000).Inotherstudies,tracingsofnasal
molecularcuesandactivityintheestablishmentoftopography, RGCs in Isl2EphA3/+ mice with altered EphA4 or EphA5 levels
butalsoshowanovelstochasticityintheestablishmentofretino- consistently showed two termination zones (Bevins et al.,
collicularconnectivity. 2011;Reberetal.,2004).However,asthemathematicalmodel
we propose here suggests, altering the sum of the EphA
HeterogeneityofRetinocollicularMapOrganizationin signaling force even slightly can have dramatic effects on the
Isl2EphA3/+HeterozygousKnockinMice consistencyoftheorganizationoftheresultingcollicularmap.
Previous investigations of retinocollicular mapping in the Inadditiontotheheterogeneityofmaporganizationsbetween
Isl2EphA3knockinmicepointedtowardarelativesignalingmodel colliculi of ls2EphA3/+ mice, the presence of mixed-type maps
ofmapformation.InheterozygousIsl2EphA3/+mice,anatomical challenges current models of map formation. Importantly, to
tracing suggested that Isl2+ and Isl2(cid:2)RGCs originating in the ourknowledge,neithertherelativesignalingnorthepermissive
nasalretinaprojectedtodistinctlocationsintheposteriorSC, arborization models predict the presence of either heteroge-
while those from temporal retina ‘‘collapsed’’ into a single neous map organizations between Isl2EphA3/+ SC or multiple
map(Brownetal.,2000).Indeed,elegantexperimentsmanipu- maporganizationswithinasingleSC.Incontrast,thestochastic
lating the expression level of other retinal EphA receptors optimization model presented here is able to replicate not
confirmthismodel,andmathematicalmodelswerederivedto only the heterogeneity of map organizations observed in the
describe these data and predict other findings (Bevins et al., Isl2EphA3/+SC,butalsomixed-typemaporganizationsinasingle
2011;Reberetal.,2004).Incontrast,ourfunctionalexperiments SC.Thisisanimportantdistinction,astheobservationofmixed-
revealextensiveheterogeneityintheorganizationofretinalin- type maps in the Isl2EphA3/+ SC suggests that the forces of
putstotheSCinIsl2EphA3/+mice.Onepotentialexplanationof molecular cues and spontaneous activity are nearly equally
thisdifferenceisthattheanatomicaltracingsinpreviousstudies in balance and that the local organization of retinal inputs
canonlysampleasmallportionofthemapatatime,whileour is determined stochastically. Incorporating this novel aspect
functionalimagingtechniqueallowsustomonitormaporgani- intofuturemodelsofretinocollicularmapformationisaneces-
zationasawhole.Thus,examiningmaporganizationatapop- sary step toward the development of accurate computational
ulation level may reveal heterogeneity that anatomical tracing simulations.
experimentscouldnot.However,wefoundsignificanthetero-
geneityintheanatomicalprojectionpatternofDiI-labelednasal Activity-DependentForces,ratherthanGenetic
RGCsinIsl2EphA3/+micethatwereconsistentwiththehetero- Modifiers,DriveHeterogeneity
geneous functional organization of the collicular map. In Our mathematical model of map formation revealed that
33.3% (6/18) of Isl2EphA3/+ animals in which we traced nasal subtle changes in the expression level of EphAs results in
Neuron87,1261–1273,September23,2015ª2015ElsevierInc. 1269