Three-Dimensional Spatial Distribution of Synapses in the Neocortex: A Dual-Beam Electron Microscopy Study.

0.87 MB·English

by  Merchan-Perez, Angel

CerebralCortexJune2014;24:1579–1588
doi:10.1093/cercor/bht018
AdvanceAccesspublicationJanuary30,2013
Three-Dimensional Spatial Distribution of Synapses in the Neocortex: A Dual-Beam
Electron Microscopy Study
AngelMerchán-Pérez1,3,José-RodrigoRodríguez1,4,SantiagoGonzález2,VíctorRobles2,3,JavierDeFelipe1,4,PedroLarrañaga5
andConchaBielza5
1LaboratorioCajaldeCircuitosCorticales,2LaboratoriodeMineríadeDatosySimulación,CentrodeTecnologíaBiomédica,
3DepartamentodeArquitecturayTecnologíadeSistemasInformáticos,UniversidadPolitécnicadeMadrid,PozuelodeAlarcón,
Madrid28223,Spain,4InstitutoCajal,ConsejoSuperiordeInvestigacionesCientíficas,Madrid28002,Spainand5Departamento
deInteligenciaArtificial,UniversidadPolitécnicadeMadrid,BoadilladelMonte,Madrid28660,Spain
AddresscorrespondencetoAngelMerchán-Pérez,LaboratorioCajaldeCircuitosCorticales,CentrodeTecnologíaBiomédica,Universidad
PolitécnicadeMadrid,PozuelodeAlarcón,28223Madrid,Spain.Email:amerchan@fi.upm.es.
In the cerebral cortex, most synapses are found in the neuropil, but plays an important role in the functional properties of sy-
relativelylittleisknownabouttheir3-dimensionalorganization.Using napses (Schikorski and Stevens 1997; Takumi et al. 1999;
anautomateddual-beamelectronmicroscopethatcombinesfocused Lüscheretal.2000;Tarusawaetal.2009).Thus,numerousre-
ion beam milling and scanning electron microscopy, we have been searchers have been trying to find simple and accurate
abletoobtain10three-dimensionalsampleswithanaveragevolume methods for estimating the distribution, size, and number of
of180µm3fromtheneuropiloflayerIIIoftheyoungratsomatosen- synapses. To this end, 2 sampling procedures are currently
sory cortex (hindlimb representation). We have used specific soft- available:Oneisbasedonserialreconstructionsandtheother
ware tools to fully reconstruct 1695 synaptic junctions present in onsinglesections.Clearly,serialreconstructionshouldbethe
thesesamplesandtoaccuratelyquantifythenumberofsynapsesper method of choice for the challenging task of unraveling the
unitvolume. These tools also allowed ustodetermine synapse pos- extraordinarycomplexityofthenervoussystem.Indeed,serial
ition and to analyze their spatial distribution using spatial statistical sectioning transmission electron microscopy is a well estab-
methods. Our results indicate that the distribution of synaptic junc- lished and mature technology for obtaining 3-dimensional
tions in the neuropil is nearly random, only constrained by the fact data from ultrathin sections of brain tissue (Stevens et al.
thatsynapsescannotoverlapinspace.Atheoreticalmodelbasedon 1980; Harris et al. 2006; Hoffpauir et al. 2007; Mishchenko
random sequential absorption, which closely reproduces the actual et al. 2010; Bocket al. 2011). It is based on imaging ribbons
distributionofsynapses,isalsopresented. of consecutive sections with a conventional transmission
electronmicroscope.However,themajorlimitationisthatob-
Keywords:dual-beamelectronmicroscopy,focusedionbeammilling/ taining long series of ultrathin sections is extremely time-
scanningelectronmicroscopy,neocortex,spatialdistributionofsynapses, consuminganddifficult,oftenmakingitimpossibletorecon-
spatialstatistics,synapses structlargevolumesoftissue.Hence,therecentdevelopment
of automated electron microscopy techniques represents
another crucial step in the study of neuronal circuits (e.g.
Briggman and Denk 2006; Knott et al. 2008; Merchán-Pérez,
Introduction
Rodriguez,Alonso-Nanclares,etal.2009).
Inthecerebralcortex,mostsynapses(90–98%)areestablished In the present study, we use a new dual-beam electron
intheneuropil(Alonso-Nanclaresetal.2008),whichismade microscope that combines a focused ion beam (FIB) column
of dendrites, axons, and glial processes. One major issue in and a scanning electron microscope (SEM). The FIB column
cortical circuitry is to ascertain how synapses are distributed directsagallium(Ga+)ionbeamtoward thesample.The col-
and whether synaptic connections are specific or not (DeFe- lision of Ga+ ions with substrate atoms results in the removal
lipe et al. 2002). Therefore, to understand the anatomical of these atoms from the substrate. Since the FIB can be
design principles of the cortical circuits, it is essential to focused and controlled on a nanometer scale, this effect can
analyze the ultrastructure of all components of the neuropil be used to mill the specimen, removing a thin layer of
and, in particular, the number and spatial distribution of sy- material.Abackscatteredelectronimageisthenobtainedfrom
napses. There are 2 major morphological types of synapses: thefreshlymilledsurfaceusingtheSEM.Themilling/imaging
Asymmetric (or Gray’s type I) and symmetric (or Gray’s type processes are automatically repeated in order to obtain a
II; Gray 1959; Colonnier 1968). The major sources of asym- longseriesofimagesthatrepresenta3-dimensionalsampleof
metricsynapsesarespinyneurons(pyramidalandspinynon- tissue. Using this methodology, we have previously shown
pyramidal cells) and extrinsic cortical afferents, whereas the that virtuallyall cortical synapses can be accurately identified
vastmajorityofsymmetricsynapsesareofintrinsicoriginand as asymmetric (excitatory) or symmetric (inhibitory) synaptic
areformedbythepopulationofaspinyorsparselyspinyinter- junctionswhentheyarevisualized,reconstructed,andquanti-
neurons. Since spiny neurons and the major cortical afferent fied from large 3-dimensional tissue samples obtained in an
systems are excitatory in function, and virtually all aspiny or automated manner (Merchán-Pérez, Rodriguez, Alonso-
sparselyspinyinterneuronsareγ--aminobutyric(GABAacid)- Nanclares,etal.2009).Sincethesegmentation,quantification,
ergic, it is assumed that axon terminals forming asymmetric and analysis of synaptic junctions are a labor-intensive pro-
synapsesareexcitatoryandthoseformingsymmetricsynapses cedure,weusedEspinasoftware,aspecificallydevelopedtool
are inhibitory (Ascoli et al. 2008). Furthermore, synaptic size thatgreatlyfacilitatesandacceleratestheseprocesses(Morales
©TheAuthor2013.PublishedbyOxfordUniversityPress.
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.org/licenses/by-nc/3.0/),whichpermitsnon-
commercialuse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.Forcommercialre-use,[email protected]
et al. 2011). For the segmentation of synaptic junctions, TendifferentsamplesoftheneuropiloflayerIIIofthesomatosen-
Espina makes use of the fact that presynaptic and especially sorycortexwereobtainedfrom3differentanimals(Table1).Toselect
postsynaptic densities are electron-dense structures. It uses a the exact location of the samples, we first obtained plastic semithin
gray-level threshold to extract all the voxels that fit the gray sections (2µm thick) from the block surface and stained them with
toluidine blue to identify cortical layers. These sections were then
levels ofthe synaptic junction. Asymmetricsynaptic junctions
photographedwithalightmicroscope.Thelastoftheselightmicro-
have a thicker postsynaptic density, so they can be distin- scope images (corresponding to the section immediately adjacent to
guished from symmetric ones, whose postsynaptic densities theblockface)wasthencollatedwithSEMphotographsofthesurface
are thinner and similar to the presynaptic densities. As a of the block. In this way, it was possible to accurately identify the
result, each synaptic junction (already tagged as asymmetric regions of the neuropil to be studied. All samples selected for FIB
or symmetric) is segmented as a flattened irregular volume milling/SEMimagingwerelocatedatmid-depthoflayerIII.Afterap-
plying a 3-dimensional unbiased counting frame and correcting for
anditsgeometrical features,including itsspatial position,are
tissueshrinkage(HowardandReed2005;Merchán-Pérez,Rodriguez,
determinedbythesamesoftware. Alonso-Nanclares, et al. 2009; Morales et al. 2011), the volume of
Pointsinspace—thesynapticjunctionsinthepresentcase— tissueanalyzedfromeachsamplerangedfrom149.13to247.58µm3
can be distributed according to 3 basic patterns: Random, (mean 180.33µm3; see Supplementary Table 1). Synaptic junctions
clustered,andregular.Arandompatternfollowsthebasicre- within these volumes were visualized, automaticallysegmented, and
reconstructed in 3 dimensions with Espina software (Morales et al.
ference model of a point process, the so-called complete
2011;Fig.1).Thissoftwarealsoprovideddatasuchasthevolumeof
spatial randomness (CSR) or homogeneous spatial Poisson
theunbiasedcountingframe,thenumberofsynapticjunctionsinside
point process (Seidel 1876). It is characterized by 2 funda-
theframe,thespatialpositionofthecentroidsorcentersofgravityof
mentalproperties:(1)Thenumberofpointsfallinginagiven thesynapticjunctions,andanestimationoftheirsizesbytheFeret’s
region follow a Poisson distribution with a constant mean diameter (the diameterof the smallest sphere circumscribing the sy-
number of points per unit volume; and (2) each point is naptic junction; Fig. 1 and Supplementary Videos 1 and 2). As pre-
equally likely to occur at any position and is not affected by viously described in detail (Merchán-Pérez, Rodriguez, Alonso-
Nanclares,etal.2009),synapticjunctionswitheitheraprominentor
the locations of the other points (Illian et al. 2008; Gaetan
thinpostsynapticdensitywereclassifiedasasymmetricorsymmetric
and Guyon 2009). In aclustered distribution, the points tend
synapticjunctions,respectively(SupplementaryVideo1).
to concentrate in groups, leaving other regions of space
emptyoralmost devoid of points. Finally, in a regularor dis-
persed pattern, every point is located as far as possible from SpatialPointPatternAnalysis
its neighbors, resulting in a lattice-like distribution of points. Toanalyzethespatialdistributionofsynapticjunctions,wecompared
Although there are no clear-cut limits between these 3 basic the actual positions of the centroids of synaptic junctions with 2
patterns, CSR represents a boundary condition between clus- theoretical point processes: CSR and random sequential adsorption
teredanddispersedspatialprocesses,soourstrategywasfirst (RSA).CSRdefinesasituationwhereapointisequallylikelytooccur
atanylocationwithinthestudyvolume,regardlessofthelocationsof
to test for CSR, trying to identify deviations from it and to
otherpoints(Diggle2003).ThemathematicalmodelunderlyingCSR
buildamodelthataccountedforthesedeviations(Illianetal. isahomogeneousspatialPoissonpointprocess.Thus,thenumberof
2008;GaetanandGuyon2009). points occurring within a finite volume, V, is a random variable fol-
lowingaPoissondistributionwithmeanλ|V|,whereλ>0and|V|is
the volume of V. The intensity λ representsthe expected numberof
MaterialsandMethods pointsperunitvolume.CSRservesasaboundaryconditionbetween
spatialprocessesthataremoreclusteredthanrandomandspatialpro-
TissuePreparationand3-DimensionalElectronMicroscopy cessesthataremoreregularthanrandom.
Male Wistar rats sacrificed in postnatal day 14 were used for this For modelingthespatial distributionof synapses,we should take
into account that synaptic junctions cannot overlap, and thus the
study.Animalswereadministeredalethalintraperitonealinjectionof
minimumintersynapticdistances(measuredbetweentheircentroids)
sodium pentobarbital (40mg/kg) and were intracardially perfused
must be limited by the sizes of synaptic junctions themselves. A
with 2% paraformaldehyde and 2.5% glutaraldehyde in 0.1M phos-
phate buffer. The brain was then extracted from the skull and pro-
cessed for electron microscopy according to a previously described
protocol (Merchán-Pérez, Rodriguez, Alonso-Nanclares, et al. 2009). Table1
All animals were handled in accordance with the guidelines for Dataonthespatialdistributionofsynapticjunctionsin10samplesoftheneuropiloflayerIII
animalresearch set out in the EuropeanCommunity Directive 2010/
63/EU,andallprocedureswereapprovedbythelocalethicscommit- Sampleno.andanimal Numberof Meandistanceto MeanFeret’sdiameter
teeoftheSpanishNationalResearchCouncil(CSIC). identification synapsesper nearestneighbor ofsynapticjunctions
cubicmicron (nm)±SD (nm)±SD
Three-dimensionalbraintissuesampleswereobtainedusingacom-
bined FIB/SEM (Crossbeam® Neon40 EsB, Carl Zeiss NTS GmbH, 1(W31) 0.9857 519.55±136.35 377.19±159.63
Oberkochen, Germany). This instrument combines a high-resolution 2(W31) 0.6936 594.07±192.28 462.18±177.52
field emissionSEM columnwithafocusedgallium ion beam,which 3(W33) 0.9279 537.43±159.20 437.62±168.04
4(W33) 1.0088 537.39±157.70 414.22±169.04
canmillthesamplesurface,removingthinlayersofmaterialonanan-
5(W33) 0.9474 597.30±174.02 466.03±215.91
ometer scale. After removing each slice (20nm of thickness), the 6(W33) 0.9399 533.21±163.29 423.38±169.83
milling process was paused, and the freshly exposed surface was 7(W33) 0.9881 487.17±172.30 397.29±168.22
imaged with a 1.8-kV acceleration potential using the in-column 8(W35) 0.7997 568.21±178.51 427.90±168.15
energyselectivebackscattered(EsB)electrondetector.A30-mmaper- 9(W35) 1.1267 501.38±156.97 378.35±166.60
10(W35) 1.0178 523.74±150.36 405.43±175.62
turewasusedandtheretardingpotentialoftheEsBgridwas1500V.
Allsamples 0.9399 535.78±166.81 417.06±175.97
The milling and imaging processes were sequentially repeated, and
long series of images were acquired through a fully automated pro- Note:Densitiesofsynapseswerecalculatedbydividingtheactualnumberofsynapticjunctions
cedure, thus obtaining a stack of images that represented a withinanunbiased3-dimensionalcountingframebythevolumeofthecountingframe.Distances
3-dimensional sample of the tissue (Merchán-Pérez, Rodriguez, tothenearestneighborwerecalculatedbetweenthecentroidsofthesynapticjunctions.
Alonso-Nanclares,etal. 2009).Image resolutionin thexy planewas TheFeret’sdiameteristhediameterofthesmallestspherecircumscribingthesynapticjunction;
3.7nm/pixel.Resolutioninthezaxis(sectionthickness)was20nm. itisusedhereasanestimateofthesizeofsynapticjunctions.
1580 Three-DimensionalDistributionofSynapses (cid:129) Merchán-Pérezetal.
Figure1. Segmentationofsynapticjunctions,estimationoftheirsizes,andextractionoftheirgeometriccentersorcentroids.(A)Anexampleofthetissuevolumesampled
andthereconstructedsynapticjunctions.Asymmetricandsymmetricsynapticjunctionsareshowningreenandred,respectively.(B)Thesmallestspherescircumscribingthe
reconstructedsynapticjunctionsservedtocalculatetheFeret’sdiameter,whichwasusedasanestimationoftheirsize.Anunbiasedcountingframewasalsodrawntofacilitate
thequantificationofthenumberofsynapsesperunitvolume.(C)Thegeometriccentersorcentroidsofthesynapticjunctionsweredeterminedtoindicatethespatialpositionof
thesynapses.Theyarerepresentedwithinthespheresthatwereusedtoestimatethesizesofsynapticjunctions.(D)Thecentroidsindicatingthespatialpositionofsynaptic
junctions are represented alone within the counting frame. The dimensions of the counting frame represented in B, C, and D are 7.16×4.58×3.98µm. See also
SupplementaryVideos1and2.
respect,an RSAprocess (Evans1993) isa kindof hard-core process
wherethepatternisconstructedbyplacingspheresin3-dimensional
spaceiterativelyandrandomly,withtheirradiifollowingaprobability
densityfunction.Ifanynewlygeneratedsphereintersectswithanex-
isting sphere, the new sphere is rejected and another sphere with a
differentcenterandradiusisgenerated.Thisprocessisstoppedwhen
therequirednumberofspheresisreached(SupplementaryVideo3).
In our case, the minimum interpoint distance would depend at
leastpartiallyonthesizesofsynapticjunctions.Thus,weobtainedthe
empiricaldistributionoftheFeret’sdiametersofsynapticjunctionsas
anestimateoftheirsizes.Wethenperformedagoodness-of-fittestto
find thetheoreticalprobabilitydensity distributionthat best fittedto
theempiricaldistribution.WefoundthatthebestfitusingtheKolmo-
gorov–Smirnov test was with a log-normal distribution with
parameters µ=5.828 and σ=0.446 (Fig. 2). The estimates of the
expectation and variance were υ=375.198nm and τ2=30,981.351
nm2,respectively(SupplementaryMethods).
Foreachofthe10differentsamplesandtheircorrespondingCSR
Figure 2. Representation of the distribution of the sizes of synaptic junctions
and RSA processes, we calculated 3 functions commonly used for
estimated by their Feret’s diameters in the 10 samples of the neuropil of layer III spatial point pattern analysis: the G, F, and K functions (Ripley and
(bluehistogram)andthecorrespondinglog-normaldistribution(redtrace).
Kelly1977;Diggle1979).
TheGfunction,alsocalledthenearest-neighbordistancecumulat-
spatialpointprocesstomodelthissituationcanbeseenasatypeof ive distribution function or the event-to-event distribution, is, for a
hard-core point process where no points can occur at a distance distance d, the probability that a typical point separates from its
smaller than a specific minimum distance (Illian et al. 2008). In this nearest-neighbor a distance of at most d. The empirical distribution
CerebralCortexJune2014,V24N6 1581
functionG*oftheobservednearest-neighbordistancesisusedtoesti- samples was 1803.32µm3, where we found 1695 synapses
matetheGfunction: (1555 asymmetric and 140 symmetric). Additional data on
X thesetissuevolumesandtheactualcountsofasymmetricand
1
G(cid:1)ðdÞ¼N IðDi(cid:3)dÞ; symmetric synaptic junctions per sample are shown in Sup-
i plementaryTable1.
Inordertoexplorethespatialdistributionpatternofsynap-
NwhtehreenDuimisbtehreodfisstyannacpesoefs,syannadpsI(e·)itthoeitisnndeicaarteosrt-nfuenigchtiboonrwsyhniacphseis, tic junctions, we first performed a nearest-neighbor analysis
oneiftheargumentistrueandiszerootherwise. on the centroids of the synaptic junctions found within each
The F function, also called the empty space function or the sampled volume. We calculated the mean distance from each
point-to-eventdistribution,is,foradistanced,theprobabilitythatthe centroid to its nearest neighbor within the counting frame.
distance of each point (in a regularlyspaced grid of L points super- Centroids that were closer to the boundaries of the counting
imposedoverthesample)toitsnearestsynapsecentroidisatmostd.
frame than to anyothercentroid were excluded from the cal-
The empirical distribution function F* of the observed empty space
distancesonagridofLlocationsisusedtoestimatetheFfunction: culations, since their nearest neighbor could lay outside the
countingframeatanunknowndistance(Baddeleyetal.1993;
X
F(cid:1)ðdÞ¼1 IðD0(cid:3)dÞ; Illian et al. 2008). The mean distance to the nearest neighbor
L i rangedfrom487.17to597.30nm(Table1).
i
Tofurtheranalyzethespatialdistributionofnearestneigh-
where D′i is the distance of grid point i to its nearest centroid. No bors,weobtainedtheGfunction(Diggle1979).Thisfunction
edgecorrectionwasusedforGandFfunctions. is estimated using the distances from each centroid to its
The K function, also called the reduced second moment function
nearest neighbor, and plotting the fraction of points in the
or Ripley’s function, is, for a distance d, the expected number of
pointswithinadistancedofatypicalpointoftheprocessdividedby sample having their nearest neighbor at a given distance or
theintensityλ.AnestimationoftheKfunctionisgivenbythemean less (Fig. 3). We then compared the experimentally observed
numberofpointswithinasphereofincreasingradiusdcenteredon GfunctionswiththetheoreticalGfunctionsthatwouldbeob-
eachsamplepoint,dividedbyanestimationoftheexpectednumber tainedifthesamenumberofcentroidswererandomlydistrib-
of points per unit volume. A common formula is the Milles–Lantue- uted according to the CSR or homogeneous Poisson process.
joul–Stoyan–Hanisch translation-corrected estimate (Baddeley et al.
Inthelatterconditions,thefunctiontakesasigmoidshape,as
1993),givenby: in the examples shown in Figure 3A,C (red traces) and Sup-
jVj2XXIðD00 (cid:3)dÞ plementary Figures 1–10. In a clustered pattern, the curve
K(cid:1)ðdÞ¼ ij ; wouldbeskewedtotheleft (shorterinterpointdistancesthan
N2 i j=i jVijj expected), while it would be shifted to the right in a regular
pattern(longerinterpointdistancesthanexpected).
wbehtewreee|nVc|enistrtohide vioalnudmeceonftrtohiedcj,ouanntdin|gVfijr|amdee,noDt″eisj itshethveodluismtaencoef The experimentallyobserved G functions showed a similar
the 3-dimensional subspace obtained as the intersection between V shapeinthe10 differentsamples.Two examplesofthemare
andthe(translated)spherecenteredatsynapseiandradiusD″ij. showninFigure3(bluetraces)andtherestareshowninSup-
Spatial analysis of the positions of the centroids of synaptic junc- plementary Figures 1–10. In all cases, when the experimen-
tionsinexperimentalandsimulateddistributionswasperformedwith tally observed G functions were compared with the G
RProject,specificallywith“spatstat”(BaddeleyandTurner2005)and
functions of the corresponding Poisson processes, the more
“fitdistplus” (Venables and Ripley 2002; Vose 2008) packages and
noticeable differences were found at short interpoint dis-
withSA3Dsoftware(Eglenetal.2008).Additionalstatisticalanalyses
tances,sinceallexperimentalsamplesshowedanemptyspace
wereperformedwithSPSS(IBMCorp.,NewYork,USA).
around centroids where no other centroids were found
(arrowsinFig.3A,C,seealsoSupplementaryFigs1–10).Due
to this empty space, the fraction of centroids having their
Results
nearest neighbor at short distances was lower than would be
Weobtained10independentsamplesbyFIB/SEMtechnology expected in a homogeneous Poisson process, while at longer
fromregionsoftheneuropiloflayerIIIofthesomatosensory distances the observed curves tended to overlap or slightly
cortex (hindlimb representation) from three 14-day-old rats. exceedthePoissoncurves.Ingeneral,20–40%ofthecentroids
From each of the 10 samples of cortical tissue used in this hadtheirnearestneighborat500nmorless,whilepractically
study,weobtainedthenumber,position,andshapeofsynap- all of them had their nearest neighbor at 1000nm or less
tic junctions inside a 3-dimensional unbiased counting frame (Fig.3A,CandSupplementaryFigs1–10).
(Howard andReed2005; Fig.1and SupplementaryVideo2). The existence of this dead space can be explained by the
Nocellsomataorbloodvesselswerepresentwithinthecount- factthatthecentroidsofsynapticjunctionsrepresentthegeo-
ing frames. In this way, we directly calculated the number of metric center of a physical volume (the volume of the recon-
synapsesperunitvolumeofneuropil.Thesedensitiesranged structed synaptic junction) instead of a dimensionless point,
from 0.69 to 1.13synapses/µm3, with a mean of 0.94sy- and thus their position cannot be independent from the pos-
napses/µm3 (Table 1). The spatial positions of the geometric ition of their immediate neighbors. In other words, centroids
barycenters or centroids of each individual synaptic junction cannotbetooclosetoeachothersincethevolumestheyrep-
(Fig.1andSupplementaryVideo2)wererecordedforfurther resent, the synaptic junctions, cannot overlap. Therefore, in
analysis.Asanestimationofthesizeofsynapticjunctions,we ordertosimulatethedistributionofsynapsesintheneuropil,
also recorded the Feret’s diameter of each synaptic junction, the empty space around the centroids of synaptic junctions
which is the diameter of the smallest sphere circumscribing had to be accounted for by a random minimum-spacing
the synaptic junction (Fig. 1, Table 1, and Supplementary distance that would depend, at least partially, on the sizes of
Videos 1 and 2). The total tissue volume studied for the 10 synapticjunctionsthemselves.
1582 Three-DimensionalDistributionofSynapses (cid:129) Merchán-Pérezetal.
Figure3. Gfunctionsestimatedfromthepositionsofthecentroidsofsynapticjunctionsof2examplesoftheneuropiloflayerIII,correspondingtosamplesno.5(AandB)and
no.10(CandD)(seealsoTable1).InAandC,thefunctionsobtainedfromtheexperimentallyobserveddata(bluetraces)havebeenrepresentedtogetherwiththefunctions
thatwouldbeobtainedifthecentroidsweredistributedaccordingtoahomogenousPoissonprocess(redtraces)andthemeanof100simulatedrealizationsofanRSAprocess
(greentraces,seetextforfurtherdetails).Inbothsamples,theexperimentallyobservedfunctionsshowanemptyspacearoundcentroidswherenoothercentroidsarefound
(AandB,arrows).AsimilaremptyspaceisalsopresentinRSAsimulations.InBandD,theexperimentallyobservedGfunctionsaredepictedinblueandthe100individual
simulatedrealizationsofRSAingreen,showingthattheexperimentalGfunctionseitheroverlappedwiththesimulatedRSAfunctions(B)orwereslightlydisplacedtotheleft
(D).SeealsoSupplementaryFigures1–10.
Toaccountforthisminimum-spacingdistancebetweencen- 2002; Gaetan and Guyon 2009). To estimatethe F function, a
troids, we simulated random distributions of points in space regular grid istraced within the 3-dimensional bounding box
using a sequential algorithm that first generates a random that contains the centroids, the distances between each grid
pointthatisthecenterofaspherewithacertaindiameter.The crossing point and its nearest neighboring centroid are
diametersusedinthesimulationswererandomlydrawnfrom measured, and the cumulative probability of having the
the probability distribution of the experimentally observed nearest centroid at a given distance or less is plotted. In a
Feret’s diameters (Table 1). This distributionwas found tobe homogeneousPoissonprocess,theFfunction takesthesame
log-normal(Fig.2).Ifthenextsimulatedpointwithitscorre- valuesastheGfunction(Baddeleyetal.1993;Fig.4andSup-
sponding Feret’s diameter does not overlap with previously plementary Figs 1–10). Values of the F function greater than
generated points, then it is accepted. Otherwise, it is rejected the Poisson value suggest that there is regularity in the point
and another random point is generated. The process termi- pattern,whilelowervaluessuggestclustering.TheKfunction
nates when the desired number of points has been reached isestimatedasthemeannumberofpointswithinasphereof
(Supplementary Video 3). This kind of process is known as increasing radius centered on each sample point (Ripley and
RSA(Evans1993). Kelly 1977). It is a rapidly growing curve in a homogeneous
Inordertocomparetheexperimentallyobserveddistribution Poisson process (Fig. 5 and Supplementary Figs 1–10), with
ofcentroidswiththeRSAprocess,100simulatedrealizationsof lower values in a regular pattern and higher values in aclus-
RSA were generated for each experimental sample, with the teredpattern.
same number of points and volumes as the original samples. In the case of F functions, the Poisson and RSA curves
Fitness between the observed G functions and the ones were very similar, and the experimentally observed curves
obtained from simulated RSA processes was better than that either overlapped with RSA curves or tended to be located
previously found with homogeneous Poisson processes, slightly to the right of them (Fig. 4 and Supplementary Figs
although the observed curves tended to be located slightly to 1–10).KfunctionswerealsoverysimilarforboththePoisson
theleftoftheRSAcurves(Fig.3andSupplementaryFigs1–10). and RSA models. The experimentally observed curves of the
Further analysis of the spatial distribution of the centroids KfunctionwereverysimilartothePoissonandRSAcurvesor
of synaptic junctions was performed by calculating the Fand were located slightly to the left of them (Fig. 5 and Sup-
K functions (Baddeley et al. 1993; O’Sullivan and Unwin plementaryFigs1–10).
CerebralCortexJune2014,V24N6 1583
Figure 4. F functions corresponding to the same samples (5 and 10) as in Figure 3. Colors of traces represent the same as in Figure 3. The F functions were similar for
the experimentallyobserved data and the Poisson and RSA processes. The observed functions eitheroverlapped with (A) or were slightly displaced to the right (C) of the
corresponding Poisson and RSA curves. Note that in both examples the observed functions were compatible with individual realizations of the RSA model (B and D).
TheFfunctionsoftherestofthesamplesareshowninSupplementaryFigures1–10.
In order to test the goodness-of-fit of the experimentally were intermingled at random (null hypothesis), the nearest
observed functions in the 10 different samples with those for neighborofanygivensynapseshouldbeasymmetricorsym-
thecorrespondingPoissonandRSAprocesses,weperformed metric with a probability that would only depend on the
a battery of 2-sample Kolmogorov–Smirnov tests (Table 2). respective proportions of both types of synapses in the
ThetestsshowedthatfitnesswasbetterforFandKfunctions sample. On the other hand, if both types of synapses were
thanforGfunctions.ComparingtheactualsampleswithRSA spatiallysegregated,theirrespectivenearestneighborswould
simulations yielded a clearly better fit than comparing with tendtobeofthesametype.Notethatinthiscasewedidnot
Poisson distributions. In fact, in the case of RSA simulations, measure the distances between centroids but counted how
26 of 30 tests yielded P-values higher than 0.950, while for many synapses had a nearest neighbor of the same or differ-
Poisson distributions 17 of 30 tests yielded P-values over enttype.These counts showedthat 704 asymmetric synapses
0.950(Table2).Onlyforsample2,thenullhypothesisofRSA had an asymmetric nearest neighborand 38 had a symmetric
was rejected for the G function (P=0.035). For the homo- nearest neighbor. In the case of symmetric synapses, 43 had
geneous Poisson process, the null hypothesis was only re- an asymmetric nearest neighbor, while 20 had a symmetric
jected for the G function of sample 10 (P=0.007). In these one.Thesedatawereused tocreatea 2×2contingencytable
samples,however,theGfunctionsshowednocleardeviations showing both types of synapses against the type of their
toward eitheraclustered or regular distribution pattern (Sup- nearest neighbor (Table 3). The 2-tailed Fisher’s exact test
plementaryFigs2and10). applied to the contingency table rejected the hypothesis that
Results were similar when all synapses (asymmetric and both types of synapses are intermingled at random
symmetric) were studied as a single group and when only (P<0.0001). In fact, the number of symmetric synapses that
asymmetricsynapseswereanalyzed(SupplementaryTable2). have a symmetric nearest neighbor was more than 4 times
This result was expected since asymmetric synapses rep- higher than expected under the null hypothesis (Table 3),
resented 91.74% of the total number of synapses found in possibly indicating that symmetric synapses tend to group
layer III. However, due to the small numberof symmetric sy- together.
napses present in our samples (the average number of sym-
metric synaptic junctions per sample was 14, see
Discussion
Supplementary Table 1), it was not possible to calculate the
G,F,andKfunctionsforthem. Using FIB/SEM technology, we have been able to accurately
Thereisasimpleway,however,totestwhetherasymmetric quantify the density and spatial distribution of synapses in
and symmetric synapses are intermingled at random. If they stacksofimagesfromtheneuropiloflayerIIIoftheyoungrat
1584 Three-DimensionalDistributionofSynapses (cid:129) Merchán-Pérezetal.
Figure5. Kfunctionscorrespondingtothesamesamples(5and10)asinFigures3and4.TracecolorsrepresentthesameasinFigure3.Theexperimentallyobservedcurves
oftheKfunctionweregenerallylocatedslightlytotheleftofthesimulatedRSAcurves,althoughtheobservedfunctionswerecompatiblewithindividualrealizationsoftheRSA
process.TheremainingsamplesareshowninSupplementaryFigures1–10.
Table2 Table3
P-valuesofthe2-sampleKolmogorov–SmirnovtestsperformedwiththeG,F,andKfunctions Contingencytableshowingthetypeofsynapticjunctionsagainstthetypeoftheirnearest
derivedfromtheactualexperimentalsamples,fromhomogeneousPoissonprocesses,andfrom neighbors
themeanof100simulatedrealizationsofRSApersample
Typeofsynapse Typeofnearestneighbor
Sampleno. Two-sampleKolmogorov–Smirnovtests(P-values) Asymmetric Symmetric Total
Experimentalsamplesversus Experimentalsamplesversus Asymmetric 704 38 742
homogeneousPoissonprocesses simulatedrealizationsofRSA 688.54 53.46 742.00
G F K G F K Symmetric 43 20 63
58.46 4.54 63.00
1 0.952 0.952 0.468 0.799 0.952 0.994 Total 747 58 805
2 0.799 0.999 0.699 0.035 0.999 0.906 747.00 58.00 805.00
3 0.998 1.000 0.994 0.952 0.999 0.994
4 0.998 0.999 0.906 0.998 1.000 0.994 Theobservedcountsofsynapses(bold)wereobtainedfromthe10samplesoftheneuropilof
5 0.998 1.000 0.699 0.999 1.000 0.994 layerIII.Theexpectedcounts(initalics)arecalculatedfromthemarginaltotals.Synapseswhose
6 0.952 0.999 0.906 0.952 0.999 0.994 nearestneighborswerenotknown—thosethatwerelocatedclosertotheboundariesthanto
7 0.236 0.952 0.994 0.134 0.998 0.994 anyothersynapseinthesample—wereexcludedfromtheanalysis.TheFisher’sexacttest
8 0.998 0.999 0.906 0.998 1.000 0.999
appliedtotheobservedcountsrejectedthehypothesisthatasymmetricandsymmetricsynapses
9 0.071 0.134 0.994 0.998 0.998 1.000
10 0.007 0.236 0.906 0.998 0.952 1.000 areintermingledatrandom(P<0.0001).Themostsalientmismatchbetweentheobservedand
expectedvalueswasthenumberofsymmetricsynapsesthathadasymmetricnearestneighbor,
whichwas4.4timeshigherthanexpected.
somatosensory cortex. In addition, virtually all synapses
present in the 3-dimensional samples could be unambigu-
ously identified since they can be visualized in consecutive from single 2-dimensional images (see for example DeFelipe
serial sections and, if necessary, they can be digitally resec- et al. 1999). Unfortunately, the mean densityof synapses per
tioned at different planes to ascertain their identity as unitvolumethatwehaveobtainedinthisstudy(meanof0.94
asymmetricorsymmetric(Merchán-Pérez,Rodriguez,Alonso- synaptic junctions/µm3) and the proportion of asymmetric
Nanclares,etal.2009).Inthisway,thetechnologyusedinthe andsymmetricsynapsescouldnotbecomparedwithprevious
present study eliminates the relatively large pool of synapses studies since no detailed electron microscope data are avail-
that were labeled as “uncharacterized” in previous reports ableinthisparticularlayeroftheratsomatosensorycortexat
sincetheycouldnotbeclassifiedasasymmetricorsymmetric theageanalyzedinthepresentstudy.
CerebralCortexJune2014,V24N6 1585
Regardingthespatialpositionofsynapses,ourresultsindi- between the neuropil and perisomatic innervation regarding
catethat thedistributionofsynaptic junctionsin theneuropil theorganizationofsynapticcircuits.Indeed,therearenumer-
is nearly random, only constrained by the fact that synapses ousglutamatergicandperisomaticGABAergicaxonterminals
cannotoverlapinspaceandsotheirgeometriccentersorcen- incloseproximityaroundthesomaandproximaldendritesof
troidscannotbetooclosetotheirneighbors.Thisconclusion pyramidal cells, providing a putative basis for nonsynaptic
isfurthersupportedbythefindingthatthespatialdistribution interactions between these 2 types of synapses (Merchán-
of the centroids of synaptic junctions can be closely modeled Pérez,Rodriguez,Ribak,etal.2009).
by a random process where overlapping is prevented by as- An issue that needs to be addressed is whether the den-
signingavolumetoeachcentroid.Inmathematicalterms,this sities of synaptic junctions and their nearly random distri-
model is known as “random sequential adsorption” (Evans bution in space have any predictive value to calculate the
1993;StoyanandSchlather2000;vanLieshout2006).Noneof possible number of synaptic inputs that a given neuron may
thefunctionsF,G,andKalonesufficeforthecharacterization receiveinlayerIII.ThisisrelatedtothesocalledPeter’srule
of a point pattern, so we have used them in combination (Braitenberg and Schüz 1998), which represents a generaliz-
(O’SullivanandUnwin2002;GaetanandGuyon2009).Visual ationtoalltypesofcorticalsynapsesbasedontheconclusion
inspectionofallthesefunctionsshowedonlysmalldeviations of Peters and Feldman (1976) regarding the synaptic connec-
betweentheexperimentaldataandtheRSAmodel,whichwas tionsofgeniculo-corticalafferentsandcorticalneuronsinthe
further corroborated by a battery of goodness-of-fit tests. In rat visual cortex: “Although thalamocortical afferents termi-
ourparticularcase,the volumesthat wererandomlyassigned nate principally in layer IV, their distribution with respect to
to each centroid were not arbitrary, but were drawn from the postsynaptic targets may be essentially random, in the sense
distributionofFeret’sdiametersofthe3-dimensionallyrecon- that no specific types of neurons receive the afferents.
structed synaptic junctions. Although the Feret’s diameter is Instead, all elements in layer IV that are capable of forming
only a rough estimate of the sizes of synaptic junctions, the asymmetric synapses may be involved” (Peters and Feldman
RSAmodelnotonlypreventstheoverlappingofsynapticjunc- 1976).
tions, but also very closely mimics the actual distribution of Our results seem to support this assertion since the pos-
synapsesintheneuropil.Moreover,sincenootherconstraints itions of synapses do not showanyspatial preference, so the
wereimposed,thepositionsofsynapsesareotherwisenearly rulewould apply to the neuropil of layer III as awhole. Our
independent of the position of their neighbors. This and the findings are also in line with the distribution of swellings
fact that the Feret’s spheres occupy only 5.85% of the total along pyramidal cell axon collaterals stained by the Golgi
volume of the neuropil help to explain why the distributions method in the mouse neocortex. In that case, the intervals
of centroids in the samples and the simulated RSA processes between the axon swellings (characterized as putative sy-
arestillverysimilartoaCSRprocess. napses) were found to follow a Poisson distribution, with a
It must be stressed that our claim that the spatial distri- dead space caused by the spatial extent of the swellings
butionofsynapsesfollowsanRSAprocessdoesnotnecessary (Hellwig et al. 1994). However, it must be pointed out that
imply that during development synapses are actually formed the densities of synapses do vary locally (Table 1), and that
and positioned in space following the same rules asthe RSA. they are randomly distributed, so local deviations from the
However, it is interesting to consider the idea that a synapse rule will arise simply by chance. In any case, it is clear that
could be formed anywhere in space where an axon terminal the formulation of Peter’s rule should take into account that
and a dendritic element may touch, provided this particular different neuron types have different bouton distributions,
spotisnotalreadyoccupiedbyapreexistingsynapse.Indeed, project preferentially to different types of neurons and/or to
asimilarmodelbasedonrandomaxonaloutgrowthandcom- different parts of these neurons (dendritic tree, soma, axon
petition for available space has already been proposed initialsegment),andthatboththeaxonterminalsanddendri-
(Kaiser et al. 2009). Nevertheless, the same end result could tic trees may or may not originate in the same cortical layer
beachievedindifferentways,includingthesynapticturnover (Anderson et al. 2002; Binzegger et al. 2004; Mishchenko
that is known to occur during cortical development (Rakic et al. 2010; Bocket al. 2011). Thus, our data represent a het-
etal.1994),providedthatsynapsesarerandomlyaddedand/ erogeneous population of synapses, and our conclusion that
orwithdrawnfromthepopulation. they are randomly distributed in space should be maintained
Sincethereseemstobenolimitationtothepositionofany only for this population as a whole, with the only possible
synapseexceptthespacealreadyoccupiedbyothersynapses, exceptionofinhibitorysynapses(seebelow).
at least a subpopulation of them would be located very close Spatial randomness does not necessarily mean unspecific
tooneanother.Thatisthecaseinoursamples,sinceGfunc- connections,sincethisdoesnotprecludetheexistenceofsub-
tions show that approximately 20–40% of synaptic junctions jacent specificities based on molecular affinities, electrical
have a nearest neighbor with an intercentroid distance of activity, the developmental history of synapses, or other
<500nm. Considering the actual size of synapses (Table 1), mechanisms not detected by our methodology. Indeed, our
thiswouldmeanthatsomeofthemwouldbelocatedsideby techniqueiscapableofdistinguishingbetweenexcitatoryand
side,openingthepossibilitythattheneurotransmitterreleased inhibitorysynapses, but thereis no indication astotheir par-
by one synapse could reach its neighbor by diffusion and ticular neuronal type of origin. Different groups of the sy-
influence its behavior(Fuxeetal. 2007; Rusakovet al.2011). napses in any given sample could come from cells located in
However, this seems to be true mostly for glutamatergic sy- the immediate vicinity, from other layers, from cortical areas
napses (asymmetric synapses, the most abundant type), outside the somatosensory cortex, from the contralateral
because the number of GABAergic synapses (symmetric sy- cortex,orfromsubcorticalregions.Ifallthesedifferenttypes
napses) is so low that very few of them were found near of synapses were to form segregated groups (e.g. DeFelipe
another asymmetric synapse. This is an interesting difference and Jones 1991), it would not be detected by our present
1586 Three-DimensionalDistributionofSynapses (cid:129) Merchán-Pérezetal.
methodology. However, we did find evidence that symmetric J, Fairén A et al. 2008. Petilla terminology: nomenclature of fea-
synapses tend to be spatially segregated from asymmetric sy- tures of GABAergic interneurons of the cerebral cortex. Nat Rev
napses. Although we could not apply the same teststoasym- Neurosci.9:557–568.
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Funding
Diaz-Cabiale Z, Jacobsen K, Tinner-Staines B, Hagman B et al.
ThestudywassupportedbyCentreforNetworkedBiomedical 2007. From the Golgi-Cajal mapping to the transmitter-based
Research on Neurodegenerative Diseases (CIBERNED, CB06/ characterization of the neuronal networks leading to two modes
of brain communication: wiring and volume transmission. Brain
05/0066) and Spanish Ministry of Economy and Competitive-
ResRev.55:17–54.
ness(grantsSAF2009-09394,SAF2010-18218,TIN2010-21289-
GaetanC,GuyonX.2009.Spatialstatisticsandmodeling.NewYork:
C02-02, TIN2010-20900-C04-04, and the Cajal Blue Brain
Springer.
Project,SpanishpartneroftheBlueBrainProjectinitiativefrom Gray EG. 1959. Axo-somatic and axo-dendritic synapses of the cer-
EPFL).FundingtopaytheOpenAccesspublicationchargesfor ebralcortex:anelectronmicroscopestudy.JAnat.93:420–433.
thisarticlewasprovidedbytheCajalBlueBrainProject. HarrisKM,PerryE,BourneJ,FeinbergM,OstroffL,HurlburtJ.2006.
Uniform serial sectioning for transmission electron microscopy.
JNeurosci.26:12101–12103.
Notes HellwigB,SchüzA,AertsenA.1994.Synapsesonaxoncollateralsof
pyramidal cells are spaced at random intervals: a Golgi study in
WethankL.ValdésandI.Fernaudfortechnicalassistance.Conflictof themousecerebralcortex.BiolCybern.71:1–12.
Interest.Nonedeclared.
HoffpauirBK,PopeBA,SpirouGA.2007.Serialsectioningandelec-
tronmicroscopyoflargetissuevolumesfor3Danalysisandrecon-
struction:acasestudyofthecalyxofHeld.NatProtoc.2:9–22.
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