Geometric and functional organization ofcortical circuits

Gordon M G Shepherd1,2,4, Armen Stepanyants2–4, Ingrid Bureau1,2, Dmitri Chklovskii2 & Karel Svoboda1,2

Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, ‘barrels’ and ‘septa’ delineate an orderly

matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections

from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions

of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections,

functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor,

however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric

overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even

for neurons of the same type. A large plasticity potential appears to be incorporated into these circuits, allowing for functional

‘tuning’ with fixed axonal and dendritic arbor geometry.

The flow of excitation in cortical neural networks is largely determinedby stereotyped synaptic connections between populations of neurons1.Because functional projections require overlap of axons and dendrites,the shapes and locations of axonal and dendritic arbors provide animportant source of specificity1. The prevailing view holds thatfor excitatory neurons, this overlap directly defines synaptic circuits:where axons and dendrites are sufficiently close, synaptic connectionsoccur2–5. This anatomical approach has long been used to constructcortical wiring diagrams based on single cell reconstructions6–8, some-times in quantitatively explicit formulations4,9–11. These wiring dia-grams made on the basis of anatomy are assumed to representfunctional circuits4,6–8,11. However, it has proven difficult to testdirectly the relationships between geometric circuits (that is, structuralcircuits based on neuronal geometry) and functional circuits (that is,circuits assayed physiologically), due to the challenges of measuringboth in the same preparation.

Here, we investigated the relationship between neuronal geometryand functional synaptic connectivity in brain slices, exploiting theprecise laminar and columnar organization of the rat’s barrel cortex inconjunction with single-cell anatomical and functional analysis tools. L4barrels, which receive thalamocortical inputs carrying excitation fromindividual whiskers, can be visualized in both living and fixed slices12.Between the L4 barrels are the septa, associated with distinct thalamo-cortical13–15 and intracortical circuits16–18. Barrels and septa demarcatebarrel- and septum-related cortical columns spanning the vertical extentof cortex (Fig. 1a). The barrel grid thus allows one to align, average andcompare measurements from different brain slices and animals.

We used laser scanning photostimulation (LSPS) to measure thestrength of functional projections to individual neurons in L2/3. For

the same projections, we also reconstructed the axonal and dendriticarbor morphology of the excitatory neurons involved and usedcomputational geometry to measure the strength of the geometricprojections. This parallel approach revealed the structure-functionrelationships across multiple cortical projections, allowing us to testwhether neuronal morphology and the overlap of dendrites and axonspredicts functional circuits.

RESULTS

Functional projections to L2/3

To measure the strength of functional projections converging on L2/3pyramidal neurons, we needed to quantify the strengths of inputs frompopulations of excitatory neurons defined by laminar and columnarlocation in the barrel cortex. For this aim, LSPS by glutamate uncagingis an effective tool17,19–22. Presynaptic neurons at each stimulation sitein the slice are selectively excited close to their cell bodies (whileavoiding axons of passage), providing sub-laminar and sub-columnarresolution. Maps of synaptic input are rapidly generated by scanningthe beam to sample hundreds of sites while recording responses from asingle postsynaptic neuron. Other electrophysiological techniques arepoorly suited for our aims here. For example, pair recording (indivi-dually testing pairs of neurons for connections) is slow and inefficient,and it reveals the strength not of a projection, but of selectedpairwise connections within a projection; extracellular electrical stim-ulation is limited by low effective resolution, because axons of passageare stimulated.

We prepared slices of rat barrel cortex (4–5 weeks old) andrecorded functional input maps (spatial maps of excitatory synapticinput) for individual L2/3 pyramidal neurons using LSPS22 (Fig. 1).

Published online 8 May 2005; corrected 15 May 2005 (details online); doi:10.1038/nn1447

1Howard Hughes Medical Institute and 2Cold Spring Harbor Laboratory, Cold Spring Harbor, New York 11724, USA. 3Department of Physics and Center for InterdisciplinaryResearch on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA. 4These authors contributed equally to this work. Correspondence should beaddressed to K.S. (svoboda@cshl.edu).

782 VOLUME 8 [ NUMBER 6 [ JUNE 2005 NATURE NEUROSCIENCE

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

We recorded from neurons in L2 and L3 above barrels and septa(Fig. 1a) while exciting clusters of neurons by photorelease ofglutamate in the focal spot of a UV laser beam on a 16 � 16pixel grid (Fig. 1b,d). The amplitudes of postsynaptic responsesindicate the strength of input to the recorded neuron from theregion of the brain slice excited by glutamate uncaging (see below).Control experiments established that LSPS input maps represent thesources of monosynaptic input with sub-laminar and sub-columnarresolution (B60 mm; see Methods; ref. 22).

At a particular spot on the grid (that is, a pixel at position x,y),photostimulation evokes a postsynaptic response (Qxy; Fig. 1c,d) that isproportional to the number of neurons stimulated, Ncell (equal to theproduct of the neuronal density, rcell, and the volume of excitedneurons, Vexc), the number of action potentials (APs) fired perstimulated neuron (SAP), and the average strength of the synapticconnection with the stimulated presynaptic neuron (qcon, defined hereas the postsynaptic charge per presynaptic neuron per action poten-tial21,22); that is,

Qxy ¼ ðrcellVexcSAPÞqcon ð1Þ

The term rcellVexcSAP gives the number of action potentials evokedin the excited presynaptic neurons and is therefore a measure ofpresynaptic excitation. Neuronal density, rcell, has previouslybeen determined23,24, and measurements of LSPS excitationprofiles (see Methods) provide Vexc and SAP. (Because Ncell ¼ rcellVexc,these measurements imply that photostimulation activated B54neurons in L4 and B34 in L5A.) Qxy is directly measured byLSPS. Therefore, LSPS, together with measurements of presy-naptic excitation, determines the strength of functional synapticprojections (qcon).

We grouped L2/3 pyramidal cells by laminar (L2 versus L3)and columnar (barrel- versus septum-related) location and averagedthe input maps (Qxy) within each group (Fig. 1e–h; see Methods).Maps were morphed to a standard barrel cortex template basedon the average dimensions of cytoarchitectonic landmarks (Fig. 1a,Supplementary Fig. 1). We restrict our attention to projectionsfrom L4 and L5A, the two main sources of translaminar input22.Neurons showed distinct spatial patterns of inputs depending ontheir particular location with respect to the columnar boundariesdefined by barrels and septa in L4. In barrel-related columns,cells in both L2 (Fig. 1e) and L3 (Fig. 1f) showed strong barrelinputs. In septum-related columns, the L5A inputs were muchstronger for L2 cells (Fig. 1g) than for L3 cells (Fig. 1h), despiteL2 cells being more distant targets; L4 inputs were weak (Fig. 1g,h). Inthe average map (Fig. 1g), but not always in the individual maps, thestrong focus of L5A input showed a small offset, extending fromdirectly below the septum anteromediad (rightward) under the neigh-boring barrel.

Responses from L5A clearly originate from L5A neurons, not fromactivation of L4 cells’ dendrites22. The density of L4 cells’ dendrites inL5A is extremely low, owing to the polarization of these dendritestowards barrel centers12, and excitation profiles (see Methods) showedthat photoexcitation of cells occurred only close to the soma and thuswithin the home layer. In addition, excitation profiles of L4 neuronslocated o50 mm from the L4/L5A border showed that the stimulationsites in L5A that were used for synaptic input mapping would not havecaused any spiking in L4 neurons22 (see Methods). Moreover, sites ofL5A input frequently occurred in isolation (that is, they did notconsistently abut sites with L4 inputs), and L5A inputs even exceededL4 inputs in the L5A-L2septum map (Fig. 1g), effectively excluding thepossibility that L4 dendrites generated the L5A signal.

L2/3

L4

L5A

e f g h

05

1015

05

1015

05

1015

05

1015

–30

0

Septum-relatedcolumn

Septum

Barrel

Pia

Barrel-relatedcolumn

x = 1.5 mm

y

c da b

–500Distance (µm)

0 500

Dis

tanc

e (µ

m)

–800

–600

–400

–200

0

200

400

600 L1

L2/3

L4

L5AL5B

L6

UV

z

2AP

0

L2/3

L4

L5A

Qxy

(pA

)

Qxy(pA)

L2barrel

cellsL2septum

cells L3septum

cellsL3barrel

cells

150

pA

Figure 1 LSPS maps of functional excitatory synaptic input (Qxy) to L2/3 neurons in different columnar positions. (a) Barrels and septa in L4 demarcate

columns. A barrel-related L2/3 pyramidal cell was reconstructed. (b) Blue dots (100 mm spacing) mark the LSPS mapping pattern. Average excitation profiles

of presynaptic cells in L4 and L5A are shown at right, indicating the resolution of photostimulation. (c) Input map for an L2/3 pyramidal neuron. Bar, 0.5 mm.

(d) During mapping, each UV flash stimulates action potentials in a small cluster of neurons (purple), some of which synaptically project to the postsynaptic

neuron (red). (e–h) Average input maps for L2/3 pyramidal cells grouped by columnar and laminar location. Plots below maps show horizontal profiles (100-mm

bins, mean 7 s.e.m.) of input from L4 (green line; data from region indicated by vertical green bar to left of map) and L5A (blue line). Barrels and laminar

boundaries drawn as dashed lines. Shown are maps for L2barrel cells (n ¼ 8, e), L3barrel cells (n ¼ 9, f); L2septum cells (n ¼ 8, g) and L3septum cells (n ¼ 7, h).

NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 6 [ JUNE 2005 783

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

Thus, in barrel-related columns, excitatorysynaptic input arrives primarily through theL4-L2/3 projection, with some input fromL5A. There is little differentiation at thecircuit level between L2 and L3 pyramids. Inseptum-related columns, the functional orga-nization is different: the L5A-L2 projectionprovides the dominant source of input, andL3septum neurons receive only weak inputfrom L4 and L5A.

Geometric projections to L2/3

Functional projections require overlap ofdendritic and axonal arbors. Does axodendri-tic overlap predict the strength of functionalprojections? To quantify the geometric pro-jections underlying the functional projectionsconverging on pyramidal neurons in L2/3, weanalyzed reconstructions of axons and den-drites of the neurons involved in the functional projections (Fig. 2) soas to compute the geometric circuits. We labeled brain slice neurons ingranular and infragranular layers and reconstructed their axonalarbors. We also reconstructed dendritic arbors of supragranular pyr-amidal neurons.

First, to characterize the basic features of the morphological orga-nization of L4 and L5A neurons’ axonal arbors, we quantified the rawreconstructions in terms of length density2,18,21,25, averaged acrossmany axonal arbors (maps in Fig. 2e–h). Inspection of reconstructionsof excitatory neurons in L2–L6 (Fig. 2a–d) together with quantitativeanalysis of the spatial distribution of axonal length density (Fig. 2e–h)led to the following observations.

Layer 4 neurons (n ¼ 26 cells; Fig. 2c) sent copious axonalprojections into L2/3, overlapping with the territory of L2/3 pyramidalneurons’ dendrites (Fig. 2b) and thus providing a structural basis forthe L4-L2/3 projection21,25–28. These L4 axons were largely containedwithin the home column, and their density decreased monotonicallywith distance from L4. Consistent with previous observations inyounger animals21, L4 axons originating in septa (n ¼ 11 cells;Fig. 2f) were fairly dense, B50% compared with axons from barrels

(n ¼ 15; Fig. 2e) and were slightly broader horizontally in L1–3.The differences between these axons could reflect cell type differ-ences (pyramid-predominant in septum versus stellate-predominantin barrel)28.

Layer 5A neurons (n ¼ 23 cells; Fig. 2d) also sent axonal branchesthat ascended to L2. Although predicted by the LSPS maps, thesesupragranular branches have not previously been considered majorcomponents of these neurons’ axonal arbors29,30. Unlike ascending L4axonal branches, ascending L5A branches targeted L2: the density ofbranches that projected towards the pia first decreased and thenincreased, reaching peak values in L2 (Fig. 2d, arrow; Fig. 2g,h).These L5A axons also fanned out horizontally across multiple columns(Fig. 2d,g,h). In the home column in L1–L2, the density of L5A axonswas one-half that of L4 axons (49%). (Relative densities of L4 versusL5A axons were calculated as the ratio of the mean values for the twoaxon types in the upper region of either the home or side columns.) Inthe immediately adjacent side columns in L1–L2, L5A axons exceededL4 axons (159%), a difference that grew more pronounced at evengreater horizontal distances from the home column (for example, 500–1,000 mm) where L5A axons continued to extend branches but L4 axons

fe

g

dcb

L2/3 cells L4cells

L5Acells 4

3

2

1

3

2

1

5A

4

3

2

1

5A

a L4 stellateL2/3 pyramid L5B pyramid L6A cellL5A pyramid

1

2

3

4

5A

5B

6AxonsDendrites

h

dc

L4cells

L5Acells

3

2

1

4

3

2

1

5A

L4 stellateL2/3 pyramid L5B pyramid L6A cellL5A pyramid

1

2

3

4

5A

5B

6AxonsDendrites

0 8000

400

L4 axons,septum

L4 axons,barrel

0

800

0 800

L1

L2/3

L4L5A

L5B/6

0 8000

200

L5A axons,barrel-related

L1

L2/3

L4L5A

L5B/6

0 8000

200

L5A axons,septum-related

0 500

Density (µm–2)

Density (µm–2)Density(µm–2)

Figure 2 Axonal and dendritic structure.

(a) Examples of reconstructed neurons from

different layers projecting axons to L2/3.

(b) Dendrites of reconstructed L2/3 pyramidal

neurons (n ¼ 13), aligned by soma position.

Bar, 0.5 mm. (c) Axons of L4 neurons (n ¼ 26).

(d) Axons of L5A neurons (n ¼ 23). Ascending

branches reached peak densities in L2 (arrow).(e) Axons of L4barrel neurons (top, n ¼ 15). Axon

reconstructions were analyzed by length density

analysis (middle; average length density of axons).

Arbors were aligned by soma position (white

circles). Plot below length density map shows

horizontal profiles (100-mm bins, mean 7 s.e.m.)

of axonal density in the lower (vertical green bar)

and upper (vertical blue bar) regions of the

supragranular layers (L1–L3). Plot to right of map

shows vertical profiles of axonal density within

home column (horizontal black bar) and the

average of the two side columns (horizontal red

bar). White scale bar, 0.6 mm. (f) Axons of

L4septum neurons (n ¼ 11). (g) Axons of L5Abarrel

neurons (n ¼ 14). (h) Axons of L5Aseptum

neurons (n ¼ 9).

784 VOLUME 8 [ NUMBER 6 [ JUNE 2005 NATURE NEUROSCIENCE

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

did not (Fig. 2). Comparison of septum-related (n ¼ 9; Fig. 2h) andbarrel-related (n ¼ 14; Fig. 2g) L5A axonal arbors revealed similarprojection patterns. This was unexpected, because functional inputfrom L5A was strongly weighted towards L5Aseptum neurons, implyingthat L5Aseptum neurons selectively connect with L2 neurons in the samecolumn. A survey of cells in L5B and L6 revealed that they alsooccasionally sent axons to supragranular layers (Fig. 2a). However,these projections are infrequent29–32 (G.S. and K.S., unpublished data),consistent with weak input seen in the input maps.

Next, we used the three-dimensional geometry of the reconstruc-tions of presynaptic axons and postsynaptic dendrites to compute‘geometric input maps’ for L2/3 neurons (Methods; Figs. 3 and 4). Ouralgorithm for deriving these permitted direct and quantitative compar-ison to the functional inputs. We based our approach on the concept ofpotential synapses2,10,33. A potential synapse is defined as a location inthe neuropil where an axonal and dendritic branch are sufficiently closethat a synaptic connection could be made (Fig. 3a; see inset). Apotential synapse is a requirement for an actual synapse, and theratio of actual to potential synapses is in the range of 0.12–0.34 indifferent cortical tissues33. The number of potential synapses, Np,formed between the axon of a presynaptic neuron and the dendriteof a postsynaptic neuron is related to the functional connectionstrength (equation (1)):

qcon ¼ Npfqsyn ð2Þ

where f is the ratio of actual to potential synapses (filling fraction) andNp f is therefore the number of actual synapses. qsyn is the average

strength (charge per action potential) per actual synapse. Np representsthe ‘macroscopic’ connectivity at the level of axonal and dendritic arborgeometry, f represents the ‘microscopic’ connectivity at the level ofaxonal boutons and dendritic spines, and qsyn is the physiologicalsynaptic weight. Combining equation (1) and (2) gives

Qxy ¼ ðrcellVexcSAPÞNpfqsyn ð3Þ

Np depends on the densities and relative positions of axonal anddendritic arbors. In the example shown (Fig. 3a), there are fivepotential synapses for the particular offset of the two arbors. For anindividual pair of neurons it is straightforward to count the number ofpotential synapses directly, but this becomes computationally ineffi-cient when large numbers of neurons with complex, dense arbors areinvolved. However, the number of potential synapses between neuronscan also be computed from the product of dendritic and axonaldensities (Fig. 3b; see Methods). For reasons of computational effi-ciency, we thus used this alternative approach (Supplementary Meth-ods). The first-principle approach (identifying potential synapsesdirectly) and the theoretical method (computing from overlap densi-ties) gave statistically indistinguishable estimates of Np (Fig. 3c).Np provides the potential connectivity between pairs of positionally

defined neurons. To generate maps of geometric input (Gxy) from Np,we ‘activate’ clusters of presynaptic neurons at different locations in L4or L5A, and ‘record’ the resulting geometric input to L2/3 neurons atdifferent laminar and columnar locations (corresponding to the loca-tions of the LSPS-mapped cells). We use the same activation parameters(that is, rcellVexcSAP) that pertain to the LSPS mapping. This allows usto compute maps of geometric input (Gxy) that are expressed in termsof the number of potential synapses times the number of presynapticaction potentials per flash: Gxy ¼ NprcellVexcSAP (Supplementary

a

L1Potentialsynapses

Dendrite ofpostsynapticL2/3 neuron

Axon ofpresynapticneuron

L2/3

L4

L5A

–200 0 200Cell displacement, x (µm)

≤ 2 µm

0.0 0.1 0.2 0.3Density (µm–2)

b

ˆ,(r n )ρ0→ ˆ,(r n )ρ →

il

ir→

in

c

Pot

entia

l syn

apse

s (N

p)

First-principle calculationDensity calculation

0

2

4

6

8

400–400Cell displacement, x (µm)

–800 8000

Figure 3 Potential connectivity. (a) Potential synapses (open circles) are

points in the neuropil where axons (red) and dendrites (blue) are close

enough to make synaptic contact (inset). For these two neurons in these

locations, there were five potential synapses. (b) Arbor density profiles.

Skeleton density of a layer 2/3 pyramidal neuron dendritic arbor is denoted

by r0. Blow-up of the dendritic segment (left) explains the notation

(Supplementary Methods). The dendritic density profile, r, is obtained by

smearing the skeleton density. The sum projection of this profile (in mm�2)is represented by the map on the right. (c) Two methods for estimating the

number of potential synapses, Np, between two arbors (axons and dendrites

from a). Np depends on arbor morphologies and their relative displacement

along the cortical surface, x. First-principle calculation (gray): for each x,

the positions of both cells are randomly moved around their origins (with

Gaussian probability, s.d. ¼ 25 mm). Np is simply the average of this

distribution; error bars represent s.d. Density calculation (black): Np is

calculated from the estimated axon and dendrite densities.

L2/3

L4

L5A

a L2barrel

cells

0

100

200

300

b

0

100

200

300

c

2500

L2septum

cells

0

100

200

300

dL3septum

cells

0

100

200

300

Np AP

Gxy

(Np

AP

)

L3barrel

cells

Figure 4 Average maps of geometric input (Gxy) for L2/3 pyramidal cells grouped by columnar and laminar location. (a) Geometric input maps for L2barrel

pyramidal neurons. Small white circles represent soma positions of L4 and L5A neurons. Black regions: insufficient data. Plot shows average horizontal profiles

of Gxy for L4 (green line) and L5A (blue line). Dashed lines represent barrels and septa. (b) L3barrel cells. (c) L2septum cells. (d) L3septum cells.

NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 6 [ JUNE 2005 785

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

Methods; Fig. 4). These geometric input maps predict the form of thefunctional input maps if the synaptic strength per potential synapse isdistributed in a spatially homogeneous manner (that is, if fqsyn

is constant).Geometric input maps were derived for the same four positionally

defined groups of L2/3 neurons that were functionally characterized(L2barrel, L3barrel, L2septum, L3septum; Fig. 4). For each group of post-synaptic L2/3 neurons, these maps show the spatial distribution ofgeometric input from L4 and L5A (‘stimulated’ using the sameexcitation parameters of resolution and intensity as in LSPS). Inspec-tion of these geometric input maps and the corresponding plots of thehorizontal profiles led to the following conclusions. In general, L2/3pyramidal neurons form vastly more potential synapses with L4 thanwith L5A axons. This applies for septum- as well as barrel-relatedcolumns and for adjacent as well as home columns. The horizontaldistributions of most projections were approximately bell-shaped andlimited to one column. The exceptions were the L5A-L2/3septum

projections (Fig. 4c,d): these had broader plateaus extending wellinto the adjacent barrel-related columns, reflecting a tendency forboth septum- and barrel-related L5A neurons axons to convergetowards L2septum pyramidal neurons.

Comparison of functional and geometric projections

To compare functional input maps and geometric input maps directly,we plotted the horizontal profiles against each other (that is, the datafor the green and blue traces below maps in Fig. 1 versus theircounterparts in Fig. 4) for each group of L2/3 neurons (Fig. 5;

Supplementary Fig. 2). Specifically, Qxy is plotted against Gxy, whereQxy/Gxy ¼ fqsyn; thus, these plots reveal the synaptic strength perpotential synapse across these projections. Steep slopes indicate strongfunctional connectivity per potential synapse.

Two input laminae (L4 and L5A) were evaluated for each of the fourgroups, so altogether eight projections were studied. Most of theindividual projections were well fit by a straight line (range of R2

values, 0.24–0.93; mean ¼ 0.72). In particular, all four of the projec-tions arising from L4 cells had R2 values of Z0.75 (Fig. 5a–d). TheL5A-L2septum projection (Fig. 5g; see also Fig. 5j) was poorly fit by astraight line (R2 ¼ 0.24). We conclude that within most projections thesynaptic strength per potential synapse was constant.

Comparing the slopes of the plots of functional versus geometricinput maps allowed us to test the hypothesis that the synaptic strengthper potential synapse is uniform across different intracortical circuitsbetween excitatory neurons; that is, whether the ratio of functional togeometric input is constant across different projections. If this were so,all the points for all the projections in these plots (Fig. 5a–h) should fallalong straight lines with identical slopes. The slopes of the regressionsshowed both similarities and differences across the eight projections.None of the four L5A-originating projections had significantly differentslopes (P4 0.05; Fig. 5j). Within the set of L4-originating projections,slopes differed up to fourfold (Fig. 5i); the L4-L2barrel projection hada significantly higher slope (Fig. 5a), and the L4-L3septum projectionhad a significantly lower slope (Fig. 5d) than the other projections(P o 0.05). Slopes were significantly higher (P o 0.05) for allprojections from L5A than from L4 (Fig. 5k) by a factor of 2.8 on

average. This observation implies highersynaptic strength per potential synapse forprojections from L5A than from L4.

To examine the spatial aspect of thesestructure-function comparisons in moredetail, we computed the average ratio offunctional to geometric input within thehome columns (Fig. 6a, gray bars; Fig. 6b,light brown bars; Supplementary Fig. 2) andcompared this to the average functional/geo-metric input ratio for the side columns (blackbars). This analysis was particularly revealingin septum-related projections (Fig. 6a), wherehome-column ratios varied 16-fold betweendifferent projections (compare L4-L3septum

and L5A-L2septum). Differences betweenhome- and side-column ratios within thesame projection were as high as fourfold(within L5A-L2septum). The maximum dif-ference observed across the entire data set wasa 28-fold disparity between home-columnL5A-L2septum and the right (anteromedial)side column of L4-L3septum. Unexpectedly,three of the eight projections (L4-L2septum,L4-L3septum, L5A-L2barrel) showed a clearleftward (posterolateral) ‘skew’, and two moreprojections showed a trend in this direction(L4-L3barrel, L5A-L3septum) (Fig. 6a,b, andSupplementary Fig. 2). Functional/geometricratios in barrel-related projections varied overa narrower range (Fig. 6b). Despite the widerange of ratios across the entire data set, theaverage functional/geometric ratios of sep-tum-related projections (Fig. 6a, dashed gray

0

5

10

0

5

10

a

R 2 = 0.93

L4→L2barrel L4→L3barrel

L5A→L2barrel L5A→L3barrel

b

0.91

d

0.75

c

0.81

L4→L2septum L4→L3septum

L5A→L2septum L5A→L3septume

0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

0.82

f

0.86

h

0.43

g

0.24

0 20 40

0 100 200 100 2000 0100 200 0 100 200

i

0.71

All L4k

All L4

All L5A

0.53

jAll L5A

0 100 200 0 100 200

→ L2barrel

→ L3barrel

→ L3septum

→ L2septum

Avg. of all0

5

10

0

5

10

0

5

10

Geometric input, Gxy (Np AP)

Fun

ctio

nal i

nput

, Qxy

(pA

)

60 0 20 40 60

0 20 40 60

0 20 40 60 0 20 40 60

Figure 5 Comparison of geometric and functional projections. Horizontal profiles of the L4 and L5A

functional inputs (Qxy; data from plots in Fig. 1e–h) are plotted against the corresponding geometricinputs (Gxy; plots in Fig. 4a–d). In general, points further from the origin are from the home column, and

points closer to the origin are from adjacent columns. R2 values are shown. (a) L4-L2barrel projection.

(b) L4-L3barrel projection. (c) L4-L2septum projection. (d) L4-L3septum projection. (e) L5A-L2barrel

projection. Note different x-axis scale for L5A-originating projections. (f) L5A-L3barrel projection.

(g) L5A-L2septum projection. Arrow: region of peak functional input. (h) L5A-L3septum projection.

(i) All L4 data plotted together. (j) All L5A data plotted together. (k) L4 data (green) and L5A

data (blue) plotted together.

786 VOLUME 8 [ NUMBER 6 [ JUNE 2005 NATURE NEUROSCIENCE

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

line) did not differ from that of barrel-related projections (Fig. 6b,dashed gray line; P 4 0.05). We conclude that the average synapticstrength per potential synapse can vary widely between differentprojections, and in some cases there is strong spatial dependenceeven within a projection.

DISCUSSION

To investigate the relationships between neuronal geometry and func-tional synaptic connectivity in cortical circuits, we have used LSPS tomeasure the strength of functional excitatory synaptic projectionsonto individual L2/3 pyramidal neurons and morphological recon-structions of labeled neurons to quantify the axonal and dendriticgeometry underlying these functional circuits. By examining functionaland geometric projections originating from two laminae (L4 and L5A)and terminating onto pyramidal neurons located in two laminae(L2 and L3) and two columns (barrel- and septum-related), wehave characterized eight positionally defined intracortical projections.This dual approach allowed us to quantitatively compare thegeometric and functional organization of multiple cortical micro-circuits (Fig. 6c).

Neuronal geometry and functional connectivity

Does neuronal geometry predict functional connectivity? By recon-structing a statistically representative sample of axons from L4 and L5Aneurons and dendrites from L2 and L3 neurons in both the barrel andseptal columnar systems, we were able to quantify the neuronalgeometry underlying eight functional projections in a cortical circuit(Fig. 6c). We used these reconstructions (Fig. 2) to compute maps ofpotential connectivity (Fig. 3) and, subsequently, geometric inputmaps (Fig. 4). Direct comparison of geometric and functional maps(Figs. 5 and 6, Supplementary Fig. 2) demonstrated complex rela-tionships both within and between the microcircuits examinedhere (Fig. 6c).

Before discussing these comparisons in detail, it is useful to considerhow geometric and functional input maps are related. Geometric inputmaps are spatial maps of Gxy, the number of potential synapses timesthe number of presynaptic action potentials per flash. They can beconverted to functional input maps by multiplying by the ‘fillingfraction,’ f, which is the ratio of actual structural synapses per potentialstructural synapse33, and by the functional ‘synaptic weight,’ qsyn, whichis the functional synaptic efficacy (that is, synaptic charge per actionpotential) per actual synapse (equation (1)). Exact values for f andqsyn are not available for the projections studied here, but if theyare approximately constant within and across projections, the shapesof geometric and functional input maps should be identical. Thus,we can directly compare geometric and functional input maps toevaluate the hypothesis that functional circuits mirror the form of theunderlying geometric circuits; that is, that ‘function follows form’ inthese projections.

Our data are consistent with this ‘function follows form’ hypothesisin the following sense. Geometric inputs typically predict functionalinputs within individual projections (Fig. 5; the clear exceptionbeing the L5A-L2septum projection; see below). Moreover, whenall the projections arising from a particular layer (L4 or L5A) arepooled, spatial correlations between functional and geometric projec-tions remain high (Fig. 5i,j). Thus, for connections between particularlayers, functional projections were largely predicted by neuronalgeometry alone.

Our data are inconsistent with the ‘function follows form’ hypothesisin three specific ways. First, synaptic strength per potential synapse islower for all projections originating from L4 axons than for thoseoriginating from L5A (Fig. 5k). Thus, this relationship depends on thelaminar source of presynaptic axons. Second, this ratio of functional togeometric input varies between the four different L4 projections(Fig. 5i): it depends on the laminar and columnar position of thepostsynaptic neuron. Third, this ratio also varies within one projection,the L5A-L2septum projection, depending on the columnar source ofthe presynaptic axons. Thus, in the absence of functional data, neuronalgeometry alone cannot be used to predict the relative strengths ofprojections, and it thus provides only a crude estimate of functionalcortical circuits. Our results are consistent with the view that functionalprojections are substructures within the scaffolds of geometric projec-tions. In other words, circuits can be refined, perhaps through activity-dependent mechanisms, yielding within them inhomogeneous rela-tionships between synaptic strength and potential synapses.

Potential connectivity and Peters’ rule

Our potential connectivity analysis pertains directly to a structuralmodel for cortical circuit organization known as Peters’ rule3–5,11,34.This concept arose from the ultrastructural observation that synapticboutons of thalamocortical axons seem to form synapses with L4dendrites in proportion to their availability (that is, density) in the

L3septum

cells

a

c

L4L5A

Home

L sid

e

R si

de

L2L3

Septum-centered

0

0.1

0.2

0.3

Septum-related column Barrel-related column

BarrelSeptum

Gxy

Qxy

PROJECTION

L4

L3

L4

L2

L5A

L3

L5A

L2

b

L4L5A

Home

L sid

e

R si

de

L2L3

Barrel-centered

0

0.1

0.2

0.3

PROJECTION

L4

L3

L4

L2

L5A

L3

L5A

L2

L4 cellsL4 cells

L5A cells L5A cells

L2septum

cellsL2barrel

cells

L3barrel

cells

1.3/32

3.5/227

3.4/31

5.6/126

8.4/33

2.8/37

15.9/290

8.3/67

1.2/18

13.3/202

6.5/71

1.6/15

Figure 6 Ratios of functional and geometric projections in barrel- and

septum-related columns. (a) Average ratio of functional/geometric

connectivity (/Qxy/GxyS) for projections to L2septum and L3septum cells.

Horizontal bars in inset show subregions averaged in horizontal profiles; for

example, home-column data (gray) were averaged over region indicated by

gray horizontal bar, and side-column data (black) were averaged over region

indicated by black bars. Dashed gray line indicates the average value of these

septum-related ratios. (b) Qxy /Gxy ratios for projections to L2barrel and L3barrel

cells. Home-column data were averaged over region indicated by light brown

horizontal bar. Gray bar indicates average value of these barrel-related ratios.(c) Average values of functional and geometric connectivity (shown inside

the boxes as /QxyS//GxyS) for L2 and L3 pyramidal neurons in septum-

related columns (left) and barrel-related columns (right). All of the home-

column and a subset of the side-column Qxy /Gxy values are shown; ratios at

the top of each box are for side-column input from L5A, ratios in the middle

are for home-column L5A input, and lower ratios are for home-column L4

input. Representative reconstructions of dendritic arbors of major excitatory

cell types are shown in gray.

NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 6 [ JUNE 2005 787

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

neuropil5,34. According to Peters’ rule, structural synapses occur whereaxons (with synaptic boutons) and dendrites overlap, with the‘strength’ of a connection following, at least to a first approximation,from the density of the overlap. In more general and quantitativeformulations of Peters’ rule, the anatomical strength of a connectionbetween two classes of neurons can be computed as the product of thedensities of axonal boutons and dendrites4,11. Peters’ rule can thus beused to calculate connection strengths between different classes ofneurons and to generate cortical circuit diagrams based on anatomyalone4,11. Although Peters’ rule makes no explicit inference about thefunctional strengths of connections, it provides a blueprint of theimplied functional circuit if the synaptic strength per unit of axon-dendrite overlap (that is, per potential synapse) is assumed to beconstant on average; that is, if function directly follows form.

Our approach here for calculating geometric circuits, based oncomputing potential connectivity from neuronal geometry, is a versionof Peters’ rule: we estimate synaptic connectivity from the spatialdistributions (densities) of axons and dendrites. The main differenceis that we used densities of axons, not of axonal varicosities. With thesimplifying assumptions that axonal varicosities and synaptic strengthper potential synapse are homogeneously distributed and roughlysimilar for different types of axons, our ‘function follows form’hypothesis is effectively a functional version of Peters’ rule.

Specificity in cortical circuits

Cortical circuits show specificity on multiple levels. Axons and dendriteneed to overlap to make connections, and geometry by itself is thereforea source of specificity (Peters’ rule, as discussed previously)3–5,11,34.Physiological experiments have further revealed that within individualprojections, cortical neurons form non-random functional networks35–37.In addition, cell type–specific biases clearly have a role in establishingcortical connections3,20,38,39. Even in the case of projections betweenexcitatory neurons, there are suggestions that the shapes of axons anddendrites do not predict function40–43. Our data show quantitativelythat the relationship between structure and functional connectionstrength depends on the laminar and columnar positions of presynapticneurons and recipient neurons, even within the same cell classes. Thisdemonstrates that circuit organization can be strongly location-specificwithin a cell type.

Functional form of septum-related projections

The strong home-column and weak surrounding-column organizationof the L5A-L2 projection raises numerous questions. Are home-column inputs strengthened, or are side-column inputs weakened?Perhaps the former, as the functional input per potential synapsefor side-column inputs originating from L5A resembles that ofL4-originating home- and side-column inputs. How do home-columninputs become relatively strengthened? What purposes do the ‘weaksurround’ projection serve? Perhaps L5A acts as a plasticity-relatedlayer; functionally weaker ‘surround’ regions in L2 beyond the homecolumn could be a substrate for experience-dependent (long-term)circuit plasticity, analogous to the barn owl’s optic tectum44. Consistentwith this, POm (the thalamic nucleus innervating L5A) may beimportant for experience-dependent plasticity in the barrel cortex45.At the level of L2, a honeycomb mosaic has been described at theL1/L2 border, associated with plasticity markers such as zinc andNMDAR1 (ref. 46); perhaps L2barrel and L2septum neurons participatedifferently in this micromodularity. Alternatively, the weak surroundcould have different synaptic properties from the center or couldreflect areas where presynaptic L5A axons preferentially connectto either inhibitory interneurons or to the apical dendritic tufts of

deeper excitatory neurons (instead of to L2/3 neurons). In anycase, our findings indicate that strong intracolumnar functional pro-jections are a fundamental organizational feature of cortical circuits47,even when abundant anatomical substrates for non-columnar projec-tions exist.

In contrast to L5A-L2, the L4-L3septum projection is unexpectedlyweak compared with the high density of geometrically available L4axons. Could the low functional/geometric ratios in this projection(lower by a factor of 3.2 compared with the average of the three otherL4-based projections; Fig. 5a–d) reflect a role in experience-dependentplasticity? Previous data support this idea: in juvenile rats, L2/3septum

cells show an approximately twofold experience-dependent gain infunctional input from septal L4 (ref. 17) not attributable to axonalarbor reorganization by branch addition25. These observations supporta model in which some combination of functional synaptic plasticity(Dqsyn) and structural re-wiring at the level of individual spines andboutons (Df)33,48 produces functional re-wiring of synaptic projections(Dqcon) in which neuronal arbor geometry is fixed (that is, Np isconstant). Thus, the extremes among the projections studied here(L5A-L2septum and L4-L3septum) demonstrate that although therelationship between functional and geometric input tends to beconserved among different projections from particular layers, excep-tions can occur, and the dynamic range (that is, the plasticity potential)in this relationship is large.

METHODSElectrophysiology and photostimulation. Detailed methods have been pub-

lished previously17,21,22. Briefly, young adult rats (Sprague-Dawley, 26–36 d

postnatal) were used according to Cold Spring Harbor Laboratory’s Animal

Care and Use guidelines. Acute brain slices, 300 mm in thickness, were cut

perpendicular to barrel rows in chilled cutting solution (consisting of, in mM,

110 choline chloride, 25 NaHCO3, 25 D-glucose, 11.6 sodium ascorbate,

7 MgSO4, 3.1 sodium pyruvate, 2.5 KCl, 1.25 NaH2PO4, and 0.5 CaCl2),

and transferred to artificial cerebrospinal fluid (ACSF, consisting of, in mM,

127 NaCl, 25 NaHCO3, 25 D-glucose, 2.5 KCl, 4 MgCl2, 4 CaCl2, and

1.25 NaH2PO4, aerated with 95% O2/5% CO2) for incubation at 35 1C

for 30 min and thereafter at room temperature (22–23 1C). The slicing

orientation yielded slices in which up to five barrels were clearly discerned in

the living slice using bright-field optics. The only slices used were those in

which the vertical axes of neurons (for example, apical dendrites of pyramidal

neurons and primary descending axons) ran parallel to the slice plane, as seen

with interference contrast optics.

LSPS by glutamate uncaging was performed as described17,21,22. Briefly, with

caged glutamate (NI-glutamate, Sigma; 0.37 mM; ref. 49) in the ACSF, cells

were patched at depths of 50–100 mm (mean, 78 mm; no significant differences

between columnar or laminar subgroups) and recorded in voltage clamp at

room temperature. Intracellular solution consisted of (in mM) 120 KMeSO3,

20 CsCl, 4 NaCl, 10 HEPES, 1 EGTA, 4 Mg2ATP, and 0.3 Na2GTP, 14 sodium

phosphocreatine, 3 ascorbate, and 0.1 Alexa-594 (Molecular Probes). The beam

of an ultraviolet laser (DPSS Lasers) was flashed at sites within the mapping

pattern, a 16 � 16 array with 100-mm spacing between sites. The map covered a

2.3-mm2 square patch of cortex centered vertically on the L4/L5A boundary,

and horizontally on the midpoint of a barrel or septum. Input maps were

repeated 2–5 times for each cell. For analysis, the mean current during a

synaptic response window (8–100 ms after stimulus) was calculated. Thus, pixel

values represent synaptic charge (coulombs); however, for consistency with

prior studies and because synaptic current is more familiar, data are expressed

as pA. Each cell’s individual maps were averaged. Sites giving direct responses,

defined as events arising within 8 ms after stimulus43, were blanked (for

example, see black pixels in Fig. 1c). Because the boundary between L2 and L3

is not cytoarchitectonically apparent, we divided L2/3 in half vertically based on

the mean vertical position of the L2/3 neurons, 546 mm above the L4/L5A

border, and we use the terms ‘L2’ and ‘L3’ to refer to the upper and lower

regions of L2/3, respectively.

788 VOLUME 8 [ NUMBER 6 [ JUNE 2005 NATURE NEUROSCIENCE

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

Calibration of photostimulation. Photostimulation was calibrated by measur-

ing with loose-seal voltage recording the excitation profiles of cells from

the major classes of excitatory neurons within the synaptic mapping area17,21,22.

Control experiments established that for the specific experimental conditions

used (such as beam profile and intensity, cage and divalent concentrations, and

animal age), there was reliable perisomatic photostimulation of presynaptic

cells while remaining well below the thresholds for photostimulation of distal

dendrites or photostimulation through synaptic (network, disynaptic) driving.

Detailed analysis of excitability parameters is presented elsewhere22. In parti-

cular, the average excitability of neurons, in terms of SAP, the average number of

action potentials per cell per flash (see equation (1)), was 1.84 7 0.34 for L4

cells (n¼ 27) and 2.59 7 0.30 for L5A cells (n¼ 27). Resolution, defined as the

mean distance from the soma of spike-eliciting sites, weighted by the number of

spikes per site, was 58 7 3 mm for L4 neurons and 64 7 2 for L5A neurons.

To gauge whether stimulation in L5A could generate spikes in L4 cells, we

also recorded excitation profiles from six cells in L4 located very close to L5A

(mean soma distance from L5A, 38 mm; range 26–52; ref. 22). Of all the spikes

generated, 98% came from stimulation at sites within L4, 2% from stimulation

at sites immediately adjacent (B13 mm) to the L4/5A border, and 0% from sites

in L5A located Z25 mm from the border.

Morphological reconstructions and analysis. Cells were loaded with biocytin

(3 mg/ml in the intracellular solution) during patch recording. Optimal

staining was achieved by patching for 2–10 min, slow retraction of the pipet

to form an outside-out patch, and incubation of the slice for 1–3 h in

oxygenated ACSF. Slices were fixed in 4% paraformaldehyde and rinsed in

phosphate buffer. For biocytin staining, after a quenching step (30 min in 1%

H2O2), samples were incubated overnight in ABC solution (ABC kit,

Vector Labs), and reacted in the presence of nickel. Samples were stained

for cytochrome oxidase for 1 h to visualize barrels and laminae. Samples

were mounted in DMSO50, and neurons were reconstructed using a 40�water-immersion objective lens and camera lucida system (Neurolucida,

MicroBrightField). Tracings were quantitatively analyzed using custom Matlab

(Mathworks) routines.

If L5A cells that were deeper in the slice had better-preserved (and more

laterally extending) axonal arbors, this would need to be factored into some of

the analyses. However, comparison of the axonal density extending horizontally

across L1–L3 of the shallower (37–73 mm, n ¼ 11) versus deeper (75–110 mm,

n ¼ 12) samples of L5A neurons showed nearly identical distributions, and

exponential fits to these data were not significantly different (P 4 0.05).

Computation of geometric projections. See Supplementary Methods for

details. Briefly, neuron tracings (axonal arbors of L4 and L5A neurons, and

dendritic arbors of L2/3 neurons) were shrinkage-corrected and morphed to a

standard barrel cortex template (based on average measured dimensions of

laminar and columnar cytoarchitectonic landmarks: that is, barrels, septa, and

laminae). The LSPS maps were similarly morphed for subsequent comparisons.

The number of potential synapses, Np, from L4 and L5A axons to individual

L2/3 neurons was computed based on the product of axonal and dendritic

arbor length density profiles (Supplementary Methods):

Npð~Ra; ~RdÞ ¼2s

Zrað~Ra; ~ra; naÞrdð~Rd; ~rd; ndÞ sinð dna; ndÞ��� ���

dð~ra �~rdÞd3rad3rddOadOd

ð4Þ

where s is the average length of dendritic spines (a value of 2 mm is used),

ra;dð~Ra;d; ~ra;d; na;dÞ are the expected axonal and dendritic density profiles, and~Ra and ~Rd are the positions of the pre- and postsynaptic somata (see also Fig. 3).

Next, we convolve the numbers of potential synapses Np with the LSPS

excitability profiles of L4 and L5A neurons, SAP, to obtain the geometric input

maps of L2/3 cells, using Gxy ¼ rcell (VexcNp) � SAP (Supplementary Methods).

Note: Supplementary information is available on the Nature Neuroscience website.

ACKNOWLEDGMENTSWe thank K. Zito and V. Scheuss for a critical reading of the manuscript,members of the Svoboda laboratory for useful discussions, J. Huang andC. Wu for access to their Neurolucida system and B.J. Burbach and C. Zhangfor technical assistance. Funded by the Howard Hughes Medical Institute

(G.S. and K.S.), US National Institutes of Health (D.C., A.S. and K.S.),Klingenstein Foundation (D.C.) and Human Frontier Science Program (I.B.).

COMPETING INTERESTS STATEMENTThe authors declare that they have no competing financial interests.

Received 1 February; accepted 31 March 2005

Published online at http://www.nature.com/natureneuroscience/

1. Douglas, R.J. & Martin, K.A.C. Neuronal circuits of the neocortex. Annu. Rev. Neurosci.27, 419–451 (2004).

2. Uttley, A.M. The probability of neural connexions. Proc. R. Soc. Lond. B 144, 229–240(1955).

3. White, E.L. Cortical Circuits (Birkhauser, Boston, 1989).4. Braitenberg, V.B. & Schuz, A. Cortex: Statistics and Geometry of Neuronal Connectivity

(Springer, Berlin, 1998).5. Peters, A. Thalamic input to the cerebral cortex. Trends Neurosci. 2, 1183–1185

(1979).6. Ramon y Cajal, S. Sur la structure de l’ecorce cerebrale de quelques mamiferes. Cellule

7, 125–176 (1891).7. Gilbert, C.D. Microcircuitry of the visual cortex. Annu. Rev. Neurosci. 6, 217–247

(1983).8. Douglas, R.J. & Martin, K.A.C. A functional microcircuit for cat visual cortex. J. Physiol.

(Lond.) 440, 735–769 (1991).9. Kalisman, N., Silberberg, G. & Markram, H. Deriving physical connectivity from neuronal

morphology. Biol. Cybern. 88, 210–218 (2003).10. Hellwig, B. A quantitative analysis of the local connectivity between pyramidal neurons

in layers 2/3 of the rat visual cortex. Biol. Cybern. 82, 111–121 (2000).11. Binzegger, T., Douglas, R.J. & Martin, K.A.C. A quantitative map of the circuit of cat

primary visual cortex. J. Neurosci. 24, 8441–8453 (2004).12. Petersen, C.C.H. & Sakmann, B. The excitatory neuronal network of rat layer 4 barrel

cortex. J. Neurosci. 20, 7579–7586 (2000).13. Koralek, K.A., Jensen, K.F. & Killackey, H.P. Evidence for two complementary patterns

of thalamic input to the rat somatosensory cortex. Brain Res. 463, 346–351(1988).

14. Chmielowska, J., Carvell, G.E. & Simons, D.J. Spatial organization of thalamocorticaland corticothalamic projection systems in the rat SmI barrel cortex. J. Comp. Neurol.285, 325–338 (1989).

15. Lu, S.M. & Lin, R.C.S. Thalamic afferents of the rat barrel cortex: a light- and electron-microscopic study using Phaseolus vulgaris leucoagglutinin as an anterograde tracer.Somatosens. Mot. Res. 10, 1–16 (1992).

16. Kim, U. & Ebner, F.F. Barrels and septa: separate circuits in rat barrels field cortex.J. Comp. Neurol. 408, 489–505 (1999).

17. Shepherd, G.M.G., Pologruto, T.A. & Svoboda, K. Circuit analysis of experience-dependent plasticity in the developing rat barrel cortex. Neuron 38, 277–289(2003).

18. Brecht, M., Roth, A. & Sakmann, B. Dynamic receptive fields of reconstructed pyramidalcells in layers 3 and 2 of rat somatosensory barrel cortex. J. Physiol. 553, 243–265(2003).

19. Callaway, E.M. & Katz, L.C. Photostimulation using caged glutamate revealsfunctional circuitry in living brain slices. Proc. Natl. Acad. Sci. USA 90, 7661–7665(1993).

20. Dantzker, J.L. & Callaway, E.M. Laminar sources of synaptic input to cortical inhibitoryinterneurons and pyramidal neurons. Nat. Neurosci. 3, 701–707 (2000).

21. Bureau, I., Shepherd, G.M.G. & Svoboda, K. Precise development of functional andanatomical columns in the neocortex. Neuron 42, 789–801 (2004).

22. Shepherd, G.M.G. & Svoboda, K. Laminar and columnar organization of ascendingexcitatory projections to layer 2/3 pyramidal neurons in rat barrel cortex. J. Neurosci.(in the press).

23. Ren, J.Q., Aika, Y., Heizmann, C.W. & Kosaka, T. Quantitative analysis of neurons andglial cells in the rat somatosensory cortex, with special reference to GABAergic neuronsand parvalbumin-containing neurons. Exp. Brain Res. 92, 1–14 (1992).

24. Keller, A. & Carlson, G.C. Neonatal whisker clipping alters intracortical, butnot thalamocortical projections, in rat barrel cortex. J. Comp. Neurol. 412, 83–94(1999).

25. Bender, K.J., Rangel, J. & Feldman, D.E. Development of columnar topographyin the excitatory layer 4 to layer 2/3 projection in rat barrel cortex. J. Neurosci. 23,8759–8770 (2003).

26. Lubke, J., Egger, V., Sakmann, B. & Feldmeyer, D. Columnar organization of dendritesand axons of single and synaptically coupled excitatory spiny neurons in layer 4 of the ratbarrel cortex. J. Neurosci. 20, 5300–5311 (2000).

27. Petersen, C.C.H. & Sakmann, B. Functionally independent columns of rat somatosen-sory barrel cortex revealed with voltage-sensitive dye imaging. J. Neurosci. 21, 8435–8446 (2001).

28. Staiger, J.F. et al. Functional diversity of layer IV spiny neurons in rat somatosensorycortex: quantitative morphology of electrophysiologically characterized and biocytinlabeled cells. Cereb. Cortex (2004).

29. Gottlieb, J.P. & Keller, A. Intrinsic circuitry and physiological properties of pyramidalneurons in rat barrel cortex. Exp. Brain Res. 115, 47–60 (1997).

30. Manns, I.D., Sakmann, B. & Brecht, M. Sub- and suprathreshold receptive fieldproperties of pyramidal neurones in layers 5A and 5B of rat somatosensory barrel cortex.J. Physiol. (Lond.) 556, 601–622 (2004).

NATURE NEUROSCIENCE VOLUME 8 [ NUMBER 6 [ JUNE 2005 789

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e

31. Zhang, Z.W. & Deschenes, M. Intracortical axonal projections of lamina VI cells of theprimary somatosensory cortex in the rat: a single-cell labeling study. J. Neurosci. 17,6365–6379 (1997).

32. Burkhalter, A. Intrinsic connections of rat primary visual cortex: laminar organization ofaxonal projections. J. Comp. Neurol. 279, 171–186 (1989).

33. Stepanyants, A., Hof, P.R. & Chklovskii, D.B. Geometry and structural plasticity ofsynaptic connectivity. Neuron 34, 275–288 (2002).

34. Peters, A. & Feldman, M.L. The projection of the lateral geniculate nucleus to area 17 ofthe rat cerebral cortex. I. General description. J. Neurocytol. 5, 63–84 (1976).

35. Song, S., Sjostrom, P.J., Reigl, M., Nelson, S. & Chklovskii, D.B. Highly nonrandomfeatures of synaptic connectivity in local cortical circuits. PLoS Biol. 3, 1–13 (2005).

36. Yoshimura, Y., Dantzker, J.L. & Callaway, E.M. Excitatory cortical neurons form fine-scale functional networks. Nature 433, 868–873 (2005).

37. Kalisman, N., Silberberg, G. & Markram, H. The neocortical microcircuit as a tabularasa. Proc. Natl. Acad. Sci. USA 102, 880–885 (2005).

38. Gupta, A., Wang, Y. & Markram, H. Organizing principles for a diversity of GABAergicinterneurons and synapses in the neocortex. Science 287, 273–278 (2000).

39. Stepanyants, A., Tamas, G. & Chklovskii, D.B. Class-specific features of neuronal wiring.Neuron 43, 251–259 (2004).

40. Yabuta, N.H., Sawatari, A. & Callaway, E.M. Two functional channels from primary visualcortex to dorsal visual cortical areas. Science 292, 297–300 (2001).

41. Schubert, D., Kotter, R., Zilles, K., Luhmann, H.J. & Staiger, J.F. Cell type-specificcircuits of cortical layer IV spiny neurons. J. Neurosci. 23, 2961–2970 (2003).

42. Sawatari, A. & Callaway, E.M. Diversity and cell type specificity of local excitatoryconnections to neurons in layer 3B of monkey primary visual cortex. Neuron 25, 459–471 (2000).

43. Schubert, D. et al. Layer-specific intracolumnar and transcolumnar functionalconnectivity of layer V pyramidal cells in rat barrel cortex. J. Neurosci. 21, 3580–3592 (2001).

44. Linkenhoker, B.A. & Knudsen, E.I. Incremental training increases the plasticity of theauditory space map in adult barn owls. Nature 419, 293–296 (2002).

45. Kaas, J. & Ebner, F. Intrathalamic connections: a new way to modulate corticalplasticity? Nat. Neurosci. 1, 341–342 (1998).

46. Ichinohe, N., Fujiyama, F., Kaneko, T. & Rockland, K.S. Honeycomb-like mosaic atthe border of layers 1 and 2 in the cerebral cortex. J. Neurosci. 23, 1372–1382(2003).

47. Mountcastle, V.B. Modality and topographic properties of single neurons of cat’s somaticsensory cortex. J. Neurophysiol. 20, 408–434 (1957).

48. Trachtenberg, J.T. et al. Long-term in vivo imaging of experience-dependent synapticplasticity in adult cortex. Nature 420, 788–794 (2002).

49. Canepari, M., Nelson, L., Papageorgiou, G., Corrie, J.E. & Ogden, D. Photochemical andpharmacological evaluation of 7-nitroindolinyl-and 4-methoxy-7-nitroindolinyl-aminoacids as novel, fast caged neurotransmitters. J. Neurosci. Methods 112, 29–42 (2001).

50. Grace, A.A. & Llinas, R. Morphological artifacts induced in intracellularly stainedneurons by dehydration: circumvention using rapid dimethyl sulfoxide clearing.Neuroscience 16, 461–475 (1985).

790 VOLUME 8 [ NUMBER 6 [ JUNE 2005 NATURE NEUROSCIENCE

ART ICLES©

2005

Nat

ure

Pub

lishi

ng G

roup

ht

tp://

ww

w.n

atur

e.co

m/n

atur

eneu

rosc

ienc

e