Oswald 2009 Spatial

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Behavioral/Systems/Cognitive

Spatial Profile and Differential Recruitment of GABAB

Modulate Oscillatory Activity in Auditory Cortex

Anne-Marie M. Oswald,1* Brent Doiron,1,2* John Rinzel,1,2 and Alex D. Reyes11Center for Neural Science and 2Courant Institute of Mathematical Sciences, New York University, New York, New York 10003

The interplay between inhibition and excitation is at the core of cortical network activity. In many cortices, including auditory cortex

(ACx), interactionsbetween excitatory and inhibitory neurons generate synchronous network gamma oscillations(30 70 Hz). Here, weshow that differences in the connection patterns and synaptic properties of excitatoryinhibitory microcircuits permit the spatial extent

of network inputs to modulate the magnitude of gamma oscillations. Simultaneous multiple whole-cell recordings from connected

fast-spiking interneurons and pyramidal cells in L2/3 of mouse ACx slices revealed that for intersomatic distances 50m, mostinhibitory connections occurred in reciprocally connected (RC) pairs; at greater distances, inhibitory connections were equally likely inRC and nonreciprocally connected (nRC) pairs.Furthermore, the GABA

B-mediated inhibition in RC pairs wasweakerthan in nRCpairs.

Simulations with a network model that incorporated these features showed strong, gamma band oscillations only when the network

inputs were confined to a small area. These findings suggest a novel mechanism by which oscillatory activity can be modulated by

adjusting the spatial distribution of afferent input.

IntroductionThe responses of cortical neurons to sensory stimuli are stronglyinfluenced by the recruitment of inhibition during network ac-tivity. Fast-spiking (FS) interneurons have a high probability ofconnection with pyramidal cells (PCs) and are thus a major

source of intracortical inhibition (Thomson et al., 1996; Goncharand Burkhalter, 1999; Beierlein et al., 2003; Holmgren et al.,2003). FSPC circuitry has been implicated in tuning receptivefields and dampening cortical responses (Gonchar and Burkhalter,1999;Beierleinet al., 2003;Swadlow,2003;Sun etal., 2006;Atencio andSchreiner,2008).Inaddition,experimental(Buhletal.,1998;SukovandBarth,2001;Hasenstaub etal.,2005;Moritaet al., 2008)andtheoreticalinvestigations (Brunel and Wang, 2003; Cunningham et al.,2004; Borgers et al., 2005) have suggested that coupled networks ofexcitatoryandinhibitory neuronssupport synchronousnetworkos-cillations. In the present study, we show how the spatial pattern ofconnectivity in FSPC microcircuits influences the recruitment ofinhibition and modulates oscillatory activity.

Oscillationsin thegammafrequency range (3070Hz)havebeen correlated with specific stimuli in auditory cortex (ACx)(Barth and MacDonald, 1996; Sukov and Barth, 2001; Brosch

et al., 2002), as well as other sensory systems [somatosensory(Jones and Barth, 2002); visual (Gray and Singer, 1989); olfac-tory (Laurent et al., 1996); electrosensory (Doiron et al., 2003)].Moreover, gamma activity in ACx is modulated by site-specificstimulation of auditory thalamus (Barth and MacDonald, 1996;

Metherate and Cruikshank, 1999; Sukov and Barth, 2001), cross-modal activation of somatosensory and visual thalamocorticalpathways (Lakatos et al., 2005, 2007), and selective attention toauditory stimuli (Lakatos et al., 2004). Responses to acousticstimuli in ACx are tonotopically ordered (Stiebler et al., 1997;Schreiner et al., 2000; Schreiner and Winer, 2007), whichsuggestsa spatial organization of inputs and circuitry within ACx couldimpart specificity and modulation of gamma oscillations.

Gamma oscillations are most prominent in the upper layers(L2L4) of ACx (Metherate and Cruikshank, 1999; Cunninghamet al., 2004; Lakatos et al., 2005) and may be mediated by PC andFS cell interactions (Sukov and Barth, 2001). Although the prop-ertiesof FSPC circuitry have been characterized in other sensory

systems (Thomson et al., 1996; Markram et al., 1998; Reyes et al.,1998; Gupta et al., 2000; Thomson et al., 2002; Holmgren et al.,2003), comparable studies have not been conducted in ACx. Weinvestigated the spatial distribution and synaptic properties ofinhibitory connections between PC and FS cells in L2/3 of ACx.When the somata of FSPC pairs were separated by50 m,most inhibitory connections occurred in reciprocally con-nected (RC) pairs. For longer distances (50100 m), RC andnonreciprocally connected (nRC) FSPC pairs occurred withequal probability. In addition, PCs in RC pairs received lessGABAB-mediated inhibition than those in nRC pairs. We incor-porated these results in a spiking network model and found max-imal gamma oscillatory power for network inputs with a spatialprofile that coincided with the 50m region dominated by RCpairs. Inputs that activated larger network areas recruited more

Received April 6, 2009; revised July 3, 2009; accepted July 8, 2009.

Thisworkwas supportedby NationalInstitutesof Health Grants DC-005787-01A1(A.D.R.)and MH-62595(J.R.)

anda Robert Leetand ClaraGuthrie PattersonTrustPostdoctoralFellowship inBrain Circuitry(A.-M.M.O.).B.D. is a

long-termfellowoftheHumanFrontierScienceProgram(LT-077).WethankJaimedelaRocha,LeonardMaler,and

Jason Middleton for useful comments on this manuscript.

*A.-M.M.O. and B.D. contributed equally to this work.

Correspondenceshouldbe addressedto Anne-Marie M.Oswald,Centerfor Neural Science,New YorkUniversity,

4 Washington Place, Room 809, New York, NY 10003. E-mail: [email protected].

A.-M. M. Oswalds present address: Department of Biological Sciences, Center for the Neural Basis of Cognition,

Carnegie Mellon University, Pittsburgh, PA 15213.

B. Doirons present address: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260.

DOI:10.1523/JNEUROSCI.1703-09.2009

Copyright 2009 Society for Neuroscience 0270-6474/09/2910321-14$15.00/0

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GABAB-mediated inhibition and reduced oscillatory activity.Our results suggest that the connectivity profile and the recruit-ment of inhibition within FSPC circuits allow the spatial profileof inputs to L2/3 to modulate gamma oscillations in ACx.

Materials and Methods

ExperimentsSlice preparation. Auditory thalamocortical slices were prepared fromSwiss Webster mice [postnatal day 14 (P14) to P29] as described byCruikshank et al. (2002). All surgical procedures followed the guidelinesdetermined by the New York University Animal Welfare Committee.Mice were anesthetized with halothane and decapitated. The brain wasexposed and two coronal cuts were made to remove the anterior 25% ofthebrainand thecerebellum. Thebrainwas then removed from theskulland immersed, anterior cut down, in ice-cold oxygenated (95% O25%CO2) artificial CSF(ACSF)(in mM: 125 NaCl, 2.5 KCl, 25NaHCO3, 1.25NaH2PO4, 1.0 MgCl2, 25 dextrose, 2 CaCl2) (all chemicals from Sigma-Aldrich). A third cut was made with a 15 medial-to-lateral slant toremove the dorsal portion of the brain leaving one hemisphere intact.The brain was submerged in ice-cold ACSF, and horizontal slices (300m) were made using a vibratome (Campden Instruments). Typically,

one or two slices contained primary ACx, the medial geniculate nucleus(MG), and the thalamocortical fiber tract. The slices were maintained inACSF at 37C for 30 min, and then rested at room temperature (2022C) for 12 h before recording (2933C).

Electrophysiology.Neurons were visualized using infrared-differentialinterference contrast microscopy (Olympus). At low magnification, theMG was visible medial to the hippocampus and posterior to the lateralgeniculate nucleus, andACx waslocated lateral to theanterior half of thehippocampus (Cruikshank et al., 2002). L2/3 was the cell-dense region100300m below thepia. Only slicescontaining theMG andACx wereused. In a subsetof slices, thelocation of ACx was verified by stimulatingthe MG and recording field potential responses in L3/4. At higher mag-nification, PCs were identified by a distinct apicaldendritethat extendedtoward L1, whereas FS cells were distinguished by ovoid somata andmultipolar dendrites. Whole-cell current-clamp recordings were made

simultaneously from up to four neurons (amplifier; Dagan; acquisitionand analysis software; IgorPro;Wavemetrics). Voltage-clamp recordingswere not performed because the addition of QX-314 (lidocaine N-ethylbromide) or cesium to the recording pipette to improve space-clampinterfereswith potassium channels and, consequently, with recordings ofGABAB. In the absence of adequate space clamp, the results of voltage-clamp recordings would not be expected to differ from current clamp.Recorded neurons were located twoto four cell layers(4070 m) belowthe surface of the slice. Pipettes were pulled from borosilicate glass (2.0outer diameter) on a Flaming/Brown micropipette puller (Sutter Instru-ment) toa resistanceof 310M. Theintracellular solution consistedofthe following (in mM): 130 K-gluconate, 5 KCl, 2 MgCl2, 4 ATP-Mg, 0.3GTP, 10 HEPES, and 10 phosphocreatine.

Stimulation.We recorded from 143 PCs and 101 FS cells. A series ofhyperpolarizing and depolarizing step currents (1 s in duration) wereinjected to measure the input resistance, time constant, and action po-tential responsesof each cell. Forthe FS cells,the average membrane timeconstant was 7 3 ms, the input resistance was 122 44 M and theresting membrane potential was 71 4 mV. To quantify spike fre-quencyadaptation in FS cells,we measured theratioof thelast interspikeinterval (ISIL) to the first ISI (ISIF) in response to a 1 s step currentinjection that evoked firing rates of 48 15 Hz. The pertinent intrinsicproperties of PCs are reported in Results and were consistent with pre-viously reported values (Oswald and Reyes, 2008).

To determine whether FSPC pairs were synaptically connected,one neuron of the pair was stimulated with five suprathreshold cur-rent pulses (0.51 nA; 5 ms pulse width) delivered at 10 Hz. Averagemembrane potential responses were compiled from 25 to 35 trials. Inconnected pairs, postsynaptic potentials (PSPs) that were temporallylocked to the presynaptic action potential were evoked in the targetcell. Connections in both directions (FS to PC; PC to FS) were tested.For each FSPC pair, one of four connection patterns was possible:

not connected, unidirectional excitatory, unidirectional inhibitory,and reciprocally connected (both an excitatory and an inhibitoryconnection).In FSPC pairs that hadan inhibitory connection, theFScell was driven to fire action potentials at a rate of 80 Hz for 500 mswhile IPSPs were recorded in the postsynaptic PC. Analyses wereperformed on the average PC membrane responses compiled from 10to 20 trials. IPSP amplitudes were taken as the difference between themembrane voltage at the peak of the IPSP and the onset of the IPSP.Short-term synaptic depression was measured by dividing the ampli-tude of each IPSP by the amplitude of the first IPSP. The intertrialinterval was sufficiently long (7 s) to ensure full recovery from short-term depression.

Pharmacology.In a subset of experiments (n 8 triplets), record-ings were performed in the presence of the AMPA/kainate receptorantagonist DNQX [6,7-dinitroquinoxaline-2,3(1 H,4 H)-dione] (20M; Sigma-Aldrich) and the GABAA receptor antagonist bicuculline(10 M; Sigma-Aldrich). Although bicuculline can nonspecificallyblock calcium-mediated potassium channels (Johansson et al., 2001),the low concentration and the membrane potentials at which theinhibitory responses were recorded (60 mV) make it unlikely thatblockade of these channels confounds our results. In four pairs,2-hydroxysaclofen (50 M; Sigma-Aldrich) was also applied andblocked the isolated GABABcomponent of the response (supplemen-tal Fig. 2, available at www.jneurosci.org as supplemental material).

Data analysis and statistics.The probability of connection (Pc) wascalculated as the number of connected pairs (Nc) divided by the num-ber of tested pairs (NT): Pc Nc/NT. We obtained the Pc versusintersomatic distance by calculatingPc SEpfor 10, 20, or 30 m binsizes between 20 and 100 m. Bin sizes were chosen such that NT 30for each bin. Since the probabilities of connection are categoricaldata, the SE for proportional data, SEp (Pc(1 Pc)/NT)

1/2, wascalculated from the binomial formula. The SEp is an indicator ofconfidence about Pc given 1 SD of the distribution and the samplesize. Fishers exact tests were used for statistical comparisons of con-nection probabilities based on the number of connected and uncon-nected pairs for each condition.

Synaptic parameters are reported as mean SD. The KolmogorovSmirnov test for normal distributions was performed on all data setsand the data did not differ significantly from that predicted for anormal distribution (p 0.14 0.67). Significance was assessed usingtwo-tailed Students t tests: paired t tests were used when the twopyramidal cells that shared common FS cell input (referred to astriplet recordings) and unpaired t tests were used for comparisonsbetween the total populations of RC and nRC pairs. In small data sets(n 10), significance was assessed using the nonparametric Wilcoxonrank test for paired data.

Biocytin fills.To verify cell identity, 0.5% biocytin was added to theintracellular solution. Sliceswere fixed in 4% paraformaldehyde for pro-cessing. The slices were rinsed with PBS, quenched with 1% H2O2in a10% MeOHPBS solution, permeabilized in Triton X-100 and then ex-posedto avidinperoxidasecomplex(ABC kit; Vector Laboratories). Theslices were rinsed (with PBS) and reacted with 3,3-diaminobenzidine,and then rinsed again. Finally, slices were mounted onto slides with

Flourmount for microscopy and cell reconstruction using Neurolucidatracing (MBF Bioscience).

ModelWe simulated a two-dimensional square sheet of 900 (30 30) PCs and225(15 15)FS cells. Each cell ijwasdistinguished by its(x,y) position,wherexij, ia,yij,ja and its cell type ( PC, FS). The neuronspacing was PC 5m and FS 10m; this maintained the densityof a three-dimensional cortical volume after compression to a corticalsheet. Thexandycoordinates of allFS cells were shifted byPC/2, sothatPC and FS cells did not occupy same point in space. The area of the sheetrepresents 22,500m2 (150 150m) of L2/3 in ACx.

PCPC cell connections were randomly distributed over the popula-tion with PCklconnecting to PCijwith probabilityPPCPC(see Fig. 5A,black curve). PCPC connections were independently and uniformlydistributed in space.In contrast,FSPC connectivity wasdistributedas a

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function of the distance d [(iPC kFS)2 ( jPC lFS)

2] 1/2

between FSPC pairs. We randomly assigned one of four possible states:nonreciprocal PC to FS connection (see Fig. 5A, connection probabilityPnRCE, green curve), nonreciprocal FS to PC connection (see Fig. 5A,connection probabilityPnRCI, blue curve), reciprocal PC and FS connec-tions (see Fig. 5A, connection probabilityPRC, red curve), or no connec-tions (1 PnRCE PnRCI PRC). The spatial profile of these probabilitydistributions approximately matched the experimentally obtained distri-butions (compare Fig. 2Awith Fig. 5A) in that, ford 50m, RC pairswere of higher probability than nRCpairs(Fig. 5A). Note that theoverallprobability of an FS to PC connection (PnRCI PRC) and PC to FS cell(PnRCE PRC) was 0.5 and independent ofd.

Each cell in thenetwork is a leaky integrate-and-fire(LIF)neuron withthe following dynamics:

CdVij,

dt gLEL V,ij gij,

AMPAtEAMPAVij,

gij,GA (t)EGAVij,gij,

GB tEGBVij,. (1)

Vij,(t) is the membrane potential of cell ij,. Spiking dynamics weregoverned by thestandard spike-reset rule, so that when Vij,(t) equalsthethreshold value of60 mV,Vij,was immediately reset toVij, 70

mV, and a spike time for cell ij, was recorded at time t. PCs had anabsolute refractory periodof 5 ms,whereas FS cells have a 2 ms refractoryperiod. The leak conductancegL 10 nS, theleak reversal potential EL70 mV, and the membrane capacitanceC 0.25 nF, yielded a passivemembrane time constant C/gL 25 ms.

The excitatory AMPA input to neuron ij,, consists of two terms asfollows:

gij,AMPA(t) gAMPA

kl

ij,kl,PC

m

KAMPA(t tkl,PCm )

m

KAMPAt tij,extm . (2)

The first term on the right-hand side of Equation 2 is excitatory input

from a presynaptic pyramidal cell, PCkl, to a postsynaptic cell ij. If asynaptic connection existed between PCkland cell ij, ij,

kl,PC was 1, andotherwise it was 0. tkl,PC

m is the mth spike time of PCkl. The second term inEquation 2 is theexternalexcitatory input to thenetwork. Forsimplicity,the external inputtimes, tij,ext

m , were chosenfrom a Poissonprocess of rateext. WedividedPC andFS cellsinto driven(D) andnondriven (ND)groups. For PCDand FSDcells,extwas 5.5 and 3.5 kHz, respectively; allND cells had ext 0.4 kHz representing spontaneous backgroundactivity. All external inputs were uncorrelated across all cells in the net-work. In this study, we always set the number of PCDneurons toNE,D64, and FSDcells toNI,D 16. Cellijwas randomly assigned to classDwith probabilitypD, ND,/(L/)

2 if cell ijwas within the squarestimulus region of length,L , centered in the middle of the network(see Figs. 5, 6). Finally, both external and internal EPSCs had an function time course, whereKAMPA(s) s s/AMPA)e

1s/AMPA with

AMPA 2.5 ms; (s) is the Heaviside function, where (s) 1 ifs 0, and otherwise (s) 0, gAMPA 0.147 nS, and the reversalpotentialEAMPA 0 mV.

The remaining two terms in Equation 1 model inhibitory activitywithin the network and were applied only to the membrane dynamics ofPC cells (thereare no FSFS connections). Notation forinhibitory inputsfollows that introduced for the excitatory inputs. The GABAA(GA) con-ductance to PCijwas as follows:

gij,PCGA (t) gGA

kl

ij,PCkl,FS

m

KGA(t tkl,FSm ). (3)

KGA(s) was an function with GA 4 ms, a maximal conductance ofgGA 0.46 nS and a reversal potential ofEGA 70 mV. All FS to PCconnections have the same GABAAcomponent.

Motivated by the experimental results (see Figs. 3, 4), the GABABcontributions to PCijwere set according to two subpopulations of FS

cells: RC or nRC. The total GABABconductance received by PCijwas asfollows:

gij,PCGB (t)

kl

m

KGB(t tkl,FSm ) gGB

RC ij,PCkl,FS kl,FS

ij,PC

gGBnRC ij,PC

kl,FS(1 kl,FSij,PC)]. (4)

AllGABAB IPSCshadthesame KGB(s) time coursewithGB 75ms,and

a reversal potential EGB 90 mV. If cell FSklwas RC with PCij(i.e.,ij,PC

kl,FS,kl,FSij,PC 1), the maximal conductance wasgGB

RC 0.0114 nS; con-versely, if it was nRC to PCij(i.e., ij,PC

kl,FS(1 kl,FSij,PC) 1), the maximal

conductance was gGBnRC 0.0343 nS. The inhibitory synapses were as-

sumed to be in a sustained depressed state.Model simulations were performed on a desktop PC with interfaced

Matlab-C (MEX) code (Mathworks) and a standard Euler time scheme,where t 0.02 ms. Neurons in the PCND population rarely elicitedaction potentials (see Fig. 5D), and therefore, the dynamics of these cellswere often notsimulated. This greatly decreasedsimulation cost, andtheresults were not affected quantitatively.

Each LIF model cell, ij, in the network produced a sequence of spike-threshold crossing times indexed bym, tij,

m m, from which we defined aspike trainyij,t mt tij,

m , where (x) i s a function centered

at x. We divided the network into four subnetworks: Y,t ij,yij,twith PC or FS andD or ND. The network has

three sources of randomness: (1) the event times of the random externalinputstij,ext

m , (2) the network connectivityij,kl, (, PC,FS), and (3)

the chosen driven and nondriven cells. We denote expectations overthese sources as tand Net, respectively; the former is the averageover time (1) and the latter an average over realizations of the networkconnectivity (2, 3). We performed 120 realizations of input and networkconnectivity. For a given realization of connectivity and input distribu-tion, the firing rate of cell ij is rij, yij,t, and the firing rate ofsubnetworkisR Yt. Spectral estimates of spike activity weredefined by theFourier transforms ofyij,(t) rij, and Y(t)R,andwritten as yij,f and Yf, respectively, where f is frequency (inhertz). To measure subnetwork spike-train rhythms, we considered thepower- and cross-spectra of the subnetwork dynamics as follows:

S ;f 1

RRYfY

* f, (5)

whereY*f is the complex conjugate ofYf. For and,S;is the power spectrum of network and is real-valued andasymptotes to 1 at very high f. For reference, a network with Poissonfiring statistics would haveS;(f) 1 for allf. When or,S;(f) is the cross-spectra between networks , and, forwhich we only show the real component, and asymptotes to 0 at high f.Finally, to measure the pairwise spike correlation between driven (D)Ecells, PCijand PCkl, we measure the spike train coherence as follows:

Cij,PC;kl,PCfyij,PCfykl,PC* f

yij,PCfyij,PC* fykl,PCfykl,PC

* f, (6)

where is the modulus. Cij,PC;kl,PC(f) is 0 for spike trains that are un-correlated at frequencyf, and 1 for spike trains completely correlated atfrequencyf.

Spectral estimates were computed with the MATLAB signal processingtoolbox (Mathworks) using a Bartlett window and spike trains digitizedat 2 kHz. For a fixed network architecture and input distribution, allspectral analyses were conducted on 70 s spike trains with the transientfirst second removed. In this study, we always show Net with errorestimates (see Figs. 6, 7, shaded regions) being 1 SD computed from theNet data ensemble (120 realizations).

ResultsWhole-cell current-clamp recordings were made from morpho-logically and electrophysiologically identified neurons in L2/3 ina thalamocortical slice preparation of ACx (Cruikshank et al.,2002). Under infrared video-microscopy, PCs were distinguished

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by a prominent apical dendrite that ex-tended to L1, whereas FS cells had multi-polar dendritic morphology (Fig. 1A).PCs responded to suprathreshold, con-stant current injectionswitha high-frequencyspike doublet followed by lowerfrequencyfiring that ranged from 6 4 Hz at rheo-

base (0.17 0.1 nA) to 51 15 Hz athigher current injections (Fig. 1 B, left). Incontrast, FS cells exhibited nonadaptingfiring rates (ISIL:ISIF 1.09 0.15;n 101) (see Materials and Methods) thatranged from 18 13 Hz at rheobase(0.26 0.09 nA) to 178 38 Hz withhigher current injections (Fig. 1 B, right).

The connections between PC and FScells were characterized by evoking actionpotentials in one cell and recording PSPsin the other (Fig. 1C). For the cells shownin Figure 1A, stimulation of the FS cellevoked IPSPs in both PC1 and PC2. Stim-ulation of the PC1, but not PC2, evokedEPSPs in the FS cell. Thus, PC1 is RC tothe FS cell and PC2 is nRC through aninhibitory connection. This study focuseson the spatial distribution and propertiesof inhibitory connections in RC (red) ver-sus nRC (blue) FSPC pairs.

Variation of connection probabilitywith intersomatic distanceWe recorded a total of 315 FSPC pairsand found 213 pairs had at least one syn-aptic connection between them. We cal-

culated the probability of excitatory (PE)and inhibitory (PI) connections as well asRC (PRC) and nRC (PnRC) pairs as a func-tion of intersomatic distance. We binneddistance in 1030m increments and, foreach bin, estimated the probability of connection (PC) by divid-ingnumber of connections (NC)ofagiventype(C:E,I,RC,nRC)by the number of connections of that type tested (NT).PE de-creased significantly between 20m (0.65 0.08) and 100 m(0.41 0.08) (Fig. 2A) (*p 0.05, Fishers exacttest), whereas PIdid not differ over the same range (0.550.47; p 0.10).

Approximately 27% of FSPC pairs were reciprocally con-nected (n 86) (Fig. 2 B, red triangles); the remaining connec-tions were unidirectional (inhibitory: n 65, blue triangles;

excitatory:n 60, black triangles; unconnected pairs are indi-cated by signs). The probability of inhibitory connections oc-curring in RC(PRC) versusnRC (PnRCI) FSPC pairs also differedsignificantly with intersomatic distance. Within the 40m ra-dius of the FS cell, RC pairs outnumbered inhibitory nRCI pairs2:1 (Fig. 2 B). Moreover, for distances 20m, thePRC wasnearly five times greater (0.45; red) (Fig. 2C)thanthe PnRCI (0.10;blue;p 0.002, Fishers exact test). Between 20 and 50m,PRCdeclined while thePnRCIincreased such thatPRC PnRCI 0.21at distances50m. The probabilityof nonreciprocal excitatoryconnections (PnRCE) over distance was comparable with PnRCI(data not shown).

The spatial profile of RC pairs parallels that of excitatory con-nectionsboth PRCandPEdecline by0.2 between 20 and 100msuggesting thatPRCdepends onPE. It has been shown that

presence of a reciprocal connection can be predicted based onexcitatoryconnectivity in primary visual cortex (V1)(Yoshimuraand Callaway, 2005). We performed similar analyses and foundthat because of the high, nearly equal numbers of excitatory (n151) and inhibitory (n 146) connections, the number of recip-rocal connections (n 86) depended equivalently onPEandPI(p 0.04, Fishers exact test). Thus, in contrast to V1, there is anequal likelihood of finding an RC pair when either an excitatoryor inhibitory connection is found. In V1, PE is much lower (0.19)

than ACx, whereasPI(0.47) is comparable in both areas (Yo-shimura and Callaway, 2005). This difference may underlie thedependence of RC pairs on excitatory connection in V1. Thedifferences inPEbetween V1 and ACx were not attributable todifferences in postnatal day age of the animals used in the twostudies [P21P26 (Yoshimura and Callaway, 2005) vs P14P29in the present study]. We found that the PI (0.45) does not varywith age, whereasPEincreased slightly from 0.40 between P14and P18 to0.55 at P19 P29 (supplemental Fig. 1A, available atwww.jneurosci.org as supplemental material).Thus, theseresultsmay reflect differences in the connection architecture of V1 ver-sus ACx rather than the age of the animal.

We further investigated whether or not reciprocal connec-tions occurred with greater probability than predicted if excita-tory and inhibitory connections occur independently. When PE

Figure 1. The intrinsic and synaptic properties of fast spiking interneurons and pyramidal cells.A, A representative FS cell

(green) that was an RC pyramidal cell (PC1; red) and an nRC to another (PC2; blue). Scale bar, 50m.B, Responses evoked with

depolarizingstepcurrentinjectionforthecellsshowninA [left,PC2,0.2nA(bottom)and0.4nA(top);right,FScell,0.6nA(bottom)

and0.8nA (top)].Calibration: vertical,40 mV;horizontal, 200ms.C, Left, Suprathreshold stimulation(10 Hz)of theFS cell (green

trace) resulted in IPSPs in both PC1 (red trace) and PC2 (blue trace). Right, Stimulation of the RC PC1 (10 Hz; red trace) producedEPSPs in the FS cell (top; green trace). Stimulation of the nRC PC2 (blue trace) did not evoke EPSPs (bottom; green trace).

Calibration: vertical, PSPs, 0.5 mV; action potentials, 40 mV; horizontal, 100 ms.



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andPIvary with distance,d, the predictedPRC(d) PE(d)PI(d)and PnRCI(d)PI(d)(1PE(d)), assuming independent connec-tivityis comparable with recorded valuesat alldistances (Table 1)(p 0.311, Fishers exact test). This result is not an artifact ofbinsize: when allconnections50m were pooled, therecordedand predicted probabilities did not significantly differ (Table 1).In summary, thehigh PRC between FSPCpairs separated by50m follows the spatial profile of excitatory connections but isotherwise consistent with the hypothesis that PC to FS and FS toPC connections occur independently.

The differences in the spatial profile ofPEand PIare not likelyattributable to cutting artifacts. Although a recent anatomicalstudy has suggested that estimates of long-range (200m) ex-

citatory connectivity are more suscepti-ble to slicing artifacts than inhibitoryconnectivity (Stepanyants et al., 2009),the present study focuses on neuronsseparated by100m. In addition, exci-tatory connectivity has been shown tobe constant between 0 and 50m below

the slice surface (Song et al., 2005), andthe majority of our neurons were locatedat least 40m below the surface. Finally,in biocytin-filled neurons, we saw mini-mal evidence of truncation (blebs) withinthe 100 m region around the recordedneurons.

The geometry of neuronal arborscould underlie the differences in the spa-tial profiles of excitatory versus inhibitoryconnections.The dendritic and axonal ar-borsof a PC (Fig. 1)and FS cell (Dumitriuet al., 2007) would be expected to overlapextensively within 100 m (Stepanyantset al., 2008). However, PC axons initiallydescend toward L5 and send collaterals toL2/3, whereas FS axons tend to be moresymmetrical. This difference could result ina nonuniform profile in excitatory connec-tivity. We ascertained the distributionsof excitatory and inhibitory connectionsgiven the relative positions of the pre-synaptic and postsynaptic cell withinthe xyplane of the slice (supplementalFig. 1 BD, available at www.jneurosci.org as supplemental material). Excitatoryconnections were more probable (0.52

0.04) when the PC was superficial (closertoL1)to the FScellthan viceversa (0.320.06;p 0.003, Fishers exact test). The probability of inhibi-tory connection did not differ with respect to the presynapticFS cell (p 0.10, Fishers exact test). This suggests that thedecline inPE could, in part, be attributed to decreased overlapbetween the vertically descending PC axon and the dendrites ofthe FS cell.

Inhibitory synaptic responsesTo compare the inhibitory synaptic responses of RC and nRCpairs, we performed simultaneous current-clamp recordingsfrom a triplet consisting of a single FS cell that was reciprocallyconnected to one PC and unidirectionally connected to a second

PC (n 19) (Fig. 3A, inset). The FS cell was driven to fire actionpotentials at 80 Hz for 500 ms (40 pulses) while the evoked in-hibitory responses were recorded in the two PCs. Both PCs re-ceived constant current injections to maintain similar holdingpotentials (RC, 61 4 mV; nRC, 62 4 mV).

In RC and nRC PCs, the IPSPs summated to produce a tran-sient onset hyperpolarization that settled to a steady-state value(Fig. 3A). The inhibitory response returned to baseline within500 ms of stimulus offset. The amplitudes of the first IPSPs of thetrains (IPSP1) were comparable in RC (0.7 0.4 mV) and nRC(0.7 0.5mV;p 0.95, paired ttest; n 19) pairs. However, forany given triplet, the strengths of IPSP1in RC versus nRC pairsoften differed in a nonsystematic manner. To correct for thisvariation and allow for direct comparisons between nRC and RCpairs, all ensuing measures of inhibitory strength are computed

Intersomatic distance (m)

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Figure 2. Variation in connection probability with distance.A, The probabilities of excitatory (PE; black circles) and inhibitory

(PI; gray circles) connections between FSPC pairs and between PCPC pairs (open circles) [from Oswald and Reyes (2008)] are

plotted against the intersomatic distance. ThePEat 20m was significantly different from that at 40, 50, 70, or 100m (*p0.05, Fishers exact test). PIwas not significantly different at any distance.B, The relative horizontal (x) and vertical (y) locations

of PCs that were reciprocally (red triangles) or nonreciprocally connected through an inhibitory (FS to PC; nRCI; blue triangles) or

excitatory (PC to FS; nRCE; inverted black triangles) synapse to FS cells (open circle) aligned to the origin. Unconnected PCs are

indicated withsigns.Thecircledenotesthe40m regionaround theFS cell.Inset,Schematicof theslice orientationwithL1at the top of the field of view andxypositions in L2/3.C, The probability of inhibitory connections occurring in RC (red) or nRCI

(blue) FSPC pairs plotted against intersomatic distance. ThePRCwas significantly greater than PnRCIbetween nearby neurons

[**p 0.002 (20m), *p 0.03 (30m), Fishers exact test]. Error bars are as follows: SEp (Pc(1 Pc)/NT)1/2, where Pcis

the connection probability andNTis the number of pairs sampled (see Materials and Methods).

Table1. Recordedand predictedprobability of connectionwith intersomatic

distance

Distance (m)

PRC PnRCI

Recorded Predicted p value Recorded Predicted p value

20 0.45 0.35 0.61 0.1 0.18 0.4730 0.32 0.27 0.65 0.14 0.2 0.5940 0.28 0.18 0.31 0.19 0.28 0.3150 0.21 0.23 1 0.23 0.27 170 0.24 0.18 0.68 0.21 0.26 0.68100 0.20 0.18 1 0.18 0.26 150 0.30 0.24 0.23 0.20 0.24 0.29

TherecordedPRC andPnRCI and predicted,PRC(d)PE(d)PI(d)and PnRCI(d)PI(d)(1 PE(d)),didnotdifferatanydistance(valuesofp0.05,two-tailed,Fishersexacttest).Recordedandpredictedvaluesalsodidnotdifferwhenconnections50m were pooled (values ofp 0.05, two-tailed, Fishers exact test).



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relative to IPSP1. The steady-state hyper-polarization (HSS) was taken as the aver-age membrane voltage in the last 200 msof stimulation (Fig. 3B). The relative in-crease in inhibition during stimulation,HSS-IPSP1, was significantly greater innRC versus RC pairs both within triplets

(nRC, 0.5 0.4 mV; RC, 0.2 0.3 mV;p 0.03; n 19; paired ttest) and over allpairs [nRC (n 22), 0.4 0.3 mV; RC(n 26), 0.1 0.3 mV; p 0.008,unpairedttest] (Fig. 3B). We measuredthe area (millivolts milliseconds) of thepostsynaptic response to 80 Hz stimula-tion normalized by the area (millivolts milliseconds) of an IPSP elicited by a sin-gle pulse (Thomson et al., 1996) (Fig. 3A,inset). The normalized inhibitory area ofRC pairs was significantly less than nRCpairs over all recordings (RC, 18 7,n 26; nRC, 24 9,n 22;p 0.013), aswell as in the triple neuron recordings(RC, 18 8;nRC,25 12;p 0.007; n19) (Fig. 3C,D).

The difference in inhibition betweenRC and nRC pairs was not attributable tothepropertiesofthePCorFScells.Withinthe triplets, PCs shared the same FS celland had similar membrane time constants(RC, 23 10 ms; nRC, 18 10 ms;p 0.3) and input resistances (RC, 175 63M; nRC, 161 68 M;p 0.6). Theinhibitory synapses within RC and nRCpairs show comparable short-term de-

pression (see Materials and Methods)during 80 Hz stimulation of the FS cell(Fig. 4A) and no long-term changes insynaptic responses (data not shown). Fi-nally, ratio of the total inhibitory areas innRC pairs versus RC pairs did not vary with age (nRC:RC atP14P18: 1.30 0.17, n 7; P19P29: 1.36 0.35, n 12;p 0.05).

The differences in inhibition between RC and nRC pairs wereattributable to differential GABABreceptor activation. The iso-lated GABABportion of the response was first inferred and thenverified pharmacologically in the following manner. The IPSPevoked with a single action potential is mediated primarily byGABAA currents (Connors et al., 1988) and can be used as a

template for GABAAreceptor activation (Fig. 4 B, middle). Foreach stimulus pulse of the train, this template was scaled by themeasured short-term synaptic depression (Fig. 4B, top). The lin-ear superposition of all the waveformsgave the predicted GABAAportion of the response (Fig. 4 B, middle, gray line). Subtractionof the predicted GABAAcomponent from the total recorded re-sponse (Fig. 4 B, bottom, gray line) yielded the predicted GABABcomponent. In a subset of triple neuron recordings (n 8), weblocked the GABAAcomponent with bath application of 10 Mbicuculline. The remaining inhibitory response was small (0.10.8 mV) and had a delayed onset consistent with GABAB-mediated responses (Connors et al., 1988) (Fig. 4 B, bottom, blueline). Thearea of the recorded GABAB components did not differfrom the predicted area values (p 0.10, Wilcoxons rank test).The GABAB receptor antagonist, 2-hydroxysaclofen (50 M),

blocked the remaining inhibitory component (n 4 pairs) (Fig.4C; supplemental Fig. 2A, available at www.jneurosci.org as sup-plemental material).

As observed for the total synaptic response (Fig. 3), the re-corded steady-state GABAB component wassmaller in RC (0.20.1 mV) versus nRC pairs (0.4 0.2 mV;p 0.02, Wilcoxonsrank test; n 8). For the majority of triplets, the predicted (filledcircles) and recorded (open circles) area of the GABABcompo-nent in the RC pair was less than that of the nRC pair (Fig. 4D).

On average, the area of the GABABcomponent in nRC pairs was2.5 times greater (range, 19) than in RC pairs (Fig. 4E) (pre-dicted area: triplets: RC, 7 5; nRC, 16 9, p 0.009; fulldataset: RC, 6 4; nRC, 16 9,p 0.00003; recorded area: RC,5 4; nRC, 12 9, p 0.025). Finally, for each triplet, thedifference in total area between RC and nRC pairs was linearlycorrelated with thedifference in thepredicted GABAB inthesamepairs (r 0.66; slope, 0.98 0.27;p 0.002) (Fig. 4 F).

In summary, we have shown that both the spatial profilesand the GABABreceptor-mediated responses differ in RC andnRC pairs. This implies that nearby neurons have a highPRCand likely receive less GABAB-mediated inhibition. As PnRCIincreases with intersomatic distance, so does the recruitmentof GABAB-mediated responses. Overall, this suggests a spatialprofile for inhibition. The amplitudes of unitary IPSPs did not

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Figure 3. Inhibitory synaptic responses in RC and nRC pairs.A, Postsynaptic responses (average of 15 trials) evoked simulta-neously (inset shows a schematic of triple recording) in RC (red) and nRC (blue) connected PCs during 80 Hz stimulation of the

presynaptic FScell.Calibration: vertical,FS cell, 40mV; PCs,1 mV;horizontal, 200ms.B,Left,Overallpairs,theamplitudesofthe

first IPSP (IPSP1) of the train did not significantly differ in RC (0.7 0.3 mV;n 26) versus nRC (0.6 0.5;n 22;p 0.77,unpairedttest) pairs. In both RC (red; *p 0.012) and nRC (blue; **p 5 106) pairs, the steady-state hyperpolarization(HSS) recorded during the last 200 ms of stimulation was greater than the amplitude of IPSP 1. Right, The increase in inhibitionduringstimulation,HSS-IPSP1, is significantlygreater innRC versusRC pairs (**p 0.008, unpaired ttest). C, Theinhibitoryarea

normalized by the area of a single IPSP (A, inset) in the RC PC is plotted versus that of the nRC PC for each triple neuron recording(n 19; black circles). In nearly all triplets, inhibitory area in the nRC pair was greater than the RC pair (i.e., below the dashedunitaryslopeline).D,TheaverageinhibitoryareawassignificantlygreaterinnRCpairsversusRCpairsintriplets(left;** p0.007,paired ttest) and over all pairs (right; *p 0.013, unpaired ttest).



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differ between RC and nRC pairs and did not vary with interso-matic distance (supplemental Fig. 2B, available at www.jneurosci.orgas supplemental material).However,therewas a trendtowardincreasing GABABresponses with intersomatic distance (supple-mental Fig. 2C, available at www.jneurosci.org as supplemental

material). Unfortunately, there were in-sufficient data in each distance binfor sta-tistical analysis of these results.

Model of L2/3 FSPC circuitryThe functional implications of the exper-imental findings were explored with a net-

work model that incorporated key aspectsof the measured FSPC circuitry andsynaptic properties (see Materials andMethods). In brief, the network was a150150msheetof900PCsand225FScells, in which each cell was modeled asa leaky integrate-and-fire neuron. Theprobability of a PC to PC connection was0.1 and spatially independent (Fig. 5A,black). The connection probability be-tween PC and FS cells depended on theintersomatic distance such that at dis-tances 50m,PRCwas high andPnRCIwas low (Fig. 5A). The GABA

A

conduc-tances were equivalent in RC and nRCpairs, whereas the GABAB conductancewas three times greater in nRC pairs (Fig.5B, left). The membrane potential re-sponses of an RC or nRC PC to an FS cellthat fired action potentials at 80 Hz for500 ms are shown in Figure 5B, right.These parameters produced a HSS,nRC/HSS,RC ratio (2.2) in model PCs that waswithin the range of recorded HSS,nRC/HSS,RC ratios (2.4 2.8) (supplementalFig. 3, available at www.jneurosci.org assupplemental material).

Exactly 64PC and 16FS cells were cho-sen at random within a square region oflength,L, positioned at the center of thenetwork (Fig. 5C, yellow cells). These cellswere driven(D) with a high rate excitatoryPoisson input; all other cells were notdriven (ND), and received a weak back-ground excitatory input (Fig. 5C, graycells). Therefore, the network consisted ofdriven/nondriven PCs (PCD, PCND), anddriven/nondriven FS cells (FSD, FSND).Sample membrane traces for driven andnondriven cells are shown in Figure 5D.Note that neurons in the PCND popula-

tion were suppressed by recurrent FS cellactivity (Fig. 5D) and did not contributeto network dynamics (data not shown).

The spatial profile of inputs modulategamma oscillationsThe combination of the RC and nRCspatial connectivity profile and the dif-ferential recruitment of GABABin thesemicrocircuits suggest that the network re-

sponse can be modulated by the spatial profile of input (Fig. 6A).Spatially focal inputs (L 40m) produced a synchronous PCDcell response (Fig. 6B, top) that oscillated strongly at gammafrequencies (40Hz),asevidencedbythelargepeakinthepowerspectrum of the PCDpopulation (Fig. 6C, top). An increase inL

1

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Figure4. GABAB-mediatedinhibitionis stronger innRC versusRC pairs.A,Themeanshort-termsynapticdepressionofsucces-

sive IPSPs normalized by the amplitude of first IPSP in RC (red;n 19) and nRC (blue;n 19) PCs during 80 Hz stimulation (40pulses) of the FS cell. Error bars were omitted for clarity. B, Top, The short-term depression (open circles) of the total inhibitory

response (blue trace; middle) of an nRC pair. Middle, The predicted GABAA(gray trace) component of the inhibitory response

obtained by convolving 40 pulses (80 Hz pulse rate) with the template IPSP (black trace) scaled by the measured short-termdepression(above).Bottom,ThepredictedGABA B component(graytrace)wasobtainedbysubtractingthepredictedGABAA component

fromthe totalinhibitoryresponse.The isolatedGABAB component(bluetrace)recordedinthepresenceof10 M bicucullineisshownfor

comparison.C, The isolated GABABcomponents in RC (red) and nRC (blue) PCs recorded in 10m bicuculline during 80 Hzfiring of the FS cell (black trace). In both PCs, this respo nse was abolished by bicuc ulline plus 50Msaclofen (RC,gray trace;

nRC,black trace). D, Forall triplets,the area ofthe predicted(filled circles) andrecorded(opencircles)GABAB response inthe nRCPCwasplottedversusthatoftheRCPC.Allpointswereonorbelowtheunitline(dashedline).Theseareaswerenormalizedbythe

areaofthefirstIPSPforcomparisonwithFigure3C. E,TheaverageareaoftheGABAB componentinRCpairs(red)wassignificantly

smallerthaninnRCpairs(blue)(recordedGABA B, *p0.025,Wilcoxonsranktest;predictedGABAB,triplets,**p0.009,pairedttest;allpairs,**p0.00003,unpaired ttest).TheareaoftherecordedGABAB inbothRC andnRCpairsdidnotsignificantlydifferfrompredictedGABAB responses(p0.10,Wilcoxonsranktest).F,ThedifferenceinthepredictedGABA BareasbetweennRCandRC pairs was correlated with the difference in total area (Fig. 3C) for the same pairs (R 0.66; slope, 0.98 0.27;p 0.002).Calibration: vertical, PC, 0.2 mV; FS, 40 mV; horizontal, 200 ms.



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decreased both the degree of PCD syn-chrony (Fig. 6 B, middle and bottom) andthe power of the network gamma oscilla-tion (Fig. 6C, middle and bottom). Thechange in power, quantified by theQfac-tor (height/width of the gamma peak)(Fig. 6 D, inset), decreased dramatically as

Lincreased from 40 to 150m (Fig. 6D).The strong gamma oscillation at L 40m was robust to perturbations in thesynaptic weights (supplemental Fig. 3,available at www.jneurosci.org as supple-mental material) and input strength (datanot shown).

Gamma oscillations in the PCD

, FSD

,and FSNDsubnetworksThe above results raised two relatedquestions. First, how do neural interac-tions within the model network generategamma oscillation? And, second, why isthe gamma band oscillatory power influ-encedbyL? To determinethe mechanismsthat underlie gamma oscillations and thedependence onL, we examined the sub-network interactions among the PCD,FSD, and FSNDpopulations (Fig. 7A).

The dependenceof gammaoscillationsonL(Fig. 6D) was not simply a result of achange in overall network activity. The heterogeneity in networkconnectivity produced a large spread in the firing rate distribu-tions (Fig. 7B). Changes inLdid not significantly influence thesefiring rates (Fig. 7B) because the relatively small difference ininhibitory strength between nRCand RC pairs wasinsufficient to

suppress firing in the PC network.Although changingLdid not affect the average firing rate, thetemporal patterning in the network activity was altered substan-tially. AtL 40m, the spike train raster plots of the PCDandFSND cells showed significant banding and the instantaneouspopulation firing rates had large-amplitude, rhythmic fluctua-tions (Fig. 7C, top and bottom). In contrast, the cells in FSDpopulation were asynchronous, and the population firing rateshad small-amplitude, aperiodic fluctuations (Fig. 7C, middle).The power spectrums of the PCD and FSND, but not the FSD,population responses had a significant peak in the gamma fre-quency band (40 Hz) (Fig. 7D, black). The PCDnetwork oscil-lation reflected synchronous activity among the PCDneurons asindicated by the high coherence between the spike trains of indi-

vidual PCDpairs (Fig. 7D, left, inset). The PCDand FSNDpopu-lation oscillations were anticorrelated (Fig. 7E, middle, black)with a phase shift of90 (data not shown). Both the PCDandFSNDpopulations were weakly correlated with the FSDpopula-tion (Fig. 7E, left and right, black curves). Finally, the oscillatorypower in all populations was reduced forL 150m comparedwithL 40 (Fig. 7CE, compare green and black curves).

GABAB recruitment modulates gamma oscillationsConsistent with previous findings (Brunel and Wang, 2003;Borgers et al., 2005; Borgers and Kopell, 2005), the anticorrelatedPCDand FSNDpopulations (Fig. 7E, middle) gave rise to gammarhythms. Synchronous input from the PCD population droveactivity in the FSND population(Fig. 8A, right, black line). After ashort delay associated with synaptic recruitment, the recurrent

inhibition from the FSNDpopulation (Fig. 8A, right, gray line)decreased PCD activity. The subsequent drive to FSNDneuronswasin turn reduced. This decreasedfeedback inhibition from theFSNDpopulation, allowing the PCDpopulation to resume firing,and repeat the cycle. In contrast, the activity of the FSDpopula-tion was dependent on external drive and was weakly influenced

by PCD activity (Fig. 7E, left). The high firing rates of the FSDinterneurons (80 Hz) (Fig. 7B, middle) prevented entrainmentof these cells to the gamma cycle (Borgers and Kopell, 2005).Consequently, the FSDpopulation acted primarily as a source offeedforward inhibition to the PCDand PCNDpopulations (Fig.8 B). The sensitivity of the network oscillation to L was qualita-tively robust to FSD firing rates of40200 Hz (supplementalFig. 4, available at www.jneurosci.org as supplemental material).

The strength of the FSDfeedfoward inhibition depended onLand provided the basis for spatial control of network oscillations.This can be seen by overlaying the PRCand PnRCIwith the prob-ability density (pd) of the intersomatic distancesof driven FSPCpairsfor L40and L150m(Fig.8 B, left).When L40m,

most of the driven PCDFSDpairs (the mass of pd) were sepa-rated by distances in the 050 m region dominated by RC pairs(gray), and thus, the majority were reciprocally connected. ForL 150m, the pd of intersomatic distances decreased in the050m range and extended to 150m (green). Consequently,the number of RC and nRC PCDFSD pairs was nearly equal.Therefore, the high number of RC pairs driven at L 40m,combined with the weak recruitment of GABAB-mediated inhi-bitionin RC pairs,resultedin minimal feedfoward GABAB to anygiven PCD (Fig. 8B, right, closed circles). As L increased, thedecrease in the number of RC pairs coupled with the increase innRC pairs increased the overall level of GABAB(Fig. 8B, right).Thisin turnsuppressed synchronous PCDdischarge,and reducedthe recruitment of the FSNDpopulation, and ultimately, attenu-ated gamma activity in the recurrent PCD/FSND subnetwork.

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Figure5. ModelL2/3 network.A,Probabilityofconnection(PC)asafunctionofintersomaticdistance.Thespatialconnectivity

profiles of PCFSpairs:PRC (red), PnRCI (blue), PnRCE (green), aswellas PPCPC (black) qualitatively matched the experimental data

(Fig.2C).B, Left,Conductancefor a singleinhibitorysynapticeventin a PCdecomposedintotheGABAA (black),andGABAB forthe

RC(red)and nRC(blue) connection.Right,Membrane potentialresponseswhena presynaptic PC(excitatorysynapse;black)or FS

cell[mixedGABAA/GABAB inhibitory synapseforRC (red)and nRC(blue)]fired actionpotentials at80 Hzfor500 ms.C,Left,SpatialprofileofinputtoPCandFSpopulations:drivencells(D)areshowninyellow,andnondriven(ND)cellsaregray.Thecellsarelocated

ongridpoints.ThesizeofthestimulusregionisgivenbyboxofsidelengthL (i.e., L70m;dashedline). D,Sample Vm tracefora cell of each class: PCD, PCND, FSD, and FSND.



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Since a large proportion of FSNDcells were nonreciprocally con-nected to the PCD population, they also provided significantGABAB inhibition. However, the recruitment of this inhibitionwasinsensitive to changes in L because the majority of FSNDPCDconnections occur between neurons separated by50m. Last,since the strength of GABAAdid not differ between RC and nRCpairs, the recruitment of GABAAwas independent ofL(Fig. 8 B,right,open circles) andthus didnot contribute to themodulation

of oscillatory activity.To verify thatL-dependent recruitment of GABABmodulatesof gamma oscillations, we applied a constant GABAB conduc-tance (H) to the PCDpopulation when L 40m (Fig. 8C, left).The strong gamma oscillation forH 0 nS (black dashed line)decreased whenH 1.2 nS (cyan line) and matched the weakoscillatory power whenL 150m andH 0 nS (green line)(Fig. 8C, middle). The decrease in gamma power with Hwasgradual, indicated by the shallow decline of the Q factor (Fig. 8C,right). Similar results were obtained in the hippocampus inwhich synaptic activation of GABABreceptors decreased the en-trainmentof neurons andpowerof gamma oscillations(Brown etal., 2007).

To explore the influence of the spatial profile of network con-

nectivity on gamma oscillations, we (1) replaced the spatiallydependent probability distributions of RC and nRC pairs withflat, spatially independent distributions (Fig. 8D) and (2) equal-ized the strength of GABAB-mediated inhibition in RC and nRCpairs (Fig. 8 E). In both cases,the influenceof spatial profile of theinput ( L) on the network oscillation was abolished. The firstmanipulation removed all spatial structure from the network,thereby makingit impossible forthe network to be sensitiveto thespatial profile of inputs. The second manipulation maintainedthe spatial profile of RC versus nRC connections, but the lack ofdifferential GABAB-mediated responses resulted in an inhibitoryfield that was insensitive to the spatial profile of inputs. In sum-mary, it is the combination of the spatial profiling of RCand nRCconnections and the differential GABABacross these two circuitsthat allowed the spatial distribution of excitatory drive to modu-

late gamma oscillatory activity throughout the model ACxnetwork.

DiscussionIn the present study, inhibitory connections between nearby(50m)PC and FS cells in ACx occurredpredominantly in RCpairs, whereas at greater intersomatic distances (50100m)RCand nRC pairs were equally probable. Furthermore, GABAB-

mediated inhibition was weaker in RC than nRC pairs. Com-bined, these results suggest that PCs within 50 m of aconnected FS cell receive less steady-state hyperpolarization dur-ing network activity. A network model incorporating this ex-perimental data showed that spatially focal inputs elicitstrong, synchronous, network gamma oscillations. Conversely,spatially broad inputs recruited more GABAB-mediated inhibi-tion that suppressed gamma band activity. These findings dem-onstrate that the connectivity and recruitment of inhibitionwithin FSPC circuits allow the spatial profile of inputsto L2/3 tomodulate gamma oscillations in ACx.

PC and FS cell connectivityThe probability of connection between L2/3 PCFS pairs in ACx

washigh(0.5) compared with the connectivity between PCPCpairs (0.11) (Oswald and Reyes, 2008). Reciprocal connectedFSPC pairs were also highly probable (up to 0.45). Similar re-sults have been reported in other cortical areas (Holmgren et al.,2003; Thomson and Lamy, 2007). Both PE and PRC decreasedsignificantly with intersomatic distance between 20 and 100m.Since PIdidnot vary with distance,it appeared that PRCdependedonPErather thanPI. However, the recordedPRCwas consistentwith the hypothesis that excitatory and inhibitory connections inRC pairs occur independently, albeit with different spatial pro-files. We propose that the spatial profile ofPE, and subsequentlyPRC, arisesbecause of the anatomical structure and orientation ofPC and FS cells. In contrast, thePEbetween FSPC pairs in V1 ismuch lower and the presence of excitatory connections is predic-tive of RC pairs (Yoshimura andCallaway, 2005). Thedifferences

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Figure 6. Spatialextent ofinputmodulatesgammaactivityin drivenPCs.A, Drivenneurons [n 64PCs(PCD)and n 16FScells(FSD)] were chosenrandomlyfrom a squarearea of lengthLcenteredin themiddleof thenetwork.Simulationresultsfor threelengths areshown:L40,70,and150m.B, Spiketrainrasterplotsand instantaneousfiringratesfor PCD forthethreevaluesofL. Instantaneous firing rateswere computed by convolvingthe network spiketrain,Y,(t) ( PC,FS;D,ND), witha Gaussian kernelwitha SDof 2ms.C,NormalizedpowerspectrumofthePCDpopulationforthethreevaluesofL.Thecurvesareaveragescomputedfrom120realizationsinwhichthenetworkconnectivityandchosendrivencellswererandomized. D,TheQ factor(QfmaxP/f) plotted against L. The gray region denotes1 SD computed across 120 realizations.



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inPEandPRCbetween V1 and ACx were not attributable to the

postnatal day age and may reflect regional differences inconnectivity.

In the present study, connections (chemical or electrical) be-tween FS cells were notexamined. It hasbeen suggestedthat theseconnections enhance synchrony among FS cells and promotegamma oscillations (Hormuzdi et al., 2001; Brunel and Wang,2003; Borgers and Kopell, 2005). Inclusion of FSFS interactionsin our model would likely increase gamma band oscillatory syn-chrony between FSD cells. However, the slow time course ofGABAB (approximately hundreds of milliseconds) comparedwith gamma frequencies would continue to suppress oscillatoryresponses to spatially broad inputs. Thus, we expect that FSFSinteractions would not qualitatively alter the sensitivity ofgamma oscillations to the spatial scale of input, unless the spatialprofile of these connections differs from PCFS interactions.

Differential GABAB

-mediated inhibition

TheGABAB-mediated inhibitoryresponses were stronger in nRCthan RC pairs. Although this difference was small for individualpairs (0.10.6 mV), the accumulation of GABABinhibition dur-ing population activity can significantly impact neural pro-cessing. For example, stimulation of neural populations inACx produces 5 mV GABAB-mediated potentials in PCs(Buonomano and Merzenich, 1998). Using a network model, weassessed the functional implications of the recorded connectivityand synaptic parameters at the population level. The model ac-counted for the relative weakness of the differential synaptic re-sponses in that increased recruitment of GABAB with spatiallybroad stimulation did not influence neural firing rates (Fig. 7 B).Nevertheless, the differential GABAB-mediated response was suf-ficient for the spatial extent of input to significantly modulatenetwork oscillations. This is consistent with the fact that weak

Figure 7. Spike train patterning in PCD, FSD, and FSNDsubnetworks.A, Schematic of the L2/3 network showing the PCD, FSD, FSNDsubnetworks and their interactions.B, Distribution of timeaveraged firingratesfor thePCD (left),FSD (middle), and FSND (right) computed from 120networkrealizations.Theensembleaverage firingrateis shownas a verticalline.The network with input

L40m(black)and L150m(green)havethesamefiringrate. C,SpiketrainrasterplotsandinstantaneousfiringratesforthePC D (top),FSD (middle),andFSND (bottom)networks.Thespikeraster plots are for the network withL 40m, whereas the firing rates are sample realizations of the network with stimulus region over L 40m (black) andL 150m (green).D,NormalizedpowerspectraforPCD (left),FSD (middle),andFSND (right)(colorsasin C). E,NormalizedcrossspectrabetweenthePC DFSD (left),PCDFSND (middle),andFSDFSND (right)subnetworks(colorsasinC).Onlythevalueoftherealcomponentisplotted.InDand E,shadedareasindicate 1SDcomputedacross120realizationsinwhichthenetworkconnectivityandchosendrivencellswere randomized.



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coupling influences spike train patterning but not firing rate(Van Vreeswijk et al., 1994). Moreover, this result was robust tovariation in the ratio of GABAB at nRC versus RC synapseswhen this ratio is varied over a range consistent with experimen-tal values, the selectivity of oscillatory activity for spatially focalinputs is maintained (supplemental Fig. 3, available at www.

jneurosci.org as supplemental material). Thus, although the dif-ferences in GABABat individual synapses are seemingly small, at

the network level, the confluence of spatial profiles in both con-nectivity and inputs amplifies the influence of differential inhibi-tion on oscillatory activity.

Currently, the mechanisms by which differential GABAB-mediated responses arise are unknown. One possibility is thatactivity patterns differin RC andnRC pairs andpromote synapticprocesses that differentially influence GABABreceptor activity.For instance, membrane-bound GABABreceptors can associate

C Feedforward modulated Gamma

A Recurrent Inhibition B Feedforward Inhibition

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Figure 8. Feedforward inhibition gates the gamma oscillation.A, The driven PCs and nondriven FS cells (PCDFSNDpopulations) participate in the gamma rhythm via recurrent excitatory

inhibitoryconnections. Theaverage GABAA conductancefromtheFSNDpopulationreceivedbyasinglePCD unit(gray),andthePCD network instantaneousfiringrate (black) showan anticorrelated

40Hzrhythm. B,ThedrivenFScell(FSD)populationsendsfeedforwardinhibitiontothePCDpopulation(top).Left,OverlapoftheRC/nRCconnectionprobability(Fig.5A)andtheprobabilitydensity,

pd,oftheintersomaticdistancebetweenapairofrandomlychosenPC DandFSD cells(shadedarea)for L40m(gray)and L150m(green).Computingpdisahypercubeline-pickingproblem

withan explicitformulafor thesquare(for details,see http://mathworld.wolfram.com/SquareLinePicking.html).Right,The average GABAAandGABAB conductancefromtheFSDpopulationtoaPCDunit as a function ofL.C, A static GABABconductance (H) applied to the PCDsimulated the extra feedforward GABABconductance whenL 150 m. Middle, The power spectrum of the PCDpopulation forL 40,H 1.2nS (cyan curve), iscomparable with that of thenetworkwhenH 0, L 150m(greencurve).ThespectrumofthePCD population response forL 40,H 0nS(blackdashedcurve), isshownfor reference. Right,TheQ factorcomputedfromthespectraofthePCD population(L 40)decreases withincreasing H. Shadedareas indicate1SDcomputedacross120 realizationsof the network connectivity.D, Theremovalof thespatialprofile inRC andnRC connections reduced theoscillatorypowerand made gammaactivityindependentofL. Left,

Flat spatialprofileforRC andnRCconnectionsin PCFScellcircuits.Right, ThePCD populationshowslowergamma power that isindependentofL. E,WhenGABAB isequivalent (gGBRC gGB

nRC0.0229 nS) in both RC and nRC PCFS pairs, the PCDpopulation shows lower gamma power that is independent ofL.



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with GABAAreceptors and undergo agonist-induced cointernal-ization at highly active synapses (Balasubramanian et al., 2004).Postsynaptic activity could also promote (de)phosphorylation ofGABAB receptors and influence membrane stability (Fairfax etal., 2004) while glutamate spillover from nearby excitatory syn-apses may decrease the expression of GABAB receptors (Vargas etal., 2008). Alternatively, differential GABA transporter activity

could affect the availability of GABA to perisynaptic GABABre-ceptors (Bernstein and Quick, 1999; Gonzalez-Burgos et al.,2009). Additional insight could be provided by studies that ad-dress mechanisms by which network activity influences postsyn-aptic GABABinhibitory responses.

Spatial scales of ACx processingIn mice, primary ACx is tonotopically organized in isofrequencybands that are centered at the best frequencies (BFs) and rangefrom 100 to 300 m in width (rostralcaudal) and up to 600 min length (dorsalventral) (Stiebler et al., 1997). Within an isof-requency contour, neurons are further clustered according tonarrow/broad frequency tuning, intensity tuning, responses tostimulus periodicity or binaural inputs, and response latencies(for review, see Schreiner et al., 2000; Schreiner and Winer,2007). Our data and model suggest that L2/3 responses are influ-enced by inputs that range from 50 to 100m. In the thalamor-ecipient layers (L3L5) that provide input to L2/3 (Wallace et al.,1991), these small scales may reflect subregions of isofrequencybands that are either narrowly tuned or selectively activated byoptimal combinations of frequency and other stimulus attributessuch as intensity or location. Alternatively, L2/3 neurons in pri-mary ACx receive nearby, long-range and contralateral connec-tions from other auditory areas (Winer, 1984, 1985; Code andWiner, 1985; Ojima et al., 1991; Budinger et al., 2000) and sen-sory cortices (Budinger et al., 2006). Small-scale activation areascould represent a spatially narrow convergence of these inputs

with feedforward drive. Finally, despite the extensive and over-lapping projections of the axonal and dendritic arbors, con-nectivity can be highly specific (Dantzker and Callaway, 2000;Shepherd and Svoboda, 2005; Song et al., 2005; Yoshimura andCallaway, 2005). In particular, RC FSPC pairs in L2/3 of V1have a high probability of receiving common input from L4(Yoshimura and Callaway, 2005), suggesting that selective, feed-forward activation of RC pairs is also possible.

There is evidence to support the prediction that the spatialscale of inputs influences gamma band activity. Gamma bandactivity is strongest when evoked by pure tone stimuli at the BFand decreases for off-BF tones (Brosch et al., 2002). Moreover,correlated neural activity decreases with spatial distance (Broschet al., 2002) between recording sites as well as for off-BF tones

(Brosch and Schreiner, 1999; Brosch et al., 2002). In contrast,click stimuli, which contain a range of frequencies andlikely drivea spatially broad area of ACx, disrupt ongoing gamma oscilla-tions (MacDonald and Barth, 1995). One caveat is that the dis-tance between recording electrodes (300m) limits the spatialresolution of these measurements.

Optical imaging and stimulation allow for the analysis andcontrol of network activityin vivowith higher spatial resolution.For instance, in barrel cortex, calcium imaging in L2/3 has shownthat stimulus-evoked synchronous activity declines substantiallywithin 100 m of the column center (Kerr et al., 2007) andneurons separated by50 m can have different receptivefield properties (Sato et al., 2007). Furthermore, targetedchannelrhodopsin-2 expression and light activation of FSPCnetworks can induce gamma band oscillatory activity in L2/3

(Cardin et al., 2009). These techniques, in combination withacoustic stimulation, could further elucidate roles for the spatialprofile of cortical microcircuits during auditory processing.

Gamma oscillations in cortical processingGamma band activity hasbeen observed in thesuperficialcorticallayers of ACx both in vivo and in vitro (Barth and MacDonald,

1996; Metherate and Cruikshank, 1999; Sukov and Barth, 2001).In addition, gamma oscillations in ACx are modulated by atten-tion (Lakatos et al., 2004), cross-modal activation of somatosen-sory (Lakatos et al., 2007)or visualinputs (Schroeder et al., 2008),and during learned discrimination tasks (Jeschke et al., 2008).However, the function of gamma oscillations during auditoryprocessing remains unclear.

There are numerous postulated roles for oscillations and syn-chrony in cortical processing (Buzsaki and Draguhn, 2004; Se-

jnowski and Paulsen, 2006).Neural populations may interact andorganize activity through network oscillations (Fries, 2005). Os-cillations could promote synchronous activity in presynapticpopulations that enhances postsynaptic responses (Salinas andSejnowski, 2001) and signal propagation in feedfoward networks(Reyes, 2003). Alternatively, oscillations may provide a clock forphase-based codes (Hopfield, 1995) and reduce spike time vari-ability to improve population discrimination tasks (Masuda andDoiron, 2007; Mazzoni et al., 2008). In all cases, the modulationof oscillatory activity by feedforward or feedback pathways isessential for the dynamic adjustment of cortical responses. Ourstudy gives a potential mechanism whereby the arrangement ofcortical circuits permits the spatial distribution of cortical inputs,to modulate synchronous oscillations across the ACx network.

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