r;CI *~mained negative to the test potential. Under theseconditions, GABAA receptor activation produced alarger CI- flux, and acetazolamide induced a -18-mVshift in the reversal potential toward Ec (n = 4).

25. M. L. Mayer and G. L. Westbrook, J. Physiol. (Lon-don) 394, 501 (1987).

26. L. Vyklicky Jr., V. Vlachova, J. Krusek, ibid. 430, 497(1990); S. F. Traynelis and S. G. Cull-Candy, ibid.433, 727 (1991).

27. GABAB antagonists enhance long-term potentiation(LTP) induction by high-frequency stimulation [C. H.Davies and G. L. Collingridge, Pharmacol. Commun.2, 98 (1992)], whereas GABAB agonists enhance

LTP induction by lower frequency stimulation [D. D.Mott and D. V. Lewis, Science 252, 1718 (1992); C.H. Davies, S. J. Starkey, M. F. Pozza, G. L. Col-lingridge, Nature 349, 609 (1992)].

28. D. M. Woodbury and J. W. Kemp, in AntiepilepticDrugs, D. M. Woodbury and J. K. Penry, Eds. (RavenPress, New York, 1982), pp. 771-789.

29. M. A. Whittington, R. D. Traub, J. G. R. Jeffreys,Nature 373, 612 (1995); H. B. Michelson and R. K. S.Wong, J. Physiol. (London) 477, 35 (1994).

30. R. L. Smith, G. H. Clayton, C. L. Wilcox, K. W. Escu-erdo, K. J. Staley, J. Neuroscience, 15, 4057 (1995).

31. M. J. During et al., Nature 376, 174 (1995).

32. A. L. Hodgkin and B. Katz, J. Physiol. (London) 108,37 (1949).

33. The small, late outward component that is not af-fected by amiloride and acetazolamide is due todiffusion of muscimol toward somatic GABAA re-ceptors, where the CI- gradient is more stable (12,19, 22).

34. We thank T. Dunwiddie and R. Nicoll for helpful com-ments on the manuscript. Supported by NIH grants(NS01573, HD27827, and AA03527) and the Amer-ican Epilepsy Foundation.

10 January 1995; accepted 30 May 1995

Recurrent Excitation in Neocortical CircuitsRodney J. Douglas,* Christof Koch, Misha Mahowald,

Kevan A. C. Martin, Humbert H. Suarezt

The majority of synapses in the mammalian cortex originate from cortical neurons. Indeed,the largest input to cortical cells comes from neighboring excitatory cells. However, mostmodels of cortical development and processing do not reflect the anatomy and physiologyof feedback excitation and are restricted to serial feedforward excitation. This reportdescribes how populations of neurons in cat visual cortex can use excitatory feedback,characterized as an effective "network conductance," to amplify their feedforward inputsignals and demonstrates how neuronal discharge can be kept proportional to stimulusstrength despite strong, recurrent connections that threaten to cause runaway excitation.These principles are incorporated into models of cortical direction and orientation se-

lectivity that emphasize the basic design principles of cortical architectures.

The basic functional architecture of theneocortex, which forms 70 to 80% of theprimate brain, is now well established: Neu-rons with similar functional properties areaggregated together, often in columns orswirling, slab-like arrangements. This archi-tecture reflects the fact that, although lat-eral connections do occur between andacross columns (1), most connections aremade locally within the neighborhood of a1-mm column, as Hubel and Wiesel (2)originally suggested (3).

The neocortex is dominated by excita-tory connections. Eighty-five percent ofsynapses within the gray matter are excita-tory and most of these synapses originatefrom cortical neurons (4). Moreover, about85% of the 5000 to 10,000 synapses madeby excitatory neurons are onto other exci-

R. J. Douglas, Institute of Neuroinformatics, Universityand Eidgenossische Technische Hochschule, Zurich8006, Switzerland; Computation and Neural SystemsProgram, 139-74, California Institute of Technology, Pas-adena, CA 91125, USA; and Center for Biological andMedical Systems, Imperial College, London SW7 ZBT,UK.C. Koch and H. H. Suarez, Computation and NeuralSystems Program, 139-74, California Institute of Tech-nology, Pasadena, CA 91125, USA.M. Mahowald, Institute of Neuroinformatics, Universityand Eidgenossische Technische Hochschule, Zurich8006, Switzerland, and Center for Biological and MedicalSystems, Imperial College, London SW7 ZBT, UK.K. A. C. Martin, Medical Research Council AnatomicalNeuropharmacology Unit, Oxford OX1 3TH, UK.

*To whom correspondence should be addressed.tPresent address: Lancet Online Corporation, KendallSquare, Cambridge, MA 02139, USA.

tatory neurons (4, 5), which suggests thatexcitatory corticocortical synapses mustcontribute strongly to the response charac-teristics of individual neurons. This view isin agreement with electrophysiologicalfindings (6). In interpretations of corticalfunction, however, feedback excitation hasbeen almost completely neglected in favorof a simple feedforward view (2, 7). But wenow know, on the basis of anatomical evi-dence, that feedforward excitation fromsubcortical structures is not prominent: Inthe primary visual cortex of cats and pri-mates, connections arising from the lateralgeniculate nucleus (LGN) make up lessthan 10% of excitatory synapses formedwith the input neurons of cortex layer IVspiny stellate cells (8). Most synapses ontospiny stellate cells originate from layer VIpyramids and other spiny stellate cells (9).

Given this massive excitation, whichhas been proposed to be a basic feature ofcortical operation (10), can we infer thefraction of neurons that make first-orderrecurrent or reciprocal connections, inwhich two neurons directly excite each oth-er (11)? We estimated the number of suchrecurrent connections for the spiny stellatecells of layer IV in the cat visual cortexfrom our detailed three-dimensional (3D)reconstructions of the axons and maps ofthe synapses they receive (9). The boutonsof these cells usually occur in a few clusters(12). Approximation of the radial density ofsynaptic boutons in the cluster surroundingSCIENCE · VOL. 269 * 18 AUGUST 1995

the soma by a 3D Gaussian distribution(characterized by its standard deviation o;Fig. 1A) enables straightforward computa-tion of the fraction of synapses onto a spinystellate cell in layer IV (Fig. 1B). Evenwhen we only consider synapses within thisprimary cluster, recurrent connectionsamong spiny stellate cells can provide asignificant source of recurrent excitation.

The electronic circuit analogy of Fig. 2Aillustrates how recurrently connected neu-rons amplify current (13). The current-dis-charge curve of a single representative neu-ron shows that the discharge frequency isproportional to the excitatory current de-livered to the soma. Discharge is represent-ed by voltage in the electronic model; here,a conductance G (the value of which isinversely related to the slope of the current-discharge curve) will yield the dischargerelation of a hypothetical linear neuron.The neuron's firing frequency F correspondsto the voltage across the conductance in-duced by the total current reaching the"soma" in our simple model of a neuron.

The simplest case of recurrent excitationoccurs in a population of identical neurons,all receiving the same feedforward inputcurrent If and forming identical synapseswith each other. Any one neuron withinthis population contributes some excitatorycurrent to each of its neighbors in the pop-ulation and receives from all of them arecurrent feedback component Irec. As asimple model of synaptic interaction, weassume that the current that flows into aneuron from an excitatory synapse is pro-portional to the discharge frequency of thepresynaptic cell. Because all synapses andneurons are assumed to be identical, we canreduce this network to a single neuron thatreceives a recurrent current Irec proportion-al to its own firing frequency F. Thislumped recurrent synapse behaves as a volt-age-controlled current source with an am-plitude of aF, where oa is the excitatoryconductance. We can think of a as a phe-nomenological "network conductance" be-cause it is generated by the activity of thenetwork of neurons. At equilibrium, thefiring rate of the network F* must obey

Iff + aF* = GF* (1)(Fig. 2B). Thus, the output of the popula-

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tion is proportional to the feedforward in-put current, according to the expression

IffF* =G a (2)G --orIf G > or, the recurrent excitation withinthe population is stable in the sense that itremains bounded without the restraint ofsaturation. In electrical engineering terms,the open loop gain, a/G, in this case is lessthan 1. By contrast, the amount by whichthe circuit amplifies Iff, the closed loop orsystem gain,

a(Iff + 'rec) {C= ~~~(3)alff G - (3)

can be much greater than 1. As a approach-es G, the total input current is mainly at-tributable to the recurrent current I rath-er than the feedforward current Iff and theresponse of the system becomes dominatedby the contribution of the recurrent path-way. If a > G, the open loop gain exceeds1 and there is no equilibrium. A smallchange in total input current generates arecurrent current that exceeds the originalchange and so the system diverges until it isdriven into saturation.

What is the open loop gain for currentamplification within a population of stellatecells? Adapted cortical neurons have a cur-rent-discharge relation that is linear overthe first nanoampere, with a slope of 100spikes per second per nanoampere to thenearest order of magnitude. Thus, G is 10pA per spike per second. Values of a arecalculated from the current delivered byeach excitatory synapse and the number ofrecurrent excitatory synapses. Each synapseprovides roughly 0.1 pA per spike per sec-ond (14). Figure 1B shows that neuronswith bouton distributions of a = 100 pzmwould make 117 first-order recurrent con-nections with as many neighbors, whichimplies that oa is 11.7 pA per spike persecond in this case. Because a > G theopen loop gain is greater than 1, and in theabsence of inhibition, the population ofcells would reach their maximal dischargerate. Removal of the initial stimulus, thefeedforward LGN input, would have no ef-fect on the subsequent activity because therecurrent excitation alone is sufficient tokeep the population active (13, 15).

Visual cortical neurons do not exhibitthis bistability; for example, they respondproportionally to changes in contrast (16).Proportional behavior can be achieved bycontrolling the recurrent amplification withsmall amounts of feedforward or feedbackinhibition that affect the open loop gain. Ifthe feedback inhibitory synapse is approxi-mated as a current source with an amplitudeof f3F, then [ acts as an inhibitory networkconductance of the opposite sign to theexcitatory network conductance. Under

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these conditions, the total recurrent currentarriving at the soma is given by irec = (a -13)F, with a steady-state firing frequency F*given by Iff + (a - [3)F* = GF* (Fig. 2B)and an amplification factor of 1/(G + P3 -

a). The feedback inhibition mediated bylinear synapses acts as a multiplicative,shunting-like inhibition that changes thegain of the cortical response to a giveninput current (Fig. 2B), whereas linear feed-

Fig. 1. Recurrent synaptic connections between spiny 70 Aneurons in cat visual cortex. (A) Radial density of synaptic 60 Layer IV spiny stellate-boutons as a function of the distance from the cell body of " 'i Layer III pyramid -two cells, a layer IVA spiny stellate and a layer Il-lll pyra- 50,midal neuron. In both cases, the axons could not be 40 i ,!completely reconstructed and the total number of bou- . 30 ,,,tons is underestimated. Nevertheless, the data show that S 20the primary cluster of boutons extends from the soma to | 10a distance of about 500 izm. The primary bouton clusters 0'"0,200 4oo 6o0 6oo100o1200 1400 166oof these cells can be described by a spherical Gaussian 200 400 600800 1000 1200 1400 1600

Radial distance (~Jm)distribution with ur between 100 and 120 pjm. Data were distance (m)obtained by computer-assisted reconstruction of neu- 400 Brons in cat striate cortex that had been labeled with 350 Recurrent synapses-horseradish peroxidase during the course of physiologi- 300 Recurrent neurons

cal experiments in vive. (B) Numerical estimate of the = 250number of first-order recurrent connections made within ~ 200the primary cluster of a spiny stellate neuron, and of the _ 150number of neighboring spiny stellate neurons that partic- 5 100ipate in these recurrent connections as a function of the 50standard deviation u of the axonal tree. For clusters with 00 50 100 150 200a = 100 pm, spiny stellate cells receive 117 recurrent Standard deviation of bouton arbor ()Standard deviation of beuten arbor (~tm)connections from as many neighbors. For a = 150 pzm,there are only 34 recurrent connections. The following parameters, drawn from the literature and our owndata, were used to calculate these estimates: 4 x 104 spiny stellate cells per cubic millimeter, 6 x 108asymmetrical (excitatory) synapses per cubic millimeter, and 5000 total synapses on the soma anddendrites of stellate cells (of which 1200 derive from other stellates). No excitatory synapses are madewithin 10 pim of the somata of spiny stellate cells. Five thousand synapses are made by the axonal arbor(of which 1200 are made onto other stellate cells). We assumed that one-third of the boutons occur in theprimary cluster and that they are homogeneously distributed in 3D space.

Fig. 2. Current amplification by recurrently connectedneurons. (A) An electronic equivalent circuit for a dis-charging cortical neuron embedded in its recurrent net-work. /g denotes the current dissipated by the spike dis-charge mechanism, which is assumed to be linear andcharacterized by conductance G. Recurrent excitationgenerates an effective "network conductance" oa, whichis represented in the schematic as a current source that iscontrolled (gray arrow) by the output voltage across G(that is, by the firing frequency of the neuron). Recurrentinhibition generates another network conductance, (3.The effective conductance of the neuron is thus Gef = G+ p3 - a. (B) Current-discharge relations characterizingthe behavior of the cortical amplifier. The 1/G line, corre-sponding to the current-discharge curve, expresses theamount of current /g dissipated across the somatic mem-brane by spike currents at discharge rate F. The 1/(G + P3)curve indicates the increased current,/g + inh, required tomaintain a given discharge rate in the presence of inhibi-tion that is proportional to the output of the neurons. The1/a curve expresses the dependence of the excitatoryfeedback current /,r measured in a particular neuron, onthe average output rate of neurons in the population. Forany particular input current/ff, the steady-state dischargerate P occurs where the equation /re + I/, = /g + /nh issatisfied. At F* the input current I/ is exceeded in ampli-tude by the recurrent current /rec. (C) Adapted (A) andunadapted (UA) current-discharge curves and feedbackcurrent /re for a population of realistic pyramidal neuronsmodeled by computer simulations (17). The adapted cur-rent-discharge and the recurrent current relation are ap-proximately linear. Because the adapted current-dis-

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charge curve does not cross /,r and the two curves diverge away from each other, the network acts asa proportional amplifier.

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·i~bforward inhibition acts more like an offsetthat reduces the input current Ii by a givenamount.

Even in the absence of inhibition, pro-portional amplification may be imposed bythe intracortical arborization of the axonaltree of the spiny stellate cells. Figure 1Bshows that recurrence (and hence the openloop gain) falls off steeply with or. For ex-ample, neurons with a bouton distributiona = 150 I.Tm make 34 first-order recurrentconnections with 34 neighboring stellatecells. Under these circumstances, a falls to3.4 pA per spike per second, the open loopgain of recurrent excitation is less than 1,and the circuit provides stable current am-plification. Although these numerical esti-mates of the open loop gain are hypotheti-cal, the spatial extent of the axonal treemay be an important factor in determiningthe amplitude of the feedback.We evaluated the performance of the

recurrent excitation model against experi-mental results by modeling direction-selec-tive neurons in a patch of cat striate cortex(17, 18). Our aim was not to study directionselectivity per se, but rather to confirm the

Fig. 3. Tests of recurrent ex-citation in a computer modelof a population of direction-selective pyramidal cells. (A)Percentage change frombaseline somatic input con-ductance during stimulationby a bar (visual stimulus)moving in the null direction inthe feedback model, com-pared with a purely feedfor-ward model (B). Conduc-tance is measured by inject-ing hyperpolarizing current.The response of the feed-back model depends onamplification of the small ex-citatory feedforward inputfrom LGN afferents. Thisfeedforward input currentcan be controlled with amoderate inhibitory conduc-tance change, in agreementwith experimental data (24).The purely feedforward

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principles described above in thla simple cortical operation wspiking neurons. The network iconsists of 40 excitatory (pyrarons and 10 inhibitory (smoo(19). Members of the pyramidaare interconnected by excitatcbut for simplicity the inhibitprovide feedforward inhibitoonly. Each neuron comprisescompartment containing the st;plement of voltage-dependentconductances found in corticathree or four passive dendritments. The spike discharge of tadapts within 50 ms. The smoare nonadapting (20).

Figure 2C shows the currecurves for the pyramidal cells arecurrent current, Ircas a funaverage discharge rate of the pylulation. Because Irec does not iadapted current-discharge curwork does not show hysteretic 1rather relaxes to its resting stainput is withdrawn. Moreover,Irec curve diverges from the a

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model receives strong excitatory input current from the LGN. The control of this large curilarge inhibitory conductance change. (C) The recurrent excitatory current (solid curve) gerpreferred stimulation, compared with the net input current (dotted curve; the difference bEtory current from the LGN and feedforward inhibitory current). In this example, the net fee(current is amplified by about 4.7 to yield the total excitatory current. (D) Histogram of direcindices of all pyramidal neurons in the normal population (solid bars), compared with tlinhibition is blocked in a single pyramidal cell (done consecutively for all cells; open bselectivity is diminished, but not lost, in agreement with experimental data (25). (E and F) Ja(26) applied a "linearity" test by comparing the modulations of somatic membranedirection-selective cell in response to a drifting sine-wave grating (1 cycle per degree,;second) (solid line) to the response predicted by summation of the modulations evokeccontrast reversal gratings at eight different spatial phases (dashed line). Cells in cat visual c¢from (26)] (E) and in the model (F) pass this test, which implies that a network with massiveunder certain limited conditions, behave linearly. Each modulation is the average of tpotential over 56 grating cycles. The same median filter was used in both cases to rpotentials.

ie context of rent-discharge curve, the neurons will am-ith realistic, plify their input in a proportional mannern our model (13). The feedforward input signal to theimidal) neu- cortical cells arises from the LGN, whoseth) neurons neurons exhibit little directional prefer-1 population ence. Cortical direction selectivity depends)ry synapses, on a spatial offset between the LGN inputsory neurons to pyramidal and smooth cells (21, 22). Inry synapses the preferred direction, excitation precedes

a somatic inhibition, which allows the neurons toandard com- begin discharging; in the null direction,membrane excitation and feedforward inhibition over-

d1 cells, and lap temporally and cancel each other.ic compart- In a purely feedforward model, feedfor-:he pyramids ward inhibition must be powerful in theoth neurons null direction to suppress the strong excita-

tion, which must be provided solely by thent-discharge LGN input. Our simulations (Fig. 3B) con-s well as the firm that this inhibition should be associat-.ction of the ed with large changes in the somatic inputramidal pop- conductance that would be almost entirely.ntersect the visible from the soma (23). Yet direct in-ie, the net- tracellular measurements have shown thatDehavior but such large shunting changes in conductancete when the do not occur (24). The paradox of massivebecause the excitation and inhibition in the preferredidapted cur- direction but only small inhibition in the

null direction is resolved within the frame-work of current amplification by corticalcircuits. In the preferred direction, the

j small LGN excitation is large enough tobring the pyramidal cells above their firingthreshold. In the model outlined above,within 100 ms the recurrent current is 4.7

V~L__ ~times the effective input current (Fig. 3C).100 150 The amplified input elicits a brisk discharge

index (%) from the neuron. In the null direction, thesmall LGN excitation overlaps in time withfeedforward inhibition and the cell remainssilent. This small amount of inhibition pro-duces only small changes in the somatic,-

,. input conductance (Fig. 3A).lIontophoretic application of bicuculline,

2 mV L_ a selective antagonist of y-aminobutyric100ms acid A (GABAA) receptors, leads to a sig-

nificant reduction or even outright elimi-nation of direction selectivity in simple

f̂\ cells in cat striate cortex (21). We obtained'IVi ~ analogous results with our model (17). In an

elaboration of Sillito's experiments, Nelsonet al. (25) blocked GABAA and GABABreceptors intracellularly in a single neuron.

erated duiring They found that direction selectivity was=tween excita- reduced, but did not disappear, in this cell.dforward input The same result holds for our model (Fig.-tion selectivity 3D), because the major fraction of the ex-he case when citatory current in a single GABA-blockedars). Direction neuron derives from other cortical cellsigadeesh et al. whose direction selectivity is unaffected.potential of a Despite the amplification inherent in2 degrees per our recurrent excitation model, it reproduc-I by stationary es the linear behavior reported by Jagadeeshxrtex [modifiedfeedback can, et al. (26). They observed that the intracel-he membrane lular potential in simple cells in response toremove action a moving sinusoidal grating is accurately

predicted by the sum of the membrane re-

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sponses to eight spatially displaced station-ary gratings (Fig. 3E). This seemingly linearbehavior was also obtained in our model(Fig. 3F); it is partly explained by the natureof the stimulus (27) and partly by the spikeconductances sinking much of the excesscurrent that would otherwise show up asnonlinear contributions to the membranepotential (17). This model demonstratesthat realistic recurrent cortical circuits canachieve proportional amplification and sta-bility, and that their directional behavioragrees with sophisticated intracellular data.The same principles of recurrent excitationhave been used in models of cortical orien-tation tuning (28).

The computational significance of recur-rence is well illustrated by the orientationcase, because in that problem the currentgain experienced by each neuron dependsnot on a single homogeneous value of x (asdescribed in Fig. 2A) but on the time-depen-dent network conductances arising out ofthe excitatory and inhibitory feedback,So,(t) and p3 (t), from cortical cells re-sponding to different orientations (here thesum is taken over all connections amongneurons i and j). The variable gain and ac-tive thresholding that arise out of these cou-plings enable the network to enhance noisyincoming signals in the following way.When a noisy input signal is presented to anorientation-selective population of corticalcells (Fig. 4A), the gains of the individual

pyramidal neurons are at first equal to eachother because their outputs are randomlycorrelated. The incoherent outputs of thepyramidal neurons are averaged by the in-hibitory interneurons, which provides aneffective threshold across the pyramidalcells. This threshold has the effect of un-coupling the pyramidal neurons as somemembers of the population that receiveonly weak input fall silent. That effectincreases the relative a% between the sur-viving pyramids, and tieir gains remainhigh or increase while the gain of isolatedfiring neurons falls. The increased outputof the survivors enables them to increasethe inhibitory threshold, thereby improv-ing the correlation in activity of the activeneurons, and so on. Initially the inhibitionis subtractive in quality because it is theaverage over incoherent pyramidal activi-ty. But as the computation converges, theinhibition becomes divisive because its ef-fect on the surviving pyramids is bettercorrelated with their discharge and theinhibitory network conductance (see P13above) is expressed.

Overall, the population of neurons co-operatively restores the incoming stimulustoward a pattern that is latent in the recur-rent connectivity; this permits meaningfuloutputs to be extracted from incomplete ornoisy input patterns by means of variablethresholding followed by amplification (Fig.4B) (29). This restoration is related to re-

Fig. 4. Signal restoration by recurrent excitation. A sec- Aond, more simplified, model network comprises 42 exci- Total-tatory and 7 inhibitory "neurons" of the kind described in °nhibitonFig. 2, A and B. The excitatory neurons are coupled to ' 0.6each other by excitatory connections falling off as a =- '

Gaussian distribution (with a cr equivalent to two neurons; 0.circular boundary conditions are used). The inhibitory 5 0.2neurons receive input from overlapping subpopulations o0' '" /"' AIof excitatory cells. The synaptic strengths of these con-nections are also Gaussian (o- = 4). All inhibitory neurons 0 5 10 15 20 25 30 3540make synapses onto the excitatory population with uni- Neuron numberform strength. The network receives a Gaussian pattern 250 Bof feedforward input currents from the LGN, and thispattern is degraded by a variable amount of noise. (A) 200Amplification of the noisy feedforward input current [sig- a= 1.2nal-to-noise ratio (S/N) = 1.8, here caused by a very c_ 150noisy oriented signal] by the recurrent network results in 100 a=0.8the net output current indicated by the solid line. After oconvergence, most of the noise is subthreshold, while the 50 0.0

o~= 0.0positive part of the signal is amplified and restored towardContthe expected Gaussian distribution. The final inhibitory 0 5 10 15 20 25 30current (dotted line) is shown as a positive current against Input S/Nwhich the feedforward LGN input signal is compared.The output of a purely feedforward model (dashed line) is simply that part of the LGN signal that exceedsthe inhibitory current without any signal restoration. (B) Signal enhancement by recurrent excitation andactive thresholding. S/N ratios of feedforward inputs and neuronal output discharges are compared insimulations similar to those described in (A). The line labeled Control indicates the parity expectedbetween input and output S/N in an ideal linear unity gain amplifier. In the absence of recurrence (oa = 0),simple feedforward inhibitory thresholding of a noisy feedforward excitatory signal provides slight signalenhancement. Increasing feedback excitation (a) improves the signal-enhancing properties of the net-work by a combination of amplification and feedback thresholding that restores the noisy input towardpatterns latent in the network connectivity. The thresholding inhibition required is relatively small becausesmall feedforward LGN inputs are amplified.

call in content addressable (associative)memories composed of sigmoidal neurons(15). However, those networks typicallyhave very strong positive feedback andmany stable attractors, whereas the corticalcircuits presented here operate in a domainwhere they can represent in a proportionalmanner various aspects of the input, such asits contrast or velocity. Functionally, therecurrent cortical architecture combines as-pects of analog signal processing ("smart"amplification) with digital signal processing(signal restoration). Similar circuits arelikely to explain receptive field propertiesin other sensory areas. The high degree ofcortical interconnectivity, compared to thesmall number of extracortical inputs, raisesthe possibility that receptive field propertiesare not so much determined by the specificpatterns of thalamic afferents but areshaped by the collective behavior of largepopulations of cortical cells. If so, the cor-tex would represent a substantially richermodifiable architecture than standard feed-forward models (30).

REFERENCES AND NOTES

1. C. D. Gilbert and T. N. Wiesel, J. Neurosci. 3, 116(1983); ibid. 9, 2432 (1989).

2. D. H. Hubel and T. N. Wiesel, J. Physiol. 160, 106(1962).

3. The majority of synapses must be made relativelyclose to their source neurons so as to minimize thevolume of axonal "wiring" and prevent an explosivegrowth of cortical volume with increasing cell number[C. Mead, Proc. IEEE 78, 1629 (1990); G. Mitchison,Trends Neurosci. 15, 122 (1992)].

4. V. Braitenberg and A. Schuz, Anatomy of the Cortex(Springer-Verlag, Berlin, 1991).

5. Z. F. Kisvarday et al., Exp. Brain Res. 64, 541 (1986);B. A. McGuire et al., J. Neurosci. 4, 3021 (1984).

6. D. Ferster and S. Lindstrom, J. Physiol. 367, 217(1985); ibid., p. 233; K. L. Grieve and A. M. Sillito,Exp. Brain Res. 87, 521 (1991).

7. P. Heggelund, Exp. Brain Res. 42,89 (1981); D. Ferster,J. Neurosci. 7, 1780 (1987); ibid. 8, 1172 (1988); R.Maex and G. A. Orban, Proc. Natl. Acad. Sci. U.S.A. 88,3549 (1991); F. Worgotter and C. Koch, J. Neurosci. 11,1959 (1991). More recently feedback inhibition hasbeen incorporated in some models; see M. Carandiniand D. J. Heeger, Science 264,1333 (1994).

8. S. LeVay, J. Neurosci. 6, 3564 (1986); E. L. White,Cortical Circuits: Synaptic Organization of the Cere-bral Cortex (Birkhauser, Boston, 1989); A. Petersand B. R. Payne, Cereb. Cortex 3, 69 (1993); A.Peters, B. R. Payne, J. Rudd, ibid. 4, 215 (1994).

9. B. Ahmed et al., J. Comp. Neurol. 341, 39 (1994).10. R. J. Douglas, K. A. C. Martin, D. Whitteridge, Neural

Comput. 1,480(1989).11. We ignore here the effects of higher order recurrent

connections that further strengthen our conclusions;see R. E. Traub and R. Miles, Neuronal Networks ofthe Hippocampus (Cambridge Univ. Press, Cam-bridge, 1991).

12. K. A. C. Martin and D. Whitteridge, J. Physiol. 353,463 (1984); J. S. Lund et al., Cereb. Cortex 3, 148(1993); Y. Amir et al., J. Comp. Neurol. 334, 19(1993).

13. See also H. H. Suarez, thesis, California Institute ofTechnology (1995) for an analysis of this system'sdynamics and the influence of nonlinearities.

14. 0. Bernander, C. Koch, R. J. Douglas, J. Neuro-physiol. 72, 2743 (1994).

15. This kind of feedback network has been studied in theartificial neural network community as the basis forcontent addressable memory [D. J. Willshaw, O. P.Buneman, H. C. Longuet-Higgins, Nature 222, 960

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(1969); D. Marr, Proc. R. Soc. London Ser. B Biol. Sci.176,161(1970); J. J. Hopfield, Proc. Natl. Acad. Sci.U.S.A. 81, 3088 (1984); S. Grossberg, Neural Net-works 1, 17(1988); J. Hertz, A. Krogh, R. G. Palmer,Introduction to the Theory of Neural Computation (Ad-dison-Wesley, Redwood City, CA, 1991)].

16. I. Ohzawa et al., Nature 298, 266 (1982).17. H. H. Suarez, C. Koch, R. J. Douglas, J. Neurosci., in

press.18. R. Maex [thesis, Leuven University, Belgium (1995)]

has simulated a similar model of cortical directionselectivity with similar results to ours.

19. The feedforward inputs from the LGN to the corticalpyramidal and smooth neurons were Poisson-dis-tributed spike trains whose instantaneous rate wasmodulated by the visual stimulus. The stimulus, usu-ally a bar or sinusoidal grating, was convolved withthe spatial-temporal receptive field characteristic ofthe LGN ON relay cells of the X type [J. D. Victor, J.Physiol. 386, 219 (1987)]. Direction selectivity wasobtained by spatially offsetting the LGN input tosmooth cells by 5' with respect to LGN inputs to thepyramidal cells. All synapses were modeled as con-ductances with appropriate reversal potentials, andtime courses and amplitudes were compatible withavailable in vitro data. The synapses providedGABAA and GABA6 inhibition and non-N-methyl-D-

aspartate (NMDA) excitation. All data presented herewere obtained with a single set of neuronal and net-work parameters.

20. D. A. McCormick et al., J. Neurophysiol. 54, 782(1985).

21. A. M. Sillito, J. Physiol. 250, 305 (1975); ibid. 271,699 (1977).

22. P. 0. Bishop, J. S. Coombs, G. H. Henry, ibid. 219,625 (1971); L. Ganz, R. Felder, J. Neurophysiol. 51,294 (1984); J. McLean, S. Raab, L. A. Palmer, VisualNeurosci. 11, 271 (1994). We do not here modellagged geniculate cells that might also contribute todirection selectivity [see D. N. Mastronarde, J. Neu-rophysiol. 57, 357 (1987); A. B. Saul and A. L. Hum-phrey, ibid. 64, 206 (1990)].

23. C. Koch et al., J. Neurosci. 10, 1728 (1990).24. Peak measured conductance changes in the null

direction are less than 25% of the somatic inputconductance [R. J. Douglas, K. A. C. Martin, D. Whit-teridge, Nature 332,642 (1988); J. Physiol. 440,659(1991); X. Pei et al., Neuroreport 2, 485 (1991); D.Ferster and B. Jagadeesh, J. Neurosci. 12, 1262(1992)].

25. S. Nelson et al., Science 265, 774 (1994).26. B. Jagadeesh et al., ibid. 262,1901 (1993). See also

R. C. Reid, R. E. Soodak, R. M. Shapley, Proc. Natl.Acad. Sci. U.S.A. 84, 8740 (1987).

27. Nonlinear Fourier components in the half-wave rec-tified responses to gratings tend to cancel out whenadded with different temporal offsets.

28. D. Somers, S. B. Nelson, M. Sur, J. Neurosci., inpress; R. Ben-Yishai, R. Lev Bar-Or, H. Sompolin-sky, Proc. Natl. Acad. Sci. U.S.A. 92, 3844 (1995).

29. R. J. Douglas, M. A. Mahowald, K. A. C. Martin, IEEEIntl. Conf. Neural Networks, 1848 (1994).

30. J. Allman, F. Miezin, E. McGuiness, Annu. Rev.Neurosci. 8, 407 (1985); B. Gulyas et al., J. Physiol.57, 1767 (1987); C. D. Gilbert and T. N. Wiesel,Vision Res. 30, 1689 (1990); C. Koch and J. Davis,Large Scale Neuronal Theories of the Brain (MITPress, Cambridge, MA, 1994).

31. We thank the U.S. Office of Naval Research fortheir long-term support of this work. In additionthis work was supported by the Air Force Office ofScientific Research, the Gatsby Foundation, theMedical Research Council, the National Institute ofMental Health, the National Science Foundation,the European Community, the Human FrontiersScience Program, the Wellcome Trust, and theRoyal Society. We thank J. Anderson for recon-structions of neurons in cat striate cortex and G.Holt for help with the graphics.

16 February 1995; accepted 5 June 1995

Object-Centered Direction Selectivity in theMacaque Supplementary Eye Field

C. R. Olson* and S. N. Gettner

Object-centered spatial awareness-awareness of the location, relative to an object, ofits parts-plays an important role in many aspects of perception, imagination, and action.One possible basis for this capability is the existence in the brain of neurons with sensoryreceptive fields or motor action fields that are defined relative to an object-centered frame.In experiments described here, neuronal activity was monitored in the supplementary eyefield of macaque monkeys making eye movements to the right or left end of a horizontalbar. Neurons were found to fire differentially as a function of the end of the bar to whichan eye movement was made. This is direct evidence for the existence of neurons sensitiveto the object-centered direction of movements.

Many behaviors and mental processes re-quire the use of spatial information definedin an object-centered reference frame. Vi-sual object recognition, for example, is gen-erally thought to require explicit encodingof the locations of parts relative to theobject (I). Visually guided motor behavioralso depends on object-centered informa-tion. The hand, in reaching around an ob-ject, must move along a trajectory definedrelative to the object. Likewise, the eyes,during scanning, may be directed to a fea-tureless point defined solely by its relationto visible details elsewhere in the scene.Evidence that localized groups of neuronsrepresent specific parts of object-centeredspace has been provided by studies of visualneglect in humans. In many cases of hemi-field neglect, patients overlook features onthe contralesional side of a visible objectDepartment of Oral and Craniofacial Biological Sciences,College of Dental Surgery, University of Maryland, Balti-more, MD 21201, USA.

*To whom correspondence should be addressed.E-mail: colson@umabnet.ab.umd.edu

even when the neglected side of the objecthas been viewed through the good hemi-field (2). Object-centered neglect mustarise from the loss of neurons that mediatedawareness of one half of the current refer-ence object rather than one half of visualspace or the retina. Such neurons could beexpected to have sensory receptive fields ormotor action fields defined with respect tothe current reference object. Previous sin-gle-unit studies have produced only limitedevidence for the existence of neurons withthese properties (3). In this report, we dem-onstrate that neurons in the supplementaryeye field (SEF) of the macaque monkeyencode eye-movement direction with re-

spect to an object-centered reference frame.The SEF is an oculomotor area on the

dorsomedial surface of the frontal lobe.Electrical stimulation of the macaque SEFelicits eye movements with complex prop-erties, including dependence on initial or-

bital position (4). Neurons in the SEF dis-charge preferentially before and during sac-

cades in a restricted range of directions (5).SCIENCE * VOL. 269 · 18 AUGUST 1995

Some SEF neurons are selectively activeduring the learning of associations betweenvisual-pattern cues and eye-movement di-rections (6). These observations suggestthat the SEF mediates processes of compar-atively high order that are related to oculo-motor control.We prepared two male macaque monkeys

for single-unit recording by standard meth-ods (7). We mapped out the SEF in bothhemispheres of one monkey and in the righthemisphere of the second monkey (8). Toassess object-centered direction selectivity,we trained the monkeys to perform an ocu-lomotor task in which the object-centereddirection of eye movements (to the left orright end of a horizontal target bar) could bedissociated from their orbit-centered direc-tion (leftward or rightward in the orbit).The sequence of events during a representa-tive trial is shown in Fig. 1A. A cue present-ed early in each trial (a spot superimposedon one end of a sample bar) instructed themonkey to look to the left or right end of thetarget bar. The target bar subsequently ap-peared at one of three locations (Fig. iB).Across eight possible conditions (Fig. 1C),eye-centered direction (leftward or right-ward in the orbit) was fully counterbalancedagainst object-centered direction (to the leftor right end of the bar) (9).

Twenty-nine neurons in one monkeywere studied while the monkey performedthis task. The neuron shown in Fig. 2 firedmore strongly when the eye movement wasto the left end of the target bar (left col-umn) than when it was to the right end(right column). This was true regardless ofthe orbital direction of the movement(rightward in the first and third rows; left-ward in the second and fourth rows). Firingwas stronger in bar-left trials, not only dur-ing the period between the cue and the

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