Lars Schwabe et al- The Role of Feedback in Shaping the Extra-Classical Receptive Field of Cortical...

8/3/2019 Lars Schwabe et al- The Role of Feedback in Shaping the Extra-Classical Receptive Field of Cortical Neurons: A Rec

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Behavioral/Systems/Cognitive

The Role of Feedback in Shaping the Extra-Classical

Receptive Field of Cortical Neurons: A RecurrentNetwork Model

Lars Schwabe,1,2,3KlausObermayer,1 AlessandraAngelucci,2* and Paul C. Bressloff3*1Fakultat IV, Electrical Engineering and Computer Science, Technische Universitat Berlin, 10587 Berlin, Germany, 2Department of Ophthalmology and

Visual Science, Moran Eye Center, University of Utah, Salt Lake City, Utah 84132, and 3Department of Mathematics, University of Utah, Salt Lake City, Utah

84112

Theresponses of neurons in sensory cortices areaffectedby thespatial context withinwhichstimuli areembedded. In theprimary visualcortex (V1),orientation-selective responsesto stimuli in the receptivefield(RF) center are suppressedby similarlyorientedstimuli in the

RF surround. Surround suppression, a likely neural correlate of perceptual figureground segregation, is traditionally thought to begeneratedwithin V1 by long-range horizontal connections.Recentlyhowever,it hasbeen shown that these connections aretoo short and

too slow to mediate fast suppression from distant regions of the RF surround. We use an anatomically and physiologically constrainedrecurrentnetwork model of macaque V1 to show howinterareal feedback connections,whichare fasterand longer-rangethan horizontal

connections, can generate far surround suppression. We provide a novel solution to the puzzle of how surround suppression can arisefrom excitatory feedback axons contacting predominantly excitatory neurons in V1. The basic mechanism involves divergent feedback

connections from the far surround targeting pyramidal neurons sending monosynaptic horizontal connections to excitatory and inhib-itory neurons in the RF center. One of several predictions of our model is that the suppressive far surround is not always suppressive,

but can facilitate the response of the RF center, depending on the amount of excitatory drive to the local inhibitors. Our model providesa general mechanism of how top-down feedback signals directly contribute to generating cortical neuron responses to simple sensory

stimuli.Key words: primary visual cortex; macaque; horizontal connections; top-down; contextual effects; surround suppression

IntroductionNeuronal responses in sensory cortices are modulated by thespatial context within which stimuli are embedded. Primary vi-sual cortex (V1) neuron responses to optimally oriented stimuliin their receptive field (RF) center are usually suppressed by iso-oriented stimuli in theRF surround (Blakemore andTobin, 1972;Nelson and Frost, 1978; Allman et al., 1985; Gilbert and Wiesel,1990; DeAngelis et al., 1994). V1 cells also exhibit contrast-

dependent size-tuning (Sengpiel et al., 1997; Kapadia et al., 1999;Sceniak et al., 1999) (i.e., the radius of a stimulus evoking thelargest response from the cell is smaller at high than at low con-trast). We refer to theoptimal radiusfor spatial summationas thehigh- or low-contrast summation RF (hsRF or lsRF, respec-tively). The RF center and surround have a number of distinctcomponents, as defined in Figure 1. In particular, we distinguish

between a near surround that extends as far as the lsRF, and asuppressive far surround extending beyond the lsRF.

Previous studies (Angelucci et al., 2002b) demonstrated thatV1 horizontal connections are spatially coextensive with the lsRFsize of V1 cells (Fig. 1), and that surround suppression can beevoked by stimuli located far beyond the monosynaptic spread ofhorizontal connections (Sceniak et al., 2001; Cavanaugh et al.,2002a; Levitt and Lund, 2002). Thus, these connections could

monosynaptically underlie the spatial summation properties ofV1 neurons at low stimulus contrast (Sceniak et al., 1999) andnear (Kapadia et al., 1995; Polat et al., 1998), but not far, sur-roundmodulation of RF center responses.Cascades of horizontalconnections are too slow (Grinvald et al., 1994; Bringuier et al.,1999; Girard et al., 2001) to account for the fast onset of suppres-sion from the far surround (Bair et al., 2003; Muller et al., 2003).The latter could instead be accounted for by longer-range (Ange-lucci et al., 2002b) and faster-conducting (Girard et al., 2001)extrastriate feedback (FB) connections to V1.Consistent with thehypothesis that FB connections could underlie the far surroundof V1 neurons, is evidence that cooling the middle temporal(MT) area reduces the suppressive effect of surround motion

stimulation in V3, V2, and V1 neurons (Hupe et al., 1998; Bullieret al., 2001). However, a role for FB connections in surroundsuppression is inconsistent with evidence that these connections

Received March 23, 2006; revised June 9, 2006; accepted July 21, 2006.

This work was supported by the Wellcome Tr ust (061113), National Institutes of Health (EY 015262), National

Science Foundation (IBN 0344569 and DMS 0515725), Research to Prevent Blindness, and BMBF (10025304). We

thank Dr. Jennifer S. Lund for her intellectual contribution to this study.

*A.A. and P.C.B. contributed equally to this work.

Correspondence should be addressed to Alessandra Angelucci at the above address. E-mail:

[email protected]:10.1523/JNEUROSCI.1253-06.2006

Copyright 2006 Society for Neuroscience 0270-6474/06/269117-13$15.00/0

The Journal of Neuroscience, September 6, 2006 26(36):91179129 9117


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arise from excitatory neurons, target almost exclusively(9798%) excitatory V1 neurons (Johnson and Burkhalter,1996), and modulate V1 responses via synaptic mechanisms inwhich excitation dominates (Shao and Burkhalter, 1996).

To pinpoint the neuronal circuitry and mechanisms underly-ingcenter-surround interactions in macaque V1,we have setup arecurrent neuronal network model whose architecture is con-

strained to fit the anatomical and physiological data describedabove. In particular, we provide a novel solution to how excita-tory FB connections could mediate far surround suppression inV1, namely by targeting excitatory neurons sending monosynap-tic horizontal connections to local inhibitors in the RF center.This is consistent with observations that horizontal connections,unlike FB connections, terminate on both excitatory and inhibi-tory neurons (McGuire et al., 1991). Our model can account fora wide range of physiological data regarding the static and dy-namic effects of surround suppression, and generates novel test-able predictions. One important prediction, consistent with ourrecent studies (Ichida et al., 2005), is that the far suppressivesurround can be facilitatory.

Materials andMethodsWe describe here the construction of our cortical network model andhow the parameters of the model are fitted to anatomical and physiolog-ical data. The values of all model parameters are summarized in Table 1.

Cortical network model. We consider a recurrent network model thatrepresents two areas of an idealizedcortex, onecorresponding to area V1(or striate cortex) and the other to an extrastriate area such as MT, witheach areabeing composedof a single layer of cells, namely layer2/3 of V1and layer 6 of MT. A schematic diagram illustrating the basic networkarchitecture is shown in Figure 2. Suppose that a particular V1 excitatoryneuron(Ectr) is identifiedas thetarget neuronwhose response propertieswe wish to determine. V1 neurons can then be labeled according to thelocation (in degrees) of their RF centers relative to the RF center of thetarget neuron. Thus, the center consists of neurons (Ectr) whose RF

centers lie within the minimum response field (mRF) of the target neu-ron, the near surround consists of neurons (Enr) whose RF centers fallwithin either the hsRF or lsRF, and the far surround consists of neu-rons(Efar) whoseRF centers liebeyond thelsRF (Fig.1).In themodel, weassume that excitatory neurons in V1 ( E) receive feedforward afferentexcitation (EFF) from other V1 layers, local recurrent excitation and in-hibition ( I), long-range excitation via slow intra-areal V1 horizontal (orlateral) connections, and FB excitation (EFB) via fast interareal connec-tions. Horizontal connections also target local interneurons, whereas FBconnections only target excitatory neurons. This is motivated by theanatomical findings that horizontal axons contact both excitatory (80%)and inhibitory (20%) neurons (McGuire et al., 1991), whereas FB axonscontact predominantly (9798%) excitatory neurons (Johnson andBurkhalter, 1996) (see Introduction). The spatial extent of interareal FBconnections is taken to be larger than that of intra-areal horizontal con-nections (Fig. 3a), following the anatomical data of Angelucci et al.(2002b). In particular, horizontal connections from the near surround,butnot thefar surround, connect to theRF centermonosynaptically, andextendas faras thelsRF of their neurons of origin,whereas extrastriate FBconnections are coextensive with the far surround of V1 neurons.

The fundamental assumption of our model is that there is an asym-metry between the properties of the excitatory cells andthose of the localinterneurons, namely, that the local inhibitory neurons have higher fir-ing thresholds and gain (Fig. 3b), and are more strongly driven by hori-zontal connections than the excitatory neurons whose output they con-trol. As a result, the inhibitory neurons generate suppression undersufficiently high levels of excitation, but are inactive at low levels ofexcitation. This is consistent with the results of electrical stimulationexperiments in slices of visual cortex showing that weaker stimulation of

horizontal connections evokes excitation in their target cells, whereasinhibition dominates after stronger stimulation (Hirsch and Gilbert,1991). There is experimental evidence for high-gain inhibitory neurons

in cortical layer 2/3. These are interneurons receiving facilitating inputsfrom pyramidal cells (Thomson et al., 1995, 2002; Markram et al., 1998;Thomson, 2003), unlike other interneurons also targeted by pyramidalcells, which instead receive depressing inputs. Whereas depressing inter-neurons receive inputs only from the local pyramids that they contact,facilitating interneurons receive inputs also from other pyramids and,thus, perhaps from those sending horizontal connections (Pouille andScanziani, 2004; Kapfer et al., 2005) (M. Scanziani, personal communi-

cation). Although the existence of higher-threshold inhibitory neuronsstrongly drivenby horizontal connections hasnot been confirmed exper-imentally, there exist a large number of different classes of interneurons,many of whose physiological properties have not yet been fully charac-terized. Similarly, we know very little about the properties of inhibitoryneurons targeted by horizontal connections. Therefore, this basic as-sumption of our model can be viewed as an experimentally verifiablehypothesis that provides a simple explanation for a wide range of phe-nomena, as described in detail in Results. It should also be noted that theinhibitory neurons with facilitating synapses have been shown to be re-cruited in the late phase of the action potential train of their presynapticpyramidal cells (Pouille and Scanziani, 2004; Kapfer et al., 2005). Thelatter could thus represent a mechanism alternative to the higher-threshold interneurons we proposed to implement the delayed recruit-ment of inhibition relative to excitation needed in our model.

For simplicity, we do not model stimulus features such as orientationandspatial frequency, because in this paper we focus on modeling thesizetuning of V1 neurons andhow this is affected by stimuluscontrast.Thus,we model experimental paradigms in which two-dimensional gratingsare presented at the optimal spatial frequency and orientation of thecenter target neuron. In real life, such stimuli activate discrete patchesacross the cortex corresponding to those cortical columns that have suf-ficiently similar orientations and spatial frequencies to that of the stim-ulus. We idealize thispatchworkstructureas a one-dimensional networkof cells along the collinear axis of the preferredorientation, in agreementwith recent data showing that horizontal (Bosking et al., 1997; Sincichand Blasdel, 2001) and FB (Angelucci et al., 2003; Shmuel et al., 2005)connections in V1 linkregions of similarorientation preference along anaxis collinear with the preferred orientation of their neurons of origin.

As a further simplification, we consider a spatially discrete model inwhich each cortical area is represented as a one-dimensional lattice ofexcitatory/inhibitory (EI) neuron pairs whose RF centers are equallyspaced between8 and8. Let N be the total number of EI pairs inthe striate ( S) and extrastriate ( X) cortex. The RF centers (indegrees) canthen be writtenasxi 8i/M

,with i0,1,. . . ,M,andN 2M 1. In our simulations we take NS 161 and NX 33. Itfollows that the RF centers of neighboring EI pairs in the striate cortexare spatially separated by 0.1, which is equivalent to 230 m in corticaldistance at 5 retinal eccentricity (see below, Spatial scales and time de-lays), and is consistent with the approximate interpatch distance of hor-izontal intracortical connections.Given this spatially coarse-grained rep-resentation of the cortex, the center is represented by the target EI pairtogether with its nearest and next-nearest neighbors, assuming the mRFhas a radius of0.2. One can think of each EI pair as the basic func-tional module of our network that incorporates the effects of local recur-rent connections. Interactions between these modules arethen mediatedby horizontal and feedback connections. Because we are focusing onsize-tuning effects in this paper, it is sufficient to take a very simple localnetwork model.However, if onewere to extendthe model to incorporateorientation tuning, for example, then it would be necessary to replaceeach EI pair with a more complicated network module such as onebased on the ring model (Ben-Yishai et al., 1995; Somers et al., 1995). Inthiscase,at least two distinct types of inhibitory neuronwould be needed(Stetter et al., 2000; Bressloff andCowan, 2002),one that is broadly tunedwith respect to orientation and one that is more sharply tuned, with thelatter playing the role of the local inhibitor in our simpler model. Ana-tomically speaking, these two classes of interneurons could be identified,respectively, as laterally projecting basket cells and vertically projecting

cells, for example, double bouquet cells.Network dynamics. The cortical network dynamics is formulated in

terms of a simplified rate model, which can be derived from a more

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detailed biophysical model as described previously (Shriki et al., 2003).Let rl

(xi, t) denote the local activity at time tof excitatory (l E) andinhibitory (l I) neurons with their RF center at xi in the striate ( S)and extrastriate (X) cortex. The activityrl

evolves according to thefirst-order rate equation as follows:

ldrl

xi , t

dt rl

xi , t FlIl

xi , t,

where l is an effective synaptic time constant (with l 8 ms), Fl( I) is

the firing rate function or frequencycurrent curve for the cell (see be-low, Firing rate function), and Il

(xi, t) is the total synaptic current intothe neuron. In the striate cortex, the synaptic current is taken to be thefollowing:

IlSxi , t

mE,I

WlmS rm

S xi , t

local inputs

ji

WlESSxixj rE

Sxj , t tSSxixj

lateral inputs within striate cortex

j

WIESXxixj rE

Xxj , t tSXxixj

feedback inputs from extrastriate cortex

hxi , tl,E

afferent inputs

,

whereas in extrastriate cortex it is of the following form:

IiXxi , t

mE,I

WlmX rm

Xxi , t

local inputs

ji

WlEXXxixj rE

Xxj , t tXXxixj

lateral inputs within striate cortex

j

WIEXSxixj rE

Sxj , t tXSxixj

feedforward inputs from striate cortex

.

Here h(xi,t) represents the afferent input to the excitatory cell with RF

center xi in striate cortex, Wlm denotes the weight of the local synapticconnection from neuron of type m to neuron of type lwithin the sameEI pair of a given cortical area , Wlm

(xi xj) denotes the non-localconnections from an EI pair with RF center xj in area to an EI pairwithRF centerxi in area,andt

(xi xj) represents the correspondingaxonal time delays. Thus, Wlm

SS and WlmXX represent the spatial distri-

bution of intra-areal (horizontal) connections, whereas WlmXS and

WlmSXrepresent the distribution of interareal feedforward and feedback

connections, respectively. The non-local weights depend on the distancebetween the RF centers xi and xj of the presynaptic and postsynapticneurons and are given by the following (Fig. 3a):

WlExixj W lE

expxi xj,

where determines the spatial scale of the connections. The values of

the weight coefficients Wlm, W lE, and space constants are listed in

Table 1. For simplicity, all recurrent connections in the extrastriate cor-tex are set to zero (W lE

XX 0 WlmX ) so that the latter effectively serves

as a relay station without further processing.The conduction time delays are given by the following:

txixj xi xj

S3Sfor lateral connections in striate cortex

xS3X

S3Xfor inter-areal connections,

where vS3S and vS3X are the conduction velocities for signaling withinthe striate cortex and between the striate and extrastriate areas, respec-tively, and xS3X is the distance between the two areas. The values as-signed to and the conduction velocities are discussed below in Spa-

tial scales and time delays.Afferent inputs. The model neurons in the recurrent network corre-

spond to neurons in layer 2/3 of area V1. Therefore, the afferent input to

these neurons arises from layer 4C. Let c( y) denote the contrast of thestimulus at the visual field location y. A typical contrast-dependent out-put current from a layer 4C neuron can be approximated by a piecewiselinear function of the following form:

Ic

0 for 0 c cth

Ilow

clow cthc cth for c

th c clow

Ihigh Ilow

chigh clowc clow Ilow for clow c

.

Below the contrast threshold cth the current is zero, whereas abovethreshold the current increases linearly with contrast at a rate thatchanges when ccrosses clow. A graph of this function is shown in Figure3c. The parameter values for the contrast-dependence of the input cur-rents are set to cth 0.1, clow 0.15, chigh 0.85, Ilow 0.58 nA, andIhigh 0.71 nA. The total input to the i th excitatory neuron with the RFcenter at xi is then given as a linear spatial summation over the distribu-tion of afferent inputs from layer 4C:

hxi Gy; xi Icyd y.

Here G( y; xi) represents the RF profile of the layer 2/3 neuron and is

taken to be a Gaussian:

Gy; xi 2aff1 expyxi2/2aff2 ,

with range aff 0.1 (Bauer et al., 1999; Angelucci et al., 2002a). Itfollows, from the form of I(c), that a necessary condition for a layer 2/3neuron to fire is that the contrast of the afferent stimulus is higher thancth.

Firing rate function. To obtain a biophysically reasonable form for thefiring rate functions FE and FI, we used a HodgkinHuxley-type neuronwith fluctuating background inputs represented by an OrnsteinUhlen-beck process, as described in detail previously (Destexhe et al., 2001;Schwabeand Obermayer, 2005). We simulated the spike response of thismodel neuron to current injections for different values of the leak con-ductance in thepresenceof thefluctuatingbackground conductance.We

considered only the already adapted responses, which were then bestfitted with thresholded polynomials. These fits were performed by min-imizingthe mean squarederrorbetween thesimulatedfiringrate andtheone predicted by the thresholded polynomials. We obtained thefollowing:

FEI max0, aEI IE

FII max0, aII II bII II2,

with aE 70.09 spikes/s (sp/s) (nA)1, IE 0.52 nA for excitatory

neurons, and aI 131sp/s (nA)1, bI28sp/s(nA)

2,andII 0.7nA for inhibitory neurons (see also Table 1). The functions FE and FIareplotted in Figure 3b. FE is a linear function, becausein the correspondingHodgkinHuxley model we included an adaptation current that linear-izes the steady-state firing rate function. In contrast, the adaptation con-ductance in the HodgkinHuxley model of the inhibitory neuron wasreduced to only 10% of the value used for the excitatory neuron. As aconsequence, the steady-state firing rate function remained nonlinear,which we captured by using a quadratic function for the fit. The currentthresholdof theinhibitory neurons is taken to be higher than the one forthe excitatory neurons. This can be implemented by assuming a higherleak conductance for inhibitory cells at rest or by assuming a differentbalance between the background excitation and inhibition for the inhib-itory neuron. Having determined the steady-state firing rate, we canincorporate the effects of synaptic dynamics into a first-order rateequation.

Spatial scales and time delays. The parameters determine the spa-tialscale of the connections between the areas a and b. Weused SS 2.3deg1 andXSSX 0.3deg1. These valuesare computed as follows.

Defining the scale of the connections between the areas a and b as thevalue x at which exp(x) 0.05, we have (x)1 ln(0.05). For horizontal connections,we usex 0.5D(mm)MF

1

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1.3 deg, and obtain SS 2.3 deg1, whereD(mm) 6 mm is theaverage lengthof horizon-tal connections in macaque V1 (Angelucci etal., 2002b), and MF 2.3 mm/deg is the corti-calmagnificationfactor(MF) in macaque V1 at5 eccentricity along the isopolar lines of visualfield representation (Van Essen et al., 1984). Ina previous study (Angelucci et al., 2002b), we

found that theaverage visuotopicextent of hor-izontal connections closelymatches the averageextent of the lsRF of their V1neurons of origin.For example, at 5 eccentricity, the physiologi-cally determined average size of the lsRF is2.6 in diameter, which is compatible with2x 2.6. For the interareal connections, weuse x 0.5 D(mm) MF

1 9.89, andobtain XS SX 0.3 deg1, where D(mm)8.9mm is theaverage cortical extentof theneu-ronal fields of FB connections to V1 within areaMT in the macaque (Angelucci et al., 2002b),and MF 0.45 mm/deg is the cortical magni-fication factorin macaque MT at 5 eccentricity(Albright and Desimone, 1987). For simplifica-tion, we assumehorizontal andFB connectionsto be translation invariant in visual space (i.e.,we do not take into account variations in theextent of the connections caused by the depen-dence of the cortical MF on retinal eccentric-ity). This is done so as to avoid distortions ofthe predicted activation profiles along the cor-tical axis. In a model with an MF varying witheccentricity, surround suppression would be-come asymmetric, with stronger suppression from cortex representingvisual field regions closer to the fovea. This is because near the fovea theMF is larger and, thus, a larger number of near surround neurons wouldexert their influence on the center neurons. In contrast, the converse istrue for cortical regions away from the fovea. Thus, a more detailed

model would predict asymmetries of surround suppression caused bythese effects. However, these are likely to become relevant only for verylarge stimuli.

For the conduction velocities used to compute the time delays t,we use vS3X 4000 mm/s for the conduction velocity of interarealconnections between V1 and MT in the macaque (Movshon and New-some, 1996; Nowak and Bullier, 1997), and xS3X 7 mm for thedistance between macaque V1 and MT (Kennedy and Bullier, 1985;Hupe et al., 1998). For the intra-areal horizontal connections in thestriatecortex, we use vS3X (200mm/s)MF

1 86.9/s (Grinvald etal., 1994; Bringuier et al., 1999; Girard et al., 2001), where MF 2.3mm/deg is the V1 cortical magnification factor at 5 eccentricity. Thesevalueslead,for example, to timedelays oft 5/(86.9/s) 57.5ms forsignals traveling a distance of 5 within the model V1 compared with adelay oft (2 7 mm)/(4000 mm/s) 3.5 ms for signals traveling a

comparable distance via feedforward connections to extrastriate cortexand back to V1.

Parameterization of the model. In the model, there are three sets ofparameters: thebiophysical single cell parameters, the parameters for thespatial scales and time delays of the intra-areal and interareal connec-tions, and the parameters determining the strengths of the connections(see Table 1). Whereas the first two sets of parameters are largely con-strained by experimental data, little is known about the last parameterset. In a model exploration, we adjusted theconnection weightssuch thatthemodel accountedfor all of theexperimental data that we simulated inthispaper. Theonly constraintswe imposed were (1) excluding feedbackto inhibitory neurons (Johnson andBurkhalter, 1996), and(2) assumingthat horizontal connections to excitatory neurons are only modulatory(Hirschand Gilbert, 1991) (i.e.,feedforward inputsto excitatory neurons

are a necessary condition for the neurons to generate action potentials).Hence, the feedforward and the local recurrent excitation of excitatoryneurons are assumed to be strong compared with that of horizontal

connections. Under these constraints, we find that only assuming stronghorizontal excitation of inhibitory neurons (Hirsch and Gilbert, 1991)can the model reproduce the experimental data (see above, Cortical net-work model, and Discussion). We also find that the strength of the feed-forward input to inhibitory neurons has a minor effect on the modelpredictions, as long as the inhibitory neurons have a higher functional

threshold than the excitatory neurons, because it is only in this regimethat the model accurately predicts the contrast-dependence of surroundsuppression (Fig. 4a). It is for simplicity that we did not assume anyfeedforward input to inhibitory neurons. It should also be noted that weare only considering one class of inhibitory neuron in our simplifiedmodel. As we have already commented above, extending our model totake intoaccount orientation tuning would requirethe introduction of atleast one additional class of interneuron representing, for example,broadly tuned basket cells. The inclusion of a direct afferent drive fromlayer 4C to interneurons would then play a more significant role.

ResultsTo elucidate the role of horizontal and FB connections in gener-ating the RF center and surround of V1 neurons, we perform

numerical simulations of the model presented in Materials andMethods. Parameters of the model are fitted to known anatomi-cal and physiological data as summarized in Table 1. Numericalsimulations are performed for stimuli of varying size and con-trast. In the figures, such stimuli are represented as gratings, tofacilitate the link with experiments. However, in our networkmodel, the size of a stimulus is simply taken to be the spatialextent (in degrees) of the feedforward afferents carrying nonzerocurrents to the V1 layer, and the contrast of the stimulus is takento be the strength of these currents (see Materials and Methods).

Iso-orientation surround suppression in V1 has traditionallybeen attributed to intra-areal horizontal connections (Gilbert etal., 1996; Somers et al., 1998; Fitzpatrick, 2000). Because these

connections terminateon both excitatory and inhibitoryneurons(Martin and Whitteridge, 1984; Kisvarday et al., 1986; McGuireet al., 1991), surround suppression has been proposed to be gen-

Table 1. Model parameters

Symbol Description Value

Network architectureN

E

S NI

S No. of excitatory and inhibitory neurons in striate cortex 161N

E

X No. of excitatory neurons in extrastriate cortex 33Size of simulated visual field representation 16 deg

Connectivity

SS

Scale of lateral connections 2.3 deg1

XSSX Scale of interareal connections 0.3 deg1

S3S

Conduction velocity of lateral connections 200 mm/sS3X

Conduction velocity of interareal connections 4000 mm/s

S3XDistance between V1 and extrastriate area MT 7 mm

aff

Spatial spread of afferent input 0.1 degFiring ratefunctions

aE Parameter for excitatory neurons 70.09 sp/s (nA)1

IE

Threshold for the excitatory neurons 0.52 nAaI Parameter for inhibitory neurons 131 sp/s (nA)1

bI Parameter for inhibitory neurons 28 sp/s (nA)2

II

Threshold for the inhibitory neurons 0.70 nA

StrengthsW

EE

SS Lateral excitation of excitatory neurons 3.38 104

WIE

SS Lateral excitation of inhibitory neurons 34 104

WEE

XSWEE

SX Interareal excitation 4.52 104

WEE

S Local excitation of excitatory neurons 85 104

WIE

S Local excitation of inhibitory neurons 34 104

WEI

S Local inhibition of excitatory neurons 122 104

WII

S Local inhibition of inhibitory neurons 12 104

No., Number.



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erated by lateral excitation of local inhibition (Lund et al., 1995;Somers et al., 1998). Thus, following previous recurrent networkmodels (Somers et al., 1998; Dragoi and Sur, 2000), we assumethat stimulation of the near surround modulates the response toa center stimulus via horizontal connections targeting both exci-tatory and inhibitory neurons in the center. The interneurons are

assumed to have a higher threshold and gain than the local exci-tatory neurons whose output they control (Fig. 3b) (see Materialsand Methods) and, thus, only generate suppression under suffi-

ciently high levels of excitation, for exam-ple, when the contrast and/or size of agrating stimulus is sufficiently large. Atlow levels of excitation, such as for smallor low-contrast stimuli, the inhibitors areinactive, and stimulation of the near sur-round facilitates the center response. The

key novel features of our model are as fol-lows: (1) FB from the extrastriate cortexprovides an additional source of excita-tion to excitatory neurons in the centerand in the near surround; (2) fast suppres-sion from the far surround is assumed tooccur via FB, rather than via a cascade ofhorizontal connections. Our model pro-vides a specific solution to the puzzle ofhow exclusively excitatory interareal FBconnections, which target predominantlyexcitatory neurons in V1, can mediate farsurround suppression of the center neu-rons; namely by targeting excitatory neu-rons inthenearsurround,which in turn,viahorizontal connections, excite the local in-hibitoryneurons in thecenter.It alsofollowsthat if the local interneurons are inactive,thenstimulation of thefarsurroundis facili-tatory. Therefore, our model also predictsthat the suppressive far surround of V1neurons is not always suppressive (see be-low, Contrast-dependent suppression andfacilitation from the far surround: a modelprediction).

Contrast-dependent spatial summation

We first use our model to simulate exper-iments in which the RF size is measured asthe stimulus radius at the peak response ofan area-summation curve (the summa-tion RF), using high- or low-contrast grat-ings. The summation RF size is known todepend on the stimulus contrast, withlower contrasts yielding larger summationRF sizes (Sceniak et al., 1999) (Fig. 1). Theresults of these simulations are shown inFigure 4a c. Increasing the size of thestimulus leads to an increased response ofthe center excitatory neurons. This facili-

tation turns into suppression as the stim-ulus size is further increased, because thelocal interneurons, now sufficiently stim-ulated, start firing (Fig. 4a). The stimulussize at which the interneurons are acti-vated, however, depends on the stimuluscontrast. At lower contrast, the firing rates

of all excitatory neurons are also lower, and so the interneuronhas to integrate over a larger area to reach its firing threshold.This accounts for the contrast-dependence of the RF size mea-sured via the area-summation curves. In order for the abovemechanism to be effective, in the model, the center interneuronsmust be strongly driven by horizontal connections, more so than

the center excitatory neurons (Fig. 4b,c). Figure 4, b and c, addi-tionally shows how, in the model, the various input currents tothe excitatory and inhibitory neurons vary with stimulus size.

Figure1. Differentcomponentsof theRF center and surround of V1 neurons andtheir hypothesized anatomicalsubstrates. Inthecenterof thefigureis a schematicdiagramof thevariouscomponentsof theRF centerandsurroundof anexampleV1 neuron;these are surrounded by four identical size-tuning curves for this neuron, over which an icon and arrow indicate the size of therespectiveRFcomponent.Blackandgraycurvesaresize-tuningcurvesmeasuredathigh-andlow-stimuluscontrast,respectively.

The white square area is the mRF or RF center; this is the RF region over which presentation of optimally oriented stimuli evokesspikesfromthecell.Experimentally,themRFismeasuredusingsmall,high-contrastmovingstimulianddelimitingtheareawherespikes are evoked from the cell (icon on the top-left size-tuning curve) (Hubel and Wiesel, 1962; Barlow et al., 1967); the arrowunderthe mRFiconindicatesthesizeof themRFrelative tothe peak ofthe high-contrast size-tuningcurve. Thedashedringis thehsRF; this is measured by presenting high-contrast gratings of increasing radius (icon on the center-left size-tuning curve) anddefined as thestimulus radiusat thepeakresponse of theneuron (arrowunderthe hsRF icon).The regionbetweenthe mRFandthehsRFistheregionoverwhichpresentationofhigh-contrastgratingsatthesameorientationasthecentergratingfacilitatestheresponseofthecelltooptimallyorientedgratingsinthecenter.ThehsRFradiusisabouttwicethatofthemRF.Thecontinuousringis the lsRF; this is measured and defined as the hsRF size, but using low-contrast gratings of increasing radius (icon on thecenter-rightsize-tuningcurve).TheregionbetweenthehsRFandthelsRFistheregionoverwhichpresentationofgratingsatthesameorientationasthecentergratingsuppressesorfacilitatestheresponseofthecelltooptimallyorientedgratingsinthecenter,

dependingonthecontrastofthegrating.Notetheshifttotherightofthepeakresponseatlowcontrast(Sceniaketal.,1999).Grayarea, RF surround. We consider two separate regions of the surround depending on their proximity to the RF center: (1) the near

surround istheregionbetweenthe mRFandthelsRF,(2)thefarsurroundis theregionoutsidethelsRFoverwhichpresentationofstimuli atthe same orientationas thecenterstimulususuallysuppresses theresponse ofthe cell tooptimally oriented gratingsinthecenter.Intra-arealV1horizontalconnections(red)arecommensuratewiththelsRFsizeoftheirV1neuronsoforigin,whereasextrastriateFB(blue)connectionstoV1arecommensuratewiththefullspatialscaleofthecenterandsurroundfieldofV1neurons(Angeluccietal.,2002b).Feedforwardgeniculocorticalconnections(datanotshown)arecommensuratewiththehsRFsizeoftheirrecipient V1 neurons (Angelucci and Sainsbury, 2006).



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Another interesting feature of the curvesshown in Figure 4a is that there is an oscil-latory component to the variation in re-sponse as a function of stimulus size. Thisis because of disinhibition of the centerexcitatory neurons caused by suppressionof the excitatory neurons in the near sur-

round driving the center inhibitory neu-rons. Such suppression in turn dependson the level of excitation of horizontalconnections to near surround neuronsarising from the center and far surround.This predicted disinhibition of the centerexcitatory neurons has been generallyoverlooked in the experimental data,partly because of the coarser sampling ofthe stimulus size used in most experi-ments compared with our computer sim-ulations, and partly because it was consid-ered as noise. However, this phenomenoncan be observed in several experimentalpapers published previously (DeAngelis etal., 1994; Li and Li, 1994; Sengpiel et al.,1997; Walker et al., 2000), although in mostcases the authors failed to appreciate it and,thus, did not comment about it. Motivatedby this specific prediction of our model, inrecent physiological studies we (Ichidaet al.,2005) have observed such an oscillatorycomponent in thesize-tuning curve of a sig-nificant proportion of V1 neurons.

In Figure 4df, we show a sequence ofdiagrams for increasing stimulus size,highlighting the network components that

are active and the major afferent pathwaysfrom the active regions to the center neu-rons. A stimulus fitted to the size of thehsRFactivates the center and part of the nearsurround (Fig. 4d). The center receives ex-citatory inputs via feedforward afferents,via horizontal connections from the activeregion of the near surround, and via FBconnections from extrastriate cortex. Athigh contrast, the local inhibitors are as-sumed to be close to threshold, so that anadditional increase in stimulus size be-yond the hsRF size, as in Figure 4e, leads to

suppression of thecenter response.In con-trast, expansion of a low-contrast stimulusbeyond the hsRF size results in facilitation,until the full extent of the near surround isactive (Fig. 4e). Finally, high- or low-contrast stimuli that extend well beyondthe lsRF activate the far surround (Fig. 4f). This suppresses thecenter via FB connections exciting neurons in the near surround,which then excitelocal interneurons in the center. In principle, inthemodel, it is possible forthe farsurroundto suppress thecentervia a cascade of horizontal connections from the far, to the nearsurround, to the center (Fig. 2). Although such a cascade is tooslow to account for the fast onset of suppression (Girard et al.,

2001; Angelucci and Bullier, 2003; Bair et al., 2003) (see Intro-duction), it could contribute to the late phase of the suppression.In our simulations, such a contribution is negligible because of

surround suppression of excitatory V1 neurons at each step in thechain, which prevents horizontal propagation of signals. How-ever, although in our model all excitatory neurons show sur-round suppression, in real V1 some neurons do not (Levitt andLund, 2002). These cells could propagate signals horizontallyand, thus, contribute to the late phase of the suppression.

Contrast-dependent suppression and facilitation from the far

surround: a model predictionTo investigate more directly the contribution of FB connectionsto the far surround of V1 neurons, we simulate an experiment in

Figure3. Functionalspecificationof thenetwork model.a,DifferentspatialscalesusedinthemodelfortheFB(black)andthelateral(orhorizontal;gray)connections.PlottedisthenormalizedstrengthoflateralandFBconnectionstoapostsynapticneuronasa functionof thedistance of theRF centers ofthe presynaptic neurons from theRF centerof thepostsynaptic neuron. Note thedifferentscalesonthexaxes(thetoponeappliestotheFBconnections,thebottomtothelateralconnections). b,FiringrateoftheV1localexcitatory(E;gray)andinhibitory(I;black)neuronsinthemodel,plottedagainsttheinputcurrent. c,InputcurrentoftheV1 excitatory neuron as a function of stimulus contrast.

Figure 2. Basic architecture of the recurrent network model. Schematic diagram of the connections used in the network model.Differentconnectiontypesareindicatedas color-codedarrows.Purpleand blackboxesrepresentpopulationsof excitatory(E)or inhibitory(I)V1neurons,respectively,labeledaccordingto thepositionof theirRF centerrelativetothatof thecenterneurons.Accordingly,ctrare theneuronsintheRFcenterormRF;nraretheneuronsinthenearsurround,ofwhichthoseclosertothecenterfallwithinthehsRFofthecenterneurons,whereasthoselocatedfartherfromthecenterfallwithinthelsRFof thecenterneurons;fararetheneuronsinthefar surround.E

FF,

ExcitatoryneuronsinotherV1layerssendingfeedforwardafferentstotheEneuronsinV1layers2/3.EFB

,excitatoryneuronsinextrastriate

cortexsendingfeedbackprojectionsto theE neuronsin V1.FBconnectionsarespatiallyhighlydivergentand convergent.Notetheabsenceofdirect FB inputs to I neurons.The latter receivemonosynapticinputsonlyfrom V1 horizontal connections(red arrows) andfrom local Eneurons via local recurrent connections (purple arrows). Icons at the bottom represent the different components of the RF center andsurround(sameconventionsasinFig.1),withredareasindicatingRFcomponentsthatarestimulatedwheneachrespectivesubmoduleis

consecutively(fromleft to right) activated bya stimulusof increasing radius.



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which afferent stimulation of the region between the hsRF andlsRF is withdrawn. This allows us to minimize the afferent driveof horizontal connections in the near surround so as to unmaskthe effect of FB connections from the far surround. To achievethis, a stimulus analogous to a high-contrast annular grating ispresented in the far surround together with a central high-

contrast stimulus fitted to the size of the hsRF (stimulus shown inFig. 5b). The inner radius of the annulus is systematically de-creased from the far surround to a size no smaller than that of thelsRF, so that near surround neurons in the lsRF but beyond thehsRF never receive afferent stimulation (Fig. 5a,b). As the innerradius is decreased, more neurons in the far surround receiveafferent stimulation. This leads to suppression of the excitatoryneurons in the center (Fig. 5a), as observed experimentally (Lev-itt and Lund, 2002). The active components in the network, andthe main pathways relaying information to the center neurons inresponse to this stimulus configuration are illustrated in Figure5e. The mechanism leading to the response suppression is thesame as that illustrated in Figure 4. Specifically, as more neurons

in the far surround are activated, excitatory neurons in the nearsurround increase their firing rate (Fig. 5b); this is caused byincreased excitation received via FB connections activated by

stimulation of the far surround. The nearsurround neurons, then, activate the cen-ter interneurons via horizontal connec-tions (Fig. 5a,e), resulting in suppression.However, our model also demonstratesthat, when a low-contrast central stimulusis presented together with a high-contrast

annulus in the far surround (stimulusshown in Fig. 5d), decreasing the inner ra-dius of the annulus (i.e., stimulating an in-creasingly larger number of neurons in thefar surround), can lead to initial facilita-tion of the center excitatory neurons fol-lowed by suppression (Fig. 5c d). This isattributable to the fact that the low-contrast central stimulus is too weak to ac-tivate the center interneurons by itself(Fig. 5c); thus, stimulation of the far sur-round initially facilitates the response ofthe center neurons, because FB inputs tothe center sum with afferent and horizon-tal inputs, until a critical annulus size isreached, beyond which the interneuronsare activated (Fig. 5c) and suppression oc-curs. It is important to emphasize thatpolysynaptic chains of horizontal connec-tions are unlikely to contribute to themodulatory effects of the far surround inthese annular grating experiments. Thisis because the excitatory neurons whoseRFs lie in the visual field location of theblank stimulus do not receive afferent driveand, thus, cannot effectively relay signals totheir postsynapticV1 neuronsbecauseof the

purelymodulatory (notdriving)effect of lat-eral connections to excitatory neurons(Hirsch and Gilbert, 1991).

One of the advantages of using a recur-rent network model is that it allows us tomake predictions regarding the popula-tion activity profile of neurons across V1

in response to visual stimuli. Figure 6a shows the predicted activ-ity profile of excitatory neurons as a function of position relativeto the center neuron population, in the case of a small high-contrast stimulus (0.4 radius; i.e., the size of the hsRF, as derivedfrom Fig. 4a) and a large high-contrast stimulus (1.5 radius; i.e.,extending into the far surround, as derived from Fig. 4a). The

responses of the neurons in the center and near surround de-crease with increasing stimulus size (thin vs thick line), as ex-pected from the simulated area summation experiments (Fig.4a). However, the responses of neurons with their RF centerslocated at theborder of thelargestimulus, in thefar surround,arenot suppressed. Figure 6b shows the predicted activity profile fora small high-contrast central stimulus (0.5 radius; i.e., just largerthan the hsRF of the neurons, but smaller than the lsRF, as de-rived from Fig. 4a) presented with and without a high-contrastannular stimulus (3.2 inner radius and 8 outer radius) in the farsurround. When the annulus is presented together with the cen-tral stimulus, the responses of the center excitatory neurons aresuppressed, whereas the responses of the excitatory neurons in

the near surround are facilitated. This can be explained by thesame mechanism illustrated in Figure 5, a and b, namely, thatactivation of FB, because of stimulation of the far surround, en-

Figure 4. Contrast-dependent spatial summationin thenetwork model.a, Response (spikes/second)of thecenter excitatory

(Ectr

; purple) and inhibitory (Ictr

; black) neurons as a function of the size of the afferent stimulus (in degrees) for two differentstimulus contrasts(85 and15%,solidand dashedlines, respectively).Iconsat thetop representthe differentcomponentsof theRF centerand surround (asin Figs.1, 2),withred areasindicating theRF regions that areactivated atthe indicatedpoints in thesize-tuning curve.Thesesameiconsare shown indfto indicate the respectiveactive network componentsand pathways.b, c,Input currents to the center excitatory neurons (b) and to the center inhibitory neurons (c) as a function of the afferent stimulussize(indegrees).Thedifferentinputtypesarecolorcodedaccordingtothelegendinf.Iconsundertheabscissain cshowthestimulususedandarevalidfor ac.df,Asequenceofdiagramshighlighting,for increasingstimulussize,thenetworkcomponentsthatare activeandthemajorafferentpathwaysfromtheactiveregionstothecenterneurons.ConventionsareasinFigure2.



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hances the response of excitatory neurons in both the center and

near surround, which in turn activate the center inhibitors (Fig.5e). It is worth emphasizing that the excitatory neurons in thenear surround are not suppressed, but are facilitated by the far

surround stimulus; this occurs because their local inhibitors, incontrast to the local inhibitors in the center, do not receive suffi-ciently high afferent drive because of the small size of the centralstimulus. Although this modulation of the cortical response pro-file predicted by our model has not been investigated experimen-tally, higher neuronal responses at the borders of stimuli com-

pared with their centers have been observed previously inexperimental data using figure-like stimuli defined by texture(Lee et al., 1998) or color (Friedman et al., 2003).

Inactivation of the feedback pathwayReversible inactivation of the extrastriate cortex had previouslyrevealed a facilitatory influence of FB connections on the RFcenter response of V1 neurons (Sandell and Schiller, 1982; Mig-nard and Malpeli, 1991; Hupe et al., 1998). The question of howinterareal FB connections contribute to suppressive contextualeffects was directly addressed in a series of experiments by Bullierand coworkers using reversible inactivation of extrastriate cortex(Hupe et al., 1998; Bullier et al., 2001). Inactivation of FB con-

nections arising from area MT greatly reduced the suppressiveeffect of surround stimulation onto the center responses of neu-rons in areas V1, V2, and V3 (in area V3, it sometimes even

Figure 5. Contrast-dependent suppression and facilitation from the far surround, in thenetwork model. a, Response (spikes/second) of the center excitatory (E

ctr; purple) and inhibi-

tory(Ictr

;black)neuronstoahigh-contrast(85%)centralstimulusof0.5radius(i.e.,justlarger

than the hsRF of the neuron; Fig. 4a) plotted against the inner radius of a high-contrast (85%)annular stimulus of an 8 outer radius presented together with the central stimulus (stimulusconfiguration shownin b).Otherconventionsare asin Figure4. b,Sameasin a,butforexcita-tory neurons inthe near surround(E

nr).Iconunderthe abscissarepresents thestimulus used in

a and b. c, Same as in a but the configuration of the stimulus used (shown in d) consists of alow-contrast (15%) central stimulus (0.5 radius) presented together with a high-contrast(85%) annular stimulus in the far surround. d, Same as in c, but for excitatory neurons in thenearsurround (E

nr).Iconundertheabscissarepresents thestimulususedin candd. e,Diagram

highlighting, forthe RFregions activatedby thestimulus(redareasin theiconat thebottom),the network components that are active and the major afferent pathways from the activeregions to the center neurons. Conventions are as in Figures 2 and 4df.

Figure6. PopulationactivityprofileoftheexcitatoryneuronsacrossV1.a,Activityprofileforasmall(0.4radius;thickline)andalarge(1.5radius;thinline)high-contrast(85%)stimulus.

Plottedarethefiringrates(spikes/second)oftheexcitatoryneuronsagainsttheirlocationinV1.b,Activityprofileforasmall(0.5radius)high-contrast(85%)centralstimuluspresentedalone(thickline)ortogether(thinline)withahigh-contrast(85%)annularstimulus(3.2and8innerand outerradius,respectively).The cortical location of theneurons werecomputedby convert-

ing the distance in degrees between their RF centers into cortical distance, using a corticalmagnification factor of 2.3 mm/ (see Materials and Methods).



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caused facilitation). The largest reduction in surround suppres-sion was observed for low-saliency stimuli.

In our network model, we can mimic the effect of FB inacti-vationsimply by setting thevalues forthe weights of theinterarealFB connections to zero. To determine the contribution of FBconnections to the center and surround of V1 neurons, we con-sider the change in response of the center excitatory neurons to a

central stimulus presented alone or together with a surroundstimulus,with andwithout activeFB connections,and forcenter-surround stimuli with different saliencies. As in the experimentalstudies (Hupe et al., 1998; Bullier et al., 2001), here we define theresponse change as follows:

100RC RCS

RC,

where RCand RCS are the responses of a neuron to the presenta-tion of the central stimulus alone and of the central stimulusshown together with a surround stimulus, respectively. Stimulussaliency here is defined as Ccenter/Csurround, where Ccenter andCsurround

are the contrasts of the central and surround stimuli,respectively. To obtain stimuli with different saliency, the sur-round stimulus is always presented at low contrast (15%),whereas the contrast of the central stimulus (15%) is changed.Note that the central stimulus is fit to the optimal RF size of theneurons whose response we wish to determine; this is defined asthe stimulus size at peak response, derived from the size-tuningcurve of the neurons, and varies with the contrast of the stimulus(Fig. 4a). Thus, for stimuli of different saliency, the central stim-ulus ranges in size from the hsRF to the lsRF, and therefore alsoincludes part of, or all of, the near surround. Figure 7, a and b,shows the response of the center neurons to a central stimuluspresented either alone or together with a surround stimulus. Theresponse with and without FB is compared under low- (Fig. 7a)

and high-saliency (Fig. 7b) conditions. In the case of the centralstimulus alone,removal of FB leads to a reductionin theresponseof the center neurons, as in the experimental findings (Sandelland Schiller, 1982; Mignard and Malpeli, 1991; Hupe et al., 1998;Bullier et al., 2001). In our model, this follows from the fact that,under normal conditions, FB excites excitatory neurons in thecenter (Fig. 2). In the presence of FB connections, the response ofthe center neurons to the central plus surround stimulus is sup-pressed relative to the response to the central stimulus alone, andthe degree of suppression is greater for high-saliency stimuli. Inthe latter case, the amount of suppression is similar with andwithout FB (Fig. 7b). In contrast,for low-saliency stimuli, there isa significant reduction in the suppression when FB is removed

(Fig. 7a). The latter result is consistent with the experimentalfindings in V1 after inactivation of FB from MT (Bullier et al.,2001). Note that the effects of FB inactivation on the responses ofV1 neurons are quantitatively different from those observed bythe same experimenters in V3 neurons (Hupe et al., 1998). Figure7cshows the response change (as defined above) as a function ofthe stimulus saliency, with and without FB connections. The re-duction in surround suppression when inactivating the FB isclearly strongest for low-saliency stimuli. In our model, the re-duction in suppression is caused by the fact that the suppressiveeffectof the farsurround is mediated by FB connections targetingexcitatory neurons in the near surround (Fig. 2). Removal of FBreduces excitation of near surround neurons and, consequently,

of the center local inhibitors that they contact. The results shownin Figure 7c are qualitatively consistent with the experimentalfindings in V1 (Bullier et al., 2001), and suggest a crucial role for

interareal FB connections in surround suppression and, possibly,figure-ground segregation. Our model predictions, however, dif-fer quantitatively from the data of Bullier et al. (2001), in that thepredicted reduction in surround suppression is restricted to sa-liency values ranging between 1 and 6, which are defined by Bul-lier et al. (2001) as low saliency (stimuli with saliency values15 were defined by these authors as high saliency). Thisquantitative difference between the actual data and our model islikely attributable to the fact that, whereas Bullier et al. (2001)used single bar stimuli in the RF center to drive the cells, in our

model we usethe equivalent of gratings stimuli optimized for sizeat each contrast value (i.e., the size of the hsRF at high contrast,and the lsRF size at low contrast). Thus, our stimuli would driveV1 cells much more vigorously than single bars. In other words,high-saliency bar stimuli used in the experiments are likely todrive V1 neurons much like the lower saliency gratings used inour model, and therefore would push the saliency-response curveof Figure 7ctoward higher saliencies.

Dynamics of contextual effectsRecently, the short-term dynamics of suppressive contextual ef-fects has been investigated in macaque V1 (Bair et al., 2003). Thelatency of suppression induced by stimuli in the far surround was

found to be almost as short as the latency of suppression inducedby stimuli in the near surround. The short delay in the onset ofsuppression induced by far surround stimulation is not consis-

Figure7. Center-surroundinteractionswithandwithoutfeedback,inthenetworkmodel.a,Response (spikes/second) of the center excitatory neurons (E

ctr) to the central stimulus alone

(small grating; 0.68 radius), and to the central stimulus presented together with a surroundstimulus (large grating; surround stimulus of 0.68 inner radius and 8 outer radius) in thepresence of FB (gray bars) or with the FB connections inactivated (white bars). The center plussurround stimuluswas presentedat lowsaliency(38 vs15% contrast;seeResults fordefinitionof saliency). b, same as in a but for a high-saliency center plus surround stimulus (77 vs 15%contrast). The size of the central stimulus was always fitted to the stimulus size at the peakresponse of the size-tuning curve (i.e., the optimal size), which varies with the stimulus con-

trast;thus,in b, thecentralstimulushad a radiusof 0.49,whichis theoptimalstimulus size at77%contrast.c,Responsechange(seeResultsfordefinition)ofthecenterexcitatoryneuronsasafunctionofstimulussaliency,withandwithoutFB.Foreachcontrast,thecentralstimuluswaspresented at the optimal size.



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tent with polysynaptic chains of horizontal connections mediat-ing this effect because of their slow conduction velocity. Theseresults suggest a role for FB connections in the generation ofsuppression from the far surround.

We simulate these experiments and investigate the modelspredictions for these delays. Figure 8a shows the response, andFigure 8b its suppression strength, of the center excitatory neu-rons to a stimulus protocol where first only an optimal centralstimulus, the size of the hsRF, is presented, and then a high-

contrast annular stimulus is flashed in the far surround, after thecenter response reaches its steady state (200 ms). The responsesuppression is strongest for annuli with smaller inner radius(i.e., simulating larger regions of the surround) (Fig. 8d). In ourmodel, the suppression from the far surround is mediated viarelaying excitation from V1 neurons in the far surround to theextrastriate area (viafeedforward connections), and fromtheretotheexcitatory neurons in thenear surround (via FB connections),which in turn excitethe center inhibitory neurons (via horizontalconnections), as in Figure 5e. The predicted responses of excita-tory neurons in the near surround and of the local inhibitoryneurons in the center are shown in Figure 8c. The dynamicsof theresponse of the inhibitory neurons in the center follows the re-

sponse dynamics of the excitatory neurons in the near surround,which drive these inhibitory neurons. Importantly, the latency ofsuppression onset in the response of the center neurons is almost

independent of the inner radius of the annulus (i.e., it is onlyweaklydependent on thelocationof stimulation in thesurround)(Fig. 8e), as observed experimentally (Bair et al., 2003). In themodel, this is because of the suppression being mediated via fastinterareal FB connections, which introduce a delay of only a fewmilliseconds.

DiscussionWe have developed an anatomically and physiologically con-strained recurrent network model of center-surround interac-tions in macaque V1. In addition to V1 horizontal connectionstypically thought to underlie the extraclassical RF of V1 cells, ourmodel includes interareal feedback projections based on recentdata implicating feedback in center-surround interactions (forreview, see Angelucci and Bullier, 2003; Shapley, 2004; Angelucciand Bressloff, 2006). We have used our model to elucidate therelative roles of horizontal and FB connections in generating thespatial summation properties of V1 neurons, their dependenceon stimulus contrast, and the timing and dynamics of center-surround interactions. Our results support the hypothesis thatextrastriate FB connections underlie the modulation of responsesof V1 neurons arising from the far RF surround. We have pro-posed a solution to the puzzle of how excitatory FB connections,targeting almost exclusively excitatory neurons in V1, can gener-ate far surround suppression, namely by targeting excitatory neu-rons in the near surround sending monosynaptichorizontal con-nections to inhibitory neurons in the RF center. While thecurrent debate is centered on whether horizontal or feedbackconnections mediate center-surround effects, our model pro-vides insights into how these two sets of connections interact togenerate responses both within and outside the classical RF.Feedback-mediated iso-orientation surround suppression is alsoconsistent with evidence in primates that FB axons link corticalterritories of broadly similar orientation preference (Angelucci et

al., 2003; Shmuel et al., 2005) (but see Stettler et al., 2002).Our model can account for a wide range of physiological data

in V1, including (1) contrast-dependent spatial summation(Sceniak et al., 1999), (2) size tuning (Sceniak et al., 2001;Cavanaugh et al., 2002a; Levitt and Lund, 2002), (3) far surroundsuppression seen in experiments in which the afferent drive tonear surround neurons is partially withdrawn by interposing ablank between the grating in the RF center and that in the farsurround (Levitt and Lund, 2002), (4) the reduction of RF centerresponse and of surround suppression after inactivation of FBconnections (Hupe et al., 1998; Bullier et al., 2001), and (5) thelack of dependence of the latency of surround suppression on thedistance of the surround stimulus from the RF center (Bair et al.,

2003).As in a previous recurrent network model of center-surround

interactions (Somers et al., 1998), as first suggested by Lund et al.(1995), we assume that stimulation of the near surround modu-lates the response to a center stimulus via horizontal axons tar-geting both excitatory and inhibitory neurons in the center, thelatter having higher threshold and gain than the local excitatoryneurons. The specific sign of the modulatory effect thus dependson the overall level of excitation reaching the local inhibitory andexcitatory neurons, with facilitation predominating for low levelsof excitation and suppression for high levels of excitation.Whereas the latter phenomenon has been observed in electricalstimulation experiments in slices of visual cortex (Hirsch and

Gilbert, 1991; Weliky et al., 1995;Shao and Burkhalter, 1996), thespecific mechanism that we have proposed for its implementa-tion (i.e., the requirement for higher threshold and gain inhibi-

Figure8. Dynamicsandlatencyofsurroundsuppressioninthenetworkmodel. a,Response(spikes/second)ofthecenterexcitatoryneurons(E

ctr)toahigh-contrast(85%)centralstimulus

(0.5 radius) first presented alone and, after 200 ms, together with a high-contrast annularstimulusin thefar surround ofvarying innerradius(2.57), plotted against thetimefromtheonset of the central stimulus. In a c, the arrow points in the direction of the decreasing innerradiusoftheannulus,asindicatedbythestimulusicon. b,Suppressionstrengthoftheresponse

of the center neurons induced by a stimulus in the far surround, plotted against the time fromthe onset of the suppression. Suppression strength is defined as 100*(R

C R

CS/R

C), where R

C

and RCS

aretheresponseof theneuronsto thepresentationof thecentralstimulusalone andofthe central stimulus shown together with the surround stimulus, respectively. c, Responses(spikes/second) of inhibitory neurons in the center (black) and excitatory neurons in the nearsurround (gray) for annuli of varying inner radius. d, Suppression strength of the steady-stateresponse of the center excitatory neurons as a function of the inner radius of the surround

annulus. e, Latency of suppression onset (defined as the time from the onset of the annulus atwhich suppression strength reached 3%) as a function of the inner radius of the surroundannulus.



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tory neurons) represents a specific model prediction partiallysupported by experimental data (see also Materials and Meth-ods). In cortical layer 2/3, high gain interneurons with facilitatingsynapses have been found whose response can only be recruitedin the late phase of the action potential train of their presynapticpyramidal cells (Pouille and Scanziani, 2004; Kapfer et al., 2005).While higher threshold interneurons are an experimentally veri-

fiable hypothesis of our model, these facilitating interneuronscould offer an alternative mechanism to implement the delayedrecruitment of inhibition that is central to our model. An addi-tional modeling assumption not yet demonstrated experimen-tally, but not inconsistent with current data, is that these facili-tating interneurons are driven by horizontal connections, andmore strongly so than local excitatory neurons. This is what al-lows surround suppression rather than facilitation to occur athigh contrast.

Our model extends the lateral model (Somers et al., 1998)by incorporating FB inputs from extrastriate cortex as an addi-tional source of excitation to excitatory neurons in the center andin the near surround. The addition of FB connections allows ourmodel to account for several aspects of center-surround interac-tions that the lateral model could not account for, namely (1) thelack of dependence of the latency of surround suppression on thedistance of the surround stimulus from the RF center (Bair et al.,2003), (2) the effects of FB inactivation on V1 neurons responsesto stimuli in their RF center (Sandell and Schiller, 1982; Mignardand Malpeli, 1991; Bullier et al., 2001) and on their modulationby stimuli in the surround (Bullier et al., 2001), (3) far surroundsuppression (Sceniak et al., 2001; Cavanaugh et al., 2002a; Levittand Lund, 2002), and (4) far surround facilitation (see below).

A novel prediction of our model is that the far surround of V1neurons is not always suppressive, but can facilitate the RF centerresponse when the amount of excitatory input to local inhibitorsis relatively low (e.g., when the center neurons are stimulated

with a low-contrast stimulus in the presence of a stimulus in thefar surround). Facilitation of the center response by iso-orientedstimuli in the surround has been reported typically when thesurround region near the RF center is stimulated (Kapadia et al.,1995; Polat et al., 1998; Chisum et al., 2003). Iso-oriented stimuliin the RF center and far surround, instead, have typically beenshown to be suppressive (DeAngelis et al., 1994; Levitt and Lund,1997, 2002; Sengpiel et al., 1998; Sceniak et al., 2001; Cavanaughet al., 2002b). Iso-orientation far surround facilitation, as pre-dicted by our model, and as confirmed by our recent physiolog-ical studies in macaque V1 (Ichida et al., 2005), is inconsistentwith difference (or ratio) of Gaussians descriptions of contextualeffects in V1 (Sceniak et al., 2001; Cavanaugh et al., 2002a).

Ourmodel nicelycaptures the finding of Bair et al. (2003) thatthe onset latency of surround suppression is nearly independentof the distance of the surround stimulus from the RF center.However, it cannot account for the finding, from the same study,that suppression from the far, but not the near, surround is pre-dominantly transient. Possibly, extending the model to includemechanisms affecting the short-term dynamics of center-surround interactions, such as firing rate adaptation, could revealtransient suppression emerging from the network dynamics.

Our model relies on intracortical inhibition to generate sur-round suppression, and does not include a feedforward compo-nent that may contribute to the suppression. Recent data (Webbet al., 2005) suggest that surround suppression in primate V1 is

likely generated by two concurrently operating mechanisms, anintracortical mechanism that is stimulus tuned and binocularlydriven, and an untuned and monocularly driven mechanism that

may result from the nonorientation-specific surround suppres-sion of LGNafferents (Solomon et al., 2002). Although we plan toexplore the contribution of feedforward mechanisms to center-surround interactionsin V1,in this study we wishedto determinethe contribution of the intracortical component alone.

A recent study in cat V1 concluded, on the basis of inactiva-tion of intracortical inhibition by GABAA receptor antagonists,

that surround suppression in V1 does notdepend on intracorticalinhibition, but results from surround suppression of LGN affer-ents (Ozeki et al., 2004). Because our model relieson intracorticalinhibition, it cannot easily account for this finding. However,although a feedforward component is likely to contribute to sur-round suppression in V1 (see above), it is difficult to fully recon-cile this finding in cat with strong experimental evidence in pri-mates for an intracortical origin of center-surround interactions.Specifically, although surround suppression in V1 is orientation-tuned and mediated dichoptically (DeAngelis et al., 1992; Seng-piel et al., 1997; Webb et al., 2005), it is not orientation-tuned inthe LGN (Solomon et al., 2002; Bonin et al., 2005) (but see Sillitoet al., 1993). Furthermore, geniculocortical afferents in macaqueare not sufficiently extensive to account for the much larger sur-round fields of V1 neurons (Angelucci and Sainsbury, 2006). It ispossible the GABA block performed by these authors was notsufficiently complete to abolish surround suppression.

An alternative mechanism to intracortical inhibition thatcombines the results of Ozeki et al. (2004) with evidence for anintracortical origin of surround suppression is withdrawal of af-ferent excitation (resulting from surround suppression of LGNafferents) to the cortical center neuron and to neurons sendinghorizontal and FB connections to the center. In this scenario, ourmodel architecture (Fig. 2) would still be valid, but withdrawal ofexcitation would replace intracortical inhibition. Withdrawal ofafferent excitation to horizontal and FB neurons projecting to thecenterneuron could also account for the orientation selectivity of

center-surround interactions, which would result from theorientation-specificity of intracortical connections. However, al-though withdrawal of afferent excitation combined with intra-cortical interactions could generate the surround suppressionseen in the spatial summation results of Figure 4a, it is difficult toenvision how such a mechanism could also account for far sur-round suppression at high contrast seen in the annulus experi-ments of Figure 5a. In the latter, the surround stimulus is locatedfar beyond the spatial extent of feedforward connections to thecenter and thus cannot directly affect the response of LGN affer-ents to the RF center; a more plausible explanation is that the farsurround stimulus suppresses the response of the center via in-tracortical feedback.

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