A-MuLV-transformed pre-B cells resultedfrom the activation of Jakl and Jak3 in theabsence of cytokines. Jakl and Jak3 wereactivated in Clone K cells treated with IL-7,whereas in A-MuLV-transformed pre-B celllines, these kinases were constitutively ac-tive (Fig. 3) (1 1). In pre-B cells transformedwith a temperature-sensitive mutant of v-abl,Jakl and Jak3 were active at permissive tem-peratures, and upon a shift to nonpermissivetemperatures, they became inactive (Fig. 3).Thus, in A-MuLV-transformed pre-B cells,the activities of Jakl and Jak3 correlate withthat of the v-Abl protein tyrosine kinase.We next investigated the possible inter-

action between v-Abl and Jakl or Jak3. JakIor Jak3 was immunoprecipitated from ex-tracts of pre-B cells expressing the tempera-ture-sensitive mutant of v-Abl. The v-Ablprotein was detected in JakI and Jak3 im-mune complexes (Fig. 4) (21). Jakl was alsodetected in v-Abl immunoprecipitates (Fig.4B). These observations were confirmedwith several other antibodies to Jakl andJak3 (1 1). We were unable to coimmunopre-cipitate either JakI or Jak3 with the 150-kDc-Abl protein in the non-A-MuLV-trans-formed pre-B cell line Clone K (Fig. 4).

Two models have been proposed for themechanism of growth factor independencein cells transformed by oncogenic forms ofAbl (5, 7, 22, 23). According to one mod-el, v-abl may increase the synthesis of RNAsencoding cytokines. Secreted cytokinescould then bind their receptors and trans-duce their signals. Alternatively, v-Abl mayabrogate the need for cytokines to bind totheir receptors by interacting with compo-nents of cytokine signal transduction path-ways. In an attempt to distinguish betweenthe two models, we assessed the amount ofRNA encoding IL-4 and IL-7 in the pre-Bcells transformed with the temperature-sen-sitive mutant of v-abl. We were unable todetect IL-4 or IL-7 mRNAs by reverse tran-scription-polymerase chain reaction (RT-PCR) in these cells (1 1). In addition, su-pernatants from cultures of A-MuLV-trans-formed pre-B cell lines did not induceGAS binding activities in Clone K cells(1l). Although, we cannot exclude thepossibility that these transformed cellsproduce other cytokines, the lack ofmRNA for IL-4 and IL-7 and our observa-tion that JakI and Jak3 coimmunoprecipi-tate with v-Abl are consistent with thelatter model. Our results suggest that A-MuLV constitutively activates the IL-4and IL-7 signaling pathways. Constitutiveactivation of Jak-STAT signaling has alsobeen observed in T cells transformed withhuman T cell leukemia virus-I (24). Ac-tivation of cytokine signal transductionpathways might be a mechanism by whichsome transforming viruses induce prolifer-ation of their target cells.

REFERENCES AND NOTES

1. J. B. Konopka and 0. N. Witte, Biochim. Biophys.Acta 823, 1 (1985); N. Rosenberg, Semin. CancerBiol. 5, 95 (1994).

2. A. Shields et al., Cell 18, 955 (1979).3. R. J. Prywes et al., J. Virol. 54, 114 (1985); E. T.

Kipreos and J. Y. Wang, Oncogene Res. 2, 277(1988); B. J. Mayer et al., Mol. Cell. Biol. 12, 609(1992); Y. Y. Chen and N. Rosenberg, Proc. Natl.Acad. Sci. U.S.A. 89, 6683 (1992); B. J. Mayer andD. Baltimore, Mol. Cell. Biol. 14, 2883 (1994).

4. A. Engelman and N. Rosenberg, J. Virol. 64, 4242(1990); Mol. Cell. Biol. 10, 4365 (1990).

5. J. H. Pierce et al., Cell 41, 685 (1985); W. D. Cook, B.Fazekas De St. Groth, J. F. A. P. Miller, H. R. Mc-Donald, R. Gabathuler, Mol. Cell. Biol. 7, 2631 (1987).

6. P. W. Kincade, G. Lee, C. E. Pietrangeli, S. Hayashi,J. M. Gimble, Annu. Rev. Immunol. 7,111 (1989).

7. J. C. Young, M. L. Gishizky, 0. N. Witte, Mol. Cell.Biol. 11,854(1991).

8. J. E. Darnell Jr., I. M. Kerr, G. R. Stark, Science 264,1415 (1994); J. N. Ihie et al., Trends Biochem. Sci.19, 222 (1994).

9. S. Pellegrini and C. Schindler, Trends Biochem. Sci.18, 338 (1993).

10. C. A. Whitlock et al., Cell 32, 903 (1983); P. Hunt etal., ibid. 48, 997 (1987); C. A. Whitlock et al., ibid., p.1009.

11. N. N. Danial, unpublished data.12. Y. Y. Chen et al., Genes Dev. 8, 688 (1994).13. The trypan blue uptake test for viability showed that

the viability of pre-B cells transformed with the tem-perature-sensitive mutant of v-abl after being shiftedto nonpermissive temperatures did not decrease.These cells also express the human BCL-2 proteinand can survive more than 2 weeks at nonpermissivetemperatures (12).

14. A. Pernis et al., J. Biol. Chem. 270, 14517 (1995).15. J.-X. Lin et al., Immunity 2, 331 (1995).

16. C. Schindler et al., EMBO J. 13, 1350 (1994).17. P. Rothman et al., Immunity 1, 457 (1994).18. J. Hou et al., ibid. 2, 321 (1995); F. W. Quelle et al.,

Mol. Cell. Biol. 15, 336 (1995).19. J. Hou et a/., Science 265, 1701 (1994).20. M. MOller et al., Nature 366, 129 (1993); 0. Silven-

noinen et al., ibid., p. 583.21. Extracts from 18.81A20 cells were immunoprecipi-

tated with antibodies against either Jak1 (directed toamino acids 797 to 817), Jak3 [directed to aminoacids 1 104 to 1 124], or Abl (directed to the COOH-terminus of the Abl protein), and the immunoprecipi-tates were immunoblotted with a monoclonal anti-body to Abl (Oncogene Science). Analysis by densi-tometry suggested that Jak3 and Jak1 immunopre-cipitates contained - 10 to 20% of the v-Abl proteinsfound in the Abl immunoprecipitations. We find thatthe v-Abl antibody depletes -90% of total cellularv-Abl from the 18.81A20 extracts. Coimmunopre-cipitation of these proteins was not disturbed byincreasing the NaCI concentration to 1 M or by add-ing 0.1 % SDS.

22. W. D. Cook et al., Cell 41, 677 (1985).23. I. K. Hariharan, S. Cory, J. M. Adams, Oncogene

Res. 3, 387 (1988).24. T.-S. Migone et al., Science 269, 79 (1995).25. F. W. Alt et al., Cell 27, 381 (1981).26. 0. R. Colamonici et al., J. Biol. Chem. 269, 3518

(1994).27. We thank C. W. Schindler and S. P. Goff for critical

reading of this manuscript and helpful discussions,N. Rosenberg for the pre-B cell line transformed withthe temperature-sensitive mutant of v-abl, J. Ihie forJakI antibody, J. O'Shea for Jak3 antibody, S. P.Goff for Abl antibody, and S. Gupta for technicalsuggestions. Supported by NIH grants Al 33540-02(P.B.R.), the Pew Scholars Program (P.B.R.), andPfizer Incorporated (P.B.R.).

7 March 1995; accepted 6 July 1995

Lateral Interactions in Primary Visual Cortex:A Model Bridging Physiology and Psychophysics

Martin Stemmler,* Marius Usher,t Ernst Nieburt

Recent physiological studies show that the spatial context of visual stimuli enhances theresponse of cells in primary visual cortex to weak stimuli and suppresses the responseto strong stimuli. A model of orientation-tuned neurons was constructed to explore therole of lateral cortical connections in this dual effect. The differential effect of excitatoryand inhibitory current and noise conveyed by the lateral connections explains the phys-iological results as well as the psychophysics of pop-out and contour completion. Ex-ploiting the model's property of stochastic resonance, the visual context changes themodel's intrinsic input variability to enhance the detection of weak signals.

A characteristic feature of primary visualcortex (V1) in primates is its topographicorganization into columns (1) of neurons

M. Stemmler and E. Niebur, Computation and NeuralSystems Program, 139-74, California Institute of Tech-nology, Pasadena, CA 91125, USA.M. Usher, Department of Psychiatry, University of Pitts-burgh, Pittsburgh, PA 15260, and Department of Psy-chology, Carnegie-Mellon University, Pittsburgh, PA15213, USA.

*To whom correspondence should be addressed.tPresent address: Department of Psychology, Universityof Kent at Canterbury, Cambridge, CT2 7NZ, UK.*Address after 1 November 1995: Krieger Mind/BrainInstitute and Department of Neuroscience, Johns Hop-kins University, 3400 North Charles Street, Baltimore, MD21218, USA.

responding to oriented stimuli within re-stricted regions of the visual field. A neu-ron's classical receptive field (CRF) is de-fined as that region of visual space in whichan individual stimulus will elicit a response.Neuroanatomical studies (2), however,have revealed an extensive network oflong-range horizontal processes that extendfar beyond the representation of the classi-cal receptive field in cortex. While theselateral connections primarily link regions ofcortex whose neurons prefer stimuli withsimilar orientations, the contribution ofthese connections in the processing of vi-sual information remains unclear. Gilbert

SCIENCE * VOL. 269 * 29 SEPTEMBER 1995

-- ------ Imimm ill womill. ll ~ --- ---

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(3), for instance, has suggested that theplexus o)f horizontal coninections providesneurons with information about the visualcontext o)f a stimulus.

The meaning of visual context can heIllustrated with two examples drawn fromncomimhf experience. Suppose the visualscene consists o)f.a large wheat field. Individ-uial stalks of wheat pale in importance comnpared to the wheat field as a whole. Only afeature in the scene that is "different" shouldstand ouit-for example, a horizontal benchamong vertical stalks-which corresponds tothe psychophysical effect o)f "po-u." Theeffect of the visual context in this case is todecrease the redundancy o)f many nearlyietclstimuli. In contrast, if the visual

scene consists of a faded o)r smudged photo-graph, the visual system needs to) use neigh-

boigvisual landmarks to complete incom-plete features, such as broken or interruptedlines in the photograph. The effect of visualcontext here is the enhancement o)f weaks-iiitmuli, rather than the suppression o)f strongstimuli. Both pop- out and enhancement o)fweak signals have been studied in the psy-chophysical literature (4, 5).We now suggest that both context ef-

fects have a neuirophy~silogi),,cal correlate atthe earliest stage of cortical visrial process-ing, namnely in Vi. Recalling that the CRFrepresents a restricted region of visual space,xvxildenote any visual stimulus within

the CIRF o)f a V 1 neuron as a center stimuit-Iris. Stimuli in the nonclassical receptivefields (outside rhe C'RF) will be referred ro assurround stimuilli.

Modulatory influences o)f surround stiml-uli oni the response o)f a cell have beenobevdin ph ilgclexperliments in cats

and primates. For high-contrast, well tunedstimuli inside the (IF, the addition of slim-ilar stimuli outside the CIRF leads to a sup-pressl(ion of the response (6, 7). On the otherhand, when weak (subthreshold) stimuli arepresent insiide the CRF, the addition o)f mul-tiple similar stimuli in the surround producesa1 wxeak increase in the response (6-8).We propose a model that explains the

reversal o)f the context effect by lox'n thenet effect o)f the logrnelateral conniec-tio)ns to be stimulus dependent. Specifically,the effect o)f lateral connections o)n a centercell is excitatory wvhen the cell receives wveakdirect input from the lateral geniculate nu-cleus (LGN), and it is inhibitory wvhen itreceives strongi-- input. This effect is a naturalconi-sequ1ence o)f the impact of noisy input o)nthe c ell's response and the differential char-acteristics o)f excitatory (pyramidi(al) cells andinhibitory neurons.

The model is a single layer netxvor o)f10,000 excitatory anid 10,000 inhibitorycells. Both excitatory and inhbtory cellsrespo~nd to~stimli o4 a preferred orienrarionwvith individual action potenitials. The net-

1878

Fig. 1. A 60 by 60 section of the 100 by 100 layerof cells. The preferred orientations of cells are giv-en by a map that was obtained by optical imagingmethods in macaque monkey (9). The color ofeach pixel corresponds to the preferred orienta-tion of the respective cell (yellow, horizontal;green, 45 red, 90 and blue, 135 ). Power spec-tral analysis of the scaled orientation map yields awavelength K (repeat distance) of 20.6 latticeunits. Superimposed in black are the connectionsmade by cells within a circular patch of radius 3 atthe center. Predominantly excitatory connections(±); predominantly inhibitory connections (-). Fit-ty nonorientation-specific local connections aremade from each excitatory cell onto excitatorycells within a Gaussian distribution of (It= 2.5lattice units. Twenty five connections are madefrom each inhibitory cell onto excitatory cells with-in a Gaussian of uT 1 .0 lattice unit. Fifty connec-tions are made from each excitatory cell onto inhibitory cells In a distributed ring A/,lattice units distant.Long-range connections are made from excitatory cells onto both inhibitory and excitatory cells; thecenters of these connections are denoted by circles. Each excitatory cell makes 15 long-range connec-tions roughly equally onto excitatory and inhibitory cells between K and 2K-, lattice units away. Theorientation preferences of target cells are taken from a Gaussian distribution with SD (-T =22.5' centeredaround the presynaptic cell's preferred orientation.

work map of orientation preferences usedwas measured by optical limaging in mna-caque mnonkey (9) and scaled to the size ofthe model network. Within each orienta-tion hypercolumn (defined as an aggregateof columns spanning all orientation prefer-ences), excitatory cottico-cortical connec-tions domninate for very nearby cells (10),xvhereas inhibitory connections are morewidl spread (1 1). Long-range excitatoryconnections are made onto excitatory aiidinhibitory cells wvith similar orientationpreferences (Fi. 1) (12).

The LGN inpuit is organized in analogyto stlimuli uised in physiological studies ofnonclassical receptive fields. We idealizethe center stimulus as input to cells in oneparticrilar orientation column. Stimulationof the nonclassical receptive field (the sur-round) is simulated by providing input tosurrounding hypercolumns. The surroundstimuluis is oriented either parallel ot or-thogonal to the center stimulus. The LGNinpuit frequency is taken to be linearly re-lated to stimuluis contrast. To test howx themodulation by the suirround depends on thecontrast of the stimulus, wxe v'ary the con-trast (input rate) of the center stlimuiluisxvhile keeping the contrast of the surroundsiuiconstant Fgie2A displays the

effect of surround stimuli on the responserate of a typical neuron wxhose preferredorientation mnarches the center stimuilus.

For high center stimulus contrast, thecell's response is suippressedl by about a fac-tot of 2 for orthogonal surround and bynearly a factor of 3 for parallel surround (6).The stronger suppression of cells tuned tothe same orientation is a physiological cot-relate of pop-out: G3iven the same surroundstimulus, the cells that code for the singular

SCIENCE * VOL. 269 * 29 SFPTEMIBER 1995

(orthogonal) center stimulus respond mnorestrongly.

For lowx center stlimulus contrast, addinga surround stimulus of the same orientationincreases the firing rate of the center cells.As shown in Fig. 2B, this increase lowersthe perceptrial threshiold of detecting astimulus when surrounded by parallel elcmnents ( 13). The time course of the responseis shoxxn in Fig. 2, C' and U), comparing amiodel nicurri to tlic averaged teimporal re-sponse of real neurons.

Our model accounts for the diOfferingeffect of the visual context on the re-sponse to weak and strong stimuli risingphysiologically plarisible mechanismns. Toanalyze the mechanisms responsible forline completion and pop-orit, wee will con-sider separately, the effect of mean netcrirrent and the effect of crirrent flricria-tions contribie by the surround.

The net crirrent fromn the surrorind con-tibrition depends on the level of activationof the cells responding to the center stimrilrus(14). Becarise the spontaneoris backgrorindinprit to inhibitory cells in the mnodel is lowerthan tr) excitatrory cells, inhibitory, cells xvillronly be activated at higher external inpritrates. Ar lowx stimuilris contrasts, the inpritfromt long-range lateral connections wvil1 onlywveakly increase the firing rates of Inhibitorynerirons; only long-range excitatiron remains,resrilting in the line comipletion effect. Be-carise the firiney rate of inhibitory nerironsincreases f-aster than that of excitatory neritons as a frinction of inprit, the surirorindcotrbrition bec )mes frinctionally inhibit

ry as the strengtht- of LGN stimrilation in-creases. The difference between nonorienta-nion- and orientation-specific inhibition isresponsible for the pop-orit effect.

01

100 200 300 400 500 600 700LGN Input frequency

Center stimulus alone

------ Center + surround-- Surround stimulus alone

1~

0 50 100 150 200 250 300Time (ms)

lUBParallel

surround stimulation90 _

80 Psychophysicalrthreshold = 75%

70

60 No surround stimulation

5C0 50 100 150 200 250 300 350 400

LGN Input frequency

Time (100 ms/div.)

Fig. 2. (A) Effect of lateral connections. The average contrast response curves of cells within the classicalreceptive field are displayed as a function of LGN input frequency (which is assumed to vary linearly withcontrast). The central stimulus is always at the preferred orientation. The dashed curve is in the absenceof any additional input. The dotted and solid lines were obtained by adding orthogonal and parallelsurround stimuli, respectively (see text). Surround input enhances the response frequency for low centerinput and suppresses it for high center input. The suppression effect is stronger for same-orientationsurround input than for orthogonal surround. (B) The addition of parallel surround stimulation lowers thedetection threshold of the center stimulus at low input contrasts. Three hundred trials were run undereach stimulus condition; the variable spike count of one cell within 150 ms of stimulus onset was recordedfor each trial. For each surround stimulus condition, the curve represents the probability, given any twotrials, one with a center stimulus, and one without, that the trial with the central stimulus produced morespikes than the trial without a central stimulus. (C) Post-stimulus time histogram. A smoothed averagetemporal response of a single unit was computed over 200 trials in response to three stimulus conditionsin an artificial (simulated) map on a smaller network: (i) input to preferred orientation within the centerhypercolumn (that is, the observed cell) alone (top curve); (ii) simultaneous stimulation of the center at thepreferred orientation and the surround at the same orientation (middle curve); and (iii) only surroundstimulation (at the preferred orientation of the center); no center stimulation (bottom curve). Stimulusonset occurred at the 50-ms mark. This figure should be compared with the experimental results in figure15 of Knierim and Van Essen (6), reproduced in (D) with permission of the Journal of Neurophysiology.

Hirsch and Gilbert (15) have shownthat the analogous experiment of varyingthe strength of horizontal inputs producessimilar results: Threshold microstimulationof the plexus of horizontal fibers results inexcitatory postsynaptic potentials (EPSPs),whereas higher stimulus currents evoke di-synaptic inhibition that can counter andeven overwhelm the laterally evoked EPSP.

As opposed to the common belief thatnoise is detrimental to information process-ing, the addition of noise by the surroundactually improves the neural sensitivity (atlow inputs) by increasing the slope of theresponse firing rate as a function of thecontrast. Using noise to extend the dynam-ic range of a system is known in physics asstochastic resonance (16, 17).

Even when the net mean current con-tributed by the lateral connections is always

inhibitory (independent of the center stim-ulus contrast), the fluctuations contributedby the surround can produce an increase inthe firing rate for low center contrast (18).The differential excitatory and inhibitorycell responses and the response to stochasticinput are thus jointly responsible for thecontext effect.

The context effect mediated by lateralconnections described here can serve as apowerful computational mechanism for bothline completion and pop-out. In the contextof psychophysics, our model predicts thatpop-out decreases for weak stimuli. Anothermodel prediction is that the perceived stim-ulus intensity in the presence of surroundstimuli is enhanced for low stimulus contrastand suppressed for high stimulus contrast;this was confirmed psychophysically (19).Physiological verification of these predic-

SCIENCE * VOL. 269 * 29 SEPTEMBER 1995

tions requires that stimulus contrast be in-cluded as an independent variable in non-classical receptive field studies (20).

REFERENCES AND NOTES

1. V. B. Mountcastle, J. Neurophysiol. 20, 408 (1957);D. Hubel and T. Wiesel, J. Physiol. 148, 574 (1959).

2. C. Gilbert and T. Wiesel, J. Neurosci. 3,1116 (1983);J. S. Lund, Y. Takashi, J. B. Levitt, Cereb. Cortex 3,148 (1993); R. Malach, Y. Amir, M. Harel, A. Grinvald,Proc. Natl. Acad. Sci. U.S.A. 90,10469 (1993).

3. C. Gilbert, Neuron 9, 1 (1992).4. J. Bergen and B. Julesz, IEEE Trans. Syst. Man Cy-

bern. SMC-13, 857 (1983).5. U. Polat and D. Sagi, Vision Res. 33, 993 (1993).6. J. J. Knierim and D. C. Van Essen, J. Neurophysiol.

67, 961 (1992).7. A. Grinvald et a/., J. Neurosci. 14, 2545 (1994).8. U. Polat and A. M. Norcia, Vision Res., in preparation.9. G. Blasdel, J. Neurosci. 12, 3139 (1992).

10. R. Douglas and K. Martin, J. Physiol. 440, 735(1991); R. Douglas, C. Koch, M. Mahowald, K. Mar-tin, H. Suarez, Science 269, 981 (1995).

11. F. Wdrgbtter et al., J. Neurophysiol. 66, 444 (1991);D. C. Somers et al., J. Neurosci. 15, 5448 (1995).

12. We chose the same number of inhibitory cells asexcitatory cells for reasons of computational effica-cy. Each cell's subthreshold membrane potential Vobeys the equation C dV/dt = - V/Ri, + gE(V - VNa)+ g(V - VCI) + 9K (V - VK), where C is the mem-brane capacitance, Rin is the cell's input resistance,gE and g, are excitatory and inhibitory synaptic con-ductances, respectively, gK is a calcium-dependentpotassium conductance, and VNa, Vcl, and VK arethe reversal potentials for sodium, chlorine, and po-tassium, respectively. Spiking is modeled by an inte-grate-and-fire mechanism in which units that reach athreshold voltage are reset by subtracting the differ-ence between the threshold voltage and the restingpotential. The conductance gE relaxes exponentiallyand depends on the number of synaptic events im-pinging on the cell. For unit i, the conductance is T6dgE/dt -g + XjwqE)(Vj threshoid) + wfi°, wherenonzero w.. indicates a connection between units iandj (the synaptic strength is uniform for each syn-apse type), O(V, - Vthreshold) is a shorthand notationfor whether the unit j spiked in the previous millisec-ond, and fP is the external input, which is weighted byw. Local, nonorientation-specific connections serveto implement the massive (excitatory) feedback ofthe canonical microcircuit (10). Inhibitory cells aremodeled as receiving fewer projections from LGNand from cortical areas other than pyramidal cells.Without stimulus input, they are further away fromfiring threshold than the excitatory cells, as indicatedby their lower spontaneous firing rate. For each celltype, the extemal input fi° follows a Poisson distribu-tion and has two components. The first is the stim-ulus-specific LGN input: Given an input orientation of0, this component scales as cos2[2(0 - 0,)], where 0,is the cell's preferred orientation. Spontaneous firingresults from the second component of fP that groupstogether all inputs from outside V1 and LGN. Excita-tory cells are subject to firing rate adaptation as givenby a simple model of the calcium-dependent potas-sium conductance: TK dg,/dt = -9K + Kg(V, -Vthreshold), where K is a positive constant. Spikesarriving from inhibitory cells open conductances withboth additive and multiplicative (shunting) effects.The time course of inhibitory conductances is anal-ogous to that for excitatory conductances: r. dgl/dt-= + X ~whe( Vthreshoid) + w/2fP. By assum

ing that inhibition occurs also on the apical shaft ofthe dendrite, we can model the shunting of excitatorycurrent phenomenologically [following L. F. Abbott,Physica A 185, 343 (1992)] by multiplying the exci-tatory current by a factor proportional to exp(- \',).

13. In analogy to the psychometric curve in two-alterna-tive forced-choice experiments (5), we measured inthe model network the "neurometric curve" (Fig. 2B)on the basis of spike countsofa single cell within theclassical receptive field to verity that the increase infiring results in a lower detection threshold for thecentral target.

1879

- 100

X 80CD

'. 60

40

20

&

200N

~ 150

cw100

0)

50

U

-n.

14. The differential response of excitatory and inhibito-ry cells can be justified physiologically. (i) As a func-tion of the injected current, the firing rate in inhibi-tory cells increases twice as fast as that in pyrami-dal cells [D. A. McCormick, B. W. Connors, J. W.Lighthall, D. A. Prince, J. Neurophysiol. 54, 782(1985)]. (ii) Inhibitory cells in vitro adapt only weakly(ibid.). (iii) Successive excitatory post-synaptic po-tentials (EPSPs) from pyramidal cells onto inhibitoryinterneurons are potentiated, whereas successiveEPSPs from pyramidal cells onto pyramidal cellsare depressed [A. M. Thomson and D. C. West,Neurosci. 54, 329 (1993); A. M. Thomson, J. Deu-chars, D. C. West, ibid., p. 347]. (iv) Long-rangeconnections terminate in the more distal regions ofthe dendritic tree of pyramidal cells [L. J. Caullerand B. W. Connors, in Single Neuron Computation,T. McKenna, J. Davis, Z. Zornetzer, Eds. (Academ-ic Press, San Diego, 1992), pp. 199-299], andconductances in these regions of high dendriticinput resistance are more likely to saturate, or to beshunted [0. Bernander, C. Koch, R. J. Douglas, J.Neurophysiol. 72, 2743 (1994)].

15. J. A. Hirsch and C. D. Gilbert, J. Neurosci. 11, 1800(1991).

16. K. Wiesenfeld and F. Moss, Nature 373, 33 (1995).17. Signal detection depends on the discrimination

between the signal plus noise and noise alone. Tofirst order, the probability of correct classification isproportional to the difference in firing rates f (I) -f (0), where f (I) is the firing rate of the cell in thepresence of a center stimulus, and f (0) is the firingrate in its absence. To second order, detectiondepends on the probability distribution of spikecounts over a finite time window. Given a near-threshold center stimulus and a fixed observationtime window, the detection probability will peak atan optimal noise level; this peak is termed the 'sto-chastic resonance."

18. For an integrate-and-fire cell, additional input vari-ance results in an increased response to weak sub-threshold stimuli, but only a negligible effect onstrong stimuli. Integrate-and-fire models capturemany of the key features of the discharge curves ofreal cells in response to noisy current injections [Z. F.Mainen and T. J. Sejnowski, Science 268, 1503(1995); A. Zador, personal communication]. In thesestudies, it has been shown that increasing the inputvariance linearizes the discharge response curve atlow firing rates, so that the cell fires even in responseto subthreshold input. The fluctuations in the lateralcortico-cortical input current are significant becauseof the irregularity in the spiking of surround cells. Ifthe surround provides a signal of constant varianceand small negative mean, at low stimulus contrastthe variance effect will dominate and lower thethreshold for detection, whereas at high stimuluscontrast the negative mean current will result in thesuppression of redundant information in a high-con-trast texture background.

19. M. Cannon and S. Fullenkamp, Vision Res. 33,1685(1993).

20. D. C. Somers et al. have independently developed amodel similar to ours [D. Somers, S. Nelson, M. Sur,Soc. Neurosci. Abstr. 20, 1577 (1994)] and verifiedsome of these predictions experimentally [D. C.Somers et al., in Lateral Interactions in the Cortex, J.Sirosh and R. Miikkulainen, Eds. (University of Texas,Austin, in press)].

21. Supported by the Howard Hughes Medical Institute,the National Institutes of Mental Health (grantsMH47566 and MH45156), the Office of Naval Re-search, the Air Force Office of Scientific Research,the National Science Foundation, the Center forNeuromorphic Systems Engineering as a part of theNational Science Foundation Engineering ResearchCenter Program, and by the Office of Strategic Tech-nology of the California Trade and Commerce Agen-cy. We thank J. Knierim, K. Grieve, F. Wbrgbtter, andC. Koch for discussions; A. Zador, U. Polat, and M.Sur for access to unpublished data; G. Blasdel forproviding the orientation map underlying Fig. 1; andC. Koch and J. McClelland for a stimulating workenvironment.

3 April 1995; accepted 27 July 1995

An Internal Model for Sensorimotor IntegrationDaniel M. Wolpert,* Zoubin Ghahramani, Michael 1. Jordan

On the basis of computational studies it has been proposed that the central nervoussystem internally simulates the dynamic behavior of the motor system in planning, control,and learning; the existence and use of such an internal model is still under debate. Asensorimotor integration task was investigated in which participants estimated the lo-cation of one of their hands at the end of movements made in the dark and under externallyimposed forces. The temporal propagation of errors in this task was analyzed within thetheoretical framework of optimal state estimation. These results provide direct support forthe existence of an internal model.

The notion of an internal model, a systemthat mimics the behavior of a natural pro-cess, has emerged as an important theoreticalconcept in motor control (1). There are twovarieties of the internal model: (i) forwardmodels, which mimic the causal flow of aprocess by predicting its next state (for ex-ample, position and velocity) given the cur-rent state and the motor command; and (ii)inverse models, which invert the causal flowby estimating the motor command thatcaused a particular state transition. Forwardmodels have been shown to be of potentialuse for solving four fundamental problems incomputational motor control. First, the de-lays in most sensorimotor loops are large,making feedback control too slow for rapidmovements. With the use of a forward modelfor internal feedback, the outcome of anaction can be estimated and used beforesensory feedback is available (2, 3). Second,a forward model is a key ingredient in asystem that uses motor outflow (also calledefference copy) to anticipate and cancel thesensory effects of movement (also called re-afference) (4). Third, a forward model canbe used to transform errors between the de-sired and actual sensory outcome of a move-ment into the corresponding errors in themotor command, thereby providing appro-priate signals for motor learning (5). Simi-larly, by predicting the sensory outcome ofthe action without actually performing it, aforward model can be used in mental prac-tice to learn to select between possible ac-tions (6). Finally, a forward model can beused for state estimation in which the mod-el's prediction of the next state is combinedwith a reafferent sensory correction (7). Al-though shown to be of theoretical use, theexistence of an internal forward model in thecentral nervous system (CNS) is still a topicof debate.

Department of Brain and Cognitive Sciences, Massachu-setts Institute of Technology, Cambridge, MA 02139,USA.*Present address to which correspondence should beaddressed: Sobell Department of Neurophysiology, Insti-tute of Neurology, Queen Square, London WC1 N 3BG,UK.

When we move an arm in the absence ofvisual feedback, there are three basic meth-ods the CNS can use to obtain an estimateof the current state-the position and ve-locity-of the hand. The system can makeuse of sensory inflow (the informationavailable from proprioception), it can makeuse of integrated motor outflow (the motorcommands sent to the arm), or it can com-bine these two sources of information by useof a forward model. To test between thesepossibilities, we carried out an experimentin which participants, after initially viewingone of their arms in the light, made armmovements in the dark. Three experimen-tal conditions were studied, involving theuse of null, assistive, and resistive forcefields. We assessed the participants' internalestimate of hand location by asking them tolocalize visually the position of their handat the end of the movement (8). The bias ofthis location estimate, plotted as a functionof movement duration, shows a consistentoverestimation of the distance moved (Fig.1). This bias shows two distinct phases as afunction of movement duration: an initialincrease reaching a peak of 0.9 cm after 1 sfollowed by a sharp transition to a region ofgradual decline. The variance of the esti-mate also shows an initial increase duringthe first second of movement after which itplateaus at about 2 cm2. External forces haddistinct effects on the bias and variancepropagation. Whereas the bias was in-creased by the assistive force and decreasedby the resistive force, the variance was un-affected.

These experimental results can be fullyaccounted for if we assume that the motorcontrol system integrates the efferent out-flow and the reafferent sensory inflow. Toestablish this conclusion, we developed anexplicit model of the sensorimotor integra-tion process, which contains as special casesall three of the methods referred to above(9). This model is based on the observerframework (7) from engineering in whichthe state estimator (or observer) has accessto both the inputs and outputs of the system.Specifically, the input to the arm is the

SCIENCE * VOL. 269 * 29 SEPTEMBER 1995

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