Functional dissection of circuitry in a neural integrator

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1 ATICES 27 Nture Publishing Group Functionl dissection of circuitry in neurl integrtor Emre Aksy 1,2, Itsso Olsgsti 3, Brett D Mensh 4, obert Bker 5, Mrk S Goldmn 3 & Dvid W Tnk 2 In neurl integrtors, trnsient inputs re ccumulted into persistent firing rtes tht re neurl correlte of short-term memory. Integrtors often contin two opposing cell popultions tht increse nd decrese sustined firing s stored prmeter vlue rises. A leding hypothesis for the mechnism of persistence is positive feedbck through mutul inhibition between these opposing popultions. We tested predictions of this hypothesis in the goldfish oculomotor velocity-to-position integrtor by mesuring the eye position nd firing rtes of one popultion, while phrmcologiclly silencing the opposing one. In complementry experiments, we mesured responses in prtilly silenced single popultion. Contrry to predictions, induced drifts in neurl firing were limited to hlf of the oculomotor rnge. We built network models with synptic-input thresholds to demonstrte new hypothesis suggested by these dt: mutul inhibition between the popultions does not provide positive feedbck in support of integrtion, but rther coordintes persistent ctivity intrinsic to ech popultion. Persistent neurl ctivity refers to sustined dischrge of ction potentils tht long outlsts briefly presented stimulus, thus representing short-term memory of the externl cue. In neurl integrtor circuits, popultions of neurons exhibiting grded levels of persistent ctivity store n ccumultion of the stimulus over time: tht is, temporl integrl. Neurl integrtors hve been chrcterized t mny levels of the nervous system, from brinstem to cortex 1 3. Two functionlly distinct popultions re typiclly observed in neurl integrtors: one tht increses firing rte s the vlue of the stored prmeter rises nd one tht decreses firing rte. In the oculomotor integrtor for horizontl eye movements, where the stored prmeter is representtion of eye position integrted from upstrem velocity commnd signls, one popultion increses its sustined firing rte nd nother decreses its firing rte s the eyes re held t different positions 4 6. In the primte prefrontl cortex (PFC) circuitry for memory of tctile vibrtions, where the stored prmeter is function of tctile frequency nd durtion, the persistent rtes in one popultion increse nd those in second decrese with higher vibrtion frequencies 7,8. This pttern is repeted gin in the lterl intrprietl re (IP) of primtes during motion discrimintion, where the stored prmeter is function of motion strength nd durtion, nd one popultion increses rte nd second decreses rte s evidence for upwrd motion ccumultes 9,1. An importnt nd unresolved question common to these systems is wht re the roles of interctions between these popultions in the process of integrtion nd the genertion of persistent neurl ctivity. To understnd this requires functionl dissection of the circuit, which is the min im of the present work. In the oculomotor integrtor, where the two popultions exhibit greter thn 7% lterliztion 4 6, ntomicl studies hve identified commissurl connections between bilterl integrtor regions 6,11, which re primrily inhibitory 11. Spike-triggered verging studies indicte functionl inhibitory connections between the two popultions 12,13, specificlly between cells with opposite directionl sensitivity. In PFC, cells with opposite frequency tuning hve firing rte fluctutions tht re nti-correlted 14. In IP, electricl stimultion of region composed primrily of one group during low coherence motion ppers to dely the time it tkes the other group to rech decision bound, gin suggesting mutul inhibition 15. These results hve motivted numerous network models tht use positive feedbck medited by mutul inhibition (disinhibition) s key element in generting persistent firing nd enbling integrtion 14, Although the ide of mutul inhibition between opposing popultions s mechnism of persistence hs been populr, other studies hve emphsized role for excittory-network interctions nd/or single-cell mechnisms intrinsic to ech individul popultion. In the oculomotor integrtor, excittory connections hve been suggested by locl xon collterls in mmmlin preprtions 11, by crosscorreltion studies 12,13 nd by intrcellulr nlyses of synptic fluctutions 22. In PFC nd IP, there re locl connections between pyrmidl cells 23 nd suggestive positive correltions in neurl ctivity during working memory 14,24. Theoreticl work hs demonstrted how cells of the sme group coupled through excittory connections cn collectively integrte through positive feedbck 25. In ddition to possible excittory-network mechnisms, there is growing understnding of how persistence could be ugmented by single-cell biophysicl processes such s cholinergiclly medited depolriztions 26,27 1 Deprtment of Physiology nd Biophysics, Weill Medicl College of Cornell University, 13 York Avenue, Box 75, New York, New York 121, USA. 2 Deprtments of Physics nd Moleculr Biology, Princeton University, Wshington od, Princeton, New Jersey 8544, USA. 3 Deprtment of Physics nd Progrm in Neuroscience, Wellesley College, 16 Centrl Street, Wellesley, Msschusetts 2481, USA. 4 Deprtment of Physicl Medicine nd ehbilittion, Hrvrd Medicl School, 125 Nshu Street, Boston, Msschusetts 2139, USA. 5 Deprtment of Physiology nd Neuroscience, New York University Medicl Center, 55 First Avenue, New York, New York 116, USA. Correspondence should be ddressed to E.A. (em24@med.cornell.edu) or M.S.G. (mgoldm2@wellesley.edu). eceived 5 Jnury; ccepted 21 Februry; published online 18 Mrch 27; doi:1.138/nn VOUME 1 [ NUMBE 4 [ API 27 NATUE NEUOSCIENCE

2 ATICES 27 Nture Publishing Group 9 c d e f b Eye te te Equilibrium eft-sccde genertor ight-eye position Conceptul circuit for integrtion eft popultion Time ight ight-sccde genertor ight popultion + Firing rtes Postsynptic ctivtions All Position (deg) nd bistble dynmics introduced with voltge-sensitive chnnels 28,29. Theoreticl work hs shown how such mechnisms my enhnce the robustness of persistent firing to vritions in synptic strength or neuronl excitbility This study seeks to functionlly dissect the role of inhibition between the two popultions from tht of mechnisms intrinsic to the individul popultions by combining phrmcologicl inctivtion with recordings of firing rte dynmics. Experiments were performed in re I of the goldfish oculomotor integrtor for horizontl eye movements 36. This integrtor hs two completely bilterlly seprted popultions of neurons (1% lterliztion). During spontneous sccdes nd fixtions, the eyes re held in more rightwrd positions s cells on the right side of re I increse their firing rtes nd cells on the left side decrese their firing rtes 6 (Fig. 1). The role of inhibition between these two popultions ws determined by complete phrmcologicl inctivtion of one popultion while recording from cells in the opposing one. In second set of experiments, subset of one popultion ws silenced while recording ctivity in the reminder of tht cell popultion. The combined results suggest tht both the left nd right popultions independently integrte over the hlf of the oculomotor rnge in which their neurons re most ctive. We therefore propose tht mutul inhibition does not provide positive feedbck contributing to persistence, but rther subserves coordintion of two hlf-integrtors. The key results were reproduced in bilterl network models bsed on the principle tht the firing rtes of neurons must exceed threshold level before they ffect their postsynptic trgets. Cumultive input k i r,i 2 E th,i 2 ight-eye position (deg) Position (deg) Firing rtes te drift ( s 1 ) 1 Tuned Position Input ight-eye position (deg) Bilterl inctivtion 2 ight-eye 2 position (deg) Unilterl inctivtion ESUTS Disrupting feedbck in trditionl models To motivte our experimentl strtegy, we first present model tht demonstrtes the functionl role trditionlly ttributed to mutul inhibition between opposing popultions in neurl integrtors 14,16 21, nd the chnges in firing rtes predicted by the model fter the inctivtion of subset of the network. Experimentlly, externl commnds to neurl integrtors with two opposing popultions increse the firing rte of one popultion nd decrese the firing rte of the opposing popultion bout bckground firing level 4 7,9 ; in the oculomotor system, this is known s push-pull rrngement of inputs 11,16. Following the offset of commnd, the firing rtes in the popultion tht ws excited by the externl input remin elevted, wheres rtes in the popultion tht ws inhibited by the externl input remin depressed. These fetures suggest tht differences between commnd inputs to the two popultions re integrted nd stored s differences between the sustined ctivities of the two popultions 37. To explin how such sustined differences cn be mintined, most studies hve strted from the ssumption tht, in the bsence of input, neuronl firing rtes rpidly relx to their bckground firing levels. To overcome this relxtion, it hs been ssumed tht there is positive feedbck between neurons such tht sustined recurrent synptic input replces the trnsient externl input to ech popultion. Two pthwys for such feedbck hve been proposed: (i) recurrent excittion in the sme popultion, such tht excited neurons send incresed, nd inhibited neurons send decresed, excittion to ech other, nd ight-eye position (deg) Figure 1 Trditionl model of feedbck for opposing popultions. () Schemtic of spontneous sccdes nd fixtions ccompnying chnges in the firing rte of two integrtor neurons, nd typicl reltionships between rte nd eye position for two right-side () neurons (red) nd two left-side () neurons (blue). (b) Conceptul circuit for n integrtor with opposing left nd right popultions which trnsforms brief eye velocity commnds from sccde genertors into sustined eye position commnds (blck, inhibitory interctions; gry, excittory). Projections crrying tonic bckground signls re not shown. (c) Construction of the cumultive input from the right popultion. Top, fits to experimentl reltionships between firing rte nd eye position for four neurons. The lines were chrcterized by slopes k i nd equilibrium rtes r,i, which set the model neuron gins nd tonic bckground inputs. E th,i, eye position threshold for recruitment of cell i. Middle, model postsynptic ctivtions provided by the presynptic neuronl firing rtes bove (see Methods). Bottom, cumultive input (mgent) t different positions is given by weighted sum of the individul ctivtions, with weights fit to stisfy the tuning condition of eqution (1). Blck trces, intermedite sums clculted from the contributions of the first n ¼ 1,3,1,2 recruited neurons. (d f) Firing rte dynmics in tuned (d) nd disrupted (bilterl, e; unilterl, f) networks. Top, stble positions re mintined wherever the totl feedbck (green), given by the difference between the inputs from the right (mgent) nd left (blue, short dshes) popultions, intersects the line representing the perfect-tuning condition (blck, dshed; eqution (1)). Middle, firing rte of right-side cell. Bottom, drift in rte during fixtions t different eye positions. NATUE NEUOSCIENCE VOUME 1 [ NUMBE 4 [ API

3 ATICES b Complete left inctivtion Eye position ight-eye position drift (deg s 1 ) ight eye 27 Nture Publishing Group eft-eye position drift (deg s 1 ) eft eye Individuls eft hlf ight hlf Chnges in eye position drift during complete left inctivtion control inctivtion c d e f Inctivtion Inctivtion Eye position (deg) Eye position (deg) difference 1 deg Eye position (deg) Figure 2 Eye position fter inctivtion of one popultion. (,b) ight nd left eye positions versus time before () nd fter (b) complete inctivtion of the left popultion. Blue shding highlights positions where the gretest chnges of eye drift during fixtions were seen with inctivtion. nd inctivtion positions re shown with the sme scle nd origin. This control ws tken fter recovery from two prior inctivtions. (c) Drift of eye position in the left nd right oculomotor-rnge hlves, for individul experiments, during control nd inctivtion (top, right eye; bottom, left eye). Points flling in the upper hlf of ech pnel indicte eye drift to the right. Corresponding dt points from n individul experiment re connected by line. (d,e) For the popultion, drift of eye position t different positions during the control (d) nd inctivtion (e) conditions. Gry points correspond to smples over.3 s during fixtion, nd blck points to verges of the gry ones in bins of 5 deg. Gry points on the horizontl boundry of the grph re from dt where the drifts exceeded the limits shown; gry points on the verticl boundry re from dt where the positions exceeded the limits shown. (f) Difference of the men inctivtion from men control dt. The 95% confidence intervls did not extend beyond the dimeter of point. (ii) mutul inhibition between popultions, such tht neurons inhibit the opposing popultion nd thereby disinhibit themselves. In previous bilterl models of the oculomotor neurl integrtor 16 18,2, the positive feedbck pthwy medited by recurrent inhibition between popultions hs been emphsized over the one medited by recurrent excittion within one popultion. These conceptul ides cn be mde explicit in simple mthemticl model for bilterl oculomotor integrtor with the rchitecture shown in Figure 1b. The model incorportes threshold-liner fits to experimentlly mesured reltionships between persistent firing rtes nd eye position 6 (Fig. 1c,top,Supplementry Fig. 1 online). For ech neuron i, the rte r i s function of eye position E ws fit s r i ¼½k i E + r ;i Š + ¼½k i ðe E th;i ÞŠ + ; ð1þ where k i is the slope of the liner reltionship, r,i is the equilibrium firing rte when the eye is t its centrl (equilibrium) position E ¼, nd [ ] + denotes tht r i is zero when the eye position is less thn E th,i. For neurons on the right, the slopes k i were positive, nd for neurons on the left they were negtive. Ech neuron is ssumed to provide input to ll of the other neurons through excittory connections to the sme popultion nd inhibitory connections to the opposing popultion. These connections re chrcterized by postsynptic ctivtion function tht defines the synptic input driven by given level of presynptic firing rte (Fig. 1c,middle). The totl input provided by the entire popultion equls the weighted sum of the individul ctivtions (Fig. 1c, bottom); connection weights were tuned to llow persistent ctivity to be sustined over continuum of firing rtes. 496 VOUME 1 [ NUMBE 4 [ API 27 NATUE NEUOSCIENCE

4 ATICES 27 Nture Publishing Group Firing rte Eye position eft eye ight eye Firing rte Eye position eft eye ight eye b Complete left inctivtion (lidocine) The key concept underlying the tuning of the model is tht the recurrent inputs to ech neuron must precisely support the chnge in firing rte produced by trnsient externl input. To do this, the recurrent inputs must counterct the relxtion to bckground firing rte level tht would otherwise occur. The greter the devition in rte from the bckground level, the greter the chnge in recurrent input tht is necessry to mintin the modified rte. This cn be grphiclly understood by considering right-side neuron: during eye fixtions, the cell receives two types of recurrent input, excittory from the right popultion (Fig. 1d, top, mgent line) nd inhibitory from the left popultion (Fig. 1d, top, blue dshed line). Note tht the excittory input increses with incresing rightwrd position, s it is constructed s the sum of postsynptic ctivtions provided by sequentilly recruited neurons (Fig. 1c, bottom). By similr construction, the mgnitude of the inhibitory input decreses for more rightwrd positions. The totl recurrent input received by the right-side neuron is the difference between the inputs from the right nd left popultions (Fig. 1d, top, green line). In this grphicl frmework, the exct tuning condition for persistent neurl ctivity to be mintined t given position, reflecting the need for greter chnge in input for greter devitions from equilibrium, is tht the totl recurrent input received by the right-side neuron hs to pproximte line with unity slope. When precisely blnced recurrent input is provided t ll positions by fitting to this line (Fig. 1d, top, blck dshed line), the firing rtes between sccdes re stble t ll eye positions (Fig. 1d, middle nd bottom). 8 1 deg Complete left inctivtion (muscimol) 1 Figure 3 Firing rtes in the right popultion fter inctivtion of the left. (,b) Neuronl pnels, firing rtes versus time of right-side cells t fine (gry) nd corse (bold blck, smoothing spline) resolution before () nd fter (b) complete inctivtion of the left popultion (top, lidocine; bottom, muscimol). Blue shding highlights firing rtes where the gretest chnges of rte drift during fixtions were seen with inctivtion. nd inctivtion rtes re shown with the sme scle nd origin. Eye pnels, s in Figure 2,b. Both controls were tken fter recovery from one prior inctivtion. 1 deg Spikes s 1 Spikes s 1 This model mkes testble predictions bout ltertions in neuronl firing rtes when feedbck pthwys re disrupted. When the inputs provided by the right nd left popultions re reduced symmetriclly by 5% (Fig. 1e, top), the totl feedbck is no longer sufficient to chieve integrtion, nd the firing rte of right-side neuron drifts downwrd when bove nd upwrd when below the equilibrium eye position (Fig. 1e, middle nd bottom). This is becuse the recurrent input is too smll t positive positions nd too lrge t negtive positions, resulting in drifts in firing rte tht re proportionl to the difference between the feedbck nd tuned-condition lines. By similr rgument, simulting disruption of the left popultion lone by reducing input from the left by 5% (Fig. 1f top) results in right-popultion neuronl firing rtes tht drift upwrd everywhere to fixed point ner the rightwrd extreme of eye position (Fig. 1f, middle nd bottom). Note tht this deficit is observed throughout the oculomotor rnge, reflecting the loss of inhibitory synptic input t ll eye positions. In the following, we demonstrte experimentlly tht this prediction does not hold; rther, deficits following unilterl inctivtion re observed cross only hlf the oculomotor rnge. We then offer pir of revised models which cn ccount for this result. The experimentl method we used for testing the effects of disruption of pthwys on firing rte dynmics ws to extrcellulrly record from neuron in one popultion, while using lidocine or muscimol to phrmcologiclly inctivte neurons in the opposing popultion or subset of the sme popultion. Estblished methods of microelectrode mpping 6 were used to define the borders of the two opposing popultions. During the experiments, the side tht ws recorded from nd the side tht ws inctivted could differ from one inctivtion to nother; in the interest of clrity the recorded side will lwys be referred to s the right side. Dt from lidocine nd muscimol experiments were first nlyzed seprtely, nd no significnt differences were found; therefore, ll summry dt re pooled. Drifts in eye position with one popultion inctivted To test the role of mutul inhibition between the two bilterlly seprted popultions, we silenced the left popultion completely by injections t the cudl nd rostrl poles of left re I in rpid succession (n ¼ 1 lidocine, n ¼ 11 muscimol, 4 to 6 n totl). We first nlyzed the effects of these injections on fixtion stbility, monitoring drift of the eyes between sccdes. eltive to control (Fig. 2), chnges in the drift pttern of the eyes were pprent within seconds of injection (Fig. 2b). The chnges depended on the eye position, nd the gretest effects occurred during fixtions in the left hlf of the oculomotor rnge (highlighted). Typiclly, ech eye showed incresed drift towrd the equilibrium position E ¼ when in the left hlf of the oculomotor rnge, nd little systemtic chnge in drift compred with control when fixted in the right hlf. Ner the leftwrd extreme of eye position, expnded rnge nd frequent sccdes compensting for strong drift were common. We used two pproches to quntify these observtions. First, nlyzing ech experiment seprtely, we ssessed drift in eye position during individul fixtions nd grouped dt into two bins, one to the left nd the other to the right of the equilibrium position. This llowed us to grphiclly nd sttisticlly nlyze s mny individul experiments s possible, nd highlighted systemtic increse in drift to the right when the eyes were fixted towrd the left (Fig. 2c nd Supplementry Tble 1 online). Next, to better resolve the chnges in drift s function of eye position, we consolidted dt from ll experiments before grouping into position bins of 5 deg width. Drifts were distributed with little position-dependent vrition during control periods (Fig. 2d). During inctivtion, drifts t positions to the left NATUE NEUOSCIENCE VOUME 1 [ NUMBE 4 [ API

5 ATICES Chnges in firing rte drift during complete left inctivtion Individuls eft hlf ight hlf b control c inctivtion d difference 27 Nture Publishing Group Firing rte drift ( s 1 ) Inctivtion Inctivtion of the equilibrium position were redistributed upwrds, indicting systemtic drift to the right, especilly t the extreme (Fig. 2e). We mde direct quntittive comprison between the consolidted control nd inctivted dtsets by clculting men drift over the individul bins. This comprison confirmed tht modifiction in verge drift occurred primrily t leftwrd eye positions (Fig. 2f, 95% confidence intervls fll within the points). Further, the drift dynmics cused by inctivtion were notbly different between the two hlves (Fig. 2f). To the left of the equilibrium position, n pproximtion with liner fit gve slopes (s 1 ) of.6 (s.e.,.1) nd.9 (s.e.,.3) for the right nd left eye, respectively, wheres to the right, liner fits gve slopes of.2 (s.e.,.1) nd.4 (s.e.,.1). These differences in drift between the left nd right hlves pper to be inconsistent with expecttions from the trditionl bilterl integrtor model, where systemtic drifts t the neuronl level were seen t ll positions (Fig. 1f). Firing rte drifts in the opposing popultion To determine how these unexpected chnges in fixtion stbility were linked to chnges t the neuronl level, we nlyzed drifts in the firing rte of the right popultion before nd during complete inctivtion of the left popultion. We used spline-fitting procedure to show the underlying trend in firing rte drift. During spontneous bck-ndforth fixtion behvior in the drk, the firing pttern consisted of series of discrete steps tht ccompnied steps in eye position (Fig. 3). Sccdes towrd the right were typiclly ccompnied by pulses in ight-eye position (deg) firing rte nd leftwrd sccdes by undershoots in rte. In the control period, there ws little systemtic drift of the rtes during fixtions. When we inctivted the left-side popultion, the stbility of neurons on the right chnged rpidly (Fig. 3b). During fixtions directed towrd the right hlf of the field of view, rtes retined stbility similr to the control cse, yet during fixtions in the left hlf, rtes typiclly drifted upwrds (highlighted), coincident with incresed drift in the eyes. Compring rte drift cross cells with widely different equilibrium rtes suggested tht the presence of upwrd drift ws closely ssocited with eye position, nd not with the bsolute levels of firing. Firing rte Eye position eft eye ight eye Firing rte Eye position eft eye ight eye ight-eye position (deg) b ight-eye position (deg) Figure 4 Anlysis of rte drift fter complete left inctivtion. () Men drift in firing rte when the eyes were in ech hlf of the oculomotor rnge for individul experiments recording from right-side cells during control nd inctivtion. Dt points below zero of the ordinte indicte times when firing rte ws decresing, nd points in the upper hlf indicte times when rte ws incresing. Corresponding dt points from n individul experiment re connected by line. (b,c) te drift t different positions during the control (b) nd inctivtion (c) conditions for the popultion. Gry points correspond to smples over.3 s during fixtion; blck points, dshes nd verticl brs correspond to mens, modes nd twice the s.d., respectively, of the gry dt points in bins of 5 deg. Dt on perimeter s in Figure 2d,e. (d) Difference of the verge inctivtion from verge control dt over seprte bins. Verticl blck segments re 95% confidence intervls, mny of which fell within the dimeter of point. Figure 5 Firing rtes in the right popultion fter inctivtion of cudl neurons. (,b) Neuronl pnels, firing rtes versus time of rostrl right-side cells t fine (gry) nd corse (bold blck) resolution before () nd fter (b) inctivtion of cudl cells in the right popultion (top, lidocine; bottom, muscimol). ed shding highlights firing rtes where the gretest chnges of rte drift during fixtions were seen with inctivtion. Eye pnels, s in Figure 2,b. No prior inctivtions occurred before the control in this lidocine experiment. The control in this muscimol experiment ws tken fter recovery from one prior inctivtion. Note tht the cell in this muscimol experiment hd high threshold, so tht when ctive it lmost lwys fired bove its equilibrium rte Cudl right inctivtion (lidocine) Cudl right inctivtion (muscimol) 9 1 deg 8 1 deg Spikes s 1 Spikes s VOUME 1 [ NUMBE 4 [ API 27 NATUE NEUOSCIENCE

6 ATICES Chnges in firing rte drift during cudl right inctivtion Individuls eft hlf ight hlf b control c inctivtion d difference 27 Nture Publishing Group Firing rte drift ( s 1 ) Inctivtion Inctivtion We quntified the chnges in persistent firing in mnner nlogous to tht in the previous section by extending the drift versus position nlysis to the domin of neuronl firing rtes. Seprtely grouping dt from leftwrd nd rightwrd fixtions for individul experiments demonstrted systemtic increse in rte drift when the eyes were fixted towrd the left (Fig. 4 nd Supplementry Tble 2 online). Consolidting dt from ll experiments nd then computing verge drifts in finer bins showed tht during control verge drifts in rte were close to zero, with slight shift downwrd t the most rightwrd eye positions (Fig. 4b). During inctivtion of the left popultion, drifts in the left hlf were redistributed towrd more positive vlues, especilly t the left extreme, with little systemtic chnge in the right Figure 7 Models with ctivtion thresholds cn explin the symmetric effects of unilterl inctivtions. Pnel fetures re s in Figure 1c,d,f. ( c) Asymmetric effects of unilterl disruption in the high-threshold model. () eft, ctivtion functions provided by the rightside neurons of Figure 1c when their firing rtes hd to cross high threshold to trigger postsynptic response. ight, with this high threshold, cumultive input from the right popultion is significnt only in the right hlf of the position rnge. Neurons re rrnged by order of synptic ctivtion. (b,c) Top, totl inputs (mgent, right; blue dshed, left; green, difference) in the tuned (b) nd 5% unilterlly reduced (c) conditions. Middle, firing rtes versus time of right-side (red) nd left-side (blue) cell. The rtes re offset by 4 spikes s 1 verticlly. Bottom, drift in rte of the right-side cell. (d f) Similr symmetry following unilterl disruption (5%) of the bistble-dendrites model. (d) eft, ctivtions provided by 3 of the right-side neurons of Figure 1c when bistble dendrites re introduced. oclized plteus turn on (up rrows) in postsynptic neuron when the presynptic neuron s firing rte exceeds threshold vlue, nd turn off (down rrows) when the rte drops below lower vlue. ight, cumultive input provided by the right side, shown explicitly for the first five ight-eye position (deg) hlf (Fig. 4c). The difference between the inctivtion nd control conditions t ech bin confirmed tht chnges in verge drift primrily occurred in the left hlf of the oculomotor rnge (Fig. 4d). Furthermore, the dependence of the drift on eye position differed between the hlves (Fig. 4d): to the left of the equilibrium position, n pproximtion with liner fit gve slope (s 1 deg 1 ) of.43 (s.e.,.14), wheres to the right the slope ws.5 (s.e.,.11). These differences of firing rte drift in the left nd right hlves mirror the mesured eye drift pttern nd disgree with predictions of systemtic rte drift t ll positions (Fig. 1f). The bove results suggest n unexpected interction between the two opposing popultions. Even though ech popultion exhibits ction neurons to cross the firing rte threshold required to ctivte their postsynptic trgets. (e,f) ecurrent input provided by ech popultion is hysteretic (tuned, e; unilterl, f). Arrows in e (top) indicte trjectory of the input provided by the left popultion s the eyes move left nd then right ight-eye position (deg) ight-eye position (deg) Figure 6 Anlysis of rte drift fter cudl inctivtion. () te drift in seprte oculomotor-rnge hlves during control nd cudl right inctivtion for individul experiments. (b,c) te drift t different positions during the control (b) nd inctivtion (c) conditions for the popultion. Gry points correspond to smples over.3 s during fixtion; blck points, dshes nd verticl brs correspond to mens, modes nd twice the s.d., respectively, of the gry dt points in bins of 5 deg. Dt on perimeter s in Figure 2d,e. (d) Difference of the verge inctivtion from verge control dt. Verticl blck segments re 95% confidence intervls, some of which fell within the dimeter of point. b te drift ( s 1 ) Postsynptic ctivtions Firing rte Tuned High-threshold model 2 2 Position (deg) Position Input 2 2 ight-eye position (deg) Cumultive input c 2 2 Position (deg) All Unilterl inctivtion ight-eye position (deg) d e Dendritic ctivtions te drift ( s 1 ) 1 Firing rte Position (deg) Bistble-dendrites model Tuned Position Input Cumultive input ight-eye position (deg) 1 Position (deg) f Unilterl inctivtion ight-eye position (deg) NATUE NEUOSCIENCE VOUME 1 [ NUMBE 4 [ API

7 ATICES 27 Nture Publishing Group Firing rtes c te, right 4 2 Tuned 2 4 te, left Midline cut potentil dischrge over the entire oculomotor rnge, the effect of the dischrge by one popultion on the other is pprent over only hlf of the oculomotor rnge. When neuron is firing below its equilibrium rte r (Fig. 1c, top), input from the opposing popultion is necessry to mintin persistent firing. In contrst, when neuron is firing bove its equilibrium rte, its persistent firing does not require the opposing popultion. Thus, it ppers tht mutul inhibition is importnt, but in fshion entirely inconsistent with role in generting positive feedbck for persistent neurl ctivity, role which predicted n influence of inhibition t ll positions (Fig. 1f). We propose insted tht the functionl role of this inhibition is to provide feedforwrd input from the high rte to the low rte popultion. A modeling implementtion building on this concept is presented below. Firing rte drifts in the sme popultion The preceding experiments were consistent with the ide tht persistent ctivity t bove-equilibrium rtes is generted in single popultion. To explore this ide further, we silenced position neurons t the cudl pole of right re I while monitoring chnges in the persistent firing of cells t the rostrl pole of the sme side (1- to 2-n stndrd solution injections; n ¼ 8 with lidocine, n ¼ 8 with muscimol; inctivtion of B3% of the popultion on one side; see Supplementry Methods online)). eltive to control (Fig. 5), chnges in firing rte drift were seen only when the eyes were to the right of the equilibrium position (Fig. 5b). The firing rte during rightwrd fixtions typiclly drifted towrd more moderte levels (highlighted), wheres drifts t lower rtes during leftwrd fixtions were reltively unchnged. Compring rte drift cross cells with widely different equilibrium rtes suggested tht the presence of upwrd drift ws closely ssocited with eye position, not with bsolute levels of firing. We nlyzed the individul nd consolidted rte drifts during cudl inctivtion nd sw (i) little systemtic chnge in drift when the eyes were in the left hlf of the oculomotor rnge nd (ii) greter negtive drift tht incresed in mgnitude s the eyes moved frther right from the equilibrium position (Fig. 6 d nd Supplementry Tble 3 online). Furthermore, the dependence of the drift on eye position differed between the hlves: in the left hlf, n pproximtion b d s 2 4 te, left Figure 8 oss of coordintion fter loss of mutul inhibition. (,b) Firing rtes of left-side (blue) nd right-side (red) neuron before () nd fter (b) midline trnsection of the high-threshold model. tes re offset by 6 spikes s 1 verticlly within ech pnel nd ligned between pnels. (c,d) te of left-side neuron versus rte of right-side neuron during fixtions before (c) nd fter (d) midline trnsection. Similr results were found in the bistble-dendrites model. 1 with liner fit gve slope (s 1 deg 1 ) of. (s.e.,.16), wheres in the right hlf the slope ws.34 (s.e.,.12) (Fig. 6d). These prtil inctivtion results re complementry to nd consistent with the results of complete inctivtion of the left popultion. Despite the presence of ction potentil dischrge in popultion throughout the oculomotor rnge, the mechnisms generting persistence in tht popultion re only effective over the hlf of the oculomotor rnge in which its cells exhibit bove-equilibrium rtes; the steps tht re observed t below-equilibrium rtes remin during prtil inctivtion. On the bsis of the results of these two experiments, we propose tht mutul inhibition, rther thn providing positive feedbck in support of persistent neurl ctivity, behves in functionlly feedforwrd mnner to coordinte two popultions tht independently generte persistence over complementry rnges. A new model for integrtors with opposing popultions In the experiments, we found tht bove-equilibrium firing rtes could be stbly mintined following inctivtion of the opposing popultion. ikewise, we found tht below-equilibrium firing rtes could be stbly mintined following inctivtion of portion of the sme popultion. Note tht in both cses stble firing occurs t times when the inctivted popultion would normlly be t below-equilibrium rtes, nd therefore contributing reltively wekly. Thus, in both sets of experiments, the persistent neurl ctivity ppered to be independent of the influence of wek signls from either popultion. To explin these observtions, we generted two new models of this system tht re bsed on the principle tht the firing rtes of neurons must exceed threshold level before they ffect their postsynptic trgets. The first model ssumes tht neuron s firing rte hs to cross high threshold before it cn cuse ny response in other cells. For cells on the right side, this shifts the postsynptic ctivtion reltionship (Fig. 1c, middle) to more rightwrd positions (Fig. 7, left). With the pproprite shift, the cumultive input provided by the right popultion is only significnt in the right hlf of the position rnge (Fig. 7, right). With similr construction for the left popultion, the two sides provide pproximtely complementry inputs (Fig. 7b, top). When the network is ppropritely tuned by fitting the difference to the line of unity slope (Fig. 7b, top), persistent firing rtes re observed t ll eye positions (Fig. 7b, middle nd bottom). Prtil disruption of one popultion cuses decrese in input from its side, but only in the hlf of the eye-position rnge for which its neurons firing rtes re bove the threshold level required to provide inputs to their postsynptic trgets. In the other hlf of the rnge, no loss of input occurs becuse, even before the disruption, neuronl firing rtes re below the ctivtion threshold. When inputs from the right side re decresed by 5% (Fig. 7c, top), firing rte drifts re only observed in the right hlf of the eye-position rnge: right-side neurons show downwrd firing rte drift tht is due to decresed excittion (Fig. 7c, middle nd bottom), nd left-side neurons show upwrd firing rte drift tht is due to decresed inhibition (Fig. 7c, middle).in summry, drift pttern more closely mtching the experimentl findings ws chieved by the introduction of high threshold for postsynptic ctivtion which segregtes input from ech popultion into seprte hlves. The second model uses more moderte thresholds, llowing ech side to contribute input over more thn hlf of the oculomotor rnge, but still produces two functionlly seprte hlves by incorporting bistble postsynptic ctivtion functions 3 32,35 (Fig. 7d, left). An exmple of such bistble process would be dendritic plteu potentil tht permits two stble levels of membrne voltge 28 :resting level when the plteu is off nd depolrized level when the plteu is 5 VOUME 1 [ NUMBE 4 [ API 27 NATUE NEUOSCIENCE

8 ATICES 27 Nture Publishing Group on. In the model, the postsynptic ctivtion in dendrite turns on when the presynptic firing rte exceeds threshold onset vlue, nd turns off when the rte drops below lower offset vlue (Fig. 7d, left). The cumultive input to ny neuron from one popultion is weighted sum of the individul ctivtion functions (Fig. 7d, right). This input forms bnd of vlues tht reflects the history dependence of the individul elements from which it ws constructed (Fig. 7e, top). For exmple, with movement to the left, the recurrent input from the left popultion follows the lower brnch; with movement to the right, the upper brnch; nd for trnsitions between left to right movement, it crosses through the interior of the bnd (Fig. 7e, rrows). As in the non-bistble networks, firing rtes cn be stbly mintined wherever the totl inputs intersect the tuned-condition line. However, in this network, the condition for intersection to occur is less stringent. Stble fixtions cn occur t ny eye position for which the totl input bnd encloses the line of slope unity (Fig. 7e). This provides robustness of the network to smll chnges in input tht distort the shpe of the bnd, but do not destroy the overlp with this line. Biophysiclly, this increse in robustness reflects tht bistble process such s plteu potentil only turns on or off in response to sufficiently lrge chnges in current. The robustness discussed bove mens tht, lthough ech popultion provides input over more thn hlf of the oculomotor rnge, the effect on persistent firing is restricted to be in only hlf of the rnge. For exmple, even with the complete removl of the left input bnd, the remining right bnd still stisfies the tuning condition t ll positions greter thn 2 deg, nerly hlf of the position rnge (Fig. 7e, top). When input from the right popultion is decresed by 5% (Fig. 7f, top), neuronl firing rtes re ltered only over pproximtely hlf the eye-position rnge (Fig. 7f, middle nd bottom). To summrize, we generted drift ptterns similr to the experimentlly mesured ones by endowing ech neuron with bistble processes tht resist smll chnges nd limit the effective contribution of ech popultion to seprte hlves. An interesting prediction of these models is generted when inhibition is removed entirely from the network by simulting midline trnsection of crossing inhibitory fibers between the two popultions. Following this perturbtion, bove-equilibrium firing rtes remin stble becuse ech hlf of the network cn independently sustin such rtes. In contrst, the below-equilibrium firing rtes seen in Figure 8 drift upwrd towrd n equilibrium vlue becuse there is no inhibitory input to prevent such relxtion (Fig. 8b). As result, it is possible for neurons on both sides of the network to simultneously sustin stble firing rtes t bove-equilibrium levels (Fig. 8b). However, becuse the two sides of the network re now decoupled, there is no mechnism for coordinting the popultions. As result, the reltionship between the firing rtes of the popultions vries over time nd is not unique (compre Fig. 8c nd d). This suggests tht inhibitory connections re importnt in coordinting the ctivity between the two popultions. In summry, previous models of neurl integrtors hve suggested tht mutul inhibitory pthwys form positive feedbck loop which cts to mintin persistent neurl ctivity. Our results insted suggest tht, s result of ctivtion thresholds, the mutul inhibitory connections re broken into two functionlly feedforwrd pthwys tht ct in lterntion s the eyes move from side to side. This feedforwrd input serves to yoke the below-equilibrium rtes in one popultion to the bove-equilibrium firing rtes in the opposing popultion, enbling commnd inputs to led to unique network output. DISCUSSION Phrmcologicl inctivtion ws used to functionlly dissect neurl integrtor to determine the roles of (i) inhibition between neuronl popultions with opposing firing rte reltionships nd (ii) persistence mechnisms intrinsic to ech popultion. Chnges in the stbility of eye movements nd firing rtes suggest severl shrp deprtures from the trditionl view of the mechnisms generting persistent ctivity in neurl integrtor. First, mutul inhibition between popultions, rther thn providing mens for positive feedbck, provides effective feedforwrd control, with the bove-equilibrium firing rtes in one popultion being necessry for persistent steps in the below-equilibrium firing rtes of the opposing popultion. Second, mechnisms intrinsic to one popultion, rther thn contributing throughout the entire oculomotor rnge, re only influentil bove the equilibrium rtes. Therefore, we propose the following hypothesis of integrtion in the full bilterl network: coordintion of the lternting pttern of ctivity between the popultions is chieved through inhibition, nd integrtion is independently chieved in ech popultion over different hlves of the eye position rnge. We hve suggested two models by which this could be ccomplished, one with high threshold in the postsynptic ctivtion function nd one with dendritic bistbility, with the common underlying principle being tht the firing rtes of neurons must exceed threshold level before they ffect their trgets. The functionl dissection of integrtor pthwys performed here builds on rich history of inctivtion nd lesion studies in the oculomotor system 18,36, As discussed previously 18,thisbodyof work hs been difficult to interpret in the context of the mechnism of integrtion, nd more directed ssessment hs been needed. Here, deficits in the integrtor were studied for the first time using combined mesurements t the behviorl nd neurl level, directly showing chnges in the cells of interest, rther thn inferring chnges from ltertions in eye movements lone. The extent of inctivtion ws determined by electrophysiologicl recording, gretly limiting the chnce of secondry effects resulting from ny spred of the drug. Network effects were ssessed beginning seconds fter confirmed neurl inctivtion, rther thn hours or dys fter, voiding confusion resulting from the pronounced nd rpid plsticity exhibited by this system 44. The bility to selectively inctivte ll or subset of individul popultions relied on their complete bilterl seprtion, determined in erlier electrophysiologicl recordings 6 ; selective inctivtion voided the difficulties of interprettion encountered when mixtures of cells from both popultions re silenced together. The role of mutul inhibition between popultions hs been clrified by these experiments. The presence of inhibitory interctions between opposing popultions in the goldfish horizontl oculomotor integrtor is supported by n ntomicl study identifying collterls from contrlterlly projecting xons of re I neurons 6,swellsphysiologicl evidence from single-unit cross-correltion studies 13. The upwrd drift observed t below-equilibrium rtes fter contrlterl inctivtion ws consistent with the removl of this inhibitory input, nd on the bsis of experimentl monitoring nd geometric considertions (see Supplementry Methods), it ws unlikely tht direct drug effects on the recorded cells were involved. The persistence tht remined t bove-equilibrium rtes ws more surprising becuse the silenced popultion normlly provided signls throughout the oculomotor rnge. We suggest tht persistence remins over hlf the rnge due to thresholding of recurrent inhibition tht mkes presynptic firing rtes ineffective when they re below their equilibrium vlues. We showed with modeling how such thresholds remove the positive feedbck suggested ntomiclly by mutul inhibitory connections, nd insted estblish two seprte NATUE NEUOSCIENCE VOUME 1 [ NUMBE 4 [ API 27 51

9 ATICES 27 Nture Publishing Group feedforwrd pthwys tht ct in lterntion s the eyes move from side to side. The roles of mechnisms intrinsic to one popultion in generting persistence were lso clrified by this work: we suggest tht, rther thn contributing throughout the entire oculomotor rnge, they re only influentil bove the equilibrium rtes. The criticl question to be ddressed next is wht excittory-network interctions 8,25 nd singlecell mechnisms underlie this persistence. In the goldfish, consensus hs not emerged concerning the existence of mechnisms in either ctegory. Antomicl evidence for recurrent excittion is lcking 6, but physiologicl evidence supports its presence 13,22. With regrd to single-cell mechnisms, direct physiologicl evidence is lcking 22, but correltion studies suggest lck of tight coupling between neurons 45. The downwrd drift observed t bove-equilibrium rtes following cudl inctivtion ws consistent with the removl of excittion from within the popultion, nd the lck of effect t belowequilibrium rtes suggests thresholding process similr to tht noted bove. The two models implemented in this study show how recurrent excittion in n individul popultion cn be medited by thresholding processes to produce persistence only t bove-equilibrium rtes, creting hlf-integrtor. Alterntively, the downwrd drift t boveequilibrium rtes could be explined by the disruption of single-cell mechnisms of persistence, s monitoring of ction potentil shpe on rostrl neurons indicted tht the injection hd direct effect on the recorded neuron in some experiments (see Supplementry Methods). A chllenge for future modeling is to determine whether bilterl network relying solely on single-cell mechnisms for persistence could reproduce the experimentl findings of this study. The new bilterl network models, developed in response to the results of the inctivtion experiments, employed n effective seprtion of function tht occurred t or ner the equilibrium firing rtes of the cells. There re severl lterntives by which this seprtion of function could rise. One possibility would be the suppression of inhibition when cells re firing t bove-equilibrium rtes, perhps through depolriztion-induced suppression of inhibition 46,47. This mechnism hs been shown to be ble to reduce the efficcy of inhibitory responses by up to 9% nd cn retrogrdely ffect input onto neighboring cells. A second possibility is drmtic fcilittion of the excittory inputs when presynptic firing is bove the equilibrium rtes 48. A third possibility, demonstrted here, relies on dendritic bistbility in multiple comprtments. Dendritic plteu potentils could nturlly rise from the voltge dependence of N-methyl-Dsprtte, clcium or persistent sodium conductnces, which hve been identified in oculomotor 29 nd other motor systems 28,49. There re severl wys in which more biophysiclly detiled models could be compred with experiments to distinguish between these mechnisms. Ech mechnism could predict slightly different behvior following inctivtion nd different responses to vestibulr stimultion (see discussion in 32 ). Furthermore, ech mechnism would likely provide different effects on spike trin cross-correltions between cells 13. A notble feture of these inctivtions ws tht neurl persistence ws never totlly bolished; even when the network ws most ffected, firing rte drifts were restricted to vlues tht corresponded to integrtor time constnts between 1 nd 2 s. Computtionl studies of distributed recurrent networks show much shorter time constnts following midline lesion 18 or perturbtions to locl excittion 25. obustness to perturbtions hs been introduced into recurrent networks by intrinsic single-cell properties like plteu potentils 3 32,35,s ws lso done here. Models incorporting bistble processes lone, however, still suffer from severe drift once the ctivity bnd moves fr wy from the line defining perfect integrtion (for exmple, Fig. 7f, top). Hence, in the models introduced here, the time constnt of intrinsic neuronl dynmics governing relxtion ws set to 1 s in order to reproduce the mesured drifts the origin of the slow dynmics is unknown nd needs to be ddressed experimentlly. An importnt question not ddressed by these experiments is wht role inhibition hs in generting the plsticity of integrtion 44.This issue hs been ddressed by following midline trnsection with visul trining (Debowy O.G. et l., Soc. Neurosci. Abstr., 71.2, 21). This work showed tht, following recovery of the integrtor time constnt, the oculr dynmics could be driven to either leky or unstble ptterns with few hours of visul trining. This suggests tht mutul inhibition is not necessry for plsticity of the integrtor either. The functionl dissection of oculomotor integrtion presented here provides results similr to those derived from the study of spinl circuits involved in locomotion. There the mechnism for oscilltory rhythms is combintion of intrinsic plteu events nd excittion in functionl unit of cells on one side of the spinl cord, with inhibition between the hemicords serving to coordinte the independently generted oscilltions 49,5. Together, these results could illustrte common functionl motif for systems of two opposing popultions: cellulr mechnisms nd intrpopultion excittion for essentil dynmics nd interpopultion inhibition for coordintion. It my be useful to consider these s blueprint s studies in PFC nd IP begin to increse our understnding of corticl memory nd decision-mking processes. METHODS Phrmcologicl inctivtion. All experiments were performed in complince with the Guide for the Cre nd Use of bortory Animls ( edu/redingroom/books/lbrts/). Specific protocols were pproved by the Institutionl Animl Cre nd Use Committee of Bell bortories. Phrmcologicl injections (n ¼ 37 nlyzed) were performed on hed-restrined goldfish (n ¼ 17 fish) while monitoring spontneous sccdes nd fixtions, nd re I position neuron ctivity. All dt during control nd inctivtion periods were cquired in the drk to eliminte optokinetic compenstion. Are I is prt of the reticulr column, nd cn be locted using rhombomeric ntomicl indictors 6. Before injections, the extent of re I ws mpped t fine scle by systemticlly serching for position neuron dischrge on grid in the rostrocudl, mediolterl plne. Cell silencing ws chieved by injection of lidocine, used in stndrd concentrtion of 7 mm, or muscimol, GABA A - receptor gonist, used in stndrd concentrtion of 1 mm in rtificil cerebro-spinl fluid. Two electrodes were used during inctivtion experiments (Supplementry Fig. 2 online): one, doubled-brreled, to inject drug nd seprtely record inctivtion, nd the other, single-brreled, to record chnges in firing rte t distl re I site, either on the opposing side or in rostrl region of the sme side. Injections of 1 to 2 n pplied through positive pipette pressure resulted in loss of spiking ctivity t the injection site. The effects on firing rte t the distl site were ssessed over subsequent window 1 to 3 s in length beginning 1 to 6 s fter the injection. ecovery of proximl dischrge begn in 3 to 1 min. Following recovery period of 1 h or more (including t lest.5 h in the light), nother inctivtion could be ttempted, lmost lwys with new monitored neuron (n ¼ 36 neurons; in the nlyzed set, one neuron ws monitored during cudl inctivtion, recovery, contrlterl inctivtion sequence). Injection of rtificil cerebro-spinl fluid lone did not lter the stbility or pttern of firing either loclly or distlly (n ¼ 3; dt not shown). Further detils of the experimentl methods s well s procedures for dt nlysis re presented in the Supplementry Methods. Computtionl modeling. The computtionl model is bilterl dpttion of two previous models 25,32. It consists of two popultions corresponding to the right () nd left () sides of the integrtor with N ¼ 36 neurons ech. The firing rte r,i of neuron i on the right side is governed by the eqution t r dr ;i dt ¼ r ;i + XN j¼1 w ;ij s ;j XN j¼1 w ;ij s ;j + T i + B i ðtþ ð2þ 52 VOUME 1 [ NUMBE 4 [ API 27 NATUE NEUOSCIENCE