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Neuroscience 124 (2004) 305–317

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ELIABLE CONTROL OF SPIKE RATE AND SPIKE TIMING BY RAPIDNPUT TRANSIENTS IN CEREBELLAR STELLATE CELLS

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. J. SUTER AND D. JAEGER*

epartment of Biology, Emory University, 1510 Clifton Road, Atlanta,A 30322, USA

bstract—Granule cell activity in cerebellar cortex directlyxcites Purkinje cells via parallel fibers, but it also inhibitsurkinje cells via cerebellar cortical interneurons. This con-

ribution of inhibitory interneurons to cerebellar cortical pro-essing remains poorly understood. In the present study wexamined the response properties of stellate cells in vitro tonput patterns that may result from granule cell activity inivo. We constructed input waveforms that represented theum of inputs from all individual synapses and applied theseaveforms to the soma of stellate cells during whole cell

ecordings in acute brain slices. The stimulus waveformsontained fluctuations in a broad range of frequencies andere applied at different amplitudes. To determine the con-

ribution of synaptic shunting to stellate cell spike responsese applied the same input waveforms either as a simulatedynaptic conductance using dynamic clamping or as a directurrent injection stimulus. Only the dynamic clamp stimulusas the shunting properties of real synapses, i.e. leads toifferent-sized synaptic current as a function of membraneotential. We found that stellate cells spike with millisecondrecision in response to fast temporal fluctuations in the totalynaptic input. Transient increases in excitatory input fre-uency led to pronounced stellate cell spike responses, in-icating that this pathway may be very responsive to evenmall assemblies of co-activated granule cells. This was ob-erved regardless of whether the input waveform was applieds a conductance with dynamic clamping, or as a directurrent injection. Thus the shunting properties of a conduc-ance input did not play a major role in determining theontrol of precisely timed spiking. In contrast, a more tonic

ncrease in excitatory conductance did not lead to a sus-ained spike response as obtained with prolonged positiveurrent injection. However, even with tonic current injectionhe precision of spiking was lost, as previously observed.verall, the synaptic response function of stellate cells sug-ests that this cell type may pick out transients in granule cellctivity, and may generate precisely timed inhibition of Pur-inje cells during behavior. © 2004 IBRO. Published bylsevier Ltd. All rights reserved.

ey words: cerebellum, granule cells, mossy fibers,nhibition, coding, dynamic clamping.

Corresponding author. Tel: �1-404-727-8139; fax: �1-404-727-880.-mail address: [email protected] (D. Jaeger).bbreviations: AMPA, �-amino-3-hydroxy-5-methylisoxazole-4-propri-nic acid; CIS, current injection stimulus; DCC, dynamic currentlamp; EGTA, ethylene-bis(oxyethylenenitrilo)tetraacetic acid; EPSC,xcitatory postsynaptic current; Esyn, synaptic reversal potential;syn, summed synaptic conductance; HEPES, N-2-hydroxyeth-lpiperazine-N�-2-ethanesulfonic acid; ISIH, interspike-interval

ristogram; PH, precision histogram; Vm, membrane potential.

306-4522/04$30.00�0.00 © 2004 IBRO. Published by Elsevier Ltd. All rights reseroi:10.1016/j.neuroscience.2003.11.015

305

nhibitory interneurons in the cerebellar cortex outnumberurkinje cells by 10:1 in the rat (Korbo et al., 1993), and up

o 50:1 in humans (Andersen et al., 1992). These interneu-ons potently inhibit Purkinje cells via fast GABAergic syn-pses, and even a single inhibitory input can shift theiming of action potentials in Purkinje cells (Hausser andlark, 1997). Because Purkinje cells provide an inhibitoryutput pathway from cerebellar cortex onto the deep cer-bellar nuclei, an increase in interneuron activity will ulti-ately disinhibit the deep nuclei and lead to an increased

erebellar output. Interestingly, Purkinje cells and interneu-ons share the same population of excitatory inputs pro-ided by granule cell axons (Ekerot and Jorntell, 2001) andlimbing fibers (Lemkey-Johnston and Larramendi, 1968;ugihara et al., 1999), as well as inhibitory inputs providedy interneurons and Purkinje cell collaterals (Lemkey-ohnston and Larramendi, 1968). In addition Purkinje cellsnd interneurons share a similar ratio of 20:1 in the numberf excitatory to inhibitory inputs (Lemkey-Johnston andarramendi, 1968). However, stellate cells receive on therder of 100 times fewer synapses than Purkinje cells. Asurkinje cells ultimately are responding to differences in

he level of excitation and inhibition (Jaeger et al., 1997;aeger and Bower, 1999) patterns of network input that

ead to stellate cell spiking but do not strongly excite Pur-inje cells at the same time are likely to code significant

nput events coded by pauses in Purkinje cell activity.An important question with respect to spike responses

riggered in stellate cells by this input situation is howpecific spike responses are to particular input patterns, orhether they code average network activity in a tonic firingode characterized by a mean rate. To allow specific

pike responses, stellate cell spiking would have to beccurately timed with respect to transient inputs from onlysmall number of granule cells. The issue of how input is

eflected in stellate cell spiking has been addressed by twother recent studies, which find conflicting results, how-ver. One report suggests only loose coupling betweenpike timing and excitatory inputs (Mann-Metzer andarom, 2002), whereas a different study showed that evensingle quantum of excitatory transmitter release can lead

o a precise spike response in these neurons (Carter andegehr, 2002).

To shed more light on what stellate cell spike re-ponses code, we systematically compare the control ofpiking between current injection and dynamic clampingith different conductance amplitudes and a wide fre-uency band of conductance fluctuations in the presenttudy. These stimuli were designed to resolve the different
esults found previously using direct current injection withved.

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K. J. Suter and D. Jaeger / Neuroscience 124 (2004) 305–317306

low input fluctuations (Mann-Metzer and Yarom, 2002) orynamic clamping with fast input fluctuations (Carter andegehr, 2002). The principal feature of dynamic clamptimuli not present with current injection stimuli consists ofshunt current that is a function of membrane potential

Robinson and Kawai, 1993; Sharp et al., 1993). Suchhunting can influence synaptic integration significantly byounteracting intrinsic voltage-gated currents (Jaeger andower, 1999) and by acting as a cellular mechanism forain control (Mitchell and Silver, 2003). In addition wexamine the response to discrete bursts in granule cellctivity, such as observed in behaving rats (Hartmann andower, 2001).

EXPERIMENTAL PROCEDURES

lice preparation

ll animal procedures were performed in accord with the Nationalnstitutes of Health Guide for the Care and Use of Laboratorynimals and were approved by the Institutional Animal Care andse Committee of Emory University. All efforts were made toinimize the number of animals used and their suffering. Maleprague–Dawley rats (14–17 days of age) were anesthetized withalothane, decapitated, and the brain was quickly removed. Sag-

ttal slices (250 �m) were cut at 6 °C using a vibratome (Sigmannlectronik, Hueffenhardt, Germany). Slices were stored at room

emperature in artificial cerebrospinal fluid containing (in mM):aCl (124), KCl (3), MgSO4 (1.9), KH2PO4 (1.2.), NaHCO3 (26),aCl2 (2) and glucose (20).

ecordings

orosilicate glass pipettes (1.5 mm outer diameter) were pulled onNarishige ME2 vertical puller, leading to resistances between 7

nd 11 M�. Electrodes were filled with intracellular solution con-aining (in mM): K-gluconate (140), HEPES (10), EGTA (0.2),aC1 (6), MgCl2 (2), NaATP (4), NaGTP (0.4), spermine (0.05),nd glutathione (5), mM cAMP (0.1) and cGMP (0.1). The additionf cyclic nucleotides was observed to result in recordings with

onger stability, and cyclic nucleotides are naturally present inon-dialyzed cells. Stellate cells were visually selected using anlympus 60� water immersion objective by location in the outer

wo-thirds of the molecular layer and by their small size (8–0 �m). Whole-cell recordings were obtained at 32 °C with anxoclamp-2B amplifier. The bridge was balanced and the voltageffset zeroed prior to recording. No correction for junction poten-ials was performed. Only cells with action potentials exceeding 50V were accepted for data collection. When a stable recordingas obtained, the slice medium was changed to include blockersf intrinsic synaptic activity (40 �M picrotoxin and 10 �M CNQX).nly cells that remained stable in spike amplitude and spike

esponse patterns throughout the presentation of the stimulus setere included in the data set described in detail.

pplication of simulated inputs

imulated input was constructed using the GENESIS (http://ww.genesis-sim.org) neural simulator. Unitary synaptic conduc-

ances gsyn (t) were modeled with a dual exponential functionsyn(t)�(A�gmax/(�2�1))(et/�2et/�1), where gmax is the peakonductance and A is a scale factor to achieve this peak conduc-ance for a given combination of rise (�1) and fall (�2) time con-tants. The time constants �1 (�2) used were 0.5 (1.2) ms forxcitation, and 1.0 (10.0) ms for inhibition, matching publishedalues for cerebellar stellate cells (Llano and Gerschenfeld, 1993).
he reversal potentials for excitation and inhibition were set at 0 a
V and 70 mV, respectively. While a reversal potential of AMPAeceptors around 0 mV is generally accepted, there have recentlyeen conflicting results regarding the Cl reversal potential intellate cells determined with perforate patch recordings in vitro,ith one group reporting 82 mV (Carter and Regehr, 2002) andnother 58 mV (Chavas and Marty, 2003). Our value of 70 mV

s a close to that estimated in many cell types, and lies in theiddle between these recent reports for stellate cells. To study the

mpact of input number and input amplitude, we constructed inputatterns that either resulted in a tonic mode of input, or in aiscrete mode with fewer but bigger unitary events (Fig. 1). Tobtain tonic-mode input, we simulated 500 excitatory synapsesnd 20 inhibitory synapses, which is a rough estimate of theumbers of synapses present on stellate cells based on theirurface area and synaptic densities (Lemkey-Johnston and Lar-amendi, 1968; Sultan and Bower, 1998). Excitatory synapsesere activated randomly at a mean frequency of 8 Hz, inhibitoryynapses at 20 Hz, to achieve an overall balance of excitation andnhibition that resulted in a physiological range of stellate cellutput spike rates. Events from each synapse were randomlyistributed using a first-order distribution and a refractory periodf 3 ms. For the discrete input mode we used 50 excitatory andve inhibitory synapses with the same activation rates but largernitary size. The peak amplitudes of unitary inputs were 50 pS forxcitation and 250 pS for inhibition in the tonic mode, and 500 pSor excitation and 1000 pS for inhibition in the discrete mode.hese values were chosen such that the average conductance for

nhibition and excitation was identical for tonic and discrete inputodes, and that the unitary events were very small or large in the

espective mode, but remained in a physiologically plausibleange (Llano and Gerschenfeld, 1993; Kondo and Marty, 1998;arter and Regehr, 2002). In addition, unitary event amplitudesere multiplied by gain factors of 0.5 or 2.0 to create additionaltimuli to examine the effect of input amplitude on spike responsesor tonic and discrete input modes. The tonic mode of many smallnputs from 500 excitatory and 20 inhibitory synapses is simulatinghe condition of all synapses on a stellate cell having a low unitaryeight and being equally active. The discrete mode in contrastould result from few synapses having large unitary weights whileany other synapses are silent. Large unitary inputs could also

esult from populations of perfectly synchronized synaptic inputs.ecause cerebellar stellate cells are very small and electrotoni-ally compact (Kondo and Marty, 1998), the conductance from allynapses can be seen as acting in the same compartment andhus the sum of all individual conductances in a single traceepresents a realistic input to this cell type. This is exactly theondition achieved in dynamic clamping, where the summed syn-ptic conductance is used to inject all simulated synaptic currentIsyn) into the soma using the equation Isyn�Gsyn(VmEreversal).n our tonic input condition the summed conductance trace Gsynas a sizeable constant baseline with added fluctuations (Fig. 1A),hereas in the discrete mode the conductance returns to zero inetween clusters of large individual inputs (Fig. 1B). A comparisonf the power spectrum of the conductance traces for both inputonditions (Fig. 1C, F) shows that in general conductance fluctu-tions are 10 times larger at all frequencies in the discrete mode.he power spectra also show that due to the summation of ran-om input trains the total conductance shows fluctuations in aroad range of frequencies, with a peak at frequencies near 20 Hzhat is more pronounced for inhibition than excitation. Only at highnput frequencies (above 100 Hz) do excitatory fluctuations ex-eed inhibitory ones. In the discrete input mode fluctuations inxcitation are shifted to higher power in relation to inhibition,lthough inhibition still has higher power at frequencies below0 Hz. It is important to note that a broad range of frequencies isresent in both excitation and inhibition for all stimulus conditionsnd that the shape of the frequency spectra of the total excitatory
nd inhibitory input conductances is only weakly dependent on the

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K. J. Suter and D. Jaeger / Neuroscience 124 (2004) 305–317 307

xact number, rates, and unitary sizes of synapses used. There-ore the exact specification of these stimulus parameters is notmportant in determining the frequency composition of the totalonductance waveforms.

In addition to the tonic and discrete random background pat-erns of input we applied brief periods of stimulus transients con-isting of added excitatory input bursts (see Results for details).hese transients were designed to examine the stellate cell output

n response to brief elevations in synaptic conductance that maye associated with a granule cell burst seen in behaving animalsHartmann and Bower, 2001).

To examine the role of synaptic shunting in controlling spikinge applied the identical input waveform either directly as conduc-

ances via the technique of dynamic clamping (Robinson andawai, 1993; Sharp et al., 1993), or as direct current injectiontimuli. The application of dynamic clamping results in synapticurrents that are voltage-dependent in real-time and thus mimicatural synaptic input. The voltage dependent term (a.k.a. drivingorce VmEreversal) needs to be updated fast enough to keep trackf changes in Vm. This was achieved using custom written soft-

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ig. 1. Characterization and comparison of tonic and discrete input mxceeding the level of excitation (black). In addition, large low-amplituS. B. The waveform of the direct CIS computed from the excitatoryonstant driving force of 51 mV for excitation and 19 mV for inhibitionhe power spectrum of inhibition (gray lines) and excitation (black lineebiased, i.e. the effect of the mean baseline conductance is removedhat the y axis is logarithmic, i.e. the power changes 10-fold betweenere about 10 times greater than fluctuations in excitatory conductanc

eads to about a two-fold amplification of excitatory fluctuations in thesterisks in E denotes the current peak resulting from a large excitato

are (for details see Jaeger and Bower, 1999), that calculates the e

riving force of input at a rate of 10 kHz and creates a simulatedynaptic current in real-time. It should be noted that dynamiclamping results in shunting currents like real synaptic input does,.e. any membrane current that drives the cell away from theynaptic reversal potential is counteracted by an increase synapticurrent in the opposing direction. Current injection stimuli (CIS)ere pre-computed from the synaptic conductances by assumingconstant membrane potential of 51 mV. This value of Vm wassed because it generated current stimuli with the same meanmplitude of current as seen with a sample of neurons recordedith dynamic clamping. Because the driving force was indepen-ent of Vm in the CIS condition, these stimuli had no shuntingroperties while retaining the temporal waveforms of the originalynamic current clamp (DCC) stimuli. Fig. 1B, E shows the directIS computed from the conductances shown in Fig. 1B, C for tonicnd discrete input modes respectively.

ata analysis

o examine the reliability of spikes triggered by the input patterns,

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he tonic mode resulted in a baseline conductance of inhibition (gray)tions in inhibition are readily apparent. The horizontal line denotes 0

ibitory conductances shown in (A). It was computed by assuming aperimental Procedures). The horizontal line denotes 0 nA current. C.of input conductances was computed using Matlab. The spectrum is

ted lines show the 95% confidence limits of the power spectrum. Notearks. Thus fluctuations of inhibitory conductance at low frequencies

ver, the larger driving force for excitatory inputs than inhibitory inputsptic current. D–F. Analogous traces for the discrete input mode. The

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imes (mean 4.7 over all recorded cells). Spikes were discrimi-ated from digitized data as events of 0.1–3.0 ms duration cross-

ng a membrane potential threshold of 20 mV. Analyses wereerformed with a customized C-program running under the Linuxperating system or with Matlab (MathWorks, Inc, Natick, MA,SA). Standard spike analysis techniques used include the con-truction of interspike-interval histograms (ISIH), spike raster plotsor multiple repeated trials, and spike triggered averaging. A novelpike precision analysis comparing spike timing across repeatedtimuli was also performed. For each spike, the time difference tohe closest matching spike in all other trials was histogrammedith 1 ms bin width. This histogram of cross-trial spike delays wasormalized by time to create a precision histogram (PH) showinghe rate at which closely aligned spikes occurred. The expectedhance rate of cross-trial spike alignment given the observed ISIistributions was derived by computing an average PH from 50epetitions of shuffling the spike-intervals in the source trials. Wealculated the percentage of spikes for each stimulus conditionhat was accurately aligned across trials within time windows of1 ms and �5 ms by dividing the rate of spikes falling within theseindows in the PH by the overall spike rate of the neuron. This

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ig. 2. Comparison of stellate cell spiking resulting from tonic and discnput amplitudes of 2.0� gain used (see Experimental Procedures). Apikes for repeated presentation of the same conductance stimulus. Thelow. The ISIH are constructed from multiple trials of 10 s of identical inpike PH indicate the alignment of spikes between repeated trials (se

he PH histograms denote the mean (black) and 2 S.D.s (gray) of binere uncorrelated (computed from shuffle predictor; see Experimentals precision above the expected chance level. B. Discrete input mod

pike rate and spike precision in comparison to the tonic input mode.

ethod leads to very similar precision scores as the cross-corre- i

ation method we have employed previously (Gauck and Jaeger,000), but it is improved in the sense that each spike in the sourcerace is only matched to a single spike in the target trace.

RESULTS

he control of spiking by tonic and discrete modesf synaptic input applied with dynamic clamping

n general, spiking of interneurons may affect Purkinje cellsn two distinct ways. A constant rate of interneuron firingeads to a steady baseline of inhibition, which together withxcitatory conductances leads to a situation of balanced

nput that stabilizes Purkinje cell spiking at a particularean rate (Jaeger et al., 1997; Jaeger and Bower, 1999).

n contrast, synchronized activity of inhibitory inputs canead to well-defined pauses in Purkinje cell spiking (Kreinernd Jaeger, 2000). It is thus important to understand how

nterneurons may translate activity of granule cell inputs

Spike rate: 5.6 HzCV = 0.9946.9 % Precision

Spike rate: 19.5 HzCV = 0.8565.6 % Precision

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uctance input patterns in one neuron. Data shown are for the maximalnput mode. Each line in the spike raster plots indicates the timing oftrace of one representative trial recorded in the same neuron is shownity. The mean spike rate and the coefficient of variation (CV) are given.ental Procedures). The bin width is 1 ms. The superimposed lines in

xpected from random spike coincidences if the spikes between trialses). The 46.9.5% indicates the percentage of spikes aligned within �1hown are from the same neuron depicted in (A). Note the increase in

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piking is controlled. As described in the Experimentalrocedures section, we applied either tonic or discrete

nput patterns consisting of both excitation and inhibitionFig. 1) to recorded stellate cells. The responses of re-orded neurons showed subthreshold membrane potentialuctuations reflecting the input pattern (Fig. 2A, B leftanels). Even though the average input conductancesere identical for tonic and discrete inputs, the larger input

ransients of discrete inputs led to sharper deflections inm, and the resulting spike responses were more pre-isely timed and the overall spike rate was higher (Fig. 2B).

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ig. 3. A–C. Spike responses of a sample neuron for increasing amplnd 2.0� correspond to unitary conductances of 250, 500 and 1000 phown are analogous to Fig. 2. Note the increase in spike precision a

his effect was quantified for three different unitary con- c

uctance amplitudes by multiplying the original conduc-ances by 0.5, 1.0, or 2.0 (see Experimental Procedures).

notable difference between tonic and discrete inputodes was that the spike rate increased with increasing

evels of inhibitory and excitatory input conductance in theiscrete input mode, but decreased in the tonic input modeFigs. 3, 4). The decrease of spiking with increased tonicnput was similar to the effects previously observed in deeperebellar nucleus neurons (Gauck and Jaeger, 2000),nd can be explained by the shunting effect exerted byonic conductances. The increase of spike rate with in-

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Spike Rate: 9.98CV = 0.8720.7% Precision

Spike Rate: 14.2 HzCV = 0.9030.3% Precision

Spike Rate: 17.8 HzCV = 1.066.1% Precision

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unitary conductances in the discrete input mode. Gains of 0.5�, 1.0�itation and 500, 1000, and 2000 pS for inhibition, respectively. Tracesrate for increasing input amplitudes.

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nput patterns, because not every individual excitatory in-ut leads to a super-threshold response at low input gains.hus an increase in input amplitudes could lead to more

nput events resulting in super-threshold responses. Evenhough inhibitory inputs were scaled up with the same gainactors, the discrete nature of the inhibitory inputs (Fig. 1D)eaves times of low inhibition available for increased exci-ation to take effect. In addition, at high input amplitudes,ingle depolarizing transients could cause multiple spikes,hich resulted in a distinct 10–20 ms peak in the ISIistogram (Fig. 3C).

The spike timing precision of stellate cells in responseo inputs was determined by applying the same input con-uctances multiple times and scoring the reliability of indi-idual spikes across repeated trials (see Experimental Pro-edures). We found that for all input patterns stellate cellpikes were aligned across trials far above chance levelFigs. 2, 3). At low input amplitudes, however, the precisionf spiking was much lower than at high input amplitudesFig. 3). Discrete inputs led to a higher spike precision thanonic inputs, and for discrete inputs at our high input gainost spikes were reliably timed within �1 ms (Fig. 4C).his finding indicates that stellate cells are well suited to

ransmit synchronized granule cell inputs as preciselyimed output spikes.

Spike-triggered averages of the input conductancesnd applied current were constructed for each stimulusondition to determine the timing of excitatory and inhibi-ory inputs in relation to output spiking (Fig. 5). Surpris-ngly, the relation of inhibitory conductance to spiking wasery similar between tonic and discrete input modes. Inoth conditions, a phasic decrease in the inhibitory inputonductance was observed starting about 20 ms beforehe spike (Fig. 5A, C). This finding indicates that inhibitorynput can make an important contribution to spike timingoth when inhibitory input consists of many small inputs, orewer discrete large inputs. Times of high inhibitory inputonductances prevent spiking, while transient periods of

ow inhibition promote spiking. It should be noted, how-ver, that not every individual spike was necessarily pre-eded by a phasic decrease in inhibition, as the traceshown present the average conductances precedingpikes (taken from three to seven trials with 6 s of dataach). In contrast to inhibition, the role of excitatory inputsas quite different in the tonic and discrete input modes.nly when individual inputs were large, did spikes show aronounced relation to fluctuations in the excitatory inputonductance. The excitatory transients preceding spikesere shorter than inhibitory transients, which is likely re-

ated to the shorter time course of unitary excitatory

nd discrete inputs at the same gain (Kruskal-Wallis test, P�0.05).he rise in precision with increasing gain within each stimulus condi-

ion was also significant (Kruskal-Wallis test, P�0.05), except for theomparison between 0.5 and 1.0 gain for discrete inputs. C. Same as, except for a more precise spike alignment window of �1 ms. At thisrecision level the rise in precision with increasing gain within eachtimulus condition was significant for all comparisons. Note that at theowest input gain the tonic input condition does not lead to a spike
lignment at the �1 ms precision level.
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ig. 4. A. Population data from 10 neurons show a significant in-rease in spike rate for increased input amplitudes (filled circles). Inontrast, the tonic input condition led to a reduction in spike rate forncreased stimulus amplitudes (open circles). B. The percentage ofpikes precisely aligned to the stimulus within a �5 ms window in-reased with increasing stimulus strength for both tonic and discretenput patterns. Asterisks indicate significant differences between tonic

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ostsynaptic currents (EPSCs) than IPSCs. The more pro-ounced responses to excitation shown by the spike-trig-ered average for discrete inputs are matched by a relative

ncrease of excitatory fluctuations for the discrete inputode in the power spectrum of the input conductances

Fig. 1). This match suggests that spikes are triggered byhe largest fluctuations present in the input conductance.mportant additional information is contained in thepike-triggered average of the input current observeduring dynamic clamping (Fig. 5B, D). First, it can beeen that the average baseline input current is around40 pA in all input conditions. In fact, recorded stellate

ells showed intrinsic pacemaker activity in the absencef any hyperpolarizing bias current, as previously re-orted (Hausser and Clark, 1997). The outward currentesulting from our applied conductances indicates thathe intrinsic pacemaker currents depolarize stellate cellseyond the combined reversal potential of inhibition andxcitation, which had an average of 51 mV across theonic stimulus condition. This finding is similar to dy-amic clamping results we previously recorded for Pur-inje cells (Jaeger and Bower, 1999). The tonic andiscrete input mode differed substantially in the transientynaptic current flowing before spike initiation. Tonicnputs triggered spikes when the inhibitory input fluctu-tions led to a small reduction in outward current, with

ittle involvement of transient in excitatory inputs. Thisesembles the situation of synaptic processing in Pur-inje cells (Jaeger and Bower, 1999), which likely re-

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ig. 5. Input conductances triggering spikes for tonic and discrete iverages of input conductances (A) and resulting applied current (B) fC) and resulting applied current (D) for the discrete input mode. Noiscrete mode. The negative current during a spike results from theotential is highly depolarized. The data shown are computed from aeurons showed remarkably near-identical waveforms of spike trigger

eive tonic excitatory and inhibitory input via parallel q

ber activity. In contrast, in the discrete input conditionpiking was initiated in response to individual strongxcitatory inputs preceding the spike by 2–5 ms. Thisffect was more pronounced when individual discrete in-uts were larger (high input gain), and explains the in-reased number of precisely timed spikes in this condition.t should be noted that for all input conditions a peak ofutward synaptic current occurred during the peak of thection potential as during this time the synaptic drivingorce was reversed even for excitatory inputs. This peak inutward synaptic current denotes the synaptic shunt cur-ent induced by the inward sodium current.

he control of spiking by tonic and discrete modesf input applied with direct current injection

urrent injection stimuli (CIS) are different from synapticnput in that changes in membrane potential have no influ-nce on the applied current. In contrast, synaptic input andynamic clamping have a driving force termdf�VmEsyn), which leads to a reduced current as Vmpproaches the synaptic reversal potential (Esyn). As wereviously showed, Esyn for tonic excitation and inhibitionan be combined in a single effective reversal potential,hich is often around 40 to 50 mV for natural inputatterns (Jaeger and Bower, 1999). Thus synaptic currentset significantly larger when Vm deviates from this value.lthough direct current injection is unrealistic for the in vivoituation of neuronal control of spiking, it is the most fre-

40 p

A0.

7 ns

DiscreteC

D

-40 -30 -20 -10 10

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es for small and large unitary conductances. A, B. Spike triggeredic input mode. C, D. Spike-triggered averages of input conductancescitatory inputs play a relatively larger role in triggering spikes in the

hift of driving forces for synaptic conductances when the membraneeuron over repeated stimulus presentations. A comparison betweenges both for conductances and currents (not shown).

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esponses. It is thus valuable to try to isolate the influencef the driving force term of synaptic input on the control ofpiking. The understanding of the involvement of drivingorces in spike control is also very important from a theo-etical point of view, as most simplified neural networkodels compute inputs without such a term. The differ-nces between conductance and current stimuli with re-pect to natural synaptic processing are in need of betternderstanding, especially since conflicting results wereescribed with respect to the control of stellate cell spiking

n previous studies (Carter and Regehr, 2002; Mann-etzer and Yarom, 2002).

To construct CIS that were only different with respecto the driving force term in comparison to dynamic clamptimuli we computed a current trace that results from ourynaptic inputs when the driving forces were fixed (seexperimental Procedures). Application of these currenttimuli to neurons (n�9) generally led to highly precisepiking responses (Figs. 6, 7), with properties that were ineneral similar to responses to dynamic clamp stimuli bothegarding spike rate and precision (Fig. 2 vs. Fig. 6) andith regard to the input waveforms triggering spikes (Fig. 5s. Fig. 8). The lack of a driving force term resulted in aack of synaptic shunt current when the neuron depolarized

100 ms

A Tonic: CIS

B Discrete: CIS

ig. 6. Stellate cell responses to direct CIS computed from tonic andample neuron for the same segment of input waveform as shown foro approximate the same average current and fluctuation level. Note

efore and during an action potential (Fig. 8C, D). Overall a

his situation led to increased spike frequencies duringeriods of depolarization and the appearance of a peak ofhort ISIs even in the tonic input mode (Fig. 6A). In addi-ion, increases in stimulus gain in the tonic input mode didot result in a decrease in spike rate as observed forynamic clamp stimuli (Fig. 4 vs. Fig. 7), presumably be-ause spike initiation was not shunted by the presence ofbaseline synaptic conductance. Nevertheless, the spike-

riggered average showed a very similar relation to a de-reases in inhibition and increases in excitation for current

njection and dynamic clamp stimuli (Fig. 8A, B).

esponses to transient increases in excitation

o understand how cerebellar interneurons may interpretranule cell input signals that drive cerebellar Purkinje cellesponses, we examined the response to brief 50 msncreases in excitatory input rate. This stimulus conditionas motivated by the observation of bursting responses inatches of granule cell layer in anesthetized (Bower andoolston, 1983) and awake (Hartmann and Bower, 2001)

ats. Our simulated granule cell burst input contained anncrease in spike frequency from 8 to 100 Hz for 25% ofxcitatory inputs to a stellate cell. This resulted in an

Spike rate: 14.0 HzCV= 0.8325.9% Precision0.06

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input patterns (see Experimental Procedures). A, B. Response of ainal conductance input in Fig. 2. The same input gain was used (2�)ng appears more bursty for CIS.

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0 ms period. We find that both for the conditions of tonicr discrete background conditions of input, the increase in

nput frequency led to a high-frequency stellate cell spikeesponse, consisting of multiple precisely timed spikesuring the input burst (Fig. 9). However, in the tonic modef baseline inputs, the burst response was more clearlyifferent from baseline activity, as similar high-frequencypike responses occurred throughout discrete input pat-erns due to large baseline fluctuations in conductanceFig. 9B open circles in spike rasters). A smaller burst inputas simulated as 10% of granule cell inputs increasing to00 Hz for 50 ms, and this input also elicited a robusthough weaker stellate cell spike response (Fig. 10A).

hen the same burst input was applied with direct currentnjection (Fig. 10B), it led to a more pronounced spikeesponse. This can be explained by the absence of hyper-olarizing shunt currents during action potentials in theurst and the lack of a reduced driving force for inputsuring membrane depolarization. Even though the cell wasriven to near-maximal firing rates as indicated by a dimin-

shed spike size, spike timing remained precisely alignedo specific features of the input. Overall, the results fromurst stimuli indicate that stellate cells can convey theresence of burst inputs from a small population of granuleells as rapid increases of Purkinje cell inhibition duringerebellar cortical processing.

A recent publication reported that cerebellar stellateells produce ‘jittery’, i.e. imprecise spike responses inesponse to excitation (Mann-Metzer and Yarom, 2002).o examine the cause of the discrepancy between precisepike responses we report in the present study and theirndings, we compared a single smooth excitatory wave-orm as used by Mann-Metzer and Yarom against ourursts of excitatory inputs simulated as AMPA-type EP-Cs. Our results replicate the finding that a single smoothxcitatory input results in a spike response that is precise

n the beginning, followed by a rapid decrease in spikerequency and imprecise spike alignment to the stimulusFig. 11B). Furthermore, this situation was exacerbatedhen the smooth excitatory waveform was applied byynamic clamping rather than by current injection as used

n the Mann-Metzer and Yarom study. Due to the shuntingomponent of the smooth conductance spiking almost en-irely ceased during the prolonged but smooth excitatorynput when applied with dynamic clamping (Fig. 11A).hese findings underscore the significance of rapid tran-ients in the input as triggers for reliably timed spikes, inarticular in the presence of synaptic shunting when aonstant level of input prevents the triggering of spikes.

DISCUSSION

t has become increasingly clear in recent years that theynaptic coding properties of neurons are non-linear anday be quite different for different types of input. Theresence and nature of fluctuations in the input has beenhown to have dramatic consequences in cortical neuronsMainen and Sejnowski, 1995; Harsch and Robinson,

1.0 2.0Gain

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ig. 7. Population data from nine neurons show that the spike rate (A) andrecision (B,C) increase with increasing input amplitude for both tonic andiscrete input patterns with current stimuli (see text). Asterisks indicate sig-ificant differences between tonic and discrete inputs at the same gainKruskal-Wallis test, P�0.05). The increase in precision with increasing gains also significant for each stimulus condition and precision window.
000; Kretzberg et al., 2001). Our own previous work in

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erebellar neurons using dynamic clamping in Purkinjeells (Jaeger and Bower, 1999) or deep cerebellar nucleuseurons (Gauck and Jaeger, 2000) showed that the levelf synchronicity in excitatory or inhibitory input pathwaysetermines the temporal precision and overall rate of out-ut spiking. Furthermore, the presence of a backgroundaseline of synaptic inputs is an important contributor tohe response function to additional synchronous input both

-40 -30 -20 -10 10

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DCC; In

DCC; Ex

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ms

ig. 8. Comparison of spike-triggered averages for conductance stonductance stimulus are shown in black. Spike-triggered conductancomputed from the same conductance traces. The comparison shows dr absence of a driving force (shunting) term. C, D. The spike-triggeretimulus (gray) are superimposed. Note that due to the driving forcepswing of the action potential.

Excitatory Input Burst:

1 nS 20

mV

A

B

excitationinhibition

Discrete background

Tonic background

ig. 9. Responses to transient bursts of inputs embedded in a tonic orrom 8 to 100 Hz input frequency for 50 ms. A. Response to input bursnput conductances for this stimulus. Representative spike responsesriggered by these input bursts in the presence of an inhibitory baselineutside of the burst are indicated by open circles. B. Same burst as in A
ode the added input burst gives a response that is less clearly separated fro
n cerebellar cells (Santamaria et al., 2002; Mitchell andilver, 2003) and cortical pyramidal neurons (Chance etl., 2002; Rudolph and Destexhe, 2003b). In cerebellarortical interneurons one set of input conditions consist-

ng of smooth increases in excitatory current led to theesult that these cells show temporally imprecise spikingatterns (Mann-Metzer and Yarom, 2002). In contrast,

he use of larger quantal inputs led to the observation of

Discrete

0.5

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B

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-40 -30 -20 -10 10

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direct CIS. A, B. Spike-triggered conductances resulting from thelso be computed for the CIS (gray traces) because this stimulus wass in features of the original stimulus that cause spiking in the presenced current resulting from the conductance stimulus (black) and current

current resulting from conductance application reverses during the

-50 mV

50 ms

-50 mV

baseline. Bursts consisted of 25% of excitatory input synapses raiseda tonic baseline input pattern. Inhibitory (gray) and excitatory (black)

neuron are shown, demonstrating the reliable coding and fast spikingtriggered during the input burst are indicated by filled circles and thoseto baseline activity in the discrete input mode. Note that in the discrete

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recise spiking controlled by single inputs (Carter andegehr, 2002). Unfortunately, the accurate temporalroperties and amplitudes of input conductances in vivoemain unknown for cerebellar stellate cells. In vivoecordings of conductances in cortical pyramidal cellsAzouz and Gray, 1999; Rudolph and Destexhe, 2003a)ndicate that the cortical networks are highly active andnduce a large fluctuating background conductance sim-lar to the stimuli employed in the present study. Al-hough in vivo data of cerebellar neural conductancesave not been published, a high level of activity shoulde anticipated as the active cerebral cortical networks
orm a major source of input to cerebellum. p
To shed more light on the coding possibilities of cere-ellar cortical interneurons, we undertook to examine spikeesponses for varying input conditions. Specifically weompared low-variability ‘tonic’ input modes vs. high-vari-bility ‘discrete’ input modes, which may result in differentoding properties as discussed above. In addition, weompared input applied as conductances via dynamiclamping with a direct current injection input using theame input waveform. Both our discrete and tonic modesre plausible patterns of input for stellate cells in vivo, ashe anatomical number of synapses is large enough toupport tonic input activity if a sizeable proportion of inputsre constantly active, or the discrete input mode if multipleynapses were co-activated in temporal patterns or largernitary events were common. Taken together, our inputatterns encompass a wide range of possible temporaluctuation frequencies and amplitudes. We found that ineneral cerebellar stellate cells show temporally precisepike responses with fast rate changes when excitatory

nput bursts occur. The only excitatory input that did notrigger spikes reliably was the condition of a smooth inputaveform with a gradual fall time similar to the conditionsed by Mann-Metzer and Yarom (2002). As reported byarter and Regehr (2002), large unitary excitatory events

eliably triggered spikes. In contrast, the low-variabilityonic input condition led to spike timing that was primarilyontrolled by gaps in the inhibitory inputs. Interestingly,hese response properties were very similar for inputsither applied with dynamic clamping or with a direct cur-ent injection. Because direct current injection is missinghe shunting properties of synaptic input, it appears thatuch shunting is not essential for stellate cell function. This

s in contrast to our observations of the control of spiking byynaptic input in Purkinje cells, where shunting waseeded to counteract strong intrinsic plateau currentsJaeger and Bower, 1999). Synaptic shunting forces Vm toollow the effective reversal potential of excitation andnhibition (Jaeger and Bower, 1999) and thus preventsntrinsic depolarizing currents to determine spike timing.ecause small cell types generally are likely to receive lessf a tonic baseline of synaptic conductance capable ofhunting intrinsic currents than large cells, their activeroperties may be tuned to allow precise responses in thebsence of shunting exerted by baseline synapticonductances.

To understand the contribution of cerebellar corticalnterneurons to cerebellar function, the coding propertiesf single cells need to be placed in the framework ofetwork activity patterns in vivo and possible algorithms ofynaptic plasticity changing the effect of interneuron outputKano et al., 1992; Kreitzer and Regehr, 2001; Hansel etl., 2001; Jorntell and Ekerot, 2002). Unfortunately, ournderstanding of these aspects of cerebellar activity is tooudimentary to assign interneurons a definite place in cer-bellar cortical computation. Nevertheless, our under-tanding of synaptic integration in Purkinje cells, the tar-ets of stellate cell inhibition, allows us to draw some

nferences about the possible functional significance of

40 pA

DCC 10% burst

100 pA

-40 mV

20 mV

A

CIS 10% burstB

ig. 10. Comparison of responses to a burst input applied with DCCr CIS. The burst applied here is weaker than in Fig. 9, and consistedf 10% of excitatory synapses being raised from 8 to 100 Hz for 50 ms., B. Top traces show the applied current, and the spike raster belowhows the response of a representative cell over repeated trials. Theoltage response of a single trial is shown below. The CIS conditionesulted in a more pronounced spike burst than the DCC stimulus.ven when stellate cells were driven to near maximal firing during CIS

nput bursts (see diminishing spike size) the spike timing remainedrecise. Note that the driving force term for DCC stimuli leads to aeduced inward current during depolarized periods and also a negativeurrent transient during action potentials. These shunting properties ofonductance input contribute to a reduced spike response in compar-son to the CIS condition.

recise stellate cell spiking. In Purkinje cells, input even

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rom single stellate cells can lead to spike suppression orhe shift of spike timing (Hausser and Clark, 1997). In theresence of a continuous baseline of inhibitory inputs,urkinje cell spiking is suppressed by synchronized inhib-

tory inputs, and precisely timed spikes are triggered byransient pauses in inhibitory input (Jaeger and Bower,999). We found that bursts in granule cell activity asxpected to occur in vivo (D’Angelo et al., 2001; Hartmannnd Bower, 2001) induced precisely timed bursts of stel-

ate cell activity, and could thus lead to equally preciselyimed pauses in Purkinje cell spiking. Glutamate spillovert stellate cells could result in a further amplification oftellate cell activation by granule cell input (Carter andegehr, 2000; Clark and Cull-Candy, 2002). In turn, the

esulting spike pauses in Purkinje cells could lead to well-imed spike responses in the deep cerebellar nucleiGauck and Jaeger, 2000). This chain of synaptic interac-ions could signify the generation of a motor command, aypothesis originally proposed by Albus (1971). Recentesearch with cerebellar patients has led to the conclusionhat cerebellar function is important to control the preciseiming of motor events down to the millisecond level (Tim-ann et al., 2001; Spencer et al., 2003). Thus, neuralctivity at the output stage of the cerebellum has to berecisely controlled at the millisecond time-scale as well.he present results indicate that cerebellar cortical inter-eurons are well suited to be involved in a precise timinglgorithm. We showed that even for random tonic input, aignificant proportion of stellate cell spiking was preciselyontrolled within a precision window of �5 ms. The preci-ion was enhanced to fall mostly inside a �1 ms window in

20 m

5

50 pA

0.5 nS

-40 mV

A DCC excitationinhibition

ig. 11. Response to a smooth prolonged increase in excitation for Deurons recorded. A. The top traces show the excitatory (black) and in

or a single response. The spike raster plot indicates that this cell genottom a single voltage response is shown. B. The top trace shows the

njection mode. The spike raster indicates that the CIS condition againn both cases the spike timing is imprecise due to the lack of tempora

he presence of larger discrete excitatory inputs. Whether N

he level of �1 ms precision of stellate cell firing is impor-ant in the accomplishment of cerebellar cortical networkomputations is unclear at the present time. Biologicallylausible network simulations could address this question

n the future.The pronounced effect of inhibitory inputs on inter-

eurons firing we observed suggests that precise inter-euron firing may be important in establishing synchro-ized activity in the interneuron network. An exact mech-nism of how this may occur is hard to specify at theresent time due to multiple uncertainties about thenatomical and physiological interconnections between

nterneurons. For instance recent measurements of thehloride reversal potential in stellate cells range from82 (Carter and Regehr, 2002) to 58 mV (Chavas andarty, 2003), which would lead to important differencesith respect to spike triggering by GABAergic inputs.urthermore, stellate cells may be connected by gap

unctions to each other, allowing direct coupling of spikeesponses (Mann-Metzer and Yarom, 1999). Thus, theverall effect of stellate cell interconnections could lead

o an increase in granule cell triggered spike correla-ions, or a limitation in excitatory responses, or both. Theresent results indicate that inhibitory network interac-

ions in cerebellar cortex should be given more attentionn the future. In particular, multi-cell recordings in vivond network modeling are likely important to define the

unctional significance of single cell properties.

cknowledgements—Supported by NIMH R29MH57256 and

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B CIS

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(Accepted 16 November 2003)

reliable control of spike rate and spike … control of spike rate and spike timing by rapid input...

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