Encoding by Response Duration in the Basal Ganglia
Naama Parush,1,2,3 David Arkadir,2 Alon Nevet,2 Genela Morris,1,2 Naftali Tishby,1,3 Israel Nelken,1,4
and Hagai Bergman1,2
1The Interdisciplinary Center for Neural Computation; 2Department of Physiology, Hadassah Medical School; 3The School of Engineeringand Computer Science; and 4Department of Neurobiology, Life Science Institute, Faculty of Sciences, The Hebrew University,Jerusalem, Israel
Submitted 25 March 2008; accepted in final form 6 October 2008
Parush N, Arkadir D, Nevet A, Morris G, Tishby N, Nelken I,Bergman H. Encoding by response duration in the basal ganglia. JNeurophysiol 100: 3244–3252, 2008. First published October 8,2008; doi:10.1152/jn.90400.2008. Several models have suggested thatinformation transmission in the basal ganglia (BG) involves gatingmechanisms, where neuronal activity modulates the extent of gateaperture and its duration. Here, we demonstrate that BG responseduration is informative about a highly abstract stimulus feature andshow that the duration of “gate opening” can indeed be used forinformation transmission through the BG. We analyzed recordingsfrom three BG locations: the external part of the globus pallidus(GPe), the substantia nigra pars reticulata (SNr), and dopaminergicneurons from the substantia nigra pars compacta (SNc) during per-formance of a probabilistic visuomotor task. Most (�85%) of theneurons showed significant rate modulation following the appearanceof cues predicting future reward. Trial-to-trial mutual informationanalysis revealed that response duration encoded reward prospects inmany (42%) of the responsive SNr neurons, as well as in the SNc(26.9%), and the GPe (29.3%). Whereas the low-frequency dischargeSNc neurons responded with only an increase in firing rate, SNr andGPe neurons with high-frequency tonic discharge responded withboth increases and decreases. Conversely, many duration-informativeneurons in SNr (68%) and GPe (50%) responded with a decreasedrather than an increased rate. The response duration was more infor-mative than the extreme (minimal or maximal) amplitude or spikecount in responsive bins of duration-informative neurons. Thus re-sponse duration is not simply correlated with the discharge rate andcan provide additional information to the target structures of the BG.
I N T R O D U C T I O N
One of the most important questions in neuroscience is howneuronal activity represents different aspects of the world(Averbeck et al. 2006; Bialek et al. 1991). It is especiallyinteresting to trace how these representations are conveyedalong a particular neuronal pathway (Barlow 1959; Chechiket al. 2006; Las et al. 2005). To examine encoding schemes inthe basal ganglia (BG), we studied neuronal activity from theexternal part of the globus pallidus (GPe) and the substantianigra pars reticulata (SNr) (central and output nuclei of the BG)and from the dopaminergic neurons of the substantia nigra parscompacta (SNc) (which modulate BG responses; Bar-Gad et al.2003; Bolam et al. 2000; McHaffie et al. 2005) during perfor-mance of a probabilistic visuomotor task (Arkadir et al. 2004;Morris et al. 2004; Nevet et al. 2004). Studying the encodingproperties of neurons in these structures can shed light on theirinterrelated computational roles and how they are imple-mented.
Most BG models use firing rate for information encoding(Albin et al. 1989; Bar-Gad et al. 2003; Berns and Sejnowski1998; DeLong 1990; Wickens 1997). These models rely onphysiological evidence that BG neurons, as in most areas of thenervous system, change their firing rate in response to behav-iorally and emotionally relevant events. However, visual ex-amination of our data suggested that response duration is alsomodulated by behavioral events (Fig. 1; also see additionalexample in Fig. 3G of Morris et al. 2004). This motivated us tostudy the response duration as an encoding strategy of BGneurons that does not necessarily rely on firing rate alone.Response duration is an attractive encoding candidate since itnaturally emerges from models of the basal ganglia that em-phasize the role of information gating in BG processing(Deniau and Chevalier 1985; Hikosaka and Wurtz 1983) andthe recent suggestion of duration encoding of reward omissionby SNc neurons (Bayer et al. 2007). Unlike rate models, gatingmodels emphasize not only the extent of the gate opening(firing rate amplitude) but also the duration of the opening(e.g., response duration). The required processing of responsefeatures, such as response duration, may result in a decrease ininformation. [According to the information processing inequal-ity, processing a response feature can decrease only the amountof information that could be provided by the original feature(Cover and Thomas 1991).] However, in gating models, thenext neuronal station will not be required to estimate theduration, but to make use of the information passed/blockedthrough the gate. We therefore used mutual information (MI)to quantify the modulation of response duration and to compareit quantitatively with other carriers of behavioral information inthe basal ganglia. The MI is a nonparametric measure of theassociation between two variables: in our case, the visualstimuli (with four different future reward conditions) and theneural responses. We used the MI as a measure of the associ-ation, since the MI is able to detect statistical dependencebeyond the linear relationships that are detected by the corre-lation coefficient. When MI � 0, the two variables are statis-tically independent and the neuronal activity does not encodeinformation regarding the cues. When the MI is equal to theentropy of the stimulus set, in our case about 2 bits (dependingon the actual frequency of the four cues, which varied some-what from session to session), the stimuli can be perfectlydistinguished by the response on a single-trial basis. Interme-diate values correspond to intermediate resolvability of the
Address for reprint requests and other correspondence: N. Parush, Depart-ment of Physiology, The Hebrew University–Hadassah Medical School, P.O.Box 12272, Jerusalem, Israel 91120 (E-mail: [email protected]).
The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
J Neurophysiol 100: 3244–3252, 2008.First published October 8, 2008; doi:10.1152/jn.90400.2008.
stimuli by observation of the neural responses on a single-trialbasis (Cover and Thomas 1991).
M E T H O D S
We studied recordings from four monkeys (Y, E, C, and G)engaged in a probabilistic visuomotor task. In each trial one of a setof four visual cues was briefly presented to monkeys in one of twopossible locations on a computer screen. After a constant delay of 2 s,a go signal instructed the monkeys to indicate the cue location bypressing one of two keys. Correct performance was rewarded in aprobabilistic (P � 0.25, 0.5, 0.75, and 1) manner, depending on thepreceding visual cue. The intertrial interval was 4–7 s. Our databaseconsisted of 61 neurons from the GPe (32 from Y and 29 from C), 56neurons from the SNr (10 from Y, 15 from E, and 31 from G), and 109dopaminergic SNc neurons (22 from Y, 71 from E, and 16 from C).The spike waveforms of all neurons were judged to be well isolatedduring the experiment and the longest period with discharge ratestability was selected off-line for each neuron. In addition, in thisstudy we included neurons that were recorded only during �10correct trials of each of the possible trial types. The behavioralparadigm, recording methods, and data preprocessing are detailed inArkadir et al. (2004), Morris et al. (2004), and Nevet et al. (2004).
We limited our study to the first 500 ms of the cue epoch to avoidthe confounding effects of the limb and the reward licking move-ments. To study the response on a trial-by-trial basis, we divided thespike trains into 50-ms bins aligned on the onset of the cue signalindicating future reward prospects. We then characterized the type of
activity in each bin of each trial as either no response, decrease infiring rate, or increase in firing rate by comparing the number of spikesin that bin to baseline activity. The baseline activity was calculated asthe mean spike count (firing rate) during intertrial intervals. In �43%of the responses, we found that the peak response deviated by �2SDs.However, the changes in firing rates could be gradual and, at theresponse onsets and offsets, the changes in firing rates were oftensubstantially smaller. Therefore decreases/increases in firing rate weredetected by changes of �1.25SD with respect to baseline activity.We repeated the same analysis with a criterion at 1.5SD, with noappreciable difference (data not shown). For each trial, we defined theduration of the negative/positive responses as the number of bins inthe longest sequence during the time period between 150 and 500 msafter cue onset (allowing single or multiple gaps of no more than onebin) in which the activity was characterized as either a negative orpositive response. We denoted this time period as the “firing rateresponse period.” Figure 1 depicts this process in five differentneurons from the three BG structures.
We estimated the MI between the cues and the neuronal responsesusing explicit bias-information loss trade-off optimization (Nelkenet al. 2005). Four response features were used: 1) response duration(as defined earlier), 2) the response spike count (the cumulative spikecount during the response period), 3) the extreme response amplitude(maximal for positive response and minimal for negative response),and 4) the total spike count (the cumulative spike count during theentire tested time period; i.e., the period between 150 and 500 ms aftercue onset). Although calculating the total spike count over a shorterepoch could have produced more information in some cases it might
trial
stri
als
trial
s
0 100 500
trial
s
raster plot response type
response duration
time (ms)time (ms) time (ms)
A
B
C
D
p=1.00
p=0.75
p=0.50p=0.25
p=1.00
p=0.75
p=0.50
p=0.25
p=1.00
p=0.75
p=0.50
p=0.25
p=1.00
p=0.75
p=0.50p=0.25
0 100 500 0 100 350
p=1.00
p=0.75
p=0.50p=0.25
E
trial
s
FIG. 1. Neural encoding of reward prospects by response du-ration in the basal ganglia: examples from recordings of 5 neurons.The visual cue was presented at time 0. For each example wepresent the neural recording raster plot in which the trials aresorted by the reward probability (first column from the left); thebinned responses, colored as either average response (white),negative response (gray), or positive response (black) (secondcolumn); and the response duration of each trial (third columnfrom the left). Response durations were calculated for the 150- to500-ms period. The rows show: A: substantia nigra pars reticulata(SNr) neuron: encoding by positive response duration (112 trials).B: SNr neuron: encoding by negative (decreased) response dura-tion (383 trials). C: substantia nigra pars compacta (SNc) neuron:encoding by positive response duration (135 trials). D: externalpart of globus pallidus (GPe) neuron: encoding by negative re-sponse duration (229 trials). E: GPe neuron: encoding by positiveresponse duration (229 trials).
3245BASAL GANGLIA GATING MECHANISMS
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
also have induced a bias between the different events and the differentneural populations. We therefore preferred the conservative choice ofa fixed window that enabled better comparison of the differentpopulations. The 150- to 500-ms time window was chosen since itcaptures the response in the tested data.
In the SNr and GPe, but not in the SNc, neurons responded to thefuture direction of movement indicated by the cue as well as to thereward probability (Arkadir et al. 2004; DeLong et al. 1983; Wich-mann and Kliem 2004). In these structures the information on thereward probability was calculated for each of the movement directionsseparately and averaged according to the number of times eachdirection occurred. Cells were scored as response duration-informa-tive if the information extracted from a cell’s positive or negativeresponse duration on future reward probability was significant whencompared with 150 surrogate shuffled MI values. (The reward prob-abilities were shuffled between trials and the significance of thenonshuffled vs. shuffled results was calculated according to theMann–Whitney test, P � 0.05.) Cells in which �20% of the trialsfrom each type had a positive/negative response were not consideredas responding by positive/negative responses. For each nucleus, wecalculated the mean response duration for duration-informative neu-rons as a function of reward probability.
To check whether the information provided by the other responsefeatures was redundant or synergistic with the information providedby response duration and to evaluate the exclusiveness of the infor-mation to one of the different response features (duration, extremeresponses, or spike count) we used a normalized synergy measure. Insynergistic encoding the information provided by two response fea-tures simultaneously is greater than the sum of the informationprovided by each one of them separately, whereas in redundantencoding the sum of information is smaller than the informationprovided by both features together. The normalized synergy betweenthe information provided by a response feature R1 on a stimulus S andthe information provided by a response feature R2 on S is given by(Schneidman et al. 2003)
This measure tests whether the information provided by R1 is redun-dant or synergistic to the information provided by R2 assuming MI(S;R1, R2) � 0. It ranges from 1 [total synergy, MI(S; R1) � MI(S; R2) �0]; through 0 [MI independent variables, when MI(S; R1) � MI(S;R2) � MI(S; R1, R2)]; to �1 [total redundancy, when MI(S; R1) �MI(S; R2) � MI(S; R1, R2)].
The synergy measurement does not indicate how the information isdistributed between the two variables. For example, norm syn(R1,R2) � �0.5 can occur in a number of scenarios: 1) both variables haveequal amount of information on S and they share two thirds of theirinformation [MI(S; R1) � MI(S; R2) � 0.75MI(S; R1, R2)]. 2) R1 hastwice as much information on S than R2 and all the information R2 hasis already provided by R1 [MI(S; R1) � MI(S; R1, R2) � 2MI(S;R2)]. In a similar way, ambiguity exists when norm syn(R1, R2) � 0(Fig. 2). We therefore also used a different measure: the normalizedcontribution. The normalized contribution of R2 to the information onS carried by the pair R1 and R2 is the fraction of information thatcould not have been extracted without R2
Norm Contrib�R2, R1� �MI�S; R1, R2� � MI�S; R1�
MI�S; R1, R2�
The normalized contribution ranges between 0 (observing R2 does notcontribute to the information in addition to R1) and 1 (none of theinformation could have been extracted without observing R2). Notethat Norm Contrib(S; R1; R2) � Norm Contrib(S; R2; R1) � 1 �Norm Syn(R1, R2), i.e., the sum of the norm.contributions is 0 in casesof total redundancy (all the information could be extracted with eitherone of the parameters alone) and 2 in total synergy (the information istotally dependent on both parameters). In addition, this measurementis not defined when MI(S; R1, R2) � 0.
In summary, we used three measures of the information encoded inthe neuronal responses regarding the prospects of future reward. The
FIG. 2. Mutual information (MI) normalized contributionvs. normalized synergy. Two examples in which the normalizedsynergy measure can describe multiple distributions of MIbetween 2 variables and the normalized contribution measurediscriminates between them: A: norm.synergy � 0 can describethe case in which the information distributes evenly (left) andthe case in which the information provided by one variable isgreater than the other (right). B: norm.synergy � �0.5 candescribe the case in which each variable has the same amount ofinformation and 2/3 is shared by both variables (left); and thecase in which the information provided by one variable is twiceas great as the information provided by the other variable, andthe latter variable does not add information that is not alreadyprovided by the former (right).
3246 PARUSH ET AL.
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
MI is a measure of the information encoded on future reward proba-bility by each of the tested reduced response measures (duration,extreme response, and response count). The normalized synergyquantifies the overlap between information encoded by two reducedmeasures of the responses and the normalized contribution indicateshow much each of the reduced measures contributes to the totalinformation.
R E S U L T S
We reanalyzed recorded data from the GPe, SNr, and SNc offour behaving monkeys to assess the encoding of rewardprobability by response duration.
Most neurons in the SNr, SNc, and GPe showed significantspike rate responses (Mann–Whitney test on spike counts ofresponse bins vs. intertrial-interval bins, P � 0.05) to theappearance of at least one of the four possible cues (Table 1, %responding neurons). Hereafter, we refer to the significantdecreases in firing rate as “negative responses” and the in-creases in firing rate as “positive responses.”
Raster plots of neural recordings revealed that the durationof the single-trial response often varied with the cue (Fig. 1).We used the MI between cue (indicating reward probability)and neuronal response to measure the amount of informationthat could be extracted from the response duration and fromother response features on the probability of future reward. Inall three BG structures, the response duration of many neuronsprovided a significant amount of information on the rewardprobabilities (Table 1, % duration informative neurons).
All of the responding SNc neurons exhibited positive re-sponses (increase in discharge rate) to the cue and thus all ofthe duration-informative neurons in the SNc showed a positiveresponse. However, twice as many of the SNr duration-infor-mative neurons (68%) responded with a negative rather than apositive response, whereas in the GPe the duration-informativeneurons distributed evenly between positive and negative re-sponses.
The average response duration in SNr and SNc duration-informative neurons exhibited monotonic increases/decreaseswith the probability of future reward (Fig. 3). Such behaviorswere not observed in the average response duration of GPeduration-informative neurons. The mean duration of the SNcpositive responses was longer for high reward probabilities andshorter for low reward probabilities (one-way ANOVA, P �0.01). The mean response duration in SNr neurons presented adifferent behavior from the SNc responses. Whereas the SNr
negative response followed the same monotonic increase asSNc neurons (duration increased for high reward probability,one-way ANOVA, P � 0.01), the positive response tended(without reaching statistical significance) to be shortened withincreased reward probability. In addition, the average durationsof the negative GPe responses in duration-informative neuronsare significantly shorter (one-way ANOVA, P � 0.01) than thepositive responses. We checked whether the negative versuspositive difference seen in response duration of SNr neuronsalso exists in other response features discussed herein. Only themean total spike count of negative duration-informative neu-rons showed a significant monotonic decrease (one-wayANOVA, P � 0.01) displaying higher values for low rewardprobabilities.
Figure 4 compares the MI between response duration andreward probability to the information provided by other re-sponse features. Since extracting response duration requiredclassifying each time bin in each single trial, we also derivedthe more standard responses (extreme response and responsespike count) of each single trial, using only those bins that wereclassified as having a significant response. Table 2 comparesthe average MI values of the different response features ofduration-informative neurons. In both Fig. 4 and Table 2 theresults are displayed separately for each of the three structuresand for positive versus negative responses. For neurons withnegative responses, duration was more informative than eitherextreme (maximal or minimal) response or response spikecount. For neurons with positive responses, extreme responseand response spike count were as informative as responseduration.
We therefore further tested whether combining responsefeatures could increase information about reward probability(Table 2). As expected, in almost all cases, there was clearredundancy between the response features (negative normal-ized synergy). Thus on average the information provided bythe extreme amplitude or by the response spike count washighly redundant with the information provided by the re-sponse duration. Unexpectedly, we found that the additionalinformation supplied by extreme response and by responsespike count when used in association with response durationwas close to zero (see METHODS and average “norm contribu-tion” in Table 2). Thus the information that can be decodedfrom response duration encompasses essentially all the infor-mation that can be decoded from response spike count orextreme amplitude.
TABLE 1. Quantitative analysis of neural responses in different basal ganglia nuclei
SNr SNc GPe
Total number of cells 56 109 61Number of responsive cells 50 93 54
(% of total cells) (89.3%) (85.3%) (88.5%)Number of duration-informative cells 21 25 16
(% of responsive cells) (42%) (26.88%) (29.3%)
PositiveResponse
NegativeResponse
PositiveResponse
PositiveResponse
NegativeResponse
Number of duration-informative cells with positive or negative 7 14 25 8 8responses(% of responsive cells) (33.3%) (66.7%) (100%) (50%) (50%)
Responsive and duration-informative neurons in the SNr, SNc, and GPe.
3247BASAL GANGLIA GATING MECHANISMS
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
Extracting response duration from single trials is rathercomplex (Fig. 1), since it involves classifying each time bin inthe responses of each single trial. Different ways of decodingthe neuronal responses may be more informative. The standardway of quantifying responses is by counting the total spikecount in a fixed, long window. Whereas total spike countencompasses time bins that may not be really important,possibly diluting the information it carries through the additionof noise, it may also take into account the responses duringtime bins that were wrongly classified as nonresponsive. Inpractice, the second effect probably dominated since we foundthat total spike count carried as much information as, or moreinformation than, the response duration. This can be seen inFig. 4 where the MI extracted from the total spike count overthe fixed 350-ms window for both positive and negative re-sponses was typically higher than the MI carried by responseduration (as also reflected in Table 2). Nevertheless, since theduration did not add significantly to the information providedby the total spike count, the information provided by both thetotal spike count and the duration is actually provided by thetotal spike count alone. Therefore the amount of informationgiven by both features exclusive to the total spike count (see“norm contribution” in Table 2: 32%, range 20–50%) is theamount of information given by the total spike count and notby the response duration, i.e., most (68%, range 50–80%) ofthe information provided by the total spike count was encodedby the response duration as well. Thus the difference betweenresponse duration and total spike count as a carrier of infor-mation was not substantial. In addition, we tested more detailed
temporal representations of the response (such as analyzing theactivity as a sequence of responsive and nonresponsive bins).However, the bias-corrected amount of information did notsignificantly increase with greater detail, suggesting that thereis no easily decoded additional information in the temporalpattern of the 50-ms bins of the BG responses (data notshown).
D I S C U S S I O N
Our results confirm previous reports of future reward prob-ability encoding in basal ganglia neurons (Arkadir et al. 2004;Morris et al. 2004). However, previous studies tested durationencoding directly only for the negative dopaminergic responses(Bayer et al. 2007). The main results of this study are 1) thedemonstration that response duration carries much of the in-formation available in responses of BG neurons about futurereward probability and 2) that there is a difference betweenencoding processes of positive and negative responses. Notethat in this study, we tested the responses only to cue-predict-ing rewards and thus evoked only positive SNc responses.However, another study of our group failed to reveal durationencoding in the responses of SNc neurons to omission ofpredicted rewards (M Joshua, A Adler, R Mitelnan, E Vaadia,and H Bergman, unpublished observations).
Evidence for the importance of response duration in thenervous system (Christensen-Dalsgaard et al. 1998; DeBusket al. 1997; Kanold and Manis 2005; Nagata et al. 2003; Rogersand Newland 2002; Zhang et al. 2004) and even specifically in
G P eS Nc
0
0.5
1S Nr
0
0.5
1
0
0.5
1
MI(reward probability; response duration)<bits>
MI(r
ewar
dpr
obab
ility
;res
pons
efe
atur
e)<b
its>
extr
eme
ampl
itude
resp
onse
spik
eco
unt
tota
lspi
keco
unt
x - positive responses. - negative responses
FIG. 4. Comparing the MI between reward probability andother response features to the MI between the reward proba-bility and the response duration. For each of the structures, weillustrate the MI between the reward probability and tworesponse features (the extreme response and the response spikecount) as a function of the MI between the reward probabilityand the response duration.
25 50 75 1000
50
100
150
200
250
S Nr
me
an
resp
on
sed
ura
tion
(ms)
reward probabilty (%)25 50 75 100
G P e
reward probabilty (%)25 50 75 100
S Nc
reward probabilty (%)
FIG. 3. Mean response duration. Mean negative and posi-tive response durations of duration informative cells in the SNr,SNc, and GPe. The error bars indicate 1SD. Square, positiveresponse; triangle, negative response.
3248 PARUSH ET AL.
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
the responses of striatal cholinergic neurons (Aosaki et al.1995; Ravel et al. 2003) and in responses of pallidal neurons(Anderson and Turner 1991) have been reported. Recently,Steuber et al. (2007) found that the best criterion to distinguishbetween different patterns of the cerebellar parallel fibers wasthe duration of the pause. O’Donnell and Grace (1998) showedthat a known psychotic modulator (phencyclidine) acts byreducing the frequency and duration of the spontaneouslyoccurring depolarized plateaus observed in the membrane po-tential of accumbens neurons. In addition, Kepecs and Ragha-vachari (2007) presented a model that can account for thegeneration of different duration up-state activity in striatalneurons. By simulating a bursting neuron model, Kepecs andcolleagues showed that bursts of different durations can codefor different stimulus features (Kepecs and Lisman 2003;Kepecs et al. 2002). Moreover, they found that synapses can betuned to preferentially respond to specific burst durations anddemonstrated the decodability of a neural code based on burstduration (Kepecs and Lisman 2004). In addition, a study ofdopaminergic neurons suggested that these neurons overcomethe limited dynamic range available for encoding of negativevalues by modification of the duration of their negative re-sponses (Bayer et al. 2007). Finally, a recent study (Person andPerkel 2005) revealed in zebra finch songbirds that high-frequency trains of pallidal spikes can drive activity in thalamicrelay neurons by rebound excitation. The latency of this re-bound is strongly affected by the duration of the pallidal spiketrain (their Fig. 4). Thus positive SNr responses will yielddifferent thalamic rebound excitation as a function of theresponse duration and, perhaps, longer SNr pauses will causelonger and probably stronger thalamic disinhibitory effects.
Our results are in line with models of the basal ganglia in whichinformation transmission is carried through gating mechanisms,where the neuronal activity determines the extent of gate apertureand its duration (Deniau and Chevalier 1985; Mink 1996). GPe isprobably involved in gating the inputs to the subthalamic nucleus,striatum, and the output structures of the BG, whereas the SNrgates the reciprocal thalamocortical neuronal loops. Contrary toother models (Mink 1996), gating models suggest that the basal
ganglia output enables, rather than selects or initiates (McHaffie etal. 2005; Mink 1996), movements or other voluntary behaviors.We suggest that the duration of the gate aperture might take partin the competition between possible actions (giving advantage tothose BG–thalamic channels with longer opened gate duration). Inaddition, reward expectation has been shown to influence re-sponse latency (Lauwereyns et al. 2002); it is thus possible thatresponse duration is part of the mechanism that modulates oraffects the action’s vigor through the multiple channels of thebasal ganglia output to the reciprocal thalamocortical networks.The significant fraction of duration-informative SNr neurons withnegative responses is compatible with this suggested role of theSNr. The SNr has GABAergic projections to the thalamus and tothe superior colliculus (Hikosaka and Wurtz 1983; Redgrave et al.1992); thus when SNr neurons decrease their activity, they disin-hibit their targets. This may be the mechanistic implementation ofthe gating mechanism, where the background tonic activity andpositive responses of SNr neurons close the gate, whereas nega-tive SNr responses open the gate (Deniau and Chevalier 1985;Hikosaka and Wurtz 1983). Our finding that the mean negativeresponse durations of duration-informative neurons monotoni-cally increases (long durations for high probability and shortdurations for low probability; Fig. 3) is also compatible with thegating model. Negative SNr responses open the gate and weexpect the gate to be opened for longer durations (and enable amovement) for the higher reward prospects. The positive re-sponses show (nonsignificant) an opposite trend. This could alsobe explained by the gating model. Since closing the gate does notdetermine the movement, its duration is less significant. Themonotonic decrease seen in the mean total spike count of negativeduration-informative neurons—displaying higher values for lowreward probabilities—is in line with the monotonic increase foundin the mean response duration of those neurons. The total spikecount consists of responsive and nonresponsive bins; thus longnegative responses that have fewer bins with normal activity andmore bins with low activity will have a low total spike count andvice versa. In addition, it has been shown that dopamine (D1receptors) inhibits SNr activity (Kliem et al. 2007). Therefore inline with SNr negative responses, the mean response duration in
TABLE 2. Comparison of information contents of the neuronal responses of duration-informative cells in different basal ganglia nuclei
Mean over positive and negative response duration-informative cells of MI, normalized synergy, and contribution between the reward probability and thedifferent response features.
3249BASAL GANGLIA GATING MECHANISMS
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
SNc (positive) responses is long for high reward probabilities andshort for low probabilities.
A negative response (i.e., response with a decrease in firingrate) has the advantage of being detectable faster than anincrease of the same magnitude (APPENDIX). However, in neg-ative responses, when the neurons decrease their firing rate toclose to zero for different time lengths, the minimal firing rateand the response spike count do not differ between differentprobabilities and thus provide little information on the rewardprobability. In this situation, the response duration remainsinformative (consequently, the total spike count that includestime bins in which short responses return to normal activitywill also be informative). On the other hand, in positiveresponses, when the neurons respond with an increase in firingrate for different time lengths, the response spike count variesbetween reward probabilities. Hence for neurons with positiveresponses, duration did not have a major advantage overmaximal firing rate or response spike count.
Spike train analyses usually have focused on two extremeschemes of neuronal encoding. Most studies have dealt withthe highly information reduced measure of spike count or rate(Ahissar et al. 2000; Georgopoulos et al. 1986; Gershon et al.1998; Shadlen and Newsome 1998). Other studies have fo-cused on information in spike patterns (Arabzadeh et al. 2006;Friedrich et al. 2004; Ikegaya et al. 2004; Jones et al. 2004;Panzeri et al. 2001; Prut et al. 1998; Victor and Purpura 1996).However, even when spike timing carries information, the useof simple reduced measures of the timing of the responses maybe sufficient (Nelken et al. 2005). Our observations demon-strate that coding schemes based on response duration areviable and that they use much of the information available inthe responses of BG neurons. Furthermore, we show that re-sponse duration encodes reward probability not only in positive(increase in firing rate, bursts) responses, but also (in the GABAe-regic BG nuclei) in negative (decrease in firing rate) responses,and that duration encoding is not a simple epiphenomenon of rateencoding. Finally, we argued that response duration may behighly relevant to the effects of BG neurons on their targetstructures. The significant amount of information encoded inresponse duration makes response duration a prominent codingelement that can mechanistically control the influence of the basalganglia on its target structures.
A P P E N D I X
This APPENDIX proves that a decrease in firing rate response can bedetected faster than an increase of the same magnitude in neurons withPoisson-like firing pattern.
The sequential probability ratio test (SPRT; Wald 1947) is a serialBayesian test designed to determine which of two hypothesizeddistributions is used to generate data samples. In this test we obtaindata samples and examine the log likelihood (the probability of agiven distribution to generate these data points) ratio of the twodistributions. The test sequentially inputs data samples until the ratiois above an acceptance or below a rejection threshold. At that time thetest can determine (with a reliability that depends solely on thethresholds) which of the two distributions generated the data.
We assume that the spike trains are generated by a Poissondistribution and that an external/internal event can cause the neuron toswitch from one firing rate (�1) to a different firing rate (�2). We seekto evaluate how many samples (spike counts/rates) are needed (usingSPRT) to determine the neuron’s firing rate after the switch hasoccurred. The likelihood ratio for the two hypotheses is
s � logL�xn��1�
L�xn��2�
where xn � (x1,…, xn) are n independent and identically distributeddata samples
p�xi��� ��xe��
x!
s � logL�xn��1�
L�xn��2�� log
�i
p�xi��1�
�i
p�xi��2�� log ��i
p�xi��1�
p�xi��2��
� �i
log �p�xi��1�
p�xi��2�� � n
1
n�
ilog �p�xi��1�
p�xi��2��
nE[log p(x��1)p(x��2)]
E� logp�x��1�
p�x��2�� � �
xp�x��1�log �p�x��1�
p�x��2��
which is also denoted as the Kullback–Leibler distance (Cover andThomas 1991)
Dklp�x��1���p�x��2�� � �x
p�x��1� log ��1xe��1/x!
�2xe��2/x!
�� �
xp�x��1��x log ��1
�2� � ��2 � �1��
� log ��1
�2�E�x��1� � ��2 � �1�
� log ��1
�2��1 � ��2 � �1�
Let nR�R(1��) denote the number of samples needed to detect a distribu-tion switch from � � R to � � R(1 � �), nR�R(1��) denote the numberof samples needed to detect a distribution switch from � � R to � � R(1 ��), and Sth denote the ratio acceptance threshold (the threshold to detect thedistribution change). We can express the required sample sizes as
nth �Sth
E�p�x��1�
p�x��2�� �
Sth
log ��1
�2��1 � ��2 � �1�
nR��R�1��� �Sth
log �R�1 � ��
R �R�1 � �� � R�
nR��R�1��� �Sth
log �R�1 � ��
R �R�1 � �� � R�
nR��R�1���
nR��R�1���
�
log �R�1 � ��
R�R�1 � �� � R�
log �R�1 � ��
R�R�1 � �� � R�
��1 � �� log �1 � �� � �
�1 � �� log �1 � �� � �
The ratio between the number of samples needed to detect a distri-bution switch from � � R to � � R(1 � �) and the number of samples
3250 PARUSH ET AL.
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
needed to detect a distribution switch from � � R to � � R(1 � �)is always �1 and reaches 2.6 as � reaches 1. Thus detecting adecrease in firing rate will require fewer data samples—i.e., less timethan detecting an increase of the same magnitude.
A C K N O W L E D G M E N T S
We acknowledge the authors’ specific contributions: N. Parush initiated anddesigned the study of response duration, developed the information theoretictools, performed the data analysis, and wrote the manuscript; D. Arkadir, A.Nevet, and G. Morris trained the monkeys for the behavioral tasks andrecorded the single-unit activity during the performance of the task; H.Bergman contributed to training of the monkeys, recording, and the writing ofthe manuscript; and N. Tishby and I. Nelken contributed to the development ofthe information analysis tools and writing of the manuscript.
G R A N T S
This study was partly supported by Netherlands Friends of the HebrewUniversity “Fighting against Parkinson” grant to H. Bergman. I. Nelken wassupported by the German–Israeli Foundation and by the VolkswagenStiftung.N. Parush and G. Morris were supported by a Horowitz fellowship and D.Arkadir and A. Nevet were supported by the MD–PhD program of the HebrewUniversity–Hadassah Medical School.
R E F E R E N C E S
Ahissar E, Sosnik R, Haidarliu S. Transformation from temporal to rate codingin a somatosensory thalamocortical pathway. Nature 406: 302–306, 2000.
Albin RL, Young AB, Penney JB. The functional anatomy of basal gangliadisorders. Trends Neurosci 12: 366–375, 1989.
Anderson ME, Turner RS. A quantitative analysis of pallidal dischargeduring targeted reaching movement in the monkey. Exp Brain Res 86:623–632, 1991.
Aosaki T, Kimura M, Graybiel AM. Temporal and spatial characteristics oftonically active neurons of the primate’s striatum. J Neurophysiol 73:1234–1252, 1995.
Arabzadeh E, Panzeri S, Diamond ME. Deciphering the spike train of asensory neuron: counts and temporal patterns in the rat whisker pathway.J Neurosci 26: 9216–9226, 2006.
Arkadir D, Morris G, Vaadia E, Bergman H. Independent coding ofmovement direction and reward prediction by single pallidal neurons.J Neurosci 24: 10047–10056, 2004.
Averbeck BB, Latham PE, Pouget A. Neural correlations, population codingand computation. Nat Rev Neurosci 7: 358–366, 2006.
Bar-Gad I, Morris G, Bergman H. Information processing, dimensionalityreduction and reinforcement learning in the basal ganglia. Prog Neurobiol71: 439–473, 2003.
Barlow HB. Sensory mechanisms, the reduction of redundancy, and intelli-gence. In: NPL Symposium on the Mechanization of Thought Processes, No.10. London: Her Majesty’s Stationery Office, 1959, p. 535–539.
Bayer HM, Lau B, Glimcher PW. Statistics of midbrain dopamine neuronspike trains in the awake primate. J Neurophysiol 98: 1428–1439, 2007.
Berns GS, Sejnowski TJ. A computational model of how the basal gangliaproduce sequences. J Cogn Neurosci 10: 108–121, 1998.
Bialek W, Rieke F, de Ruyter van Steveninck RR, Warland D. Reading aneural code. Science 252: 1854–1857, 1991.
Chechik G, Anderson MJ, Bar-Yosef O, Young ED, Tishby N, Nelken I.Reduction of information redundancy in the ascending auditory pathway.Neuron 51: 359–368, 2006.
Christensen-Dalsgaard J, Jorgensen MB, Kanneworff M. Basic responsecharacteristics of auditory nerve fibers in the grassfrog (Rana temporaria).Hear Res 119: 155–163, 1998.
Cover TM, Thomas JA. Elements of Information Theory. New York: Wiley, 1991.DeBusk BC, Debruyn EJ, Snider RK, Kabara JF, Bonds AB. Stimulus-
dependent modulation of spike burst length in cat striate cortical cells.J Neurophysiol 78: 199–213, 1997.
DeLong MR. Primate models of movement disorders of basal ganglia origin.Trends Neurosci 13: 281–285, 1990.
DeLong MR, Crutcher MD, Georgopoulos AP. Relations between move-ment and single cell discharge in the substantia nigra of the behavingmonkey. J Neurosci 3: 1599–1606, 1983.
Deniau JM, Chevalier G. Disinhibition as a basic process in the expression ofstriatal functions. II. The striato-nigral influence on thalamocortical cells ofthe ventromedial thalamic nucleus. Brain Res 334: 227–233, 1985.
Friedrich RW, Habermann CJ, Laurent G. Multiplexing using synchrony inthe zebrafish olfactory bulb. Nat Neurosci 7: 862–871, 2004.
Georgopoulos AP, Schwartz AB, Kettner RE. Neuronal population codingof movement direction. Science 233: 1416–1419, 1986.
Hikosaka O, Wurtz RH. Visual and oculomotor functions of monkey sub-stantia nigra pars reticulata. IV. Relation of substantia nigra to superiorcolliculus. J Neurophysiol 49: 1285–1301, 1983.
Ikegaya Y, Aaron G, Cossart R, Aronov D, Lampl I, Ferster D, Yuste R.Synfire chains and cortical songs: temporal modules of cortical activity.Science 304: 559–564, 2004.
Jones LM, Depireux DA, Simons DJ, Keller A. Robust temporal coding inthe trigeminal system. Science 304: 1986–1989, 2004.
Kanold PO, Manis PB. Encoding the timing of inhibitory inputs. J Neuro-physiol 93: 2887–2897, 2005.
Kepecs A, Lisman J. Information encoding and computation with spikes andbursts. Network 14: 103–118, 2003.
Kepecs A, Lisman J. How to read a burst duration code. Neurocomputing 58:1–6, 2004.
Kepecs A, Raghavachari S. Gating information by two-state membranepotential fluctuations. J Neurophysiol 97: 3015–3023, 2007.
Kepecs A, Wang X-J, Lisman J. Bursting neurons signal input slope.J Neurosci 22: 9053–9062, 2002.
Kliem MA, Maidment NT, Ackerson LC, Chen S, Smith Y, WichmannT. Activation of nigral and pallidal dopamine D1-like receptors modu-lates basal ganglia outflow in monkeys. J Neurophysiol 98: 1489 –1500,2007.
Las L, Stern EA, Nelken I. Representation of tone in fluctuating maskers inthe ascending auditory system. J Neurosci 25: 1503–1513, 2005.
Lauwereyns J, Watanabe K, Coe B, Hikosaka O. A neural correlate ofresponse bias in monkey caudate nucleus. Nature 418: 413–417, 2002.
McHaffie JG, Stanford TR, Stein BE, Coizet V, Redgrave P. Subcorticalloops through the basal ganglia. Trends Neurosci 28: 401–407, 2005.
Mink JW. The basal ganglia: focused selection and inhibition of competingmotor programs. Prog Neurobiol 50: 381–425, 1996.
Morris G, Arkadir D, Nevet A, Vaadia E, Bergman H. Coincident butdistinct messages of midbrain dopamine and striatal tonically active neu-rons. Neuron 43: 133–143, 2004.
Nagata T, Suzuki H, Zhang R, Ozaki M, Kawakami Y. Mechanicalstimulation activates small fiber mediated nociceptive responses in thenucleus gigantocellularis. Exp Brain Res 149: 505–511, 2003.
Nelken I, Chechik G, Mrsic-Flogel TD, King AJ, Schnupp JW. Encodingstimulus information by spike numbers and mean response time in primaryauditory cortex. J Comput Neurosci 19: 199–221, 2005.
Nevet A, Morris G, Saban G, Fainstein N, Bergman H. Discharge rate ofsubstantia nigra pars reticulata neurons is reduced in non-parkinsonianmonkeys with apomorphine-induced orofacial dyskinesia. J Neurophysiol92: 1973–1981, 2004.
O’Donnell P, Grace AA. Phencyclidine interferes with the hippocampalgating of nucleus accumbens neuronal activity in vivo. Neuroscience 87:823–830, 1998.
Panzeri S, Petersen RS, Schultz SR, Lebedev M, Diamond ME. The role ofspike timing in the coding of stimulus location in rat somatosensory cortex.Neuron 29: 769–777, 2001.
Person AL, Perkel DJ. Unitary IPSPs drive precise thalamic spiking in acircuit required for learning. Neuron 46: 129–140, 2005.
Prut Y, Vaadia E, Bergman H, Haalman I, Slovin H, Abeles M. Spatio-temporal structure of cortical activity: properties and behavioral relevance.J Neurophysiol 79: 2857–2874, 1998.
Ravel S, Legallet E, Apicella P. Responses of tonically active neurons in themonkey striatum discriminate between motivationally opposing stimuli.J Neurosci 23: 8489–8497, 2003.
Redgrave P, Marrow L, Dean P. Topographical organization of the nigro-tectal projection in rat: evidence for segregated channels. Neuroscience 50:571–595, 1992.
Rogers SM, Newland PL. Gustatory processing in thoracic local circuits oflocusts. J Neurosci 22: 8324–8333, 2002.
Schneidman E, Bialek W, Berry MJ. Synergy, redundancy, and indepen-dence in population codes. J Neurosci 23: 11539–11553, 2003.
3251BASAL GANGLIA GATING MECHANISMS
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
Shadlen MN, Newsome WT. The variable discharge of cortical neurons:implications for connectivity, computation, and information coding. J Neu-rosci 18: 3870–3896, 1998.
Steuber V, Mittmann W, Hoebeek FE, Silver RA, De Zeeuw CI, HausserM, De Schutter E. Cerebellar LTD and pattern recognition by Purkinjecells. Neuron 54: 121–136, 2007.
Victor JD, Purpura KP. Nature and precision of temporal coding in vi-sual cortex: a metric-space analysis. J Neurophysiol 76: 1310 –1326,1996.
Wald A. Sequental Analysis. New York: Wiley, 1947.Wichmann T, Kliem MA. Neuronal activity in the primate substantia nigra
pars reticulata during the performance of simple and memory-guided elbowmovements. J Neurophysiol 91: 815–827, 2004.
Wickens J. Basal ganglia: structure and computation. Network Comput NeuralSyst 8: R77–R109, 1997.
Zhang R, Tomida M, Katayama Y, Kawakami Y. Response durationsencode nociceptive stimulus intensity in the rat medial prefrontal cortex.Neuroscience 125: 777–785, 2004.
3252 PARUSH ET AL.
J Neurophysiol • VOL 100 • DECEMBER 2008 • www.jn.org
