population coding in somatosensory cortex - cog sciajyu/teaching/cogs160_sp10/... · from single...

Population coding in somatosensory cortex Rasmus S Petersen*†, Stefano Panzeri‡ and Mathew E Diamond*

Presenter: Crane Huang05/20/2010

Introduction

• A fundamental challenge in neurobiology is to discover the essential differences in the neural representations of two perceptually discriminable stimuli.

• Aim: To compare candidate cortical population codes by identifying features of the neural response that might underlie stimulus discrimination.

Introduction

• Is information encoded by a widespread network or by a restricted subset of neurons?

• Are stimuli encoded by spike count or does the ms precision convey additional information?

• Does each spike code independently, or do correlated spike patterns convey additional information?

Outline

• Spatial organization of neural coding

• The role of spike timing

• The role of spike correlations

Spatial organization of neural coding

• Is the activity within the stimulated whiskerʼs homotopic cortical column sufficient to specify the stimulus site (restricted subset of neurons)?

• Is the activity essential to specifying stimulus site distributed across many columns (a widespread network)?

ANN can reproduce arbitrary mappings between input andoutput and hence, in principle, can accurately representthe ideal decoder. In practice, due in part to the need toavoid ‘overfitting’, an ANN will perform worse than theideal decoder by an unknown amount [8].

The ANN was much more accurate in decoding the loca-tion of a whisker deflection for networks generated fromensembles of ~30 simultaneously recorded neurons thanfrom single neurons [7•]. This observation, together withthe multicolumnar distribution of single-whisker activity,might seem to favour the notion that the population codefor stimulus location depends on cells located across a largepart of barrel cortex. However, an alternative hypothesis isthat the widespread distributed activity, although informa-tive, is redundant with the activity that a stimulus evokesin its homotopic column.

Another recent study addressed this issue. The corticalresponse to single-whisker deflection in cortical layers 3–4was measured by a 100-microelectrode array [6•]. Theamount of discriminability between a given pair ofwhiskers was measured with population d’. This quantityis the difference in the mean number of spikes evoked bytwo stimuli normalised by the spike count variability (seeFigure 2a–c). Electrodes were classified as being locatedeither in an ‘on-centre’ barrel column topographicallymatched to one of the two stimuli, or in an ‘off-centre’ column. The first result was that whisker pairs could bediscriminated above chance even if responses limited tooff-centre barrel columns were considered. This shows

that activity beyond the homotopic column is indeed informative and supports the existence of distributed, multicolumnar coding. However, is this an essentialcomponent of the cortical representation? To answer this,population d’ of the entire cortical response was comparedto that of only on-centre columns. The result was that>90% of the discriminability was accounted for by the on-centre columns; only a modest (10%) increase in dis-criminability was due to the off-centre columns (Figure 2d).In layers 3–4, the essential code for stimulus location thusappears to be founded on spatially localised activity.

Role of spike timing in population codingOne widely accepted view of sensory coding is that messages are conveyed by the number of spikes (‘spikecount’) that neurons fire within a period of time (perhaps100 ms or more), which is long compared to typical inter-spike intervals. The precise firing of spikes within thistime interval is assumed to reflect random processes, unrelated to stimulus encoding [9]. An alternative view isthat precise firing times are an additional, informativedimension of the response [10]. To distinguish betweenthese possibilities, it is necessary to quantify and comparethe stimulus discriminability afforded by timing and spikecount codes.

The general method is to choose a window, say 0–40 ms(where the stimulus onset is 0 ms) and to measure theresponse in a way that directly compares the two codes(Figure 3a). For a spike count code, the response on a trialis simply the number of spikes that the neuron fires

442 Sensory systems

Figure 1

Spatial organisation of the barrel cortical codefor stimulus location. (a) Four stimulus sites,whiskers C 1– C 4. (b) Response maps forstimulation of whiskers C 1– C 4 based onspikes simultaneously recorded through100 microelectrodes in the thalamorecipientlayers of barrel cortex [6•]. The activity evokedat each electrode in the 10!10microelectrode array (0–40 ms post-stimulus)has been averaged over trials withinterpolation between the electrodes. Theseresults illustrate that the cortical response towhisker deflection is partially localised, but notlimited to a single barrel column. Two alternateviews of widespread activity are portrayed.F irst, the widespread activity outside thehomotopic barrel column might play anessential role in stimulus coding: in panel(c) note that the activity at no single electrodeis sufficient to judge stimulus site, so that theobserver must take the pattern into account.In contrast, off-centre activity might be non-essential: in panel (d) the activity at the on-centre electrode is sufficient to identify thestimulus; all patterned activity in surroundingcolumns is redundant. Colour scale followspanel (b).

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Stimulus Redundantsurround

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(a) (b) (c) (d)

Current Opinion in Neurobiology

• ANN: more accurate in decoding from ensembles of ~30 simultaneously recorded neurons than single neurons.

• Seem to favor fig1(c), that the population code depends on a large part of barrel cortex.

• But...might be redundant.

Spatial organization of neural codingANN method

Spatial organization of neural codingPopulation d’

within the window. For a spike timing code, the window issubdivided into bins, and the occurrence or absence of aspike in each bin is registered; the response, instead ofbeing a single number, is a sequence of numbers. If spiketiming is important, then the estimated stimulus discrim-inability will improve as spike times are registered withincreasing precision.

Using the ANN method, it was found that stimulus discrim-inability, based on responses of ensembles of ~30 neurons,improved as bin size was decreased from 40 ms to 6 ms, indicating that precise spike timing may indeed play animportant role in cortical coding of stimulus location.

Information theory offers the possibility of directly quanti-fying the role of spike timing in stimulus discriminability.The quantity known as ‘mutual information’ is the mostrigorous measure of stimulus discriminability [11]. Themutual information is a non-parametric measure of howwell an ideal observer of neuronal responses can, on average, discriminate which stimulus occurred, based on aresponse observed on a single trial. If responses to differ-ent stimuli are similar, the mutual information is low; if theresponses are very different, it tends to be high. It has theadvantage over d’ of not assuming Gaussian-like responses

and the advantage over ANNs of not underestimating idealobserver performance.

Because neurons in barrel cortex fire few spikes perwhisker deflection, the mutual information can be wellapproximated by an expression — the series expansion —that depends only on the statistics of single spikes — thepost-stimulus time histogram (PSTH) — and pairs ofspikes (joint PSTH) [12,13•]. This series expansion formutual information (SEMI) estimation has been used tocompare spike count coding with spike time coding in barrel cortex [14••,15••]. The result, shown in Figure 3b,was that the activity of single neurons reported 44% moreinformation about stimulus identity (among nine possiblewhiskers) when the 40 ms post-stimulus window was considered with 5 ms precision [14••]. The informationgain from finer time bins was confirmed for simultaneouslyrecorded pairs of neurons [15••]. These results confirmthose obtained using the ANN method.

Are the spikes occurring in each, small time bin equallyimportant? The population d’ reveals how discriminabilityevolves during the course of the ensemble response [6•].Evaluation of the index as a cumulative function of timeindicates that d’ peaks within 12–16 ms of stimulus onset

Population coding in somatosensory cortex Petersen, Panzeri and D iamond 443

Figure 2

Studying stimulus location coding usingpopulation d’. (a) In the simplest case,d’ measures discriminability between a pair ofstimuli based on the number of spikes fired byone neuron: in this case, d’ is simply thedifference between the mean spike counts,normalised by the standard deviation of the spikecount. When the conditional probability of thespike count given each stimulus is approximatelyGaussian, d’ is a simple and useful measure ofdiscriminability. (b) How can d’ be generalised topopulations? If the neurons are uncorrelated,d’ is computed for each neuron individually andthe population d’ is simply the square root of thesum of the squared single neuron d’ values.However, neuronal responses are usuallysomewhat covariated, as shown schematicallyhere. (c) Provided that the covariance structureis similar for different stimuli, this can be takeninto account by transforming the responses to acoordinate system in which the variables areuncorrelated. For the example of (b), this isachieved by a 45º rotation. Panel (c) shows theprojection of the response distributions of (b)onto these new coordinates, in which theindividual d’s can be combined as in theuncorrelated case. (d) We applied thepopulation d’ method schematised in parts (b)and (c) to data simultaneously recorded from100 microelectrodes implanted in ratsomatosensory cortex. The contribution ofon-centre (homotopic) and off-centre(non-homotopic) neurons to stimulus sitediscrimination is shown. Reproduced withpermission from [6•].

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Post-stimulus time (ms)

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(b) (d)

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held at a consistent level by monitoring hindpaw withdrawal, corneal reflex,and respiration rate. Supplemental doses of urethane (0.15 gm/kg) wereadministered as necessary. With the subject placed in a stereotactic appa-ratus (Narashige, Tokyo, Japan), the left somatosensory cortex was ex-posed by a 7-mm-diameter craniotomy centered on a point 2 mm posteriorto bregma and 6 mm from the midline. The dura mater was left intact.

The array (Bionic Technologies, Salt Lake City, UT) consisted of a 10 !10 grid of 1.0- or 1.5-mm-long electrodes with a 400 !m inter-electrodedistance. Electrode array fabrication is described in Jones et al. (1992).The vibrissal region of left somatosensory cortex was identified accordingto vascular landmarks and stereotactic coordinates (Hall and Lindholm,1974; Chapin and Lin, 1984), and the array was positioned with theelectrode tips, perpendicular to the surface of cortex, pressing very lightlyagainst the dura at the target location. Then it was implanted by using apneumatic impulse inserter (Bionic Technologies) (Rousche and Nor-mann, 1992) such that the electrodes tips reached those layers receivingafferents from the ventroposterior nucleus of the thalamus, i.e., layer IVand the lower part of layer III (Lu and Lin, 1993). A wire positioned in thecortex served as a reference. From photographs of the inserted arrays, theminimum and maximum depths of electrode penetration were found to be400 and 900 !m. Figure 1 B illustrates one case.

Array placement was examined in histological sections. At terminationof the recording session the subjects were perfused with saline and 4%paraformaldehyde. After post-fixation in 20% sucrose, the cortex wasremoved, flattened, and frozen. The block of tissue was cut in 40 !msections in the tangential plane and stained with cresyl violet.

Electrophysiolog ical data acquisition. Individual whiskers were stimu-lated 3 mm from their base by a piezoelectric wafer (Morgan Matroc,Bedford, OH) that was controlled by a voltage pulse generator (A.M.P.I.,Jerusalem, Israel). The stimulus, an up–down step function of 80 !mamplitude and 100 msec duration, was delivered at 1 Hz.

Initially, each macrovibrissa (A1–4, B1–4, C1–5, D1–5, E1–5, ", #, $, and %)was stimulated 50 times. The subset of whiskers for which the barrel-columns were penetrated by the array received a greater number ofstimulus trials (279–500). Whiskers for which the barrel-columns lay at theedge of the array and for which the representations hence would have beensampled incompletely, were excluded from further analysis. The presentresults are based on the responses to 33 whiskers (rat r28: A1–2, B1–4, C1–4,D1–3, and E1–3; rat r30: C1–3, D1–3, and E1–2; rat r32: C1–4, D1–3, and E2–3).

The data acquisition system (Bionic Technologies) (Guillory and Nor-mann, 1999) consisted of a 100-channel amplifier (gain " 5000, filtered atbandpass 250–7500 Hz), a digital signal processor (DSP), and Pentium PC.Voltage thresholds for each channel were set by using the PC. The DSPdetected when the signal on any channel crossed threshold. It then ex-tracted 1.5 msec of analog signal (0.5 msec before the threshold crossing,1.0 msec after) and digitized it at 30,000 samples/sec per channel. Digitizedwaveforms were transmitted to the PC for storage. In off-line analysis,spike-sorting programs were used to select the activities of multiple singleunits on each electrode. Waveforms characteristic of thalamic afferents[initial negative deflection with short duration and high spontaneous ac-tivity (Simons and Carvell, 1989)] were recorded rarely and, if encoun-tered, were excluded by spike sorting. To reduce the bias introduced by theselection of single neurons (i.e., to eliminate the decision of which units to“discard” when constructing the whole-array response maps; see below),we summated the neural waveforms of the multiple neurons recorded oneach electrode to form a neural cluster. That is, the multiunit activity on agiven electrode was treated as a single composite unit (for details, see alsoRousche et al., 1999).

Analysis of neuronal responses. The first step was to form peristimulustime histograms (PSTHs) by using neural data collected at each electrodeacross all trials for a given stimulus site. For the purposes of illustration,neural data from all electrodes were used to form whole-array responsemaps (see Figs. 2 B, 3, 6). However, for the quantification of corticalresponse parameters (see Figs. 4, 5, 7), only those electrodes at which theneural cluster gave a statistically significant response were included.Responding electrodes were identified by comparing the trial-by-trial post-stimulus (0–100 msec) and prestimulus (#100 to 0 msec) multiunit spikecounts, using the Wilcoxon signed ranks test ( p $ 0.01 accepted as asignificant response).

On the basis of the observation that the principal whisker of a givenbarrel-column evokes the greatest response, we estimated the columnar

location of each electrode (Ghazanfar and Nicolelis, 1999) (see alsoLebedev et al., 2000). An electrode was defined as being in the barrel-column of a given whisker if that whisker elicited a statistically significantresponse (0–100 msec) that was at least 50% greater than that to all otherwhiskers. It was also useful to classify the set of electrodes responding toa given whisker as being “on-center” or “off-center.” For a specific whisker,an electrode was designated as “on-center” if the response to that whiskerwas 66% or more of the maximum evoked at that electrode for anywhisker. The set of off-center electrodes for a given whisker was simply theset of all responding electrodes that were not on-center.

For all responding electrodes the response onset latency was calculatedby using a method similar to that of Maunsell and Gibson (1992). ThePSTH was constructed with 1 msec bins from #100 to %100 msec (stimulusonset " 0 msec). Onset latency was defined as the earlier of the first twoconsecutive poststimulus bins of the PSTH in which the spike countexceeded ( p $ 0.01) the count that would be expected from a Poissonprocess with mean spike count equal to that of spontaneous firing. Rate ofspontaneous firing was determined from the 100 msec interval precedingstimulus onset. Because the rising phase of the PSTH was very sharp (seeFig. 4A), latency measurement was relatively insensitive to the critical pvalue that was chosen. However, response latency is somewhat sensitive tothe number of trials, as is the Wilcoxon test of response magnitude. Thesemeasurements were always based on 279 stimulus trials (the minimumnumber used in any experiment) to make them comparable across allwhiskers of each rat. The bias attributable to using small numbers of trialswas evaluated by repeating the latency analyses on randomly chosensubsets of 50 trials.

To enable comparison with published data, we also estimated modallatencies, using the method of Armstrong-James and Fox (1987). Theanalysis was restricted to those cases for which the onset latency was welldefined. By measuring the time to first spike after stimulus onset on everytrial, we constructed a first-spike time histogram with 1 msec bins in theinterval 0–100 msec poststimulus. The modal latency was defined as themode of this histogram.

Discriminabilit y of cortical population response patterns. To determinethe discriminability among the neural responses to different whiskers, weadapted the signal detection measure d& (Green and Swets, 1966). d& quan-tifies how discriminable two events are, based on responses to them. For asingle dependent response variable, d& is simply the absolute differencebetween the mean responses to the two events divided by the average SD.In the present case the events are stimuli presented to two differentwhiskers, and the dependent response variable is the spike count at anelectrode of interest. If the mean values of response for stimuli x and y aremx and my, respectively, and if the SD across both stimuli is &, then:

d& '!mx ( my!

&. (1)

This measure has been used to study how well single sensory neuronsdiscriminate among relevant stimulus features (Tolhurst et al., 1983; Essickand Whitsel, 1985).

When more than one response variable is available, it is necessary toconsider possible covariation among them across trials. If the responses toa given stimulus are statistically independent, then the population d& issimply the square root of the sum of the squared individual response d&s(Green and Swets, 1966):

d& ' "#i

d&i2 , (2)

where d&i is the discriminability at the ith response variable (electrode).Equation 2 also has been applied to sequentially recorded neurons, whereno information about covariance was available (Zohary, 1992; Geisler andAlbrecht, 1997). However, neocortical neurons are not, in general, statis-tically independent (Gawne and Richmond, 1993; Zohary et al., 1994; Leeet al., 1998). For a given set of stimuli the response covariance canconstitute either redundancy or synergy (Snippe, 1996; Oram et al., 1998;Abbott and Dayan, 1999), in which case Equation 2 will overestimate (forredundancy) or underestimate (for synergy) the true discriminability.

Table 1. Consistency of principal results across subjects

Experiment

Evoked spikesper stimulusmedian (IQR)

Number of respondingelectrodes median(IQR)

Response onsetlatency median(IQR)

Responseoffset timemean (SD)

Peak d&mean (SD)

r28 6.0 (4.3–10.3) 14 (8–15) 8 (5–8) 45.8 (19.0) 4.8 (1.0)r30 4.6 (2.6–5.7) 10 (7–12) 6 (5–17) 44.0 (12.4) 3.4 (0.9)r32 6.0 (3.3–6.0) 13 (10–13) 9 (7–12) 40.6 (9.3) 3.3 (0.7)ALL 5.7 (3.3–8.1) 12 (8–15) 8 (6–12) 43.9 (15.1) 4.3 (1.2)

Response latency and response offset time in msec. Standard deviation, SD; interquartile range, IQR.

6136 J. Neurosci., August 15, 2000, 20(16):6135–6143 Petersen and Diamond • Spatial–Temporal Activity and Stimulus Coding in Rat SI

held at a consistent level by monitoring hindpaw withdrawal, corneal reflex,and respiration rate. Supplemental doses of urethane (0.15 gm/kg) wereadministered as necessary. With the subject placed in a stereotactic appa-ratus (Narashige, Tokyo, Japan), the left somatosensory cortex was ex-posed by a 7-mm-diameter craniotomy centered on a point 2 mm posteriorto bregma and 6 mm from the midline. The dura mater was left intact.

The array (Bionic Technologies, Salt Lake City, UT) consisted of a 10 !10 grid of 1.0- or 1.5-mm-long electrodes with a 400 !m inter-electrodedistance. Electrode array fabrication is described in Jones et al. (1992).The vibrissal region of left somatosensory cortex was identified accordingto vascular landmarks and stereotactic coordinates (Hall and Lindholm,1974; Chapin and Lin, 1984), and the array was positioned with theelectrode tips, perpendicular to the surface of cortex, pressing very lightlyagainst the dura at the target location. Then it was implanted by using apneumatic impulse inserter (Bionic Technologies) (Rousche and Nor-mann, 1992) such that the electrodes tips reached those layers receivingafferents from the ventroposterior nucleus of the thalamus, i.e., layer IVand the lower part of layer III (Lu and Lin, 1993). A wire positioned in thecortex served as a reference. From photographs of the inserted arrays, theminimum and maximum depths of electrode penetration were found to be400 and 900 !m. Figure 1 B illustrates one case.

Array placement was examined in histological sections. At terminationof the recording session the subjects were perfused with saline and 4%paraformaldehyde. After post-fixation in 20% sucrose, the cortex wasremoved, flattened, and frozen. The block of tissue was cut in 40 !msections in the tangential plane and stained with cresyl violet.

Electrophysiolog ical data acquisition. Individual whiskers were stimu-lated 3 mm from their base by a piezoelectric wafer (Morgan Matroc,Bedford, OH) that was controlled by a voltage pulse generator (A.M.P.I.,Jerusalem, Israel). The stimulus, an up–down step function of 80 !mamplitude and 100 msec duration, was delivered at 1 Hz.

Initially, each macrovibrissa (A1– 4, B1– 4, C1–5, D1–5, E1–5, ", #, $, and %)was stimulated 50 times. The subset of whiskers for which the barrel-columns were penetrated by the array received a greater number ofstimulus trials (279–500). Whiskers for which the barrel-columns lay at theedge of the array and for which the representations hence would have beensampled incompletely, were excluded from further analysis. The presentresults are based on the responses to 33 whiskers (rat r28: A1–2, B1–4, C1–4,D1–3, and E1–3; rat r30: C1–3, D1–3, and E1–2; rat r32: C1–4, D1–3, and E2–3).

The data acquisition system (Bionic Technologies) (Guillory and Nor-mann, 1999) consisted of a 100-channel amplifier (gain " 5000, filtered atbandpass 250–7500 Hz), a digital signal processor (DSP), and Pentium PC.Voltage thresholds for each channel were set by using the PC. The DSPdetected when the signal on any channel crossed threshold. It then ex-tracted 1.5 msec of analog signal (0.5 msec before the threshold crossing,1.0 msec after) and digitized it at 30,000 samples/sec per channel. Digitizedwaveforms were transmitted to the PC for storage. In off-line analysis,spike-sorting programs were used to select the activities of multiple singleunits on each electrode. Waveforms characteristic of thalamic afferents[initial negative deflection with short duration and high spontaneous ac-tivity (Simons and Carvell, 1989)] were recorded rarely and, if encoun-tered, were excluded by spike sorting. To reduce the bias introduced by theselection of single neurons (i.e., to eliminate the decision of which units to“discard” when constructing the whole-array response maps; see below),we summated the neural waveforms of the multiple neurons recorded oneach electrode to form a neural cluster. That is, the multiunit activity on agiven electrode was treated as a single composite unit (for details, see alsoRousche et al., 1999).

Analysis of neuronal responses. The first step was to form peristimulustime histograms (PSTHs) by using neural data collected at each electrodeacross all trials for a given stimulus site. For the purposes of illustration,neural data from all electrodes were used to form whole-array responsemaps (see Figs. 2 B, 3, 6). However, for the quantification of corticalresponse parameters (see Figs. 4, 5, 7), only those electrodes at which theneural cluster gave a statistically significant response were included.Responding electrodes were identified by comparing the trial-by-trial post-stimulus (0–100 msec) and prestimulus (#100 to 0 msec) multiunit spikecounts, using the Wilcoxon signed ranks test ( p $ 0.01 accepted as asignificant response).

On the basis of the observation that the principal whisker of a givenbarrel-column evokes the greatest response, we estimated the columnar

location of each electrode (Ghazanfar and Nicolelis, 1999) (see alsoLebedev et al., 2000). An electrode was defined as being in the barrel-column of a given whisker if that whisker elicited a statistically significantresponse (0–100 msec) that was at least 50% greater than that to all otherwhiskers. It was also useful to classify the set of electrodes responding toa given whisker as being “on-center” or “off-center.” For a specific whisker,an electrode was designated as “on-center” if the response to that whiskerwas 66% or more of the maximum evoked at that electrode for anywhisker. The set of off-center electrodes for a given whisker was simply theset of all responding electrodes that were not on-center.

For all responding electrodes the response onset latency was calculatedby using a method similar to that of Maunsell and Gibson (1992). ThePSTH was constructed with 1 msec bins from #100 to %100 msec (stimulusonset " 0 msec). Onset latency was defined as the earlier of the first twoconsecutive poststimulus bins of the PSTH in which the spike countexceeded ( p $ 0.01) the count that would be expected from a Poissonprocess with mean spike count equal to that of spontaneous firing. Rate ofspontaneous firing was determined from the 100 msec interval precedingstimulus onset. Because the rising phase of the PSTH was very sharp (seeFig. 4A), latency measurement was relatively insensitive to the critical pvalue that was chosen. However, response latency is somewhat sensitive tothe number of trials, as is the Wilcoxon test of response magnitude. Thesemeasurements were always based on 279 stimulus trials (the minimumnumber used in any experiment) to make them comparable across allwhiskers of each rat. The bias attributable to using small numbers of trialswas evaluated by repeating the latency analyses on randomly chosensubsets of 50 trials.

To enable comparison with published data, we also estimated modallatencies, using the method of Armstrong-James and Fox (1987). Theanalysis was restricted to those cases for which the onset latency was welldefined. By measuring the time to first spike after stimulus onset on everytrial, we constructed a first-spike time histogram with 1 msec bins in theinterval 0 –100 msec poststimulus. The modal latency was defined as themode of this histogram.

Discriminabilit y of cortical population response patterns. To determinethe discriminability among the neural responses to different whiskers, weadapted the signal detection measure d& (Green and Swets, 1966). d& quan-tifies how discriminable two events are, based on responses to them. For asingle dependent response variable, d& is simply the absolute differencebetween the mean responses to the two events divided by the average SD.In the present case the events are stimuli presented to two differentwhiskers, and the dependent response variable is the spike count at anelectrode of interest. If the mean values of response for stimuli x and y aremx and my, respectively, and if the SD across both stimuli is &, then:

d& '!mx ( my!

&. (1)

This measure has been used to study how well single sensory neuronsdiscriminate among relevant stimulus features (Tolhurst et al., 1983; Essickand Whitsel, 1985).

When more than one response variable is available, it is necessary toconsider possible covariation among them across trials. If the responses toa given stimulus are statistically independent, then the population d& issimply the square root of the sum of the squared individual response d&s(Green and Swets, 1966):

d& ' "#i

d&i2 , (2)

where d&i is the discriminability at the ith response variable (electrode).Equation 2 also has been applied to sequentially recorded neurons, whereno information about covariance was available (Zohary, 1992; Geisler andAlbrecht, 1997). However, neocortical neurons are not, in general, statis-tically independent (Gawne and Richmond, 1993; Zohary et al., 1994; Leeet al., 1998). For a given set of stimuli the response covariance canconstitute either redundancy or synergy (Snippe, 1996; Oram et al., 1998;Abbott and Dayan, 1999), in which case Equation 2 will overestimate (forredundancy) or underestimate (for synergy) the true discriminability.

Table 1. Consistency of principal results across subjects

Experiment

Evoked spikesper stimulusmedian (IQR)

Number of respondingelectrodes median(IQR)

Response onsetlatency median(IQR)

Responseoffset timemean (SD)

Peak d&mean (SD)

r28 6.0 (4.3–10.3) 14 (8–15) 8 (5–8) 45.8 (19.0) 4.8 (1.0)r30 4.6 (2.6–5.7) 10 (7–12) 6 (5–17) 44.0 (12.4) 3.4 (0.9)r32 6.0 (3.3–6.0) 13 (10–13) 9 (7–12) 40.6 (9.3) 3.3 (0.7)ALL 5.7 (3.3–8.1) 12 (8–15) 8 (6–12) 43.9 (15.1) 4.3 (1.2)

Response latency and response offset time in msec. Standard deviation, SD; interquartile range, IQR.

6136 J. Neurosci., August 15, 2000, 20(16):6135–6143 Petersen and Diamond • Spatial–Temporal Activity and Stimulus Coding in Rat SI

Following the arguments of Green and Swets (1966), the generalization ofEquation 2 that takes covariance into account is:

d! ! !"mx " my#TC$1"mx " my# , (3)

where mx and my are mean response vectors across all electrodes, C is thematrix of covariances between pairs of electrodes, and T denotes matrixtransposition. In the pattern recognition literature this measure of popu-lation d! is sometimes known as the Mahalanobis distance (see Duda andHart, 1973).

In practice, means and covariances must be estimated from data. If thereare electrodes at which neurons do not respond or respond very weakly,then the inverse covariance matrix can become subject to serious samplingerror. In our case this problem was avoided in large part by repeating eachstimulus many times (279 –500 trials per whisker) and by restricting theanalysis to electrodes for which the neurons yielded a significant response.Thus, if there were 10 responding electrodes in the 100-electrode array,then mx and my would be 10-dimensional, and C would be 10 % 10. In thefew cases in which the covariance matrix remained singular, we computeddiscriminability in the subspace in which it was invertible (Metzner et al.,1998), using the singular value decomposition (see Strang, 1988):

d! ! !"mx " my#TQ&$1QT"mx " my# . (4)

Given that C is a N%N matrix with rank R, then Q is the N%R matrix forwhich the columns are the R eigenvectors of C with non-zero eigenvalue,and & is the R%R diagonal matrix of corresponding eigenvalues.

Bias is another issue that arises when estimating d! from a finite set ofdata. Suppose that the identical stimulus is delivered across two sets oftrials. Ideally, the discriminability between the two sets of responses wouldbe zero. In practice, however, the difference between the two sample meanresponses inevitably will be non-zero, resulting in a non-zero value of d!.In this light, it was important to estimate the chance d! value obtained bycomparing response sets taken from the same stimulus. This was accom-plished by randomly assigning the responses obtained for a given stimulusto two sets and estimating d! between these two sets. The procedure wasrepeated 10 times for each stimulus site, yielding estimates for the meanand SD of the chance d!. Thus, for each pair of stimulus sites a true d!estimate and two separate chance d! values were obtained (see Fig. 7A).Finally, the significance of the true d! was evaluated by computing z scores.

RESULTSCortical population response to a single whiskerThe vibrissae of the snout are arranged in rows A–E, readilyidentifiable in all subjects (Fig. 1A), and neighborhood relations

among whiskers are conserved in the local topographic relation-ships among the barrel-columns in contralateral primary somato-sensory cortex (Woolsey and Van der Loos, 1970; Welker, 1971). Inthe present experiments the 400 #m spacing between the elec-trodes of the array resulted in each column being penetrated by oneto three electrodes; a cortical column lying within the array gridwas never excluded (Fig. 1C).

In each of the three experiments the neurons residing in '20–30cortical columns were recorded. This permitted us to generatemaps representing the spatial distribution of the cortical populationresponse as a function of stimulus site. Figure 2, A and B, illustratesthe method by using rat r28 as an example. Vibrissa C1 wasstimulated 279 times, and a PSTH with 2 msec bins was generatedat each electrode for the interval from 40 msec before, until 40msec after, stimulus onset. All 100 PSTHs are illustrated in Figure2A. Those electrodes for which neurons gave the largest responseare evident by the peak values in the PSTHs. Response magnitudeevoked at each electrode was calculated as the average spike countfor the 40 msec interval after stimulus onset minus the averagespike count in the 40 msec prestimulus interval. In Figure 2B, thesevalues have been plotted at the corresponding electrode positions,on a color scale, to create a “response map.” The total number ofresponding electrodes was 14 (see Materials and Methods forstatistical criteria).

To learn about the unfolding of the cortical response over time,Figure 3 (top) illustrates neuronal activity in sequential 2 msecsegments after upward deflection of whisker C2 in rat r32. In thetime window 4–6 msec after stimulus onset, the cortical responseemerged as a small central core focused on one electrode. In thetime windows 8–10 and 10–12 msec after stimulus onset, the zoneof activation expanded laterally to include an area of eight elec-trodes (1.28 mm 2). Thereafter, the cortical activation—both inarea and in magnitude—diminished rapidly. The low level ofactivity evident at 14–16 msec persisted until 36 msec after stim-ulus onset (data not shown). Release of the whisker from theupward position produced a response to “stimulus offset,” illus-

Figure 1. Sampling of the cortical vibrissal representation with a 10 % 10 electrode array. A, Disposition of the whiskers (shown as stubs) on the snout.Rows are labeled with letters A (dorsal) to E (ventral). B, Array position for rat r30 based on a photomicrograph of the preparation. Light gray shading isthe dura mater exposed by the craniotomy. A 500 #m length of the electrodes is visible (shown in black), and the remaining 500 #m length (shown in white)is implanted in the tissue. C, Placement of the 10 % 10 microelectrode for rat r28. A barrel map was drawn from a nitric oxide synthetase-labeled tangentialsection (Valtschanoff et al., 1993) and used as a template. Then an electrode grid template was positioned to give the best fit to the physiological data; i.e.,each electrode was ascribed the columnar location that matched its principal whisker (see Materials and Methods). tr, Trunk; hl, hindlimb; fl, forelimb;ul, upper lip; ll, lower lip; no, nose; rv, rostral vibrissae.

Petersen and Diamond • Spatial–Temporal Activity and Stimulus Coding in Rat SI J. Neurosci., August 15, 2000, 20(16):6135–6143 6137

C is the covariance matrix between pairs of electrodes

Peterson RS, Diamond ME, 2000

Spike timing in population coding

• Spike count or spike timing?

• The precise firing of spikes (within inter-spike interval) is to reflect random processes, or is an additional, informative dimension of the response?

• ANN method: stimulus discriminability improves as bin size decreased from 40 ms to 6 ms---->spike timing may play an important role.

• Information theory: SEMI estimation confirm ANN method.

Spike timing in population coding

(Figure 2d). Given that most neurons would be expectedto fire at most a single spike within 12–16 ms of stimulusonset, the d’ time course suggests that these single, short-latency spikes are an important component of the neuralcode. This was directly tested using the SEMI method, byestimating the degree of discriminability based on thewhole spike train compared to that of the first spike (time)by itself [14••,15••]. 90% of the information transmitted bythe whole spike train (both for single cells and cell pairs)could be accounted for by just the timing of the first post-stimulus spike in each cell. Moreover, although laterspikes were potentially informative (the second spike contained ~45% of the total spike train information), theircontributions were almost completely redundant with the first.

To summarise, data from ANN, information theory, andpopulation d’ all argue that the cortical code for stimuluslocation is based not simply on the spike count, but on themillisecond precision timing of the spikes. The latter twoanalyses described above additionally suggest that the timing of the first stimulus-evoked spike of individualneurons might be particularly important.

Role of correlated spike patterns in populationcodingThe presence of correlated population activity in rat barrelcortex [16] raises the possibility of synergistic coding,where the information conveyed by an ensemble of spikesis more than the sum of the information conveyed by theindividual spikes (Figure 4). However, the relationshipbetween correlated activity and neural coding is complex:under different circumstances, correlations can cause the

spikes in an ensemble to exert synergistic or redundanteffects [12,17–19]. A simpler type of cortical populationcode is one in which spikes encode stimuli independentlyof one another. The key question, for our purposes, iswhether correlations provide the ideal decoder with additional information beyond that already available in theindividual spikes.

Synergistic coding of stimulus location has been testedusing ANN and SEMI methods. A particularly useful feature of the SEMI is that it quantifies the contribution ofcorrelated spike patterns separately from that of individualspikes. What role do spike patterns play in the encoding of stimulus location by pairs of barrel cortex neurons?Averaged over 52 pairs of cells located in barrel column D2,individual spikes carried 83% of the overall information[15••] (Figure 4c). Similar results were found for neuronpairs in different columns. The series expansion allowedthe 17% of total information that originated in synergy tobe split it into ‘within-cell’ (Figure 4b) and ‘cross-cell’(Figure 4a) contributions. Synergy was entirely attributableto spike patterns occurring within individual cells: cross-neuron spike patterns provided no additional contributionbeyond that supplied by individual spikes (Figure 4d).

The role of cross-correlations in encoding stimulus site hasbeen tested using a variant of the ANN method — ‘lineardiscriminant analysis’ — by comparing performance on theactual simultaneously recorded data (~30 neurons) versusperformance on randomly ‘trial-shuffled’ data [7•]. The latter procedure conserves the time-varying firing rate ofeach neuron but destroys any structure in the cross-cell

444 Sensory systems

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Role of spike timing in coding stimulus site. (a) Spikes fired by a neuronin barrel column D2 in response to 10 deflections of whisker D2.Neuronal response is quantified to allow spike count and spike timingcodes to be compared (see text for details). (b) Mutual information

conveyed by both codes about stimulus site was estimated using theSEMI method [14••] and is plotted as a cumulative function of post-stimulus time, averaged over 106 single units in barrel column D2.Reproduced with permission from [15••]. Bars denote standard errors.

Correlated spike patterns in population coding

• Question: whether correlation provide additional information beyond that already available in the individual spikes.

correlations. The result was that after trial-shuffling, ANNperformance was either unchanged or slightly improved,consistent with the demonstration [15••] that cross-cellpatterns are not synergistic.

Conclusions: principles of population codingWe have explored which components of somatosensory cortical population activity encode stimulus location. Theagreement among the observations gleaned from differentanalysis strategies encourages us to give concrete answers tothe questions posed at the outset. What is the spatial organi-sation of the neural code? Neurons beyond the principalcolumn of the stimulated whisker carry some informationabout stimulus location, but this information is largely redundant with that present at shorter latencies within theprincipal column (Figure 2d). The available data thus argue

that patterned activity distributed across the cortex might notbe an essential element of the code, supporting the modelillustrated in Figure 1d. What is the role of spike timing?Precise spike timing (to at least 5 ms) conveys considerableinformation beyond that available only in the spike count(Figure 3b). The time of the first post-stimulus spike is par-ticularly informative. What is the role of spike correlations?Within the neuronal population, the most important functional unit for stimulus localisation is the individualspike (Figure 4c). Such synergy as exists (giving rise to about17% of all available information) derives from within-cellspike patterns (Figure 4d); there is no current evidence forsynergy at the cross-neuronal level in this system.

It is important to establish whether these coding principlesapply more generally to other sorts of stimuli and to other


Figure 4

Role of correlated spike patterns in stimuluslocation coding. (a) A cross-cell spike patternmeans that the probability of unit 1 firing aspike at time t1 and unit 2 firing a spike at timet2 differs from the level expected were thespikes to occur independently. An illustrativejoint PSTH for two neurons (left) is comparedto the joint PSTH predicted from independentfiring (right): the higher values along thediagonal in the left plot reveal synchronisedcross-cell patterns. (b) A within-cell spikepattern means that the probability of the unitfiring a spike both at time t1 and at time t2differs from the level expected were thespikes to occur independently. Comparison ofthe joint PSTH and its predictor shows thatthe cell has spike patterns characteristic ofrefractoriness. (c) Using the S EMI method,the contributions of independent spikes,cross-cell spike patterns and within-cell spikepatterns were estimated separately for52 pairs of cells recorded simultaneously frombarrel column D2 [15••]. The contribution ofindividual spikes to the total mutualinformation is compared to that of both typesof spike pattern considered together.(d) Contributions of cross-cell and within-cellpatterns are compared directly. Bars denotestandard errors.

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ConclusionPrinciples of population coding

• Spatial organization of the neural code: Figure 1d

• Role of spike timing: Figure 3b

• Role of spike correlations: Figure 4 c,d

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