{"title": "Binary Coding in Auditory Cortex", "book": "Advances in Neural Information Processing Systems", "page_first": 117, "page_last": 124, "abstract": null, "full_text": "Binary Coding in Auditory Cortex \n\nMichael R. DeWeese and Anthony M. Zador \n\nCold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724 \n\ndeweese@cshl.edu, zador@cshl.edu \n\nAbstract\n\nCortical neurons have been reported to use both rate and temporal \ncodes. Here we describe a novel mode in which each neuron \ngenerates exactly 0 or 1 action potentials, but not more, in response \nto a stimulus. We used cell-attached recording, which ensured \nsingle-unit isolation, to record responses in rat auditory cortex to \nbrief tone pips. Surprisingly, the majority of neurons exhibited \nbinary behavior with few multi-spike responses; several dramatic \nexamples consisted of exactly one spike on 100% of trials, with no \ntrial-to-trial variability in spike count. Many neurons were tuned to \nstimulus frequency. Since individual trials yielded at most one \nspike for most neurons, the information about stimulus frequency \nwas encoded in the population, and would not have been accessible \nto later stages of processing that only had access to the activity of a \nsingle unit. These binary units allow a more efficient population \ncode than is possible with conventional rate coding units, and are \nconsistent with a model of cortical processing \nin which \nsynchronous packets of spikes propagate stably from one neuronal \npopulation to the next. \n\n1 B i n a r y c o d i n g i n a u d i t o r y c o r t e x \n\nWe recorded responses of neurons in the auditory cortex of anesthetized rats to \npure-tone pips of different frequencies [1, 2]. Each pip was presented repeatedly, \nallowing us to assess the variability of the neural response to multiple presentations \nof each stimulus. We first recorded multi-unit activity with conventional tungsten \nelectrodes (Fig. 1a). The number of spikes in response to each pip fluctuated \nmarkedly from one trial to the next (Fig. 1e), as though governed by a random \nmechanism such as that generating the ticks of a Geiger counter. Highly variable \nresponses such as these, which are at least as variable as a Poisson process, are the \nnorm in the cortex [3-7], and have contributed to the widely held view that cortical \nspike trains are so noisy that only the average firing rate can be used to encode \nstimuli. \n\nBecause we were recording the activity of an unknown number of neurons, we could \nnot be sure whether the strong trial-to-trial fluctuations reflected the underlying \nvariability of the single units. We therefore used an alternative technique, cell-\n\n\fa\n\nc\n\nMulti-unit\n\nb\n\nSingle-unit recording method\n\n10 kHz\n\nSingle-unit\n\n.\n\n. ... .. ... ... ....... . ...\n\nV\nm\n5\n\n1sec\nRaw cell-\nattached\nvoltage\n\nIdentified\n\nspikes\n\nThreshold\n\nHigh-pass\n\nfiltered\n\n28 kHz\n\nd\n\nSingle-unit\n\n38 kHz\n\n0\n\n40\n\n120 160 200\n\n80\nTime (msec)\n\ne\n\n)\nl\na\ni\nr\nt\n/\ns\ne\nk\ni\np\ns\n(\n \nn\na\ne\nm\n/\ne\nc\nn\na\n\ni\nr\na\nv\n\n \n\ne\ns\nn\no\np\ns\ne\nR\n\n4\n\n3\n\n2\n\n1\n\nb\n\ni\n\nn\n\na\n\nr\n\ny\n\nN = 29 tones\n\nPoisson\n\nN = 11 tones\n\n0\n\n1\n\n0\nMean response (spikes/trial)\n\n2\n\n3\n\nFigure 1: Multi-unit spiking activity was highly variable, but single units obeyed binomial \nstatistics. a Multi-unit spike rasters from a conventional tungsten electrode recording showed \nhigh trial-to-trial variability in response to ten repetitions of the same 50 msec pure tone \nstimulus (bottom). Darker hash marks indicate spike times within the response period, which \nwere used in the variability analysis. b Spikes recorded in cell-attached mode were easily \nidentified from the raw voltage trace (top) by applying a high-pass filter (bottom) and \nthresholding (dark gray line). Spike times (black squares) were assigned to the peaks of \nsuprathreshold segments. c Spike rasters from a cell-attached recording of single-unit \nresponses to 25 repetitions of the same tone consisted of exactly one well-timed spike per \ntrial (latency standard deviation = 1.0 msec), unlike the multi-unit responses (Fig. 1a). Under \nthe Poisson assumption, this would have been highly unlikely (P ~ 10-11). d The same neuron \nas in Fig. 1c responds with lower probability to repeated presentations of a different tone, but \nthere are still no multi-spike responses. e We quantified response variability for each tone by \ndividing the variance in spike count by the mean spike count across all trials for that tone. \nResponse variability for multi-unit tungsten recording (open triangles) was high for each of \nthe 29 tones (out of 32) that elicited at least one spike on one trial. All but one point lie \nabove one (horizontal gray line), which is the value produced by a Poisson process with any \nconstant or time varying event rate. Single unit responses recorded in cell-attached mode \nwere far less variable (filled circles). Ninety one percent (10/11) of the tones that elicited at \nleast one spike from this neuron produced no multi-spike responses in 25 trials; the \ncorresponding points fall on the diagonal line between (0,1) and (1,0), which provides a strict \nlower bound on the variability for any response set with a mean between 0 and 1. No point \nlies above one. \n\nattached recording with a patch pipette [8, 9], in order to ensure single unit isolation \n(Fig. 1b). This recording mode minimizes both of the main sources of error in spike \ndetection: failure to detect a spike in the unit under observation (false negatives), \nand contamination by spikes from nearby neurons (false positives). It also differs \nfrom conventional extracellular recording methods in its selection bias: With cell-\n\n\fattached recording neurons are selected solely on the basis of the experimenter(cid:146)s \nability to form a seal, rather than on the basis of neuronal activity and \nresponsiveness to stimuli as in conventional methods.\n\nSurprisingly, single unit responses were far more orderly than suggested by the \nmulti-unit recordings; responses typically consisted of either 0 or 1 spikes per trial, \nand not more (Fig. 1c-e). In the most dramatic examples, each presentation of the \nsame tone pip elicited exactly one spike (Fig. 1c). In most cases, however, some \npresentations failed to elicit a spike (Fig. 1d). Although low-variability responses \nhave recently been observed in the cortex [10, 11] and elsewhere [12, 13], the \nbinary behavior described here has not previously been reported for cortical \nneurons.\n\nThe majority of the neurons (59%) in our study for which statistical significance \ncould be assessed (at the p<0.001 significance level; see Fig. 2, caption) showed\nnoisy binary behavior(cid:151)(cid:147)binary(cid:148) because neurons produced either 0 or 1 spikes, and \n(cid:147)noisy(cid:148) because some stimuli elicited both single spikes and failures. In a \nsubstantial fraction of neurons, however, the responses showed more variability. We \nfound no correlation between neuronal variability and cortical layer (inferred from \nthe depth of the recording electrode), cortical area (inside vs. outside of area A1) or \ndepth of anesthesia. Moreover, the binary mode of spiking was not due to the \nbrevity (25 msec) of the stimuli; responses that were binary for short tones were \ncomparably binary when longer (100 msec) tones were used (Fig. 2b).\n\na\n\n)\nl\n\na\n\n1.4\n\nN = 3055 response sets \n\nb\n\ni\nr\nt\n/\n\ni\n\ns\ne\nk\np\ns\n(\n \nn\na\ne\nm\ne\nc\nn\na\n\n/\n\ni\nr\na\nv\n\n \n\ne\ns\nn\no\np\ns\ne\nR\n\n1.2\n\n1\n\n0.8\n\n0.6\n\n0.4\n\n0.2\n\n0\n\n0\n\nPoisson\n\n28 kHz - 100 msec\n\nb\ni\nn\n\na\n\nr\n\ny\n\nNot assessable\nNot significant\nSignificant (p<0.001)\n\n0.2 0.4 0.6\nMean response (spikes/trial)\n\n0.8\n\n1\n\n1.2 1.4\n\n28 kHz - 25 msec\n\n0\n\n40\n\n120\n\n80\nTime (msec)\n\n160\n\n200\n\nFigure 2: Half of the neuronal population exhibited binary firing behavior. a Of the 3055 \nsets of responses to 25 msec tones, 2588 (gray points) could not be assessed for significance \nat the p<0.001 level, 225 (open circles) were not significantly binary, and 242 were \nsignificantly binary (black points; see Identification methods for group statistics below). All \npoints were jittered slightly so that overlying points could be seen in the figure. 2165 \nresponse sets contained no multi-spike responses; the corresponding points fell on the line \nfrom [0,1] to [1,0]. b The binary nature of single unit responses was insensitive to tone \nduration, even for frequencies that elicited the largest responses. Twenty additional spike \nrasters from the same neuron (and tone frequency) as in Fig. 1c contain no multi-spike \nresponses whether in response to 100 msec tones (above) or 25 msec tones (below). Across \nthe population, binary responses were as prevalent for 100 msec tones as for 25 msec tones \n(see Identification methods for group statistics).\n\nIn many neurons, binary responses showed high temporal precision, with latencies \nsometimes exhibiting standard deviations as low as 1 msec (Fig. 3; see also Fig. 1c), \ncomparable to previous observations in the auditory cortex [14], and only slightly \n\n\fmore precise than in monkey visual area MT [5]. High temporal precision was \npositively correlated with high response probability (Fig. 3).\n\na\n\n)\nc\ne\ns\nm\n\n(\n \nr\ne\nt\nt\ni\nJ\n\n14\n\n12\n\n10\n\n8\n\n6\n\n4\n\n2\n\n0\n\nN = 32 tones\n\n0\n\n0.2\n\n0.4\n\n0.6\n\n0.8\n\n1\n\nMean response (spikes/trial)\n\nb\n\n40\n\n30\n\n20\n\n10\n\n)\nc\ne\ns\nm\n\n(\n \nr\ne\nt\nt\ni\nJ\n\n0\n\n0\n\nN = (44 cells)x(32 tones)\n\n0.4\n\n0.8\n\n1.2\n\n1.6\n\n2\n\nMean response (spikes/trial)\n\nFigure 3: Trial-to-trial variability in latency of response to repeated presentations of the \nsame tone decreased with increasing response probability. a Scatter plot of standard \ndeviation of latency vs. mean response for 25 presentations each of 32 tones for a different \nneuron as in Figs. 1 and 2 (gray line is best linear fit). Rasters from 25 repeated presentations \nof a low response tone (upper left inset, which corresponds to left-most data point) display \nmuch more variable latencies than rasters from a high response tone (lower right inset;\ncorresponds to right-most data point). b The negative correlation between latency variability \nand response size was present on average across the population of 44 neurons described in \nIdentification methods for group statistics (linear fit, gray).\n\nThe low trial-to-trial variability ruled out the possibility that the firing statistics \ncould be accounted for by a simple rate-modulated Poisson process (Fig. 4a1,a2). In \nother systems, low variability has sometimes been modeled as a Poisson process \nfollowed by a post-spike refractory period [10, 12]. In our system, however, the \nrange in latencies of evoked binary responses was often much greater than the \nrefractory period, which could not have been longer than the 2 msec inter-spike \nintervals observed during epochs of spontaneous spiking, indicating that binary \nspiking did not result from any intrinsic property of the spike generating mechanism \n(Fig. 4a3). Moreover, a single stimulus-evoked spike could suppress subsequent \nspikes for as long as hundreds of milliseconds (e.g. Figs. 1d,4d), supporting the idea \nthat binary spiking arises through a circuit-level, rather than a single-neuron, \nmechanism. Indeed, the fact that this suppression is observed even in the cortex of \nawake animals [15] suggests that binary spiking is not a special property of the \nanesthetized state. \n\nIt seems surprising that binary spiking in the cortex has not previously been \nremarked upon. In the auditory cortex the explanation may be in part technical: \nBecause firing rates in the auditory cortex tend to be low, multi-unit recording is \noften used to maximize the total amount of data collected. Moreover, our use of \ncell-attached recording minimizes the usual bias toward responsive or active \nneurons.\n\nSuch explanations are not, however, likely to account for the failure to observe \nbinary spiking in the visual cortex, where spike count statistics have been \nscrutinized more closely [3-7]. One possibility is that this reflects a fundamental \ndifference between the auditory and visual systems. An alternative interpretation(cid:151) \n\n\fa1\n\n100 spikes/s\n\nb\n\ny\nt\ni\nl\ni\n\n \n\nb\na\nb\no\nr\np\ne\ns\nn\no\np\ns\ne\nR\n\n2 kHz\n\n0\n\n100\n\n300\n\n200\nTime (msec)\n\n400\n\n500\n\n20\n\n16\n\n12\n\ns\ne\nz\ni\n\ns\n\n \nl\n\no\no\np\n \nf\no\no\ni\nt\na\nR\n\n \n\na2\n\nPoisson simulation\n\nc\n\nPSTH\n\na3\n\nPoisson with refractory period\n\nd\n\n0\n\n40\n\n120 160 200\n\n80\nTime (msec)\n\n8\n\n4\n\n0\n\n0.2\n\n1\nMean spike count per neuron\n\n0.6\n\n0.4\n\n0.8\n\ny\nt\ni\nl\ni\n\nb\na\nb\no\nr\np\n \ne\ns\nn\no\np\ns\ne\nR\n\nN = 32 tones\n\n1\n\n0.8\n\n0.6\n\n0.4\n\n0.2\n\n0\n\n2.0\n\n3.8\n\n7.1\n\n13.2 24.9 46.7\n\nTone frequency (kHz)\n\nFigure 4: a The lack of multi-spike responses elicited by the neuron shown in Fig. 3a were \nnot due to an absolute refractory period since the range of latencies for many tones, like that \nshown here, was much greater than any reasonable estimate for the neuron(cid:146)s refractory \nperiod. (a1) Experimentally recorded responses. (a2) Using the smoothed post stimulus time \nhistogram (PSTH; bottom) from the set of responses in Fig. 4a, we generated rasters under \nthe assumption of Poisson firing. In this representative example, four double-spike responses \n(arrows at left) were produced in 25 trials. (a3) We then generated rasters assuming that the \nneuron fired according to a Poisson process subject to a hard refractory period of 2 msec. \nEven with a refractory period, this representative example includes one triple- and three \ndouble-spike responses. The minimum interspike-interval during spontaneous firing events \nwas less than two msec for five of our neurons, so 2 msec is a conservative upper bound for \nthe refractory period. b. Spontaneous activity is reduced following high-probability \nresponses. The PSTH (top; 0.25 msec bins) of the combined responses from the 25% (8/32) \nof tones that elicited the largest responses from the same neuron as in Figs. 3a and 4a \nillustrates a preclusion of spontaneous and evoked activity for over 200 msec following \nstimulation. The PSTHs from progressively \ntones show \nprogressively less preclusion following stimulation. c Fewer noisy binary neurons need to be \npooled to achieve the same (cid:147)signal-to-noise ratio(cid:148) (SNR; see ref. [24]) as a collection of \nPoisson neurons. The ratio of the number of Poisson to binary neurons required to achieve \nthe same SNR is plotted against the mean number of spikes elicited per neuron following \nstimulation; here we have defined the SNR to be the ratio of the mean spike count to the \nstandard deviation of the spike count. d Spike probability tuning curve for the same neuron \nas in Figs. 1c-e and 2b fit to a Gaussian in tone frequency.\n\nless responsive groups of \n\nand one that we favor(cid:151)is that the difference rests not in the sensory modality, but \ninstead in the difference between the stimuli used. In this view, the binary responses \nmay not be limited to the auditory cortex; neurons in visual and other sensory \ncortices might exhibit similar responses to the appropriate stimuli. For example, the \n\n\ftone pips we used might be the auditory analog of a brief flash of light, rather than \nthe oriented moving edges or gratings usually used to probe the primary visual \ncortex. Conversely, auditory stimuli analogous to edges or gratings [16, 17] may be \nmore likely to elicit conventional, rate-modulated Poisson responses in the auditory \ncortex. Indeed, there may be a continuum between binary and Poisson modes. Thus, \neven in conventional rate-modulated responses, the first spike is often privileged in \nthat it carries most of the information in the spike train [5, 14, 18]. The first spike \nmay be particularly important as a means of rapidly signaling stimulus transients. \n\nBinary responses suggest a mode that complements conventional rate coding. In the \nsimplest rate-coding model, a stimulus parameter (such as the frequency of a tone) \ngoverns only the rate at which a neuron generates spikes, but not the detailed \npositions of the spikes; the actual spike train itself is an instantiation of a random \nprocess (such as a Poisson process). By contrast, in the binomial model, the \nstimulus parameter (frequency) is encoded as the probability of firing (Fig. 4d).\n\nBinary coding has implications for cortical computation. In the rate coding model, \nstimulus encoding is (cid:147)ergodic(cid:148): a stimulus parameter can be read out either by \nobserving the activity of one neuron for a long time, or a population for a short time. \nBy contrast, in the binary model the stimulus value can be decoded only by \nobserving a neuronal population, so that there is no benefit to integrating over long \ntime periods (cf. ref. [19]). One advantage of binary encoding is that it allows the \npopulation to signal quickly; the most compact message a neuron can send is one \nspike [20]. Binary coding is also more efficient in the context of population coding, \nas quantified by the signal-to-noise ratio (Fig. 4c).\n\nThe precise organization of both spike number and time we have observed suggests \nthat cortical activity consists, at least under some conditions, of packets of spikes \nsynchronized across populations of neurons. Theoretical work [21-23] has shown \nhow such packets can propagate stably from one population to the next, but only if \nneurons within each population fire at most one spike per packet; otherwise, the \nnumber of spikes per packet(cid:151)and hence the width of each packet(cid:151)grows at each \npropagation step. Interestingly, one prediction of stable propagation models is that \nspike probability should be related to timing precision, a prediction born out by our \nobservations (Fig. 3). The role of these packets in computation remains an open \nquestion. \n\n2 I d e n t i f i c a t i o n m e t h o d s f o r g r o u p s t a t i s t i c s \n\nWe recorded responses to 32 different 25 msec tones from each of 175 neurons from \nthe auditory cortices of 16 Sprague-Dawley rats; each tone was repeated between 5 \nand 75 times (mean = 19). Thus our ensemble consisted of 32x175=5600 response \nsets, with between 5 and 75 samples in each set. Of these, 3055 response sets \ncontained at least one spike on at least on trial. For each response set, we tested the \nhypothesis that the observed variability was significantly lower than expected from \nthe null hypothesis of a Poisson process. The ability to assess significance depended \non two parameters: the sample size (5-75) and the firing probability. Intuitively, the \ndependence on firing probability arises because at low firing rates most responses \nproduce only trials with 0 or 1 spikes under both the Poisson and binary models; \nonly at high firing rates do the two models make different predictions, since in that \ncase the Poisson model includes many trials with 2 or even 3 spikes while the binary \nmodel generates only solitary spikes (see Fig. 4a1,a2). Using a stringent \nsignificance criterion of p<0.001, 467 response sets had a sufficient number of \nrepeats to assess significance, given the observed firing probability. Of these, half \n(242/467=52%) were significantly less variable than expected by chance, five \nhundred-fold higher than the 467/1000=0.467 response sets expected, based on the \n\n\f0.001 significance criterion, to yield a binary response set. Seventy-two neurons had \nat least one response set for which significance could be assessed, and of these, 49 \nneurons (49/72=68%) had at least one significantly sub-Poisson response set. Of this \npopulation of 49 neurons, five achieved low variability through repeatable bursty \nbehavior (e.g., every spike count was either 0 or 3, but not 1 or 2) and were \nexcluded from further analysis. The remaining 44 neurons formed the basis for the \ngroup statistics analyses shown in Figs. 2a and 3b. Nine of these neurons were \nsubjected to an additional protocol consisting of at least 10 presentations each of \n100 msec tones and 25 msec tones of all 32 frequencies. 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