Binary Spiking in Auditory Cortex

Multiunit recordings

We first recorded multiunit activity with conventional low-impedance tungsten electrodes (Fig. 1a). The number of spikes in response to each pip fluctuated markedly from one trial to the next, as though governed by a random mechanism such as that generating the ticks of a Geiger counter. Such highly variable responses are comparable to those recorded throughout the visual cortex (Tolhurst et al., 1983; Softky and Koch, 1993; Buracas et al., 1998; Shadlen and Newsome, 1998; Stevens and Zador, 1998) and have contributed to the widely held view that cortical spike trains are so noisy that only the average firing rate can be used to encode stimuli.

Cell-attached single-unit recordings

Because we were recording the activity of an unknown number of neurons, we could not be sure of the relationship between the strong trial-to-trial fluctuations observed in the population and the underlying variability of the single units. We therefore used an alternative technique, cell-attached recording with a patch pipette (Otmakhov et al., 1993; Friedrich and Laurent, 2001; Margrie et al., 2002), to ensure single-unit isolation (Fig. 2). This recording mode minimizes both of the main sources of error in spike detection: failure to detect a spike in the unit under observation (false negatives) and contamination by spikes from nearby neurons (false positives). Although single-unit isolation can also be obtained using high-impedance tungsten electrodes, cell-attached recording also differs from conventional extracellular recording methods in its selection bias. With cell-attached recording, neurons are selected solely on the basis of the experimenter's ability to form a seal, rather than on the basis of neuronal activity such as spontaneous activity or responsiveness to particular stimuli, as in conventional methods.

Surprisingly, single-unit responses were far more orderly than suggested by the multiunit recordings; responses typically consisted of either 0 or 1 spikes per trial, and not more. In the most dramatic examples, each presentation of the same tone pip elicited exactly one spike (Fig. 1b). In most cases, however, some presentations failed to elicit a spike (Fig. 1c). Thus, these single-unit responses could be characterized as a noisy binary process: “binary” because neurons produced either 0 or 1 spikes, and “noisy” because some stimuli elicited single spikes on some trials, but no spikes on others.

Eleven of the 32 tones presented to this neuron elicited at least one spike on at least one trial (out of 27 repetitions). For these eleven tones, we compared the mean spike count to the Fano factor (the ratio of the variance to the mean of the distribution of spike counts on individual trials). The Fano factor for any neuron that displays binary spiking is the same as for a binomial process with the same probability of spiking per trial, p, and is given by variance/mean = [p (1 - p)]/(p) = 1 - p, independent of the number of trials. Thus, on a plot of p versus Fano factor, a collection of perfectly binary responses (i.e., trials consisting of no multispike responses) falls along the diagonal (1 - p) connecting the top left and bottom right corners of the unit square (Fig. 3a). For this neuron, 10 of the 11 tones elicited perfectly binary responses and so fell exactly along the diagonal, whereas one point deviated slightly from the diagonal because of a lone double-spiked response.

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Figure 3.

Multiunit spiking activity was highly variable, but single units obeyed binomial statistics. a, Response variability for the multiunit tungsten recording (triangles) was high for all tones that evoked any response from the neurons being recorded. All points lie near or above one (horizontal line), the value expected from a Poisson process. Single-unit responses recorded in cell-attached mode were far less variable (circles; same neuron as in Fig. 1b,c). All but one of the 11 tones that elicited at least one spike never produced a multispike response in 25 trials, as one would expect from a binary process (diagonal line). b, Spike probability tuning curve for the same neuron as in Figures 1, b and c, and 3a fit to a Gaussian tuning curve.

By comparison, most of the multiunit responses fell far above the diagonal on this plot (Fig. 3a). Indeed, all but one of the multiunit responses fell above the horizontal line corresponding to the Fano factor of unity, indicating trial-to-trial variability in excess of that expected from Poisson spiking. Below we show how the multiunit and single-unit responses can be reconciled by assuming correlations between units (see Reconciling multiunit and single-unit recordings below).

The probability of firing a single spike was related to stimulus frequency (Fig. 3b) (Calford and Semple, 1995). This suggests that the conventional notion of a tuning curve, in which spike rate is related to some stimulus parameter, can readily be extended to binary responses.

The majority of responses are binary

How prevalent were binary responses such as those illustrated by Figures 1, b and c, and 3a? One approach to answering this question would be to assess directly the degree to which our data were consistent with binomial statistics. However, in a real experimental setting, small deviations from perfectly binary spiking are to be expected, and we do not have a good noise model to account for these deviations. For example, although it might seem reasonable to model the deviant spikes that occur during tones as “spontaneous”, i.e., as occurring at the same rate as the spikes that occur during the intertone interval, such a model includes an implicit assumption about the additivity of noise during spontaneous and evoked activity. An ideal statistical test would include no such strong ad hoc assumptions.

We therefore adopted an alternate approach. We devised a statistical test to distinguish binary responses from those consistent with a Poisson process (the null hypothesis). We formulated the question in terms of deviations from the null hypothesis of a Poisson process by asking whether the observed variability was significantly below that expected from a Poisson process (see Materials and Methods for details). Expressed this way, establishing significance requires that two conditions be satisfied. First, the amount of data had to be sufficient (given the observed firing rate and number of repetitions) to distinguish Poisson from binary firing. This is because, at low firing rates, Poisson and binary firing are indistinguishable given limited data (Fig. 4); thus only some responses can be classified, whereas others must be regarded as potentially consistent with either hypothesis. Second, the neuronal variability (as quantified by the Fano factor) had to be sufficiently low that the chances of observing such variability was less than some statistical confidence level. Intuitively, our test assessed whether, when plotted as in Figure 3a, points were significantly below the horizontal (Poisson) line, in the direction of the diagonal (binary) line. This test is highly conservative, because a perfectly binary response might nonetheless be characterized as unclassifiable if the response probability were too low or the sample size too small.

Figure 4 (compare c, d) emphasizes the difference, evident at high firing rates, between Poisson and binary spiking. In each set of simulated trials there are exactly 20 spikes; thus, the mean spike count is one spike per trial in both cases. In the Poisson set (Fig. 4c), some trials have no spikes at all, some have one, some two, and some three spikes. By contrast, in the binary set (Fig. 4d), the same 20 spikes are arrayed over the 20 trials in a much more orderly manner, with exactly one spike per trial. The two sets of rasters are thus clearly different, even in the case where there is on average one spike per trial. It is this difference that our statistical test captures.

The majority of response sets (370/624 = 59%) for which statistical significance could be assessed (at the p < 0.01 significance level) were well characterized as binary (Fig. 5a). We emphasize that, by definition, <1 of 100 responses (i.e., no more than ∼6 of the 624 for which significance could be assessed) would have been expected to show such low variability by chance, given the null hypothesis of a Poisson process. Moreover, the majority of the 91 neurons (75/91 = 82%) for which significance could be assessed showed at least one significantly sub-Poisson response (p < 0.01). Even using a more stringent criterion of p < 0.001, half (239/458 = 52%) of the response sets and 68% (49/72) of the neurons were still significantly sub-Poisson. Therefore, low-variability spiking was not an anomalous finding, characteristic of a limited subset of neurons or responses, but was instead a typical mode of firing among neurons in our sample.

Most responses with sub-Poisson variability consisted of either one or zero spikes on nearly every trial, as in Figure 1, b and c, and thus were well characterized as binary. However, 13 neurons achieved low variability for at least one tone by firing stereotyped multispike bursts in which nearly every spike count was, for example, either 0 or 3, but not 1, 2, 4, or greater (Fig. 5b). Such bursty responses have been previously described in the anesthetized cat (Phillips and Sark, 1991). Note that we use the term burst here phenomenologically, with no suggestion of the mechanism underlying the multispike response.

Approximately 41% of the responses were not significantly sub-Poisson. In some cases response variability was supra-Poisson (i.e., Fano factor greater than unity), as expected from recordings in other cortical regions. Heterogeneity in response variability has also been reported in the primary visual cortex of the anesthetized cat, in which only well isolated and well driven layer 4 neurons show markedly sub-Poisson variability (Kara et al., 2000). However, we found no comparable dependence of response variability on recording depth. Although our depth measurements were not validated with electrolytic lesions (cf. Kara et al., 2000) and should therefore be treated as crude estimates only, our data do not support the hypothesis that binary spiking in the auditory cortex is limited to a particular layer, but suggest instead that it is a general feature of the entire neuronal population recorded using patch electrodes.

We wondered whether binary spiking resulted from the brevity (25 msec) of the stimuli we typically used. We therefore subjected 12 neurons to an additional protocol consisting of at least 10 interleaved presentations each of 100 msec tones and 25 msec tones of all 32 frequencies (Fig. 5c). Of the 100 msec stimulation response sets, 45 were found to be significantly sub-Poisson at the p < 0.05 level, in good agreement with the 47 found to be significant among the responses to 25 msec tones. Thus, binary spiking was not attributable to the brevity of the stimuli. Moreover, even complex stimuli with rich spectrotemporal structure can produce binary behavior (Fig. 5d).

Response timing

In many neurons, binary responses showed high temporal precision, with latencies sometimes exhibiting SD values as low as 1 msec (Fig. 6) (see also Fig. 1b,c), comparable to previous observations in the auditory cortex (Heil, 1997), and only slightly more precise than in visual area MT (Buracas et al., 1998) of the alert monkey. High temporal precision was positively correlated with high response probability, both within (Fig. 6a) and across (Fig. 6b) cells.

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Figure 6.

Trial-to-trial variability in response latency to repeated presentations of the same tone decreased with increasing response probability. a, Scatter plot together with best linear fit of SD of latency (jitter) versus mean response for 25 presentations each of 32 tones for the same neuron as in Figure 2. Rasters from 25 repeated presentations of a low response tone (top left inset, which corresponds to leftmost diamond) display much more variable latencies than rasters from a high response tone (bottom right inset; corresponds to rightmost diamond). b, The negative correlation between latency variability and response size was present on average across the population of 62 significantly binary neurons described in Results; the best linear fit is also shown.

Poisson model with refractory period

The low trial-to-trial variability ruled out the possibility that the firing statistics could be accounted for by a simple rate-modulated Poisson process (Fig. 5a). To illustrate this, we compared the observed spike rasters (Fig. 7a) with simulated spike trains generated using a rate-modulated Poisson process whose event rate was fit to the smoothed PSTH derived from the observed rasters. As expected, the simulated spike trains contained several multispike responses (Fig. 7b). The simulated spike trains seen here are qualitatively similar those observed in visual area MT during presentation of dynamic stimuli (Buracas et al., 1998).

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Figure 7.

The lack of multispike responses elicited by the same neuron as in Figures 2 and 6a was not caused by an absolute refractory period, because the range of latencies for many tones, like that shown here, was much greater than any reasonable estimate for the refractory period of the neuron. a, Experimentally recorded responses to multiple presentations of the same tone contain no multispike responses. b, A representative example of rasters generated under the assumption of Poisson firing and the same PSTH as a includes four double-spike responses (arrows at left) of 25 trials. c, Representative rasters generated by a Poisson process subject to a hard, 2 msec refractory period still include one triple-spike and three double-spike responses.

In other systems, low trial-to-trial variability has sometimes been explained in terms of a Poisson process followed by a post-spike refractory period (Berry et al., 1997; Kara et al., 2000). In the present context, if the underlying firing rate were elevated for a time shorter than the refractory period, then at most one spike per trial could be generated. Thus, whether a refractory period can provide a full account of binary spiking depends critically on whether the refractory period is longer than the period of elevated firing.

During periods of spontaneous firing, and occasionally during stimulus-evoked responses, interspike intervals as short as 2 msec were observed, as expected from previous cortical recordings. These short interspike intervals provide an upper bound on the hard refractory period, which is presumably caused by the intrinsic properties (for example, the time course with which sodium channels recover from inactivation) of the spike-generating mechanism of the neuron. The inclusion of such a hard refractory period did not substantially reduce the variability of the simulated Poisson process; several multispike responses were still observed (Fig. 7c).

These simulations suggest that binary spiking did not result from the intrinsic properties of the spike-generating mechanism of the neuron. Rather, the fact that stimulus-evoked responses consisted of at most a single spike was more likely the result of circuit-level mechanisms. Tones elicit a precisely timed sequence of excitation, followed by strong inhibition (Wehr and Zador, 2002); the inhibition quenches the response and thereby enforces a very short window for temporal integration during which only a single spike can occur. However, this inhibition typically decays within 50-100 msec, and is therefore unlikely to account for the long-lasting suppression observed after a stimuli that elicit spikes with high probability (Fig. 8); such longer-lasting suppression may be attributable, at least in part, to short-term synaptic depression (Chung et al., 2002).

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Figure 8.

Spontaneous activity is reduced after high-probability responses. The PSTH (top; 0.25 msec bins) of the combined responses from the 25% (8/32) of tones that elicited the largest responses from the same neuron as in Figures 1, b and c, 3, and 5c illustrates a preclusion of spontaneous and evoked activity for over 200 msec after stimulation. The PSTHs from progressively less responsive groups of tones show progressively less preclusion after stimulation.

Reconciling multiunit and single-unit recordings

How can the highly variable multiunit recordings (Fig. 1a) be reconciled with the single-unit binary recordings (Fig. 1b,c)? According to the simplest model, each multiunit response would consist of the summed activity of several single-unit recordings. If responses from enough low firing probability, statistically independent binary units are combined, then the trial-to-trial variability of the population approaches a value close to unity. Thus, we should expect the multiunit data to be about as variable as a Poisson process, even if the individual units are statistically independent of one another.

However, more careful examination of the multiunit responses reveals that the observed variability for most responses actually exceeds that of a Poisson process (i.e., the Fano factor exceeds unity) by a substantial margin. This supra-Poisson variability suggests that neurons are correlated with each other (Zohary et al., 1994; Abbott and Dayan, 1999). A simple simulation illustrates how positive correlations can lead to supra-Poisson variability. Figure 9 shows a simulated multiunit recording consisting of five noisy binary neurons, each with a per trial spiking probability of 0.2. The responses of the neuron were designed so that a fraction of the spikes of each neuron was shared by all neurons. For example, the point at the far left of the graph corresponds to the case of five statistically independent neurons; at the far right, the activity of each neuron is identical. The simulated multiunit variability increased with the fraction of shared spikes. Thus comparison of single- and multiunit data support the idea that binary units are positively correlated.

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Figure 9.

A comparison between the multiunit (Fig. 1a) and single-unit (Figs. 1b,c, 3a) recordings suggests that neurons are correlated with each other (Zohary etal.,1994; Abbott and Dayan, 1999). We illustrate this with a simple model in which many binary single units are combined to produce a highly variable multiunit recording. If responses from N statistically independent binary units, each with firing probability p, are combined, then the Fano factor of the population response is given by variance/mean = [Np(1 - p)]/(Np) = 1 - p. However, introducing positive correlations between neurons leads to higher trial-to-trial variability, as seen in our multiunit recordings. We simulated a multiunit recording consisting of five noisy binary neurons, each with a per trial spiking probability, p, of 0.2. The responses of the neurons were designed so that a fraction of the spikes of each neuron occurred on the same trials as spikes in all other neurons. For example, the point at the far left of the graph corresponds to the case of five statistically independent neurons; in this case, coincidences happen at the level of chance. At the far right, the activity of every neuron is identical up to differences in the response latency of each neuron, which allow the individual spikes to be detected; an example of a typical response set for this case is [0,0,5,0,5,0,0,0,0,0...]. The variability of this multiunit simulation increased with the degree of correlation between the neurons.

Relation to previous studies of auditory cortex

Response variability has been extensively studied in the visual cortex (Heggelund and Albus, 1978; Dean, 1981; Tolhurst et al., 1983; Buracas et al., 1998; Oram et al., 1999), where with three exceptions (Gur et al., 1997; Gershon et al., 1998; Kara et al., 2000), Poisson or supra-Poisson variability has been observed. However, the trial-to-trial variability of single units has not been previously assessed in the auditory cortex, although the variability of stimulus-evoked local field potentials (LFPs) has been considered (Kisley and Gerstein, 1999).

It has long been known that tone-evoked responses in the auditory cortex can be transient. For example, in one early study of auditory cortical responses, it was noted that “nearly 95% of the neurons responded with a single spike, or short bursts of 2 to five spikes, to pure tones delivered monaurally or binaurally regardless of the duration of the tone” (Brugge et al., 1969). Subsequent work over the intervening three decades has supported the view that transient responses are common (Calford and Semple, 1995; Heil, 1997; Sutter et al., 1999), although more sustained responses are also sometimes observed, even in the anesthetized preparation (Phillips and Sark, 1991; Furukawa et al., 2000) (Fig. 5b).

However, the binary responses we describe are not simply transient. To demonstrate the transient nature of auditory spiking, it would have sufficed to show PSTHs, because the brevity of the response can be fully assessed by the mean activity. “Transient” refers to the time course and the mean spike count per trial, whereas “binary” makes a statement about the variance of the spike count as well. Our study thus establishes for the first time that transient responses in auditory cortex can be described as a binary process, rather than as a highly variable Poisson process.

Anesthesia and transient responses in auditory cortex

Although there has recently been renewed interest in the stimulus dependence of sustained spiking in the awake auditory cortex [particularly in response to complex stimuli (deCharms et al., 1998; Lu et al., 2001)] purely transient responses have also commonly been reported in this preparation since they were observed in single-unit recordings over 40 years ago (Hubel et al., 1959; Abeles and Goldstein, 1972; Dear et al., 1993). Such transient responses can be seen, for example, in early studies on responses to complex vocalizations (Wollberg and Newman, 1972; Creutzfeldt et al., 1980). Particularly clear examples of purely transient spiking are evident in an early study of attentional modulation of auditory cortical responses (Hocherman et al., 1976). In the awake rat, up to 50% of neurons show phasic short-latency responses such as those observed here (Talwar and Gerstein, 2001). Indeed, even in a recent study focusing on the contrast dependence of the sustained component, a substantial fraction of neurons show purely transient responses under all stimulus conditions (Barbour and Wang, 2003). Thus transient firing per se is not an artifact of anesthesia. However, none of these earlier studies distinguished between Poisson and binary responsiveness, and so provide no insight into the reliability of cortical coding.

There is nevertheless little doubt that sustained responses are less common in the anesthetized preparation. Unfortunately, there have been relatively few studies in which the activity of individual single units is compared when the animal is in different states of arousal. In one study comparing single-unit activity in sleeping to awake rats, most response properties remained primarily unchanged, with at least some neurons remaining transient under all conditions (Edeline et al., 2001).

Interestingly, firing rates observed with cell-attached and whole-cell recording methods in the awake preparation (Margrie et al., 2002) are much lower than previously reported based on conventional extracellular recordings, supporting the idea that these methods differ in their selection bias. There is at present no evidence to suggest that responses of well isolated transient responders are any less reliable in the awake preparation, and it remains an open question whether the subpopulation of transient responders in the auditory cortex of awake animals show the binary behavior we describe here.

Relation to other areas

Transient responses are also observed in other cortical areas. However, in contrast to the present results, transient responses in other cortical areas typically show the same high trial-to-trial variability as sustained responses and can, to first approximation, be considered to result from a rapidly modulated Poisson process. For example, in area MT of the awake monkey, even when the response to a brief stimulus consists of on average only a single spike per trial, individual trials may show as many as two or three spikes (Buracas et al., 1998). These area MT responses thus have more in common with the simulated responses shown in Figure 7, b and c, than with the binary auditory responses described here.

Whereas this is the first description of binary spiking, there have been several reports of low variability spiking. Under some (de Ruyter van Steveninck et al., 1997) but not all (Warzecha and Egelhaaf, 1999) stimulus conditions, motion-sensitive neurons in the fly visual system can show sub-Poisson firing. Similarly, neurons in the vertebrate retina (Berry and Meister, 1998; Kara et al., 2000) and thalamus (Kara et al., 2000) have been reported to respond with low variability under some conditions. There have also been three reports describing sub-Poisson variability in the cortex (Gur et al., 1997; Gershon et al., 1998; Kara et al., 2000), although even the least variable neurons from these studies do not approach the extremely low variability attainable by the binary units we describe here. It is interesting to note that variability of responses reported in the auditory nerve is high (typical Fano factors are of order unity) (Teich et al., 1990), indicating that in the auditory system spike count variability decreases centripetally; in contrast, in the visual system spike count variability shows the opposite trend, increasing from the retina to the visual cortex.

Cortical physiology and circuitry are similar across many different cortical regions, and it is tempting to speculate that basic cortical computations are, as a result, also similar. It is therefore somewhat puzzling that different regions should differ so strikingly in so fundamental a characteristic as the operating fidelity. One possibility is that auditory and visual processing are indeed fundamentally different. An alternative interpretation is that the difference results not from the sensory modality, but instead from the difference between the stimuli used. In this view, the binary responses may not be limited to the auditory cortex; neurons in visual and other sensory cortices might exhibit similar responses to the appropriately punctate stimuli. Conversely, auditory stimuli analogous to edges or gratings (Kowalski et al., 1996; deCharms et al., 1998) or other complex stimuli (Lu et al., 2001) may be more likely to elicit conventional, rate-modulated Poisson responses in the auditory cortex.

Sparse and efficient representations

The first spike is privileged in that it often carries most of the information in the spike train (Heil, 1997; Buracas et al., 1998; Panzeri et al., 2001). In fact, it has been suggested that complex image recognition can occur with only a single spike per neuron (Delorme and Thorpe, 2001). Because in the binary mode we have described each spike is a “first spike,” binary spiking is an efficient or sparse representation (Olshausen and Field, 1996; Hahnloser et al., 2002).

Because binary responses consist of at most a single spike, no possible information can be contained in the precise substructure of the spike train, ruling out the possibility of a privileged role for bursts (Martinez-Conde et al., 2000) or temporal multiplexing (Richmond and Optican, 1987) as has been reported in visual cortex; a stimulus parameter, such as the frequency of a tone, is encoded as the probability of firing a single spike (Fig. 3b). From the perspective of a single neuron, this probability fully specifies the response and implies that any additional information about the stimulus can be decoded only by looking over the neuronal population.

Implications for cortical processing

The well established observation that neuronal firing in the visual cortex typically shows Poisson or supra-Poisson variability has often been assumed to be a general principle true of all cortical areas (Shadlen and Newsome, 1998) or even every cortical neuron (Pouget et al., 2000). High variability is thus often taken as a starting point for a general theory of cortical dynamics, a constraint that any biologically plausible theory must satisfy. Natural questions then become: what biophysical (Softky and Koch, 1993) or circuit (van Vreeswijk and Sompolinsky, 1996) mechanisms allow such variability to arise or propagate (van Rossum et al., 2002) and how can populations of noisy neurons represent sensory stimuli with fidelity (Pouget et al., 2000)? On the other hand, if such high variability is not a necessary feature of cortical function, then inquiry turns naturally to the question of why one area or modality should show high variability whereas another does not, or to the dependence of variability on stimulus parameters.

High variability greatly constrains the kinds of processing that might occur at the level of a single neuron and may complicate models in which separate computations are performed on major dendritic branches (Shepherd and Brayton, 1987; Mel, 1994). For example, consider a hypothetical patch of dendrite in which the appropriate complement of voltage-dependent channels are arrayed to produce a logical AND gate of the activity of two nearby inputs (Shepherd and Brayton, 1987). In other words, suppose that the arrival of two presynaptic action potentials to one or both of these synapses within a short time period can result in a much greater signal to the soma than twice the affect of one action potential alone. In conventional high-variability models of cortical processing, a response that, on average, consisted of a single spike in input A would, on particular trials, often consist of a pair of spikes, and so would be indistinguishable from the simultaneous firing of A and B. If, however, each input neuron A and B reliably produced either zero or one spike, then such a scheme could sensibly signal the presence of simultaneous activity in both neurons. Similarly, some models for harnessing the computational power of dynamic synapses depend on temporally precise, low-variability spiking (Maass and Zador, 1999). Thus, binary spiking provides a possible substrate for models requiring a degree of control over spike number that, heretofore, had not been documented in the cortex.

The precise organization of both spike number and time we have observed suggests that cortical activity consists, at least under some conditions, of packets of spikes synchronized across populations of neurons. Theoretical work (Marsalek et al., 1997; Diesmann et al., 1999; Kistler and Gerstner, 2002) has shown how such packets can propagate stably from one population to the next, but only if neurons within each population fire at most one spike per packet; otherwise, the number of spikes per packet (and hence the width of each packet) grows at each propagation step. Interestingly, one prediction of stable propagation models is that timing precision should increase with increasing spike probability, a prediction born out by our observations (Fig. 6). The role of these packets in computation remains an open question.