Binary spiking in auditory cortex

Abstract

Neurons are often assumed to operate in a highly unreliable manner: a neuron can signal the same stimulus with a variable number of action potentials. However, much of the experimental evidence supporting this view was obtained in the visual cortex. We have, therefore, assessed trial-to-trial variability in the auditory cortex of the rat. To ensure single-unit isolation, we used cell-attached recording. Tone-evoked responses were usually transient, often consisting of, on average, only a single spike per stimulus. Surprisingly, the majority of responses were not just transient, but were also binary, consisting of 0 or 1 action potentials, but not more, in response to each stimulus; several dramatic examples consisted of exactly one spike on 100% of trials, with no trial-to-trial variability in spike count. The variability of such binary responses differs from comparably transient responses recorded in visual cortical areas such as area MT, and represent the lowest trial-to-trial variability mathematically possible for responses of a given firing rate. 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. These results demonstrate that cortical architecture can support a more precise control of spike number than was previously recognized, and they suggest a re-evaluation of models of cortical processing that assume noisiness to be an inevitable feature of cortical codes.

Figure 2.

Spikes recorded in cell-attached mode were easily identified from the raw voltage trace (top) by applying a high-pass filter (bottom) and thresholding. Spike times (dots) were assigned to the peaks of suprathreshold segments. The stimulus consisted of a pseudorandom sequence of 25 msec tones presented every 500 msec (stimulus envelope at bottom; see Materials and Methods). Note long time scale compared with most rasters in other figures.

Figure 5.

The majority of the neuronal population exhibited binary firing behavior. a, Of the 3055 sets of responses to 25 msec tones, 2431 (gray points) could not be assessed for significance at the p < 0.01 level, 254 (red points) were not significantly binary, and 370 were significantly binary (black points) (see Materials and Methods). All points were jittered slightly so that overlying points could be seen in the figure. Gray points were plotted with Fano factors recalculated with N (number of trials) rather than N-1 in the denominator of the variance so that response sets containing no multispike responses fell on the diagonal line even for small N. Figure is truncated at top and right. b, Spike rasters from a neuron different from those shown in previous figures show non-binary but highly repeatable multispike responses to repeated presentations of the same tone. c, The binary nature of single-unit responses was insensitive to tone duration. Twenty additional spike rasters from the same neuron (and tone frequency) as in Figure 1b contain no multispike responses whether in response to 100 msec tones (above) or 25 msec tones (below). Across the population, binary responses were as prevalent for 100 msec tones as for 25 msec tones. d, Binary cortical responses are not restricted to loud stimulus onsets. High probability single-spike responses (red boxes) can be triggered by wide-spectrum transients embedded in complex natural sounds (vocalization of the common nightingale); greater spectral power is represented by darker regions of spectrogram (bottom). Note long time scale compared with most rasters in other figures.

Figure 1.

Single-unit responses were far less variable than the multiunit responses. a, Multiunit spike rasters from a conventional tungsten electrode recording showed high trial-to-trial variability in response to 10 repetitions of the same 50 msec duration, 10 kHz pure tone stimulus (stimulus envelope at bottom). Darker hash marks indicate spike times within the response period, which were used in the variability analysis (see Materials and Methods). b, Spike rasters from a cell-attached recording of single-unit responses to 25 repetitions of the same tone consisted of exactly one well timed spike per trial, unlike the multiunit responses (a). c, The same neuron as in b responds with lower probability to repeated presentations of a different tone, but there are still no multispike responses.

Figure 4.

Poisson statistics are practically indistinguishable from binomial statistics for low probability of firing, p, but they are easily distinguished for high p. a, b, Typical examples of simulated spike rasters from Poisson and binomial processes for low p are statistically indistinguishable. c, d, Repeating both simulations for high firing probability (p = 1) nearly always results in spike rasters for which Poisson and binomial spiking can be clearly distinguished.

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.

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.

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.

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.

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.