INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The spike patterns of auditory cortical neurons vary systematically as a function of sound-source location. At low sound levels, some neurons show somewhat restricted spatial receptive fields in the sense that the neurons respond with high spike probability (i.e., high spike count) to sounds presented from some locations and respond with low probability or not at all to sounds presented from other locations (e.g., Imig et al. 1990; Middlebrooks and Pettigrew 1981; Middlebrooks et al. 1998; Rajan et al. 1990). At moderate sound level, however, most neurons show above-background responses to sound sources from any location. In addition to location-dependent variation in spike counts, neurons also show location-dependent variation in the distribution of spikes in time relative to stimulus onset. In previous studies (Furukawa et al. 2000; Middlebrooks et al. 1994, 1998; Xu et al. 1998), we have used a pattern-recognition algorithm (an artificial neural network) to recognize location-dependent spike patterns and, thereby, to estimate the locations of sound sources. The accuracy of location estimates provided an empirical measure of the location-related information carried by spike patterns. In many cases, accuracy was degraded substantially when spike patterns were replaced by mean spike countsthat is, when we eliminated any stimulus-specific characteristics of the timing of spikes. That result indicated that spike timing was important for stimulus coding but did not reveal the particular features of spike patterns that might be important. For instance, the previous analysis did not permit us to quantify the relative importance of first-spike latencies, interspike intervals, or other higher-order temporal features.

The goal of the present study was to quantify the relative amounts of information about sound-source location that are carried by spike counts and by spike timing and to identify particular temporal features of spike patterns that might transmit stimulus-related information. We recorded the responses of single units in area A2 of the auditory cortex of anesthetized cats. We focused on area A2 because neurons there tend to show broad frequency tuning (Schreiner and Cynader 1984), suggesting that they might integrate location cues across broad frequency ranges. Also, we have considerable previous data from area A2 indicating that neurons can signal the locations of sound sources in azimuth (Furukawa and Middlebrooks 2001; Furukawa et al. 2000; Middlebrooks et al. 1998) and elevation (Xu et al. 1998) and that neurons respond to spectral-shape cues for sound-source elevation (Xu et al. 1999) and paired clicks (Mickey and Middlebrooks 2001a) in a way that parallels human localization judgments. We have shown previously that ensembles of ~100 A2 neurons can signal sound-source azimuth with accuracy comparable to the behavioral localization accuracy of cats (Furukawa et al. 2000). Nevertheless, we are aware of no conclusive demonstration of a role of area A2, or of any other cortical area, in localization behavior. For that reason, the present results should be regarded as pertaining to information-bearing features of spike patterns in one particular cortical fieldwe cannot claim to have evaluated every possible cortical spatial representation.

In the present study, we recorded the spike patterns of single neurons elicited by noise bursts that varied in location throughout 360° in the horizontal plane. We quantified the location-specific information that was transmitted by full-spike patterns and by spike patterns that were processed to degrade stimulus-related spike counts or spike timing. We also measured the information transmitted by three unidimensional parameters: mean spike count, mean spike latency, and the dispersion of spike latency. The results demonstrated that, for many neurons, spike timing transmitted more stimulus-related information than did spike count. The feature that transmitted the most stimulus-related information was the latency of the first spike in each spike pattern, often transmitting as much information as did the full-spike pattern.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Stimulus generation

The experimental apparatus for stimulus generation was identical to that detailed previously (Furukawa et al. 2000; Middlebrooks et al. 1998). Briefly, experiments were controlled with an Intel-based personal computer. Acoustic stimuli were synthesized digitally at a sampling rate of 100 kHz using equipment from Tucker-Davis Technologies (TDT; Gainesville, FL). Experiments were conducted in a sound-attenuating chamber that was lined with acoustical foam (Illbruck, Minneapolis, MN) to suppress reflections of sounds at frequencies >500 Hz. Sounds were presented from 18 calibrated loudspeakers, 1 loudspeaker at a time. Loudspeakers were positioned in the horizontal plane with angular separation of 20° 1.2 m from the animal's head. The speaker location directly in front of the animal was labeled 0°, and positive azimuths indicated speakers on the right side of the animal, which was ipsilateral to the recorded cortical hemisphere.

Noise bursts were 80 ms in duration with abrupt onsets and offsets. Tone bursts were 80 ms in duration, ramped on and off with 5-ms rise/fall times. Noise and tone bursts were presented once every ~800 ms.

Animal preparation

This report presents data from 14 purpose-bred adult cats of both sexes. The animal preparation was identical to that detailed previously (Middlebrooks et al. 1998). In brief, isoflurane anesthesia was used during surgery, and -chloralose was used for unit recording. All recordings were made from the right cortical hemisphere. The animal was positioned in the center of the sound-attenuating chamber, with its body supported in a sling that also held a heating pad and its head supported from behind by a bar attached to a skull fixture. Thin wire supports were used to push the external ears into a forward position (Middlebrooks and Knudsen 1987). The position of the ears was constant throughout each experiment.

At the end of each experiment, the animal was killed. The cortex was immersed in buffered formalin and later inspected visually to confirm the region of cortex recorded.

Data acquisition and spike sorting

Procedures for unit recording and for spike sorting were identical to those detailed by Furukawa et al. (2000). Briefly, unit activity was recorded extracellularly with silicon-substrate multichannel probes (Anderson et al. 1989). Each probe had one shank along which 16 recording sites were located in 100- or 150-µm intervals. Neural waveforms were amplified, digitized (16 bits, sampling rate of 25 kHz), and stored on computer disk. Spikes were detected on-line for monitoring purposes. Off-line custom software (Furukawa et al. 2000) was used to discriminate spikes for detailed analysis. The spike-sorting procedure used a template-matching algorithm. Spike waveforms were expressed as weighted sums of principal components, spikes were selected from plots of the weights of first and second principal components, and then waveform templates were computed from those spikes. The analysis in the present study, except when stated otherwise, was restricted to well-isolated single units that were identified according to the following two criteria. First, the first and second principal components of the spike waveforms formed a discrete cluster. Second, the distribution of interspike intervals formed across all trials peaked at >2 ms. An example of a single-unit recording is shown in Furukawa et al. (2000). In a separate analysis, we used recordings of two or more unresolved units. Those multiunit recordings were sampled from the same placements of the multichannel recording probe as those that yielded the single units, but the single units and multiple units were recorded from different recording sites. The final data set consisted of 40 single units and 111 multiunit clusters from 28 electrode placements in 14 cats.

Experimental procedure

Recordings were made from cortical area A2. Electrode penetrations passed dorsoventrally, oblique to the cortical surface near the crest of the middle ectosylvian gyrus, ventral to area A1. Area A2 was distinguished from area A1 by the absence of tonotopic organization and by frequency response bands that were one or more octaves wide at signal levels 40 dB above threshold (Reale and Imig 1980; Schreiner and Cynader 1984). Search stimuli consisted of broadband noise bursts, presented in the region of 0° to contralateral 40° azimuth. The recording probe was adjusted in cortical depth so that spike activity could be recorded simultaneously from as many recording sites as possible; typically, single- or multiunit responses were observed at ~10 of 16 recording sites in each probe penetration. We assume that recordings were predominantly from layers III and IV based on the recording depths and the presence of active units in this anesthetized preparation.

Study at each probe placement began identifying a stimulus location from which noise bursts elicited a strong response, usually 0° or contralateral 40° azimuth. Frequency sensitivity was tested using tones varied in 1/3-octave steps of frequency. Thresholds for noise bursts were estimated to the nearest 5 dB by inspection of on-line poststimulus time histograms and of plots of spike counts versus noise-burst sound level. When thresholds differed among recording sites at one probe position, we adopted the modal threshold as representative for that probe position. Usually, the range of thresholds at any probe position was 10 dB across all recording sites. Finally, we measured the spatial sensitivity using stimuli presented from 18 azimuths in the horizontal plane (180-160° in steps of 20°) at five sound levels ranging from 20 to 40 dB above the units' threshold. Stimuli were presented in pseudorandom order such that all locations were tested at all sound levels once before repeating all stimuli again in a different random order. Each combination of location and sound level was tested 40 times.

Study at each probe placement typically lasted ~2 h. Data for other experiments (e.g., unit recording using other auditory stimulus sets) (Furukawa and Middlebrooks 2001; Mickey and Middlebrooks 2001a; Xu et al. 1999) normally were collected from the same animals. For that reason, experiments typically lasted 2-5 days.

Data analysis

Analysis of spike data from each unit consisted of the following steps: representation of spike patterns as lists of spike times; (optional) manipulation of spike patterns to degrade putative information-bearing features; formation of multiple bootstrap samples of eight response patterns; isolation of selected unidimensional features or low-pass filtering of average response patterns followed by re-sampling with 1-ms bins; pattern recognition with artificial neural networks to estimate sound-source locations; and computation of transmitted information from joint stimulus-response matrices.

REPRESENTATION OF SPIKE PATTERNS. In off-line spike sorting, spike times were stored with 20-µs precision as latencies relative to the onset of sound at a loudspeaker. The response to each stimulus therefore was represented by a spike pattern consisting of a list of spike times. The arrival of sound at the cat's head was delayed by ~3.5 ms because of the acoustical travel time. The range of spike times used for the analysis was between 10 and 80 ms after the stimulus onset. For the purpose of testing the artificial-neural-network recognition of response patterns (described later), we assigned the spike patterns for odd- and even-numbered trials to training and test sets, respectively. Thus 40 trials yielded 20 training trials and 20 test trials for each stimulus. The separation of training and test sets provided a cross-validation of the pattern recognition scheme.

DEGRADATION OF PUTATIVE INFORMATION-BEARING FEATURES. The goal of this study was to quantify the relative amounts of stimulus-related information transmitted by specific features of spike patterns. For that reason, we processed spike patterns either to isolate particular unidimensional features (described in the following text) or to degrade particular features.

FORMATION OF BOOTSTRAP SAMPLES. Under the conditions of animal preparation and anesthesia that were used, cortical neurons typically responded to a noise burst with only one or a few spikes at the onset of the sound. The sparseness of spike patterns made it difficult to estimate sound-source locations on the basis of responses of single neurons to single sound presentations. For that reason, a bootstrap sampling procedure was used to form average response patterns within the test (or training) set (Efron and Tibshirani 1991; Middlebrooks et al. 1998). Each average response pattern was formed from a sample of spike patterns on eight trials, drawn randomly with replacement from a training set (or test set) of 20 responses to each combination of stimulus location and sound level. The samples of spike patterns were averaged together according to procedures described in the following two paragraphs. We chose eight as the number of trials to average because, in our previous study (Middlebrooks et al. 1998), the precision of stimulus identification tended to increase with averages across increasing numbers of trials, but for most units the rate of increase tended to slow beyond averages of around eight trials. We repeated the bootstrap sampling procedure to form 20 test and 20 training samples for each stimulus condition for each unit.

ISOLATION OF UNIDIMENSIONAL FEATURES. Three unidimensional features were isolated from bootstrap samples of response patterns. The mean spike count was the arithmetic mean of the number of spikes per trial averaged over each bootstrap sample of eight trials. The mean first-spike latency was computed by, first, selecting all the spike patterns in each bootstrap sample that contained one or more spikes and, then, computing the geometric mean of the latency (with 20-µs precision) of the first spike in each such pattern. The geometric mean was used for latencies, rather than the arithmetic mean, because the distribution of first-spike latencies tended to be highly skewed, having a long tail toward longer latencies with variance increasing with increasing latency. The spike dispersion was the SD of all the spike times in each bootstrap sample. The spike-dispersion measure was influenced by the durations of spike patterns as well as by the trial-by-trial variability in spike latencies. No first-spike latency was computed in cases in which the eight trials of a bootstrap sample contained no spikes, and no spike dispersion was computed in cases in which the eight trials contained a total of no more than one spike; in those cases, the numbers of training or test patterns that were available were reduced. In rare instances in which no latencies or dispersions could be computed from any of the responses to a particular combination of stimulus location and sound level, that stimulus condition was eliminated from further analysis. The impact of that situation on measurements of transmitted information was tested and found to be negligible.

LOW-PASS FILTERING AND RE-SAMPLING. The four types of spike patterns (control and 3 degraded conditions) consisted of lists of spike times. For further analysis, those lists of spike times were converted to vectors of 1's and 0's, representing the presence or absence of spikes in 100-µs time bins, and those vectors were averaged across the eight trials in each bootstrap sample. In the case of first-spike patterns, patterns that contained no spike were omitted from the average so all average first-spike patterns had unity magnitude. Next, the vectors of 1's and 0's were low-pass filtered by convolution with a unit Gaussian impulse ( = 1 ms) and re-sampled with 1-ms precision. The low-pass filter operation is a conventional signal-processing procedure that is necessary to attenuate aliased high frequencies. Low-pass filtering also served to smooth the otherwise sparse spike-density vectors. An identical procedure has been followed in our previous studies (Middlebrooks et al. 1998; Xu et al. 1998). The resulting spike patterns, regardless of the type of manipulation, consisted of 70-element spike density vectors that represented the probability of a spike in each of 70 1-ms time bins from 10 to 80 ms relative to stimulus onset. The 100-µs precision of the underlying spike latencies influenced the distribution of each Gaussian impulse across 1-ms time bins. For that reason, the effective precision of the resulting spike density vectors was 100 µs. Figure 1 illustrates an example of a sample of eight spike patterns (represented by rasters) converted to a spike density vector (represented by a bar plot).

View larger version (7K): [in this window] [in a new window]   Fig. 1. Computation of a spike density vector. Eight spike patterns, represented in a raster plot, were combined, low-pass filtered, and re-sampled with 1-ms precision to form a spike density vector (bar plot at bottom).

ARTIFICIAL-NEURAL-NETWORK RECOGNITION OF SPIKE PATTERNS. We used an artificial neural network (ANN) to identify sound-source locations by recognizing spike patterns. The ANNs were implemented with the MATLAB Neural Network Toolbox (The Mathworks, Natick, MA). The ANN architecture consisted of inputs, a competitive layer, and a linear layer. The inputs were spike density vectors or single numbers representing unidimensional features. The competitive layer had one hidden unit and one output unit for each stimulus location, i.e., there were 18 hidden units and 18 output units. Each hidden unit was specified in 70 dimensions or 1 dimension, depending on the form of the input. The ANN was trained, using the learning vector quantization (LVQ) training algorithm (Demuth and Beale 1998; Kohonen 1987) to classify the unit responses and to assign each class to 1 of the 18 sound-source locations (i.e., locations from 180 to 160° in 20° steps). The learning rule, in essence, positioned each hidden unit in 70- or 1-dimensional space to minimize the mean squared Cartesian distance to the input vectors that corresponded to a particular stimulus. Nicolelis and colleagues (1998) used a similar network design for study of encoding of tactile information, and we have used such a design for study of cortical coding of cochlear-implant stimuli (Middlebrooks and Bierer 2002)

COMPUTATION OF TRANSMITTED INFORMATION. The estimates of stimulus locations by the ANN were summarized as joint stimulus-response probability matrices, which were used to compute the transmitted information. In the present study, transmitted information (also known as mutual information) was a measure of the reduction in the uncertainty in stimulus location due to knowledge of unit responses and classification by an ANN (Cover and Thomas 1991). The information (I) transmitted about a stimulus set, S, given a response set, R, is defined as

(1)

where

Here, s_i and r_j represent, respectively, the ith stimulus condition and the jth class of unit response (i.e., ANN estimate of stimulus location); p(s_i), and p(r_j) represent the probabilities that stimulus and unit response take values s_i and r_j, respectively, and p(s_i|r_j) represents the conditional probability of s_i given r_j. H(S) is the entropy of the stimulus set (indicating the uncertainty about the stimulus), and H(S|R) is the conditional entropy of the stimulus set, given the response set (indicating the uncertainty about the stimulus after knowing the response). From Eq. 1, we can compute the transmitted information directly from the joint probability matrix of stimulus and ANN response. The unit of transmitted information is bits.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The analysis presented here was derived primarily from 40 single units recorded from 14 cats. A supplementary analysis used data from 111 multiunit clusters. We begin by describing the spatial sensitivity of single units and by quantifying the information about sound-source azimuth that could be derived from full-spike patterns, which preserved the magnitude and timing of unit responses. Then we quantify the degree to which information transmission depended on spike timing, and we evaluate the relative importance of the first and later spikes in the spike pattern. Next, we quantify the information carried by three unidimensional features of spike patterns: spike counts, first-spike latencies, and temporal dispersion of spike patterns. Finally, we evaluate the significance of two details of the experimental design: analysis of single trials versus averages across multiple trials and single- versus multiunit recording.

Azimuth information transmitted by full-spike patterns

Figure 2 represents the responses of three single units to noise bursts that were presented at various azimuths. Each unit is represented by a horizontal row of panels, and the left-most three panels in each row are raster plots that represent responses to sound levels that were 20, 30, and 40 dB above each unit's threshold. Each horizontal row of dots in the raster plots represents the spike pattern elicited by an 80-ms noise burst. Responses to eight stimulus presentations are shown for each azimuth. The three illustrated units are representative of the range of variation in spike patterns across the unit sample. Unit 9806/18/13a (top), responded to 80-ms noise bursts with bursts of spikes lasting ~10 ms, whereas unit 0003/130/13a (middle) typically produced only one or two spikes on each trial. Spike patterns of unit 9804/24/2a (bottom) consisted of a single spike at stimulus onset, a pause, then a burst of a few additional spikes. Note that even the longest-lasting spike patterns ended well before the end of the 80-ms noise burst.

View larger version (64K): [in this window] [in a new window]   Fig. 2. Examples of unit responses. Each row of panels represents the responses of 1 unit. Raster plots (3 left columns of panels) show responses at sound levels 20, 30, and 40 dB above each unit's threshold. In the raster plot, each dot represents 1 spike, and each row of dots represents a spike train elicited by 1 presentation of stimulus. The vertical dimension plots sound-source azimuth, with 8 examples of spike patterns at each azimuth. The 3 right columns of panels show spike count, first-spike latency, and spike-dispersion as a function of sound-source azimuth. In each panel, empty circle, ×, and empty triangle represent sound levels 20, 30, and 40 dB above threshold.

In the examples in Fig. 2, one can see azimuth-dependent changes in mean spike counts per trial, in the first-spike latency, and in the dispersion of spikes in time. Those three dependent variables are plotted as a function of source azimuth in the three right columns of panels in Fig. 2; the computation of those unidimensional features is described in METHODS. The three curves in each panel represent the responses to sounds at the three sound levels. All three of the variables were modulated to various degrees by the sound-source azimuth as well as by the sound level.

Several characteristics of spatial sensitivity were common to most of the sampled population. Generally, units were broadly tuned for sound-source azimuth, responding to near-threshold sounds presented throughout the contralateral half or frontal-contralateral quadrant of space. At higher sound levels, spatial receptive fields tended to expand to 360°. Even within a 360° receptive field, however, sounds tended to elicit spike patterns that varied in the number of spikes and in the distribution of spikes in time.

We used an ANN to identify sound-source locations by recognizing unit responses, and then we quantified the azimuth-related information that was transmitted by each unit. Details of the ANN analysis and of the computation of transmitted information are provided in METHODS.

Figure 3 shows examples of joint histograms obtained for the full-spike patterns of units shown in Fig. 2. In each panel, the abscissa and ordinate indicate the stimulus locations and the ANN assignment of responses to locations, respectively. The areas of the filled squares are proportional to the joint probability of stimulus and ANN response. The loci corresponding to perfect ANN identification of source locations lay on the positive major diagonal of the plot. For the examples in Fig. 3, the ANN estimates generally clustered around the diagonal. Clusters of responses in the top-left and bottom-right corners of each panel correspond to stimuli that were mislocalized to the wrong side of the rear midline but were correctly localized to the rear; note that azimuths 180 and +160° were adjacent locations even though they appear far apart in the illustration. The middle panel shows a situation in which responses to stimuli around 160° azimuth were systematically mislocalized to around +60° azimuth. Those responses can be understood by referring to the raster plots in Fig. 2, middle. That particular unit responded similarly to stimuli around 160° and to those around +60° by producing a spike only infrequently. Despite those few classes of errors, it is noteworthy that the full-spike patterns of these units signaled sound-source locations with varying degrees of accuracy throughout nearly 360° of azimuth. The percentage of correct localizations, averaged across all stimulus locations, ranged from 17.8 to 23.5% in the examples shown in Fig. 3. That is substantially better than the value of 5.6% correct predicted from random-chance selection from among 18 locations.

View larger version (24K): [in this window] [in a new window]   Fig. 3. Joint probability of stimulus locations and neural network estimates of stimulus locations. Examples are for the 3 units shown in Fig. 2. The horizontal and vertical dimensions represent actual stimulus location and network response, respectively. The joint probability of each combination of stimulus and response is indicated by the area of a filled square.

The transmitted information in the cases shown in Fig. 3 ranged from 1.03 to 1.24 bits. Figure 4 shows the distribution across the entire sample of 40 units of the transmitted information for the full-spike patterns. The transmitted information ranged from 0.24 to 1.33 bits and averaged 0.81 ± 0.25 (SD) bits. To provide some feeling for those numbers, perfect identification of the 18 sound-source locations would have required 4.17 bits of transmitted information, and 1 bit would have permitted perfect discrimination of left from right. Empirically, we found that units discriminated left from right somewhat imperfectly but discriminated many of the locations within each hemifield. On average, the units transmitted 19.4 ± 6.0% of the total entropy in the stimulus set. The distribution of transmitted information was essentially unimodal, so there was no basis for distinguishing distinct classes of units that were particularly good or bad localizers. Across the sample of 40 units, the percentage of correct localizations ranged from 7.7 to 23.5% and averaged 15.0 ± 3.5% correct. The percent correct was correlated with the transmitted information (correlation coefficient r = 0.84). The transmitted information for chance-level performance was estimated by randomizing the correspondence between spike patterns and stimulus locations. That procedure yielded a chance level of 0.12 ± 0.01 bits, which was substantially less than the information transmitted by any unit.

View larger version (12K): [in this window] [in a new window]   Fig. 4. Information transmitted by full-spike pattern. The histogram shows the distribution of the transmitted information measure among the sample of 40 units.

Importance of spike-timing information

The examples illustrated in Fig. 2 demonstrated that spike timing, as well as spike counts, could vary with stimulus location. In this section, we explore the contribution of spike timing to transmitted information. First, we test a condition in which the stimulus dependence of spike timing was disrupted entirely, leaving only the stimulus-related information carried by spike counts. Then we estimate the relevant time scale of stimulus-dependent spike timing by systematically degrading the precision of spike times.

We disrupted spike timing by forming shuffled spike patterns, as described in METHODS. The shuffled spike patterns included no stimulus-related information carried by spike timing but maintained any information that was carried by stimulus-specific spike counts and maintained the first-order statistics (i.e., the mean and SD) of spike times across all spike patterns. The stimulus-related information contained in shuffled spike patterns was evaluated with an ANN-classification procedure identical to that used for the full-spike patterns.

Figure 5 plots the information transmitted by shuffled patterns and by full-spike patterns. The shuffled patterns consistently transmitted less information about sound-source azimuth than did the full patterns. The transmitted information in the shuffled condition averaged 0.51 ± 0.19 bits (compared with 0.81 ± 0.25 bits in the full-spike-pattern condition; paired t-test; P < 0.001). The information transmitted in the shuffled condition averaged only 65 ± 18% of that transmitted in the condition in which stimulus-related spike timing was intact. We interpret that result to say that, on average, only 65% of location-related information in the full-spike pattern was available from spike counts alone. That result indicates that spike timing carried 35% of the information. We show later that spike timing carried additional information, beyond the 35%, that was redundant with that carried by spike counts.

View larger version (18K): [in this window] [in a new window]   Fig. 5. Information transmitted by the full-spike pattern and by the shuffled spike pattern. , 1 unit. (n = 40)

We estimated the stimulus-related temporal precision of spike times by forming within-interval-shuffled spike patterns, as described in METHODS. The recording window corresponding to 10-80 ms after stimulus onset was divided into equal intervals with durations of 1, 2, 4, 8, 16, 32, or 70 ms. The within-interval-shuffling procedure preserved stimulus-related spike counts and first-order temporal statistics within each interval but disrupted any stimulus-related temporal structure within intervals. The width of the shuffling interval determined the temporal precision of the surviving spike-timing representation.

Figure 6, top, shows the information transmitted by spike patterns of four units, shuffled with various temporal precision; the transmitted information for the unshuffled condition also is shown. Three of the units are those that were presented in Fig. 2, and the fourth is the unit that showed the median amount of transmitted information across the sample of 40 units (0.84 bits). In each case, transmitted information decreased with increasing interval width (i.e., with decreasing precision). Figure 6, bottom, shows the distributions across 40 units of the transmitted information at various levels of precision. In that plot, transmitted information at each interval width is expressed as a fraction of the information in the unshuffled condition, and the distributions are represented with box plots. Each of the illustrated increases in interval width resulted in a significant decrease in transmitted information (P < 0.005 for 1 vs. 2 ms, P < 0.001 for all other pair-wise comparisons, paired t-test). At the 4-ms interval width, the median fraction was 0.91, indicating that half of the units lost >9% of transmitted information when the temporal precision was degraded by that amount. At the 16-ms interval width, the median loss was 22% and the spike patterns of 25% of units showed a loss of >39% of their transmitted information.

View larger version (18K): [in this window] [in a new window]   Fig. 6. Top: transmitted information as a function of the interval width for within-interval-shuffled spike patterns. Each symbol type and line represents 1 unit. Symbols without lines represent the full-pattern condition. Bottom: distribution of transmitted information for various interval widths as a fraction of that for the 1-ms condition. Each box-and-whisker plot indicates the distribution of the fractions of 40 units for 1 interval width. The lower and the higher ends of the whiskers represent the 10th and 90th percentiles, respectively. The horizontal lines in a box represent the 25th, 50th, and 75th percentiles. The circles represent the means.

Dominance of the first spike

The analyses in the previous sections demonstrated that spike timing carried appreciable amounts of stimulus-related information. The majority of spike patterns consisted of no more than a single spike. Specifically, across all 40 single units and all stimulus presentations, 44% of spike patterns had no spikes, 35% had one spike, and only 21% of responses had two or more spikes. In response to the stimulus that produced the highest spike count for each unit, 26 of the 40 units showed median spike counts of <2 per trial. We tested the hypothesis that most of the stimulus-related information in spike patterns is carried by the latency of the first spike. In this section, we test spike patterns in which all but the first spike were deleted. In the next section, we evaluate the information carried by a unidimensional representation of first-spike latency.

We compared the information transmitted by full-spike patterns and by patterns that contained only the first spikes (first-spike patterns; described in METHODS). The first-spike patterns preserved first-spike latency and the trial-by-trial dispersion of first-spike latency, but any information from spike probabilities was eliminated. Figure 7 compares the information transmitted by first-spike patterns with that transmitted by full-spike patterns; * and , respectively, indicate units that showed median spike counts of 2 or <2 spikes in response to optimal stimuli. Many of the points lie near the diagonal line, indicating that for many units, the first spike in the response pattern carried nearly all the stimulus-related information. Across all 40 units, the information carried by the first-spike patterns averaged 89 ± 21% of the information carried by the full patterns. That is, ~89% of the transmitted information was available from a measure that transmitted no information in the form of spike counts or interspike intervals. The higher-count units (*) showed a somewhat greater loss of transmitted information in the first-spike condition. If all units are considered, the ratio of transmitted information between first-spike and full conditions was not significantly lower for the higher-count units than for the lower-count units (P = 0.06), but the difference was significant (P < 0.01) after excluding the one outlying point that showed ~0.2 bits of transmitted information in the full-pattern condition.

View larger version (19K): [in this window] [in a new window]   Fig. 7. Information transmitted by 1st-spike patterns and full-spike patterns. * and , units that exhibited median spike counts of 2 or <2 spikes, respectively, in response to an optimal stimulus.

Unidimensional features of spike patterns

We evaluated the stimulus-related information carried by features of spike patterns that could be represented by unidimensional measures, specifically mean spike count, mean first-spike latency, and spike dispersion (see METHODS for computation of those measures). The information carried by each unidimensional term was evaluated using ANNs and measures of transmitted information as presented in the preceding text. In the present section, however, the ANNs were configured with a single input (for 1 of the unidimensional terms) or with two or three inputs (for combinations of 2 or 3 of the terms). We first wished to validate the efficiency of the ANN analysis for low-dimensional inputs. For that reason, we duplicated the analysis of the unidimensional features using maximum-likelihood classification (Green and Swets 1966). Results from the ANN and maximum-likelihood analyses were highly correlated, with correlation coefficients (r) of 0.98 for spike counts and 0.96 for first-spike latency; the correlation between ANN and maximum-likelihood analysis was lower for spike dispersion (r = 0.57). The transmitted information identified with the ANN procedure, however, was significantly greater (P < 0.001, paired t-test), ranging from 0.02 to 0.14 bits greater than that identified with maximum likelihood classification. For that reason, the results presented in this section were those obtained with the ANN procedure.

Figure 8, top, represents the means and SD of the information transmitted by the three individual features and by combinations of the features. Of the three single features tested (the 3 leftmost bars), the first-spike latency showed the greatest transmitted information on average: 30 of 40 units showed the greatest information carried by first-spike latency. One might have expected the information that was carried by unidimensional spike counts and first-spike latencies to be roughly equivalent to that carried by the shuffled spike patterns and by the first-spike patterns, respectively. Nevertheless, the transmitted information that was computed was significantly less for both of the unidimensional features (P < 0.001). We attribute the differences to sensitivity of the ANN to the structure of inputs to the ANN; the shuffled-spike and first-spike patterns were 70-elements vectors, whereas spike count and first-spike latency were single numbers. Also, the first-spike patterns would have shown stimulus-dependent variation in the dispersion of first-spike latencies that would not have been evident in the mean-latency measure.

View larger version (16K): [in this window] [in a new window]   Fig. 8. Top: means and SD (n = 40 units) of information transmitted by for various individual features (left 3 bars) and for combinations of 2 or 3 features (right 4 bars). Middle: means and SDs of the information transmitted by various combinations of features as a fraction of the sum of information transmitted by the individual features. Bottom: means and SDs of the squared correlation coefficients (R2) for the pairs of response features.

Transmitted information could be increased by combining unidimensional features, as indicated by the four rightmost bars in Fig. 8, top. For instance, a neural network that had both latency and spike-count inputs could identify stimulus locations more accurately than a network that had either of those inputs alone. The information transmitted by combinations of two or three features (latency and dispersion, latency and count, dispersion and count, all 3) always was greater than the greater of the information transmitted by any of the individual features (P < 0.001; paired t-test). This indicates that those three features carried at least some information that was independent among the features. The combined information, however, was never as great as the sum of the information carried by individual features. That is demonstrated in Fig. 8, middle, which shows the information transmitted by combined features as a fraction of the sum of the individual values of transmitted information. The fraction always was less than unity, indicating that the features carried mutually redundant stimulus-related information. The mutual redundancy of stimulus-related information was expected from the correlation between individual features. Figure 8, bottom, shows the means and SD of the squared correlation coefficients (R²). On average, the greatest correlation was between latency and spike count. That correlation can be seen in the Fig. 2's raster plots, which show that stimuli that produced the highest spike counts tended to elicit spikes with the shortest latencies. Nevertheless, latency and spike count transmitted enough mutually independent information that addition of a spike-count input to an ANN improved localization based on latencies (i.e., Fig. 8, top). First-spike latency and dispersion showed the lowest mutual correlation, and the information carried by those features combined showed the highest fraction of the information summed between the individual features.

Significance of procedural details

In this section we evaluate the impact on results of two elements of the experimental design: the use of averages across stimulus presentations and the use of single-unit compared with multiunit responses. The analyses presented to this point were based on spike patterns averaged across eight trials. That was done because cortical units generally responded to each stimulus with no more than a few spikes locked to the stimulus onset. The sparseness of the responses would have made it difficult to estimate the stimulus dependence of spike probabilities and to form accurate representations of spike timing. Also, the response of one unit averaged across multiple trials can be regarded as a surrogate for the responses of multiple isolated units on a single trial. Here we repeated some of the analyses presented in earlier sections in this case, applying them to spike patterns recorded on single trials, that is, to nonaveraged spike patterns.

Figure 9 shows the information transmitted by full-spike patterns, by first-spike latencies, and by spike counts in the single-trial condition compared with the bootstrap-averaged condition. As expected, the transmitted information was markedly less in the nonaveraged condition for all three of these representations (P < 0.001; paired t-test). The consequences of not averaging differed between the spike-count and latency representations of responses. The information transmitted by spike counts was particularly degraded by the lack of averagingtransmitted information in the single-trial condition was only 21 ± 35% of that computed in the averaged condition. The principal reason for that result is that, in the single-trial condition, spike counts could take on only one of a few numbers, most often 0, 1, or 2. The quantal nature of spike counts was ameliorated to a large extent by averaging across trials. In contrast, the distribution of first-spike latencies measured on single trials formed a continuum. Information transmitted by latencies in the single-trial condition was 71 ± 13% of that transmitted in the averaged condition. Presumably the main benefit of averaging in the case of spike latencies is that averages across trials permitted a more accurate estimate of the central tendency of latency.

View larger version (21K): [in this window] [in a new window]   Fig. 9. Information transmitted by full-spike patterns, mean latencies, and mean spike counts in nonaveraged and bootstrap-averaged conditions.

In previous studies of cortical coding of sound-source location (e.g., Furukawa et al. 2000; Middlebrooks et al. 1998), we based much of the analysis on recordings from unresolved clusters of multiple units. Here, we evaluated the impact of single- versus multiunit recording on conclusions concerning transmission of stimulus-related information. One hundred and eleven multiunit recordings were obtained from the same electrode placements that yielded the 40 single-unit data recordings; the single- and multiunit recordings were made simultaneously from different recording sites on the multichannel recording probes. Comparisons between the single-unit and the multiunit recordings are shown in Table 1 for several representations of unit responses. Generally, the multiunit recordings transmitted somewhat less information than did the single-unit recording. We assume that the summation of spike patterns from two or more units that showed somewhat different spatial sensitivity would have resulted in an apparent decrease in spatial sensitivity resulting in the decrease in transmitted information. Nevertheless, the relative amounts of transmitted information among the various response representations were similar between single- and multiunit conditions. For instance, the shuffled-spike conditions showed similar fractions of the full-pattern transmitted information: ~65% and ~71% for the single-unit and multiunit conditions, respectively. Similarly, of the three unidimensional features of neural responses (spike count, latency, and dispersion), latency transmitted the greatest amount of information in both single- and multiunit conditions.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The present results demonstrate that the spike patterns of single neurons transmit substantial amounts of stimulus-related information, in many cases enough to identify sound-source locations throughout 360° of space. Tests of various degraded spike patterns demonstrate the relative amounts of information transmitted by spike counts and spike timing. A rather unexpected result was that, for many neurons, the timing of the first spike carried as much stimulus-related information as did the full-spike pattern. In DISCUSSION, we begin by relating the present results to those of previous studies of auditory spatial sensitivity. Next, we assess the relative importance of spike counts and spike times. We consider the significance of across-trial averages of spike counts and of spike times clocked relative to stimulus onset for an animal that must make location judgements on the basis of single stimulus presentations and that has no independent reference to stimulus onset. Finally, we evaluate possible characteristics of a neural code for sound-source location.

Relation to previous studies of auditory spatial sensitivity

In the present results, single units in area A2 showed broad spatial tuning, most often showing spatial receptive fields that occupied much of the contralateral hemifield at low sound levels and expanded to 360° at levels 30-40 dB above threshold. Similarly broad spatial tuning has been encountered previously in studies of the cat's area A2 (Furukawa and Middlebrooks 2001; Middlebrooks et al. 1998) and other auditory areas (area A1: Brugge et al. 1994; Imig et al. 1990; Middlebrooks and Pettigrew 1981; Rajan et al. 1990; area AES: Korte and Rauschecker 1993; Middlebrooks et al. 1994, 1998). We have demonstrated previously that the spike patterns of single units or clusters of units can signal sound-source locations throughout 360° of azimuththat is, that single units localize sound sources panoramically. In our previous work, we have classified unit responses using an ANN that consisted of a feed-forward perceptron with either linear (Middlebrooks et al. 1994) or nonlinear (Furukawa and Middlebrooks 2001; Middlebrooks et al. 1998; Xu et al. 1998) transfer functions in the middle layers. The advantages of that particular ANN design were that it produced a continuously varying estimate of sound-source location and that it could interpolate between untrained stimulus locations. Those properties facilitated comparison of ANN estimates of location with localization judgements in psychophysical experiments (Furukawa et al. 2000; Mickey and Middlebrooks 2001a; Xu et al. 1999). A different ANN architecture was used in the present studyone that produced discrete outputs that were restricted to the set of discrete values in the stimulus set. The discrete outputs were more appropriate to the goals of the present study in that we were able to evaluate the contribution of particular features of spike patterns to stimulus-related transmitted information.

In our previous studies (e.g., Furukawa and Middlebrooks 2001; Furukawa et al. 2000; Middlebrooks et al. 1994, 1998), many of the recordings were from unresolved clusters of multiple units. For that reason, we were concerned that those studies might have overestimated the breadth of spatial tuning and underestimated the accuracy of panoramic sound localization. Indeed, in the present study, the single units showed somewhat more accurate sound-source localization and somewhat greater transmitted information than did multiunit clusters. Nevertheless, all the conclusions regarding the relative amounts of information transmitted by various features of spike patterns agreed between single- and multiunit conditions.

Relative amounts of information transmitted by spike counts and by spike timing

The present study demonstrated that features of spike patterns related to spike timing tended to transmit more stimulus-related information than did features related to the count of spikes per trial. The first-spike patterns, which preserved first-spike timing but lacked any spike-count information, transmitted more information than did the shuffled patterns, which preserved spike counts but lacked any stimulus-dependent temporal structure. Among the unidimensional features, first-spike latency transmitted more information than did mean spike counts. Spike dispersion, which was another feature determined only by spike timing, typically transmitted about the same amount of information as did spike counts.

Spike counts were particularly ineffective in transmitting information in the condition in which single trials were analyzed, i.e., in which there was no across-trial averaging. That result highlights the point that, given spike patterns that contain no more than one or two spikes, a single response does not provide a useful estimate of spike count (i.e., of spike probability); that point also has been raised by Brugge and colleagues (1994). Experimentally, the spike count of a single neuron is informative when averaged across multiple stimulus presentations. In the context of an animal's perceptual judgement, which normally must be based on a single stimulus presentation, the mean spike count of a single neuron is significant only as a surrogate for the response of a population of neurons. That is, one might regard an average of the responses of one neuron across many presentations as representative of the average of responses across many identical neurons on a single presentation. In a previous study of sound-source localization based on full-spike patterns (Middlebrooks et al. 1998), we showed that the accuracy of localization estimates increased with increases in the number of stimulus presentations across which spike patterns were averaged. We assume that much of that improvement was a result of more accurate representation of mean spike counts. Recanzone and colleagues (2000) have presented a model of the primate auditory cortex in which a localization judgement was based on the sum of spike counts across multiple sequentially recorded neurons. In that study, the sums across multiple neurons discriminated between pairs of sound-source locations more accurately than did spike counts of single neurons on single stimulus presentations. We have shown a similar result in cats (Furukawa et al. 2000). We found, moreover, that sound-source localization is more accurate when the patterns of relative spike counts across neurons are classified than when all spike counts are simply added together. Classification of relative spike counts exploits any differences among neurons in their stimulus specificity, whereas between-neuron differences degrade the accuracy of a grand sum.

Several previous studies of the auditory cortex and of other cortical areas have demonstrated the importance of spike timing for stimulus coding. One way to demonstrate the importance of spike timing has been to degrade the temporal information in spike patterns and to quantify the resulting degradation in stimulus identification. We have demonstrated previously that the accuracy of sound-source localization by cortical neurons is reduced substantially when spike patterns are reduced to unidimensional spike counts (Middlebrooks et al. 1994, 1998; Xu et al. 1998) or when spike patterns of ensembles of neurons are represented by vectors of spike counts (Furukawa et al. 2000). In the somatosensory cortex, degradation of the temporal structure in spike patterns reduces the accuracy of discrimination of tactile stimuli by ensembles of cortical units (Ghazanfar et al. 2000; Nicolelis et al. 1998). In the visual cortex, degradation or elimination of temporal features of spike patterns particularly reduces the information transmitted about stimulus contrast, whereas degradation of spike-count information has a greater impact on transmission of information about stimulus orientation (Gawne 2000; Gawne et al. 1996; Reich et al. 2001). In the present study, we confirmed that disruption of temporal structure (the shuffled spike pattern and within-interval-shuffled conditions) or elimination of temporal information (the spike-count condition) results in a substantial reduction in transmitted information.

The importance of spike timing for stimulus coding also has been demonstrated by tests of specially constructed representations of spike patterns that contain only timing information. In the visual cortex, Richmond and Optican (1987, 1990) represented spike patterns by principal components. Generally, the first principal component (i.e., the component that accounted for the most variance across all spike patterns) correlated highly with spike counts. Nevertheless, the second- and higher-order components alone were demonstrated to carry stimulus-related information. Those components, by definition, were largely independent of spike count and thus presumably reflected only the time structure of spike patterns. Also in the visual cortex, Reich and colleagues (2001) demonstrated that first-spike latencies carried considerable information about stimulus contrast, often as much information as that carried by full-spike patterns. In the present study, we found that all of the representations of spike patterns that deleted direct influence of spike counts (i.e., the 1st-spike patterns, 1st-spike latency, and spike dispersion) transmitted substantial amounts of stimulus-related information.

In the present study, first-spike latencies appeared to transmit more stimulus-related information than did any other feature of spike patterns. The analysis of "first-spike patterns" revealed that, for most units, spikes that follow the first spike transmit little or no stimulus-related information that is not available from the first spike. To a large extent, that result must reflect the low mean spike count that was observed in the anesthetized preparation that was used. That is, across all units and all trials, only 21% of spike patterns contained two or more spikes, so it is not surprising that the second and later spikes transmitted little information. In preliminary results of recordings from awake cats (Mickey and Middlebrooks 2001b), we find that units often fire in a more sustained fashion than do neurons in the anesthetized condition and that sustained portions of spike patterns tend to be modulated by stimulus azimuth. It remains to be seen whether or not the sustained portions of spike patterns transmit stimulus-related information that is not available from the onsets of spike patterns.

Two observations from the visual cortex literature, one in anesthetized animals and one in awake animals, suggest that the dominant role of the first spike in information transmission is not entirely a result of low spike counts. First, Reich and colleagues (2001) studied visual cortex responses in an anesthetized-monkey preparation that showed considerably more tonic activity than we observed in the cat auditory cortex. They reported that coding of stimulus contrast was dominated by information in the first-spike latency with little contribution of "transient, tonic, and off" responses. Second, Gawne and colleagues (Gawne 2000; Gawne et al. 1996) found in unanesthetized monkeys that elimination of mean first-spike-latency information severely impaired signaling of stimulus contrast by visual cortex responses.

Experimentally, spike latencies can be recorded with great precision relative to the onset of the stimulus. In contrast, the nervous system has no independent measure of stimulus onset. For that reason, information carried by latencies presumably is available to an animal only in the form of interspike intervals in the spike patterns of single neurons and relative spike times among multiple neurons. The contribution of interspike intervals to information transmission in the present study must have been small, because only ~20% of spike patterns contained two or more spikes. The relative lack of importance of interspike intervals was demonstrated by the relatively small loss of transmitted information that resulted from elimination of all interspike intervals (i.e., the 1st-spike-pattern condition).

We presume that spike-latency information is available to an animal predominantly in the form of relative spike timing between neurons. The present study did not examine directly the stimulus dependence of between-neuron spike timing. Nevertheless, if we regard across-trial averages of spike patterns as surrogates for recordings from multiple neurons, we can treat the "spike dispersion" term as one indicator of the stimulus-related synchrony of firing among neurons. The results showed that spike dispersion transmitted roughly the same amount of information as did spike counts. In the cat's cortical area A1, Brugge and colleagues (Brugge et al. 1996; Jenison 1998) have demonstrated that first-spike latencies show systematic gradients as a function of sound-source location within single-neurons' spatial receptive fields. In their model, spike-time differences between neurons with differing spatial gradients could carry information about sound-source location. We have shown previously (Furukawa et al. 2000) that in many cases small ensembles of cortical neurons can signal sound-source location with approximately equal accuracy regardless of whether spike times are recorded relative to stimulus onset or relative to the first spike in the ensemble response. That is an empirical demonstration of effective stimulus coding by between-neuron spike times. A similar relative-timing representation has been modeled formally by Jenison (2001).

Combined spike-count and -timing signaling of stimulus location

One of the goals of this study was to evaluate the importance of spike timing for stimulus coding. For that reason, we went to