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Humboldt University Berlin, Institute of Behavioural Physiology, Department of Biology, Berlin, Germany
Submitted 16 December 2004; accepted in final form 7 February 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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, 2003; Ronacher et al. 2004). Intrinsic variability results from stochastic processes during sensory transduction, spike generation, and synaptic transmission (Lestienne 2001). To quantify intrinsic neuronal variability, two measures of spiking responses are commonly employed, that is, the interspike-interval distribution and the spike-count distribution (Dayan and Abbott 2001; Gabbiani and Koch 1998). In numerous studies, especially on the visual systems of vertebrates, the spike-count variability was quantified by the Fano factor (FF) (e.g., Kara et al. 2000; Vogels et al. 1989). As a standard quantification of the interspike-interval variability, the coefficient of variation (CV) is calculated (Softky and Koch 1993). While the FF reflects the response reliability for multiple stimulus presentations, the variability of an ongoing neuronal response is expressed by the CV. If spike generation follows a renewal process, the FF should correspond to the square of the CV (Gabbiani and Koch 1998). Thus the relation between these two measures may help to characterize a neuron's spiking response.
It is important, however, to note that in spite of their general use the two measures of variability suffer from a possible draw back: they rely on very long stimuli or on manifold repetitions of an identical stimulus. This is in contrast to the normal operation of nervous systems, which usually have to process sensory inputs quickly (Ronacher et al. 2004). Hence, by measuring variability over time, it is quite conceivable that one obtains a misleading picture of neuronal variability. Slow changes of the internal physiological state, for example, may lead to an overestimation of the actual variability, which is relevant for the task at hand. If the magnitude of variability is compared along successive stages in a sensory pathway, it might be problematic to compare data that were recorded at different times. A reasonable strategy to circumvent such an overestimation of neuronal variability is to perform simultaneous recordings from at least two neurons at successive processing levels. Although the investigation of variability across different processing levels with simultaneous recordings does not relieve the problem of long stimulation times, it allows a comparison under identical physiological conditions.
To assess the magnitude and possible impact of intrinsic spike train variability in a model sensory pathway, we focused on the metathoracic auditory system of acridid grasshoppers, which is an intensively studied model system for investigating the processing of acoustic stimuli (Ronacher et al. 1986; Stumpner et al. 1991). The metathoracic auditory network is characterized by a separation into two hemispheres and a hierarchical organization consisting of receptor neurons, segmental, and ascending interneurons, which can be identified as individuals on the basis of their characteristic morphology and physiology (Fig. 1A). Receptor neurons project onto segmental interneurons, which then serve as presynaptic elements to ascending neurons (Römer and Marquart 1984; Stumpner and Ronacher 1991; Stumpner and von Helversen 2001). The latter transmit information to the brain where the final evaluation of acoustic information takes place (Bauer and von Helversen 1987; Ronacher et al. 1986). Hence, the set of ascending neurons constitutes a bottleneck for the transmission of auditory information (Fig. 1A). At the level of ascending interneurons, a functional separation in elements coding for the sound pattern (Fig. 1B, top 2 traces, ascending interneurons) and those carrying directional information (AN1, Fig. 1B, 3rd trace) has been reported (Ronacher and Stumpner 1993). The patterns of spiking responses differ substantially among receptors and segmental and ascending interneurons (Fig. 1B).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Animals were adult female and male locusts (Locusta migratoria), which were obtained from a commercial supplier and held at room temperature (22–25°C). After removal of head, legs, and wings, the animals were fixed with their dorsal side up onto a holder. The thorax was opened dorsally and the metathoracic ganglion was exposed and stabilized by a small NiCr platform. The whole torso was filled with locust Ringer solution (Pearson and Robertson 1981). The temperature of the preparation was adjusted by means of a Peltier element at 30 ± 2° C.
Intracellular recordings from auditory receptors, and interneurons were obtained in the auditory nerve and the frontal auditory neuropil of the metathoracic ganglion, respectively. For simultaneous recordings of two neurons, we used standard electrophysiological equipment (Krahe and Ronacher 1993). After amplifying the intracellular voltage signal (Bramp-01, NPI), it was fed through a 10-kHz low-pass filter. The tips of the glass microelectrodes (Clark Electromedical Instruments) were filled with a 3–5% solution of Lucifer yellow (Aldrich) in 0.5 M LiCl. This dye was injected after completion of the physiological recordings by applying hyperpolarizing current. After an experiment, the thoracic ganglia were fixed in 4% paraformaldehyde, dehydrated, and cleared in methylsalicylate. Stained cells were identified under a fluorescence microscope based on their characteristic morphology (terminology after Römer and Marquart 1984). Although both neurons were filled with the same dye, an unambiguous identification was possible by combining the knowledge about response characteristics and recording sites.
Acoustic stimulation
The preparation was placed in a Faraday cage lined with reflection-attenuating pyramidal foam and was acoustically stimulated via two loud speakers (D2905/9700a, Scanspeak), situated laterally at a distance of 30 cm from the preparation. Sound intensities were calibrated with a Brüel and Kjær microphone (1/2 in) positioned at the place of the animal, and a Brüel and Kjær measuring amplifier (type 2209). Intensities are given in dB re 2 * 10–5 N/m2 (dB SPL). All stimuli were stored digitally and delivered by custom software (Labview, National Instruments) using a 100-kHz D/A-converter (PCI-MIO-16E-4, National Instruments).
Neurons were considered as auditory if their spike rate depended on the occurrence of an acoustic search pulse. Two different stimulus paradigms were applied. First was the intensity response paradigm (short stimulus paradigm): for intensity-response curves, rectangular pulses of 100-ms duration (including 2-ms rising and falling ramps) filled with white noise (bandwidth: 0.5–30 kHz) were presented at intensities ranging from 30 to 70 dB increasing in 10-dB steps. At each intensity, the stimuli were repeated 10 or 15 times. The stimuli were separated by 300-ms interstimulus intervals. Data from a total of 16 cell pairs were obtained. In addition, single-cell recordings were used to complete the results of dual recordings. Altogether the responses from 33 low-frequency receptor neurons and 25 segmental and 21 ascending interneurons were recorded.
Second was the long stimulus paradigm: the stimuli of this set of experiments consisted of 400 ms (including 2-ms rising and falling ramps) rectangular pulses filled with white-noise carrier (bandwidth: 0.5–30 kHz). In contrast to the short stimulus paradigm, these stimuli were presented at a single intensity only. This intensity was adjusted at 
20 dB above the neuron's response threshold (in most cases between 60 and 70 dB, in a few cases at 50 dB SPL). The stimuli were repeated eight times with stimulus intervals of 1 s. We analyzed the single-cell recordings of 18 receptor neurons and 27 segmental and 31 ascending interneurons.
Data analysis
Spiking responses were digitized with 0.05-ms precision (A/D converter, PCI-MIO-16E-4, National Instruments). From the digitized recordings, the spike times were determined by means of a voltage threshold criterion. The resulting spike trains represented the basis for all subsequent analysis procedures. The statistical analyses considering the spike-train variability were based on the evaluation of the interspike-interval and the spike-count distributions at each intensity. Mean spike count and variance were computed by counting the spikes on a trial-by-trial basis within a time window of the stimulus duration to which the response latency was added. The interspike-interval distribution was determined by joining all consecutive trials. The mean interspike interval and SD were determined from this distribution. The spike rate was evaluated within the entire time window of analysis.
Spike train statistics
The CV of the interspike-interval distribution is defined as the quotient of SD and mean value. The FF was calculated as the quotient of variance and mean value of spike number per trial. Because most of the distributions of CV and FF were not fitted by a normal distribution, we applied the nonparametric Mann-Whitney U test or the Wilcoxon signed-rank test. However, for reasons of clarity, in most cases, we plotted mean and SD of the CVs and FFs in the figures. A Bonferroni correction was applied if more than two tests were performed (Sachs 1999).
To increase the reliability of the CV estimates a number of 
50 interspike intervals were demanded for the interspike-interval distribution. This lower threshold corresponds to a mean spike rate of 50 Hz at a stimulus duration of 100 ms and a repetition number of 10 (6 spikes or 5 ISI) or 15 (>4 spikes or 3.3 ISI), respectively. In the following, it is termed the "50 Hz-criterion" (see Fig. 2 ). If at a certain intensity a neuron fired fewer spikes so that the interspike-interval distribution was based on <50 events, the respective CV value for this intensity was excluded from further analysis. Compared with vertebrate neurons, the spike rate criterion of 50 Hz may appear rather high as a lower limit. However, the maximum spike rates of grasshopper auditory interneurons range between 150 and 300 Hz, and at spike rates <50 Hz, the firing becomes highly irregular. For simultaneous recordings, we plotted the CVs for those intensities where both neurons fired at least at 50 Hz (Fig. 3, A and D). The same criterion was applied to the calculation of the FF. Most of the auditory neurons show only a little spontaneous activity (Stumpner and Ronacher 1991). However, in a few cases the spontaneous activity was >50 Hz (Fig. 1B, AN4). Such cases did not influence our data analysis and conclusions because a confounding influence of spontaneous activity would have been relevant only at very low stimulus intensities, whereas our statistical analysis is based on stimulus intensities evoking maximal spike rates (Fig. 3, B and E) or spike rates of 140 or 210 Hz (Fig. 7) or were obtained at distinctly suprathreshold intensities (20 dB above threshold for the long stimulus paradigm, Fig. 8).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Variability of interspike intervals
The variability of the interspike-interval distributions of simultaneously recorded neurons was quantified by the CV (Fig. 3A). The majority of the paired recordings showed an increase of CV from one processing level to the next (data of simultaneously recorded cells are connected by lines). However, the increase of variability from receptors to segmental neurons is clearly more pronounced than the increase from segmental to ascending interneurons. In this latter comparison, one-third of the data even exhibited a reduction of variability (Fig. 3A, right). Figure 3A contains data between one and five intensities for each cell pair tested (data from the same cell pair are indicated by the same symbols). The wide spread of data points along the y-axis results from differences in spike rates between different neurons of the same type on one hand and on the other hand for the same neuron at different intensities corresponding to their intensity-response (rate-level) functions. In Fig. 2, the intensity-response functions of two simultaneously recorded cells are shown. Auditory neurons exhibited very different response characteristics with respect to response thresholds, maximal spike rates, or the overall shape of the response functions. Whereas receptor neurons typically exhibit a saturation response type of intensity-response curve (Römer 1976), interneurons in the auditory pathway of locusts often show peaked optimum curves (Fig. 2). Because both neurons of a pair rarely showed the same intensity dependency of the spike rate, it was not possible to obtain the CV values in a simultaneous recording for both neurons at their respective "best" intensity. Taking this into account, it turned out that a drop of CV values between segmental and ascending neurons was correlated with the fact that in seven of nine cases, the ascending interneuron fired at higher rates than the respective segmental interneuron (see Fig. 3A). This finding indicates a strong impact of the spike rate on the variability of neuronal responses and will therefore be examined in more detail in the following text.
A statistical examination of the data set in Fig. 3A is problematic because dependent data (same cell pair at different intensities) and independent data (different cell pairs) are combined in this plot. However, the analysis of single-cell recordings in Fig. 3B does not suffer from this problem. Here the data from all neurons (see METHODS) were pooled to calculate the mean CV for receptors and segmental and ascending interneurons, respectively. For each neuron, only the CV calculated at the maximal spike rate was included (Fig. 3B, see also Fig. 2). This kind of evaluation confirmed the picture emerging from Fig. 3A and allowed the application of standard statistical tests because now each neuron contributed only a single value. The CV increased significantly from receptor neurons to segmental interneurons and ascending interneurons (see legend Fig. 3; mean values of 0.20 for receptor neurons and 0.37 for segmental, and 0.48 for ascending interneurons, respectively). For comparison, Fig. 3C gives the complete CV data of these neurons, obtained at different sound levels, with the same 50-Hz criterion as in Fig. 3A (see also Fig. 2 and METHODS). The same tendency is visible as in Fig. 3B; however, the mean CVs are shifted to somewhat higher values.
Spike-count variability
The variability of the spike count reflects the reliability of neuronal responses with respect to successive stimulus repetitions. Figure 3, D–F, is organized in the same manner as A–C, with the same recordings as data basis and the same evaluation criteria. Again one can observe an increase of variability from peripheral to higher processing levels (Fig. 3, D–F). The increase of spike-count variability was significant between receptor neurons and segmental and ascending interneurons, respectively (Fig. 3E; mean values of 0.04 for receptor neurons, 0.08 for segmental and 0.19 for ascending interneurons, respectively).
As mentioned in the preceding text, at the level of ascending interneurons, one can distinguish two types of cells: neurons that are specialized in the processing of sound direction and, on the other hand, neurons with low directionality, obviously suited to encode features of the sound patterns (Ronacher and Stumpner 1993; Stumpner and Ronacher 1994). Examples of spiking responses of a direction coding (AN1) and a sound pattern coding ascending interneuron (AN11) are shown in Fig. 4. In general, the spiking patterns of direction coding interneurons are characterized by strong inhibitory inputs resulting in highly variable spiking responses (Rheinlaender and Mörchen 1979; Römer and Marquart 1984). Although pattern coding interneurons may receive inhibitory inputs as well, this inhibition usually is more precisely timed (Franz and Ronacher 2002). In contrast to the analysis of the interspike intervals, the spike-count variability between ascending interneurons coding for direction and pattern differed significantly (Fig. 3E, P < 0.05). In the examples of Fig. 4, the FF of AN1 was more than three times as high as that of AN11.
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A comparison of Fig. 3, B and E with C and F indicates that the spike rate had a strong impact on the variability of neuronal responses and suggests a negative relationship between spike rate and variability. Such a negative correlation is not unexpected because at high spike rates the refractory period delimits spike intervals and may lead to more regular spike trains. In the context of the increasing variability at higher processing levels, it is important to note that the maximal spike rates decreased considerably from a mean of 300 Hz for receptor neurons to 250 Hz for segmental and 170 Hz for ascending interneurons (Fig. 5A, compare also Fig. 2). As these differences in spike rates may have a profound influence on neuronal variability, this parameter is taken into account in the following. In a first step, we explored whether the reduction of spike rates at the level of ascending interneurons may have been caused by a prolonged refractory period in these neurons. The minimal interspike intervals, which were determined at each cell's maximal spike rate even showed significantly higher values at the level of receptor neurons than at the level of segmental interneurons (Fig. 5B). Thus there was no indication that the decrease of spike rate was caused by a change of the refractory period.
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210 Hz the ascending interneurons failed to show a tendency for higher mean values (Fig. 7B). In no case, significant differences between the processing levels were found, hence the differences in spike-count variability between processing levels observed before (Fig. 3) can be attributed mostly to differences in spike rates. Impact of the evaluation time window on variability
Previous studies of spike train variability reported a relationship between the time window for analysis and the measured variability (Gabbiani and Koch 1998; Kara et al. 2000). The stimuli used so far had a duration of 100 ms and were presented at different intensities. With a set of long stimuli (400 ms), we investigated the impact of the evaluation time window on variability. For the long stimulus paradigm, the interval between the stimulus presentations was 1 s because this time span has been shown to suffice for a extensive recovery from adaptation (Benda 2001; Ronacher and Krahe 1998). The same increase of variability at higher processing levels was observed as with the short stimuli (compare Fig. 3, C and F with Fig. 8, A and D ). However, the absolute values were shifted to higher values for the long stimulus paradigm. This may be due to the fact that the intensity that was used for stimulation did not necessarily elicit the cells maximal spike rate. Furthermore, with long stimulus durations adaptation may influence the neurons response more strongly.
The analysis of interspike-interval variability in time windows ranging from 25 to 400 ms shows a decrease of variability for very small time windows. The CV reached a saturation at a window size of 100 ms, whereas the difference among the three processing levels persisted over all window sizes (Fig. 8B). In contrast to the saturating interspike-interval variability, the enlargement of the evaluation time window did not result in a saturation for the spike-count variability, which showed a steady increase with the window size (Fig. 8E). As already observed for the short stimulus paradigm, both measures of variability yield different results when separating ascending interneurons into pattern and direction coding types. Although no difference between both groups of neurons was observed for the interspike-interval variability (Fig. 8C), the pattern coding ascending interneurons showed significantly lower FF values than direction coding interneurons (Fig. 8F).
Comparison of interspike-interval and spike-count variability
So far, for both measures of spike train variability, CV and FF, an increase was observed from the periphery to higher processing levels. If the spike generation follows a renewal process, the FF should approximately correspond to the square of the CV (Gabbiani and Koch 1998). To see whether the variability data followed this rule, individual FF and CV2 values are plotted in Fig. 9. Indeed, for the short stimulus paradigm, the data of individual receptor neurons scatter around the 45°-line (Fig. 9A). In contrast, for segmental interneurons, the FF was in most cases smaller than the expectation derived from CV2 (Fig. 9A). To illustrate this, we calculated the ratio between the individual FF and CV2 values and plotted the median of this distribution in Fig. 9E (left). As can be seen in this figure, both receptors and segmental interneurons showed median ratios lower than one. In the case of the segmental interneurons, the deviation from one was highly significant while for receptor neurons no significant difference was found (compare the 25 or 75% interquartile distances in Fig. 9E). Interestingly, the two groups of ascending interneurons differed considerably in this respect (Fig. 9, B and E). While for direction coding ascending interneurons the ratio between FF and CV2 was larger than one, for the pattern coding interneurons the FF was by a factor 3 lower than CV2 (Fig. 9E). In the latter case, there even existed a significant difference between FF and CV2.
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). For real neurons, this assumption is not realistic because adaptation reduces the neuronal activity even when a constant stimulus is presented. Benda et al. (2001) have shown that in auditory receptors adaptation occurs mainly during the first 80–100 ms. Thus for the short stimulus paradigm, the assumption of stationarity of the spike rate certainly was not fulfilled (Fig. 9, A and B). Therefore we considered data from the long stimulus paradigm and rejected the first 200 ms of a 400-ms neuronal response to get rid of adaptation-caused spike rate changes. Indeed, the ratio between FF and CV2 is very similar to the short stimulus paradigm for all the groups of neurons and clearly below one (Fig. 9E, right), although there was no significant difference from one in any case (Fig. 9, C and D). However, it has to be mentioned that pattern coding ascending interneurons almost approached significance (P < 0.06). Thus it remains to be seen whether a comparison with a renewal process may be an appropriate description for this group of neurons. |
DISCUSSION |
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The higher variability of ascending neurons was unexpected because these neurons form a bottleneck for the information transfer to the brain, and therefore one may have expected that the precision rather than the variability of spike responses should increase at this level. Before focusing on these findings and the consequences for neural processing, however, a more general technical question concerning our approach to measuring variability shall be discussed.
Do our procedures capture the relevant variability?
Performing simultaneous recordings in the auditory system of locusts was important with regard to establishing identical physiological conditions for a comparison of the neuronal variability at different processing levels. However, the measures that were used to quantify the magnitude of variability may not be ideally suited to capture the influence variability has on the processing tasks because they determine variability from repeated stimulus presentations (FF) or from sustained stimuli (CV). This is a situation quite different from the actual processing tasks performed by sensory systems, which normally have to rely on single events and have to come to quick decisions. The long stimulation periods used for determination of FF and CV therefore may lead to an overestimation of the actual variability relevant for the animal. Even by performing simultaneous recordings, it is conceivable that the excitability of only one of both simultaneously recorded neurons changes slowly (Pollack 1986, 1988; Römer and Krusch 2000). Moreover, differences might exist in the synaptic coupling strength between different pairs of neurons. A strong excitatory synapse between both neurons, for example, is likely to cause covariations of their spiking responses over time. In this case, the animals would have to cope with distinctly lower neuronal variability than expected from a longer measurement series with repeated stimuli as we have done in our study.
In the context of pattern recognition, the interspike-interval variability possibly does not capture the most important aspects of neuronal coding. Here, the processing of signal features could enforce, as a byproduct, large differences in interspike intervals, while the recognition may be based on the reliability of spike count and, possibly also, spike timing (Berry et al. 1997; De Ruyter van de Steveninck et al. 1997; Reinagel and Reid 2002; Warzecha and Egelhaaf 1999; Warzecha et al. 2000). However, the evaluation of interspike-interval variability in the nervous systems is of particular interest for theoreticians because they may gain insight into neural processing mechanisms or into the properties of synaptic transmission (Softky and Koch 1993; Teich et al. 1997).
Influence of spike rate on variability
The data presented in Figs. 5–7 suggest that the increase in variability from the periphery to consecutive processing levels can to a large degree be attributed to a parallel reduction of mean and maximal spike rates between receptors and ascending neurons. A negative correlation between interspike-interval variability and spike rate has been reported for the visual system (Barlow and Levick 1969; Frishman and Levine 1983; Kara et al. 2000; Rodieck 1967). The reduction of the interspike-interval variability at high spike rates is at least partly due to the influence of the refractory period that regularizes the spike distances. Obviously, this was the case for receptor neurons at higher spike rates (Fig. 1B). Interestingly, the strength of correlation between response variability and spike rate changed from a very strong one in receptor neurons to a weak or nonexisting correlation in ascending interneurons. The lower spike rates in ascending neurons did, however, not result from physiological limits such as an extended refractory period (Fig. 5B). Rather it appears that the lower spike rate of ascending interneurons is a consequence of signal processing mechanisms. To what extent this assumption is corroborated by further observations will be discussed in the following.
Implications of the observed variability for information processing
With the stimuli used here both variability measures yielded values clearly below one, which would be expected if spikes were generated according to a Poisson process. Moreover, it is very unlikely that a Poisson process yields a good description for the spike-generating mechanisms in real nerve cells because this model lacks a refactory period (Lestienne 2001). A very simple model, which incorporates a refractory period, is the renewal process (Cox 1962; Gabbiani and Koch 1998). Schaette et al. (2005) have shown that the spiking responses of auditory receptor neurons in locusts are well described by a renewal process. The comparison of FF and CV2 is a simple indicator of whether the spike train corresponds to a renewal process. For receptor neurons, the present evaluation revealed a very close agreement with the work of Schaette et al. (2005) (Fig. 9C). Even the adaptation effective within the first 100 ms did not result in a significant difference between FF and CV2 (Fig. 9A). Schaette et al. (2005) found minimal CV values of 0.2 for the interspike-interval distribution in response to constant stimulation. This value corresponds well to the CVs found in our study (see Fig. 3B). For segmental interneurons, the relationship between FF and CV2 showed a pronounced deviation from one. However, this deviation was significant only for the short stimulus paradigm (Fig. 9E compare left and right). This means that the neurons' responses in the adapted state resemble a renewal process while a strong onset response does not match this theoretical model. For pattern coding ascending interneurons, the same tendency as for segmental neurons was observed. The ratio between FF and CV2 remained very low even in an adapted state, although significance was just missed. However, at present it remains speculative if there exist active mechanisms in spike generation that increase the reliability of neuronal responses.
Apart from the strong tendency of pattern coding ascending neurons to emphasize the onset of a stimulus (see Figs. 1B and 4B), the responses of most ascending interneurons are shaped by both excitation and inhibition (Fig. 1B) (Franz and Ronacher 2002; Römer and Dronse 1982; Römer et al. 1981). Inhibitory inputs seem to be indispensable for information processing in the auditory system of grasshoppers as well as other animals (for review, see Hennig et al. 2004). The increasing impact of inhibition may be a major reason for both decreasing spike rates and increasing interspike-interval variability at higher processing levels. However, these inhibitory inputs do not necessarily also decrease the spike-count reliability. This can be deduced from a comparison of ascending interneurons that code for sound direction and for sound pattern (Fig. 3). For both classes of ascending neurons, the interspike-interval variability was virtually the same (Fig. 3B). In contrast, the FF of neurons coding for the sound pattern was only marginally larger than that of receptor neurons and significantly lower than that of neurons coding for sound direction (Fig. 3E, P < 0.05). Hence, the pattern coding interneurons show a remarkable reliability in the spike count for different presentations of a stimulus in spite of rather variable interspike intervals (Fig. 3B). Again, inhibitory inputs seem to be responsible for these differences. In the group of pattern encoding neurons, the inhibition occurs rather precisely in time, whereas in directional neurons, without need for precise timing, strong inhibitory inputs appear to reduce the spike count on one side (Römer and Dronse 1982; Römer et al. 1981). The directional information can then be represented simply by the differences in spike count between mirror image counterparts. As long as the difference of spike count between both neurons is sufficient, the precise number and timing of spikes may not be a crucial factor (Ronacher et al. 1986; see also Römer and Krusch 2000). In an extreme case, this would result in lateralization, that is, excitation from one side and inhibition from the other. Indeed, in grasshoppers this kind of lateralization has been shown for a direction coding interneuron as well as in the behavior of these animals (von Helversen 1997; for review see Hennig et al. 2004).
Finally, the pooling of data from different identified neurons into larger classes deserves a comment, in particular for the class of pattern coding ascending neurons. The classes of receptors and segmental and ascending neurons are anatomically defined and correspond also to the stages of information flow within the metathoracic processing module (Fig. 1A). Among ascending neurons, the distinction between directional and pattern encoding neurons was introduced earlier based on their different response properties (Ronacher and Stumpner 1993). The two direction coding interneurons known so far resemble each other in their response properties. Both neurons are excited from one hemisphere and inhibited from the other, and, in view of their variable responses, seem hardly suited to transmit information about the song pattern (Stumpner and Ronacher 1991, 1994). The class of pattern coding neurons is larger and encompasses more different response characteristics, but these neurons share a common feature in that they transmit little or no directional information (Ronacher and Stumpner 1993). In particular, the small SD for the FF of pattern coding elements (Figs. 3E and 8D) is a hint that pooling of these neurons captures some more general properties of the auditory network.
Comparison with vertebrate sensory systems
The results reported here show interesting parallels to the visual system of vertebrates. Increasing spike-count variability has also been reported for successive processing levels in the cat primary visual pathway on the basis of simultaneous recordings in retinal, thalamic, and cortical neurons (Kara et al. 2000). This increase of variability was also accompanied by a decrease of mean spike rate in the respective neurons. However, the responses of cortical neurons are often highly variable with respect to the spike number and their temporal occurrence. Numerous studies in the visual cortex of cats report FFs larger than one (Bair and O'Keefe 1998; Buracas et al. 1998; Heggelund and Albus 1978; Oram et al. 1999; Skottun et al. 1987). In other studies, FFs smaller than one were found (Gershon et al. 1998; Gur et al. 1997; Kara et al. 2000). Kara et al. (2000) discuss the ineffectiveness of stimuli as a reason for a higher neuronal variability as observed in former investigations. In our study, we deliberately chose noise pulses without AM to separate the intrinsic sources of variability from stimulus-induced ones. The responses of neurons to amplitude modulated stimuli will be the subject of another paper (Vogel and Ronacher, unpublished data).
In comparison to the grasshopper auditory system, where the processing of different stimulus features occurs in a network of ascending interneurons, in the vertebrate nervous system, the encoding of different stimulus parameters is often organized in different anatomical nuclei. However, in contrast to the visual system of vertebrates and to the results of our study, deWeese et al. (2003) found most reliable spiking responses in the auditory cortex, which is the highest stage of the auditory pathway. This reliability is based on a binary spiking mode, which means "spike" or "no spike" in response to an acoustic stimulus. For some stimuli, those auditory neurons fired with the highest reliablility one spike per trial. In this case, FF is zero. However, this kind of representation requires high functional separation between the neurons. This means that every cell is coding a certain limited aspect of the stimulus (Covey and Cassaday 1991; Oertel 1999; Takahashi et al. 1984; Viete et al. 1997). Besides a functional separation of ascending interneurons in the metathoracic ganglion, we also found a pronounced decrease of the spike rate at this processing level. This decrease is accompanied by an increase of the phasic response component. However, it remains speculative whether at higher processing levels in the brain of the grasshopper this mechanism is further intensified finally leading to a kind of binary spiking and thus to a massive decrease of variability. In another sensory system of the locust, such a decrease of spike rate at higher processing levels was observed. The Kenyon cells, which represent the highest stage of the odor-processing system, respond with only a single spike when their respective odor is presented (Stopfer et al. 2003). In this context, it seems worth to investigate the response characteristics of auditory brain neurons in the future.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Address for reprint requests and other correspondence: A. Vogel, Humboldt University Berlin, Institute of Behavioural Physiology, Dept. of Biology, Invalidenstr. 43, 10115 Berlin, Germany (E-mail: astrid.vogel{at}rz.hu-berlin.de)
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