Discrimination of behaviorally relevant signals by auditory receptor neurons

Christian K. Machens$^{1,2}$, Petra Prinz$^2$, Martin B. Stemmler$^{1,2}$,

Bernhard Ronacher$^{1,2}$, and Andreas V. M. Herz$^{1,2}$

$^1$ Innovationskolleg Theoretische Biologie and $^2$ Institut für Biologie,

Humboldt-Universität zu Berlin, 10099 Berlin, Germany

Abstract

An organism's ability to distinguish natural stimuli is limited by bottlenecks in the transmission of sensory signals. To quantify how much auditory receptor neurons in a grasshopper species represent a bottleneck, we tested the capability of single receptors to discriminate calling songs from conspecific grasshoppers. Spike trains elicited from different songs were studied using the metric-space analysis of Victor and Purpura (1997). The natural songs can be distinguished perfectly after a mere 100 ms if spike trains are evaluated on time scales of about 10 ms. This time scale is well matched to the temporal structure of these grasshopper songs.

Results

Many sensory systems are faced with the task of distinguishing stimuli based on the responses of only a few neurons. Whether natural stimuli evoke sufficiently different responses can be best investigated when these stimuli are well characterized by a small set of parameters. The acoustic communication signals of grasshoppers fulfill this requirement, making grasshoppers an ideal candidate for correlating neurophysiology and behavior.

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Figure 1: Sections of two grasshopper songs (sound pressure level versus time)

Grasshoppers must detect and discriminate the calling songs of conspecific potential mates. Male grasshoppers of the species Chorthippus biguttulus rhythmically generate sound consisting of many repetitions of a basic pattern, termed ``syllables''. Every syllable, in turn, is composed of six elementary pulses. Among individual grasshoppers of this species, syllables vary considerably in their length (60-120 ms), their substructure, and their frequency content. Behavioral experiments show that female grasshoppers prefer certain male songs over others, even when all songs are equally loud (R. Balakrishnan, personal communication). While it is not known which of the song differences are most relevant in the female's decision, the grasshopper's ability to discriminate between different songs should be visible in the neural responses at all levels of the auditory pathway.

Here we focused on the distinguishability of spike trains recorded from single auditory receptor neurons. Eight different songs were repeatedly presented to a grasshopper while keeping the peak sound intensity constant. Spike trains were recorded intracellularly from an auditory receptor and subsequently analyzed using the metric-space analysis introduced by Victor and Purpura (1997) (Network: Comput. Neural. Syst. 8:127-164).

The metric-space analysis consists of two steps: (1) A distance is calculated between every two spike trains by a stepwise transformation of one spike train into the other. Each step consists of inserting, deleting, or shifting a spike and is associated with a cost. Insertion and deletion cost one unit each, while a shift in time of $\Delta t$ costs $q \Delta t$ units, where $q$ is a free parameter that weights how important the precise timing of spikes is. The distance between two spike trains is defined as the minimal cost of transforming one train into the other. (2) A supervised clustering algorithm is applied, sorting spike trains close to each other into one group. The resulting groups are then compared with the groups sorted by stimulus, allowing us to calculate the mutual information between the two sets, one sorted by metric distance, the other by stimulus. For eight songs the maximum information, indicating perfect discrimination, is 3 bits since $2^3=8$. The complete analysis depends on the parameter $q$; therefore, the value of $q$ that results in optimal stimulus discrimination determines the precision with which spike times should be evaluated.

For $q=0$, the distance between two spike trains corresponds to the difference in the number of spikes. In this case, the spike trains fall into two groups (yielding a mutual information of less than 1 bit); spike trains of the group with fewer spikes were evoked from songs that had considerably less power in the preferred frequency band ($\sim$5 kHz) of the auditory receptor. A better discrimination of the set of stimuli, however, is not possible based on spike count alone.

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Figure 2: Contour plot of distinguishability (measured in terms of the mutual information) as a function of window length $T$ and cost factor $q$.

Beyond the spike count, two additional factors influence how well stimuli can be distinguished: the timing of spikes, whose importance is weighted by the factor $q$, and the length of the stimuli. To investigate how the latter influences distinguishability, only the first $T$ milliseconds of each spike train were taken into account, where $T$ was varied from 0-500 ms. An analysis varying both $T$ and $q$ yields the contours shown in Fig. 2, outlining the regions in $(T,q)$ space that have a mutual information of at least 1, 2, 2.5, or 3 bits. One needs to observe about a hundred milliseconds of each spike train to distinguish the songs perfectly when a cost factor of $q\approx 100\;$s$^{-1}$ is used, as can be observed from the 3 bit contour. Within this time, only one to two syllables of each song have been played back to the grasshopper. Therefore, under these ideal conditions, all songs can be perfectly discriminated after the first two syllables. A cost factor of $q\approx 100\;$s$^{-1}$ implies comparing spike trains at a time scale of about 10 ms. This time scale corresponds well to the substructure of each syllable (6 pulses of length 10-20 ms). We conclude, therefore, that the substructure plays a vital role in discrimination. Note also that beyond the first 100 ms window, longer samples of the spike trains only improve discrimination ability marginally, as can be seen by the nearly horizontal contours in Fig. 2.

This study demonstrates that the information present in the songs, namely the syllable length and syllable substructure, is well preserved in the spike trains of the receptor neurons. How grasshoppers make use of this information, however, cannot be decided at this stage. The computation presented is only a lower bound on the discrimination abilities of single auditory receptor neurons, as the ensemble of natural stimuli was restricted in size. With a population of thirty to forty auditory receptors per tympanum, the discrimination ability of the animal as a whole could be even greater. Interestingly, under ideal conditions male grasshoppers can perfectly distinguish calling songs of males and females after only 2-3 syllables (Ronacher and Krahe (1998). J. Comp. Physiol. A 183, 729-735). Our study shows that this achievement can be explained at the level of single auditory receptor neurons. Whether further syllable repetitions are needed in noisy environments is an open question and calls for more experiments in both behavior and physiology.