Predicting the temporal responses of non-phase-locking bullfrog auditory units to complex acoustic waveforms
Abstract
Axons from the basilar papilla of the American bullfrog (Rana catesbeiana) do not phase lock to stimuli within an octave of their best frequencies. Nevertheless, they show consistent temporal patterns of instantaneous spike rate (as reflected in peristimulus time histograms) in response to repeated stimuli in that frequency range. We show that the second-order Wiener kernels for these axons, derived from the cross-correlation of continuous (non-repeating), broad-band noise stimulus with the spike train produced in response to that stimulus, can predict with considerable precision the temporal pattern of instantaneous spike rate in response to a novel, complex acoustic waveform (a repeated, 100-ms segment of noise, band-limited to cover the single octaves above and below best frequency). Furthermore, we show that most of this predictive power is retained when the second-order Wiener kernel is reduced to the highest-ranking pair of singular vectors derived from singular-value decomposition, that the retained pair of vectors corresponds to a single auditory filter followed by an envelope-detection process, and that the auditory filter itself predicts the characteristic frequency (CF) of the axon and the shape of the frequency-threshold tuning curve in the vicinity of CF.
... Wiener-kernel analysis is a technique that is able to disentangle inhibition that is hidden within the excitatory passband (Eggermont, 1993; van Dijk et al., 1997;Yamada and Lewis, 1999;Temchin et al., 2005;van Dijk et al., 2011). To apply this analysis, neural responses from the auditory system to broadband Gaussian noise are measured. ...
... These kernels characterize the linear and nonlinear responses of the auditory system up to the location where the response was measured. In order to separate excitatory and inhibitory contributions, a singular value decomposition (SVD) can be applied to decompose the second-order kernel into a number of parallel subsystems (Yamada and Lewis, 1999). Each subsystem is characterized by a filter function (an eigenvector of the kernel matrix) and a gain function (the corresponding eigenvalue; see Fig. 1). ...
... Correspondingly, the system described by the kernel can be regarded as a number of parallel subsystems, which all consists of a linear filter (with an impulse response equal to an eigenvector u i ), a squaring device, and a weight factor (equal to the eigenvalue w i ). Subsystems with a positive and negative eigenvalue reflect excitation and inhibition of a neuronal response, respectively (Yamada and Lewis, 1999). Subsystems often occur in quadrature pairs, ranked consecutively as indicated by the dashed red squares. ...
Noise-induced tinnitus and hyperacusis are thought to correspond to a disrupted balance between excitation and inhibition in the central auditory system. Excitation and inhibition are often studied using pure tones; however, these responses do not reveal inhibition within the excitatory pass band. Therefore, we used a Wiener-kernel analysis, complemented with singular value decomposition (SVD), to investigate the immediate effects of acoustic trauma on excitation and inhibition in the inferior colliculus (IC).
... Along with the stimulus is shown the PSTH (solid gray figure) of the unit's response (derived from 9,270 spikes) and the predicted PSTH (ragged dark line along the upper edge of the PSTH). The prediction was derived by adding the zero-order and second-order terms of the Wiener series (Yamada and Lewis, 1999). Note that the presence of the non-repeating background acoustic noise in this case was sufficient to prevent the sort of clipping (at zero spikes per second) seen in the PSTH of Fig. 1. ...
... We also made predictions (not shown) from a simplified version of the second-order term, computed by convolving the stimulus waveform with a linear-filter function (the highest-ranking eigenvector from singular-value decomposition of the second-order kernel), then taking the square of the envelope of the result (the filtered waveform). In fact, the predictions obtained in this way consistently were more faithful (in terms of rms error) than those obtained from the entire kernel (Yamada and Lewis, 1999). ear, that impose randomness (dithering) on the responses to the stimulus waveform. ...
... pattern can be predicted remarkably faithfully by Wiener series (de Boer and de Jongh, 1978;Wolodkin et al., 1996). When the dithering is not sufficient, as is true of many frog auditory units, it often can be made sufficient by addition of external (acoustic) noise to the stimulus waveform (Yamada, 1997;Yamada and Lewis, 1999). For primary auditory units, the kernels of the Wiener series traditionally are based on reverse correlation between the spike-train response and a stimulus comprising continuous white noise (de Boer and de Jongh, 1978;van Dijk et al., 1994). ...
We present examples of results from our studies of auditory primary afferent nerve fibers and populations of such
fibers in the frog and gerbil. We take advantage of the natural dithering effect of internal noise, where it is sufficient,
to construct highly predictive descriptive models (based on the Wiener series with kernels derived from white-noise
analysis). Where the internal noise is insufficient, we enhance dithering by applying external acoustic noise together
with our stimuli. Using acoustic noise as a background sound, orthogonal to the stimulus waveform, we show that
under some circumstances such background sound can enhance the ability of individual fibers and populations of
fibers to encode the stimulus waveform. © 2000 Elsevier Science Ireland Ltd. All rights reserved.
... That function represents the second-order nonlinear behavior of the ear. When employed as the kernel for convolution in the second-order term of the Wiener series, it predicts the second-order distortion components of the ac (phase-locked) spike-rate response and positive and negative dc spikerate responses (shifts in the mean spike rate) (Yamada and Lewis, 1999; Lewis et al., 2002a,b). The second-order kernel also can be converted to a graph of the spectrotemporal receptive Weld for the unit—displaying secondorder non-linear behavior in time and frequency (Lewis and van Dijk, 2004; see also Hermes et al., 1981; Eggermont et al., 1983a,b). ...
... The recorded data were digitized with a 10 kHz sampling rate. Spike times were identiWed automatically by means of a threshold and peak-detection algorithm (Yamada and Lewis, 1999). The digitized continuous noise stimuli and corresponding times of spike peaks were used to generate discrete Wrst and second-order Wiener kernels for each auditory axon. ...
... For each of the 37 auditory units presented here, the number of spikes included in the analysis ranged from approximately 1500–20,000. Through singular-value decomposition, each secondorder Wiener kernel (h2) was decomposed into a set of normalized singular vectors and a set of their corresponding amplitudes (Yamada and Lewis, 1999). From these, separate excitatory and inhibitory subkernels were constructed (Lewis et al., 2002a,b). ...
Second-order reverse correlation (second-order Wiener-kernel analysis) was carried out between spike responses in single afferent
units from the basilar papilla of the red-eared turtle and band limited white noise auditory stimuli. For units with best excitatory frequencies
(BEFs) below approximately 500Hz, the analysis revealed suppression similar to that observed previously in anuran amphibians. For
units with higher BEFs, the analysis revealed dc response with narrow-band tuning centered about the BEF, combined with broad-band
ac response at lower frequencies. For all units, the analysis revealed the relative timing and tuning of excitation and various forms of
inhibitory or suppressive effects.
... The frequency carriers, the fine structure, which were used for the DMR sound span a frequency range of 1-48 kHz. In previous studies, the entire auditory sound waveform was considered for the reverse correlation analysis (van Dijk et al., 1994;Yamada and Lewis, 1999) or for derived information theoretic approaches (Andoni and Pollak, 2011). In the present work however, the reverse correlation method is applied to the spectrotemporal envelope, individually for each frequency carrier. ...
... The difference between a covariance and outer product is that for the covariance, for each (τ 1 , τ 2 )-combination the mean of each segments is subtracted before multiplication, whereas for the outer product it is not. The outer product can be used for the spike-triggered covariance analysis (Yamada and Lewis, 1999). The outer product is computed for each temporal DMR envelope segment of length τ which elicited a spike at time t i=1...N , and averaged across all N obtained matrices, for each frequency channel, schematically shown in Fig. 3. ...
Neurons in the main center of convergence in the auditory midbrain, the central nucleus of the inferior colliculus (ICC) have been shown to display either linear significant receptive fields, or both, linear and nonlinear significant receptive fields. In this study, we used reverse correlation to probe linear and nonlinear response properties of single neurons in the cat ICC. The receptive fields display areas of stimulus parameters leading to enhanced or inhibited spiking activity, and thus allow investigating the interplay to process complex sounds. Spiking responses were obtained from neural recordings of anesthetized cats in response to dynamic moving ripple (DMR) stimuli. The DMR sound contains amplitude and frequency modulations and allows systematically mapping neural preferences. Correlations of the stimulus envelope that preferably excite neurons can be mapped with the spike-triggered covariance. The spike-triggered average and -covariance were computed for the envelope of the DMR, separately for each frequency carrier (spanning a range of 0-5.5 octaves). This enables studying processing of the sound envelope, and to investigate whether nonlinearities are more pronounced at the neurons' preferred frequencies rather than at other frequencies. We find that more than half of the neurons (n=120) display significant nonlinear response properties at least at one frequency carrier. Nonlinearities are dominant at the neuron's best frequency. The nonlinear preferences can have either the same or opposite temporal receptive field pattern (e.g. on-off) as the linear preferences. No relationship to other neural properties such as feature-selectivity, phase-locking, or the like has been found. Thus, these nonlinearities do not seem to be linked to a specific type of neuron but to be inherent to ICC neurons indicating a diverse range of filtering characteristics.
... The physiological data used in this paper were taken from a¡erent auditory axons of the American bullfrog (R. catesbeiana). The experimental methods used to obtain the data appear in a previous paper (Yamada and Lewis, 1999) 1 . The nUn second-order Wiener kernels were computed from the data in the manner described by Eq. 1. ...
... vectors presented in the earlier paper (Lewis et al., 2002). The tuning and timing represented in Fig. 17 is thoroughly consistent with that of the highest-ranking singular vectors of the underlying Wiener kernel and subkernels (see Yamada and Lewis, 1999, for kernels and singular vectors from similar units). ...
The spectro-temporal receptive field [Hear. Res 5 (1981) 147; IEEE Trans BME 15 (1993) 177] provides an explicit image of the
spectral and temporal aspects of the responsiveness of a primary auditory afferent axon. It exhibits the net effects of the
competition between excitatory and inhibitory (or suppressive) phenomena. In this paper, we introduce a method for derivation of
the spectro-temporal receptive field directly from a second-order Wiener kernel (produced by second-order reverse correlation
between spike responses and broad-band white-noise stimulus); and we expand the concept of the spectro-temporal receptive field
by applying the new method not only to the second-order kernel itself, but also to its excitatory and inhibitory subkernels. This
produces separate spectro-temporal images of the excitatory and inhibitory phenomena putatively underlying the competition.
Applied, in simulations, to models with known underlying excitatory and suppressive tuning and timing properties, the method
successfully extracted a faithful image of those properties for excitation and one for inhibition. Applied to three auditory axons
from the frog, it produced images consistent with previously published physiology.
: 2003 Elsevier B.V. All rights reserved.
... Multiple filters can be derived by maximizing the amount of mutual information they jointly convey. MIDs have the advantage that they are not biased by stimulus correlations when non-Gaussian stimuli are applied, including environmental and communication sounds (Steveninck and Bialek 1988;Yamada and Lewis 1999;Slee et al. 2005;Fairhall et al. 2006;Schwartz et al. 2006;Maravall et al. 2007;Sharpee et al. 2011a). Alternative approaches, which may incorporate processing constraints, have also been shown to yield conjoint, multidimensional RFs of auditory cortical neurons that capture more information and enable better response predictions (Harper et al. 2016;Kozlov and Gentner 2016;Atencio and Sharpee 2017). ...
Classic spectrotemporal receptive fields (STRFs) for auditory neurons are usually expressed as a single linear filter representing a single encoded stimulus feature. Multifilter STRF models represent the stimulus-response relationship of primary auditory cortex (A1) neurons more accurately because they can capture multiple stimulus features. To determine whether multifilter processing is unique to A1, we compared the utility of single-filter versus multifilter STRF models in the medial geniculate body (MGB), anterior auditory field (AAF), and A1 of ketamine-anesthetized cats. We estimated STRFs using both spike-triggered average (STA) and maximally informative dimension (MID) methods. Comparison of basic filter properties of first maximally informative dimension (MID1) and second maximally informative dimension (MID2) in the 3 stations revealed broader spectral integration of MID2s in MGBv and A1 as opposed to AAF. MID2 peak latency was substantially longer than for STAs and MID1s in all 3 stations. The 2-filter MID model captured more information and yielded better predictions in many neurons from all 3 areas but disproportionately more so in AAF and A1 compared with MGBv. Significantly, information-enhancing cooperation between the 2 MIDs was largely restricted to A1 neurons. This demonstrates significant differences in how these 3 forebrain stations process auditory information, as expressed in effective and synergistic multifilter processing.
... Because the second-order model does not require explicit knowledge of the nonlinearities in the system, this model class has been widely applied in system identification studies of early sensory systems. In the auditory system, second-order models have explained the envelope response in the papilla of bullfrogs (Yamada and Lewis, 1999), inferior colliculus of owls (Keller and Takahashi, 2000), A1 of ferrets (Kowalski et al., 1996), and auditory forebrain of songbirds (Sen et al., 2001). The second-order model has been used to describe frequency-specific modulations in the auditory nerve fiber of cats (Young and Calhoun, 2005). ...
The functional relationship between an input and a sensory neuron's response can be described by the neuron's stimulus-response mapping function. A general approach for characterizing the stimulus-response mapping function is called system identification. Many different names have been used for the stimulus-response mapping function: kernel or transfer function, transducer, spatiotemporal receptive field. Many algorithms have been developed to estimate a neuron's mapping function from an ensemble of stimulus-response pairs. These include the spike-triggered average, normalized reverse correlation, linearized reverse correlation, ridge regression, local spectral reverse correlation, spike-triggered covariance, artificial neural networks, maximally informative dimensions, kernel regression, boosting, and models based on leaky integrate-and-fire neurons. Because many of these system identification algorithms were developed in other disciplines, they seem very different superficially and bear little obvious relationship with each other. Each algorithm makes different assumptions about the neuron and how the data is generated. Without a unified framework it is difficult to select the most suitable algorithm for estimating the mapping function. In this review, we present a unified framework for describing these algorithms called maximum a posteriori estimation (MAP). In the MAP framework, the implicit assumptions built into any system identification algorithm are made explicit in three MAP constituents: model class, noise distributions, and priors. Understanding the interplay between these three MAP constituents will simplify the task of selecting the most appropriate algorithms for a given data set. The MAP framework can also facilitate the development of novel system identification algorithms by incorporating biophysically plausible assumptions and mechanisms into the MAP constituents.
Auditory perception depends on multi-dimensional information in acoustic signals that must be encoded by auditory nerve fibers (ANF). These dimensions are represented by filters with different frequency selectivities. Multiple models have been suggested; however, the identification of relevant filters and type of interactions has been elusive, limiting progress in modeling the cochlear output. Spike-triggered covariance analysis of barn owl ANF responses was used to determine the number of relevant stimulus filters and estimate the nonlinearity that produces responses from filter outputs. This confirmed that ANF responses depend on multiple filters. The first, most dominant filter was the spike-triggered average, which was excitatory for all neurons. The second and third filters could be either suppressive or excitatory with center frequencies above or below that of the first filter. The nonlinear function mapping the first two filter outputs to the spiking probability ranged from restricted to nearly circular-symmetric, reflecting different modes of interaction between stimulus dimensions across the sample. This shows that stimulus encoding in ANFs of the barn owl is multidimensional and exhibits diversity over the population, suggesting that models must allow for variable numbers of filters and types of interactions between filters to describe how sound is encoded in ANFs.
In this chapter I shall attempt to explore the ways in which several vertebrate groups utilize vibrational or seismic signals Specifically, I hope to encourage the study of animals other than those used in the standard mammalian preparations by emphasizing that an animal’s natural acoustic behavior often leads to insights concerning the underlying physiological mechanisms. Applied across a wide range of taxa, this neuroethological approach has yielded a great deal of information about vertebrate behaviors including bat echolocation, sound localization by owls, electrolocation and object avoidance in electric fishes, song learning in passerine birds, and frog acoustic and vibrational communication. Among the vertebrates, strong evidence for seismic signal detection and/or communication has been documented for only a handful of cases. These animals appear to rely on surface (Rayleigh) waves to transmit vibrational signals. In Leptodactylus and perhaps in Crotalus, the apparatus for detecting these signals resides both in the sensory epithelium of the inner ear and in its associated sensory structures and appears to take advantage of the multimodal response properties of the sensory hair cells. Methods used to explore these responses and new behavioral evidence for seismic cue detection in several animal groups are discussed.
It is shown that noise can be an important element in the translation of neuronal generator potentials (summed inputs) to neuronal spike trains (outputs), creating or expanding a range of amplitudes over which the spike rate is proportional to the generator potential amplitude. Noise converts the basically nonlinear operation of a spoke initiator into a nearly linear modulation process. This linearization effect of noise is examined in a simple intuitive model of a static threshold and in a more realistic computer simulation of spike initiator based on the Hodgkin-Huxley (HH) model. The results are qualitatively similar; in each case larger noise amplitude results in a larger range of nearly linear modulation. The computer simulation of the HH model with noise shows linear and nonlinear features that were earlier observed in spike data obtained from the VIIIth nerve of the bullfrog. This suggests that these features can be explained in terms of spike initiator properties, and it also suggests that the HH model may be useful for representing basic spike initiator properties in vertebrates.
SUMMARY Acoustic response characteristics of single fibres were studied in the Vlllth cranial nerve of adult and early post-metamorphic bullfrogs (Rana catesbeiana). Based on the distribution of units' best excitatory frequencies, three populations of auditory fibres were found in each group of frogs. The sharpness of the tuning curves and temporal firing patterns of primary fibres were similar in both adults and froglets. However, the distributions of the populations were different between the two groups, and it was found that froglets responded to higher frequencies than did adults. There were also differences in the distributions of thresholds of excitation between the froglets and adults. The excitation thresholds of low-frequency selective and high-frequency selective fibres tended to be higher in froglets. Low- frequency selective fibres in both groups of frogs exhibited two-tone inhibi- tion, and the best inhibitory frequencies were higher in froglets than in adults. These results demonstrate that changes in the response properties of primary auditory fibres occur during the development of the bullfrog. These func- tional changes presumably reflect morphological changes which may occur in the peripheral auditory system.
Discharge patterns of cat auditory‐nerve fibers were elicited with a series of synthesized speech sounds as stimuli. The sounds differed in the starting frequencies of formants two (F2) and three (F3), or in the duration of the transition. Fibers with characteristic frequencies (CF's) less than 800 Hz respond primarily to components near the first formant (F1), or, for the lowest CF's, to the fundamental frequency (F0). The responses of fibers with higher CF's may include several prominent components. For CF's between 800–1600 Hz, the response is usually dominated by a component near F2 at low intensity, but as F2 changes or intensity increases, F1 may dominate. If the frequency of F3 is low, F3 may also dominate: as F3 rises, the dominant component abruptly switches to F2. For CF above 1600 Hz, all formants may be represented in the response. Again, increases in intensity or changes in the instantaneous frequencies of the formants may alter the relative contributions of response components. [Supported by...
Hair cells, the primary receptors of the auditory, vestibular, and lateral-line sensory systems, produce electrical signals in response to mechanical stimulation of their apical hair bundles. We employed an in vitro preparation and intracellular recording to investigate the transduction mechanism of hair cells in the sacculus from the inner ear of the bull-frog (Rana catesbeiana). When stimulated directly by mechanical deflection of their hair bundles, these cells gave graded responses up to 15 mV in amplitude; the peak sensitivity was about 20 mV/µm deflection. The depolarizing component of the receptor potential corresponded to stimuli directed towards the kinocilium. Depolarizing responses were associated with a membrane resistance decrease, and hyperpolarizing responses with a resistance increase. Action potentials, possibly calcium spikes, were occasionally evoked in hair cells by mechanical or electrical stimulation.
A population study of auditory nerve responses in the bullfrog, R a n a c a t e s b e i a n a, analyzed the relative contributions of spectral and temporal coding in representing a complex, species‐specific communication signal at different stimulus intensities and in the presence of background noise. At stimulus levels of 70 and 80 dB SPL, levels which approximate that received during communication in the natural environment, average rate profiles plotted over fiber characteristic frequency do not reflect the detailed spectral fine structure of the synthetic call. Rate profiles do not change significantly in the presence of background noise. In ambient (no noise) and low noise conditions, both amphibian papilla and basilar papilla fibers phase lock strongly to the waveform periodicity (fundamental frequency) of the synthetic advertisement call. The higher harmonic spectral fine structure of the synthetic call is not accurately reflected in the timing of fiber firing, because firing is ‘‘captured’’ by the fundamental frequency. Only a small number of fibers synchronize preferentially to any harmonic in the call other than the first, and none synchronize to any higher than the third, even when fiber characteristic frequency is close to one of these higher harmonics. Background noise affects fiber temporal responses in two ways: It can reduce synchronization to the fundamental frequency, until fiber responses are masked; or it can shift synchronization from the fundamental to the second or third harmonic of the call. This second effect results in a preservation of temporal coding at high noise levels. These data suggest that bullfrog eighth nerve fibers extract the waveform periodicity of multiple‐harmonic stimuli primarily by a temporal code.
Discharge patterns of single eighth nerve fibers in the bullfrog, Rana catesbeiana, were analyzed in response to signals consisting of multiple harmonics of a common, low‐amplitude fundamental frequency. The signals were chosen to reflect the frequency and amplitude spectrum of the bullfrog’s species‐specific advertisement call. The phase spectrum of the signals was manipulated to produce envelopes that varied in their shapes from impulselike (sharp) to noiselike (flattened). Peripheral responses to these signals were analyzed by computing the autocorrelation functions of the spike trains and their power spectra, as well as by constructing period histograms over the time intervals of the low‐frequency harmonics. In response to a phase aligned signal with an impulsive envelope, most fibers, regardless of their characteristic frequencies or place of origin within the inner ear, synchronize to the fundamental frequency of the signal. The temporal patterns of fiber discharge to these stimuli are not typically...