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Center for Neurodynamics, 1Department of Physics and Astronomy, and 2Department of Biology, University of Missouri at St. Louis, St. Louis, Missouri 63121-4499
Submitted 31 July 2003; accepted in final form 10 October 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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26 Hz in power spectra of spontaneous afferent firing. The second type of oscillator resides in afferent terminals, is seen as a noisy peak at fa 30–70 Hz that dominates the power spectra of spontaneous afferent firing, and corresponds to the mean spontaneous firing rate. Sideband peaks at frequencies of fa ± fe are consistent with epithelia-to-afferent unidirectional synaptic coupling or, alternatively, nonlinear mixing of the 2 oscillatory processes. External stimulation affects the frequency of only the afferent oscillator, not the epithelial oscillators. Application of temperature gradients localized the fe and fa oscillators to different depths below the skin. Having 2 distinct types of internal oscillators is a novel form of organization for peripheral sensory receptors, of relevance for other hair cell sensory receptors. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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). Odorants evoke synchronized oscillations in populations of olfactory receptor neurons in catfish (Nikonov et al. 2002). The membrane potential and hair bundles of auditory and vestibular hair cells of turtles, eels, and frogs can undergo spontaneous oscillations (Crawford and Fettiplace 1980, 1985; Martin et al. 2001, 2003; Rüsch and Thurm 1990). The mammalian ear may employ a "cochlear amplifier" involving basilar membrane oscillations driven by outer hair cells, to increase sensitivity and frequency selectivity (Eguíluz et al. 2000). Nonmammalian vertebrates may achieve similar amplification using oscillations in single auditory hair cells (Camelet et al. 2000; Manley 2001; Manley et al. 2001; Martin and Hudspeth 1999; Ospeck et al. 2001). Such oscillatory processes indicate that these sensory receptors are complex systems, acting as stimulus preprocessors with nonlinear properties.
The sensory epithelia of ampullary electroreceptors of marine cartilaginous fishes (ampullae of Lorenzini; see Zakon 1986) produce oscillations, like other hair cell receptors cited above. These are self-sustained (continuously ongoing) transepithelial oscillations at 10–35 Hz, depending on temperature, which can be recorded as voltage or current fluctuations in the canals leading from skin pores to sensory epithelia (Clusin and Bennett 1979a,b; Lu and Fishman 1995). However, Broun and Govardovskii (1983) and others have disputed the existence and significance of the epithelial oscillations, regarding them as artifacts of reducing the electrical loading on the epithelia, as when the skin is raised into the air (Bennett 1967; Obara and Bennett 1972).
The axon terminals of certain sensory afferents possess a different type of oscillatory mechanism, implicated in the bursting discharges of mammalian cold receptors (Bade et al. 1979; Darian-Smith et al. 1973; Heinz et al. 1990) and in the periodicity of afferent firing in ampullary electroreceptors of catfish (Schäfer et al. 1995) and dogfish sharks (Braun et al. 1994). The hypothesized oscillator has been modeled (Braun et al. 2000; Feudel et al. 2000) as arising from slow ion channels in the membranes of afferent terminals, giving rise to approximately 50-Hz waves of membrane potential, tending to drive periodic firing. Different modes of afferent firing (tonic, doublet, bursting) have been attributed to the dynamics of the slow ion channels. Membrane potential oscillations in somata of primary sensory neurons have been used as a model for events in afferent terminals (Amir et al. 2002).
In this report, we demonstrate 2 distinct types of oscillatory processes in the ampullary electroreceptors (ERs) of paddlefish (Polyodon spathula). These primitive fish have thousands of ERs on their rostrum, a flattened antennal structure projecting anterior of the head, as well as on the head and gill covers. As diagrammed in Fig. 1 A, the receptive field of an ER afferent consists of a cluster, usually only one, of skin pores on the rostrum. Short (about 0.2 mm) canals lead from the skin pores to sensory epithelia composed of hair cells and support cells. Based on their ultrastructure (Jørgensen et al. 1972) and their polarity sensitivity of being excited by cathodal stimuli (Wilkens et al. 1997), paddlefish ERs are similar to the ampullae of Lorenzini of marine elasmobranch fishes (Zakon 1986) and to the ERs of sturgeon (Jørgensen 1980; Teeter et al. 1980). The polarity sensitivity implies that external electric fields are presumably sensed by the apical membranes of hair cells (Bennett and Obara 1986). From their basolateral membranes, the hair cells synaptically excite the terminals of primary afferents by ribbon synapses. Each cluster is innervated by 2–4 afferents (Russell et al. 2003). A primary afferent fires continuously ("spontaneously") at a nearly fixed frequency in the range of 30–70 Hz, varying for different afferents, fish, and temperatures. Afferent axons form the large anterior lateral line nerve (ALLn) on each side (Norris 1925), which enters the dorsal octavolateralis nucleus of the medulla for CNS processing of electrosensory information (New and Bodznick 1985). Afferents respond best to external sine-wave stimulus frequencies of 1–10 Hz, maximally at about 5 Hz, with declining sensitivity out to 0.1–30 Hz (Pei et al. 1998; Wilkens et al. 1997). Threshold has been estimated from behavioral tests as approximately 0.5 µV/cm (Russell et al. 1999, 2001). The ERs form a passive sensory system used for detection and capture of planktonic prey (Russell et al. 2001; Wilkens et al. 1997) and avoidance of metal obstacles (Gurgens et al. 2000). Kalmijn (1974) demonstrated that paddlefish avoid electric dipoles.
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). Both types of oscillators affect the firing of primary afferents, resulting in stochastic biperiodic output, normally showing both fundamental frequencies. An advantage of the paddlefish electroreceptor system is that it permits simultaneous recording from sensory epithelia and single afferents, which allowed us to study interactions of the epithelial and afferent oscillators. Such dual data are unavailable for other types of hair cell–primary afferent receptors. In sum, we have recognized a novel type of organization for a sensory receptor, of having 2 different types of embedded oscillators. Our findings illustrate that peripheral sensory receptors of vertebrates can be surprisingly complex nonlinear systems. Our findings are of general interest for understanding the roles of oscillations in other sensory receptors (e.g., the hair cell–primary afferent receptors for hearing and balance). |
METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Paddlefish were obtained from the Missouri Dept. of Conservation, and raised in large aquaria at 23–27°C. The data were from in vivo experiments on 20 paddlefish, of 37.3 ± 4.4 cm total length, and 12.8 ± 1 cm rostrum length. A protocol for these experiments was approved by the institutional animal care and use committee. The protocol called for a fish to be anesthetized during surgery with 3-aminobenzoic acid ethyl ester methanesulfonate (0.1 g/l). The fish was immobilized with 0.6 mg curare administered intramuscularly. It was artificially ventilated with dechlorinated tap water of 500–600 µS/cm conductivity, bubbled with 100% O2, flowing into the mouth by gravity from an elevated reservoir. An in-line chiller regulated the water temperature at about 22°C. Water hoses were routed so as to minimize the loop area of the water circuit. The fish was in an elongated 6 x 15 x 55 cm (H x W x L) all-plastic experimental chamber, in water about 5 cm deep. The entire rostrum was always submerged under 5–10 mm of water, such that there was normal electrical loading on the ERs. The chamber was on an air-support vibration-damping table, inside a Faraday cage made of ferrous hardware cloth. The plastic braces holding the fish did not compromise the skin, and did not compress the rostrum, important for maintaining its blood supply. Water motion around the rostrum was attenuated by partitioning the chamber transversely, at the base of the rostrum, with a slab of electrically conductive 2% wt/vol agarose. The sensory ganglion of an ALLn was exposed, lateral to the medulla, and a 12-M
tungsten microelectrode was advanced into the ganglion to obtain single-unit recordings of afferent spikes. To insulate electrically the body interior from the water, the water level was adjusted to have the cranial opening in air; petroleum jelly was applied topically to the skin around the opening; and saline flow onto the brain was discontinued during data collection. A 50 x 50-mm chlorided silver plate under the head led to system ground.
A unit’s modality as an electroreceptor, and the location of its receptive field, were established by presenting 5-Hz sinusoidal electrical stimuli from a 2.5-mm local dipole electrode, connected to a battery-powered constant-current linear stimulus isolation unit. The isolator’s internal noise was 0.1 nA rms over the relevant 0.1- to 100-Hz band. Recordings of oscillatory potentials from a canal were made by pressing a heat-polished glass pipette filled with water, having a tip diameter of 150–200 microns, into a canal opening at the skin. Spikes and canal signals were digitized at 20–22 kHz and 5–16 kHz, respectively, using an interface and Spike2 software from Cambridge Electronic Devices (Cambridge, UK).
Data analyses to detect and characterize oscillations
All the data presented here were from fresh in vivo preparations <16 h old. Values are stated as means ± SD. Kolmogorov–Smirnov (K-S) statistical tests were run using Systat v.9 software. PH0 refers to the probability of the null hypothesis in statistical tests.
Afferent spike times were derived off-line using Spike2 software to identify the peaks or troughs of digitized action potentials, by fitting parabolas, interpolating between samples to a time resolution of 5 µs. As a result, a sequence of spike times tn, n = 1, ... , N, was obtained. The total number of afferent spikes N in a 5- to 30-min data recording was 1–8 x 104. The single-unit nature of such afferent recordings was indicated by similar shapes and heights of spikes, and by the lack of interspike intervals (ISIs), Tn = tn+1 – tn, shorter than 5 ms.
Several types of time series analyses were used to detect and characterize oscillations and noise in ERs, using custom software programmed in Fortran77 and run on a Sun workstation, or programmed in the Spike2 script language and run on a PC. Most time series analyses require that data be stationary (i.e., have consistent properties) over the duration of a recording. To minimize nonstationarity, our analyses were applied to data segments 200–900 s in length, in which a simple moving average of the afferent firing rate over a 10-s window fluctuated less than ±2% from the mean rate for the data, and showed no trend, and in which the instantaneous firing rate revealed no gaps or unusual transients.
The coefficient of variation (CV, dimensionless) of afferent firing, a widely used measure of variability, was calculated as the SD of ISIs divided by the mean ISI: CV = 
/
Tn
, where var is the variance and angled brackets denote averaging. The mean firing frequency (
) in a data segment was calculated from the time between the first and last spike. As computational controls, renewal processes were generated from spike time series by repeatedly shuffling the order of ISIs (shuffled surrogates; Dolan et al. 1999). Shuffling did not alter the ISI histogram. Renewal processes have no memory, such that each ISI is uncorrelated with earlier or later ISIs.
Power spectra of afferent spike trains were calculated as in Douglass et al. (1993) and Gabbiani and Koch (1998). A spike train was represented as a sequence of delta-like functions centered at the spike times: a(t) = 
(t – tn) A list of spike times was converted into a sampled waveform having a baseline value of "0", assigning to a single sample nearest to each spike time the value 1/
t, where t is the sample interval (usually 50 µs). The power spectrum of this series of delta functions was calculated from overlapping windows, usually of size w = 218 samples, applying a raised-cosine window filter. Power was normalized to the mean number of spikes per window 
= wt, to have similar scaling for different afferents, yielding units for power spectral density (PSD) of: (spikes/s)2/(spike Hz–1). We usually displayed spectra with logarithmic vertical scales and assigned units of –dB relative to the maximum.
The center frequency f0 of a power spectrum peak was estimated by bisecting the peak area if it was asymmetrical, or by fitting Lorentzians for a sharp symmetrical peak, S(f) = c/[(f – f0)2 + d2], where c and d are parameters to be fitted. The width of a peak f50 was calculated as f50 = 2d, or was measured at 50% of its maximum above an estimated baseline (from linear spectra, after minimal smoothing). The quality factor of a spectral peak was calculated as Q = f0/f50. The quality factor is widely used to describe the sharpness of a peak; higher values correspond to sharper peaks.
The coherence function is useful for characterizing the correlation properties of 2 stochastic processes in the frequency domain (see Gabbiani and Koch 1998). We used it to look for corresponding oscillations in canal and afferent activity. Coherence ranges from 0 (none) to 1 (maximal coherence). The coherence function 
(f) was calculated as the ratio of the square of the absolute value of the cross-spectrum of a canal signal and corresponding spike train, to the product of their power spectra (Bendat and Piersol 2000): (f) = |Sas(f)|2/[Saa(f)Sss(f)], where Sas(f) is the cross-spectrum and Saa(f), Sss(f) are the power spectra of the afferent spike train a(t) and the canal signal s(t), respectively.
An alternate approach to analyzing the oscillatory firing patterns of ER afferents, which does not rely on power spectral analysis, was to map the phase angles 
(n) (Glass and Mackey 1988; Janson et al. 2001) between sequential pairs of ISIs, from return maps (below). In any oscillatory system, it is possible to represent the periodicity as a map of observed and preferred values ("attractors") in a multidimensional phase space. Phase angles measure the "rotation" (if any) of vectors connecting sequential points in a return map of afferent ISIs, around a center, (n) = arctan [(Tn+1 – Tn)/(Tn – Tn)]. If an afferent’s firing has 2 independent frequencies (i.e., is biperiodic), plots of (n + 1) versus (n) should exhibit invariant curves (attractors), as the projection of a 2D torus, given that the phases of 2 oscillators give the 2 angles needed to describe a torus. If there is a rational (integer) relation between the frequencies of 2 oscillators, then the phase angle map should demonstrate "fixed points" (i.e., loci) where the values cluster. If there is only one oscillatory component to an afferent’s firing, a phase angle map with no structure (uniform distribution of points) would be predicted.
The normalized cross-correlation function G(
) was used to characterize statistical relations between signals recorded from 2 canals, and was calculated as follows: G() = [s1(t) – s1][s2(t + ) – s2]/
, where is the time lag and angled brackets stand for averaging over time t. G() ranges from +1 (completely correlated) to zero (no correlation) to –1 (completely anticorrelated), and is a sensitive measure.
The correlation properties of sequences of ISIs were analyzed using 2 approaches. Return maps plotted an interval Tn against the subsequent interval Tn+1, in a pairwise manner. The dynamics of correlations over longer sequences of ISIs were revealed using the normalized autocorrelation function of ISIs, also known as the serial correlation coefficient C(k), C(k) = (Tn+kTn – Tn2)/var [Tn], where k is the lag after a given ISI expressed as the number of elapsed ISIs (Tuckwell 1988). C(k) ranges from +1 (complete correlation) to zero (lack of correlation) to –1 (complete anticorrelation). A renewal point process (e.g., from randomly shuffling the order of ISIs) shows no correlations between event intervals, such that C(k) = 1 for k = 0 (that is, an ISI is correlated with itself) and C(k) = 0 for k 
0.
The reverse correlation [revcor, R() ] reveals an average stimulus (canal signal, in our case) occurring before spikes (see Gabbiani and Koch 1998). We applied revcor analysis to paired recordings from canal and afferent. Pretriggered averaging was carried out on canal signals, using as a timing reference the afferent spikes recorded at the ALLn ganglion near the brain. This was equivalent to calculating R() = (1/N) s(tn – ), where is the lead or lag time relative to spike times tn.
Coupling of afferent firing to canal oscillations was also revealed by statistical analysis of their relative timing, using the concept of an analytic signal and the Hilbert transform (Bendat and Piersol 2000; Pikovsky et al. 2001). If there is no interaction (coupling) between these 2 processes, then there should be no preferred phase, and thus a uniform distribution is expected; otherwise, if there is coupling, the phase distribution must exhibit a peak at a preferred phase. Each cycle of canal oscillation was considered as 2
radians, and the probability density of the relative instantaneous phase of the canal oscillation at each afferent spike (
P) was calculated. The complex analytic signal z(t) was constructed, with the real part being the original canal signal and the imaginary part being its Hilbert transform: z(t) = s(t) + isH(t) = A(t)ei(t), where A(t) and (t) are the instantaneous amplitude and phase, respectively, and sH(t) is the Hilbert transform of the canal signal sH(t) = (1/) 
[s(u)/(t – u)]/du. The instantaneous phase (t) is the argument of the analytic signal, and was calculated at each afferent spike, P = (t = tn).
The frequency response of an ER afferent was measured using stimulus reconstruction (Bialek et al. 1991; Gabbiani and Koch 1998). A long (10-min) broadband Gaussian noise stimulus waveform 
(t) was applied to an ER. This stimulus was then estimated from the ER afferent firing using optimal Wiener–Kolmogorov filtering (Bendat and Piersol 2000) of the spike train. The optimal filter with the response function h(t) was applied to each spike to give an estimate of the stimulus: est(t) = h(t – tn). The response function of the filter is given in the frequency domain by h(f) = Sa(–f)/Saa(f), where Sa(f) is the cross-spectrum of the stimulus noise and the afferent spike train and Saa(f) is the power spectrum of the afferent spike train. The encoding capacity of an ER was then judged from the effective noise, the difference between the original and estimated stimulus: e(t) = (t) – est(t). The signal-to-noise ratio (SNR) at different frequencies was calculated as the ratio of the stimulus power spectrum to the power spectrum of the effective noise, SNR(f) = S(f)/See(f). The SNR as a function of frequency equals 1 when there is no encoding, and attains large values for good encoding.
Thermal gradients
Focal streams of water were used to create temperature gradients through the rostrum, taking advantage of its thin planar geometry. Thermally evoked changes in the frequency of spontaneous firing were analyzed for afferents from visible receptive fields on the dorsal surface of the rostrum. The water flowed by gravity onto a receptive field, through 4-mm ID nozzles, at 350 ml/min, from elevated reservoirs containing oxygenated water already chilled or heated to the desired temperature. The high flow rate ensured good temperature control. In some experiments, a second nozzle was positioned underneath the receptive field, to direct water vertically upward onto the ventral surface of the rostrum. Tubing from the nozzles led to plastic valves, including a latching solenoid valve that was energized only momentarily and so did not heat the water. The temperature was monitored using an electronic thermometer with a thin plastic-coated short-latency probe placed near the skin receiving a flow of water. Because the data (i.e., afferent spike times) were nonstationary, afferent power spectra were represented as time-evolution waterfall displays, using DISLIN software (DISLIN) to code power spectral density (scaled as dB) as colors, such that red/blue represent high/low power, respectively.
A steady laminar flow of ambient-temperature water directed orthogonally down onto a receptive field had little or no effect on an afferent’s background firing. However, pulsatile water flow was strongly stimulatory, and so we took steps to minimize pulsations, including immobilizing the water tubing and nozzle, gravity flow of water from elevated reservoirs, and the use of a latching solenoid valve to switch rapidly between 2 sources of water (at different temperatures) such that water flowed continuously onto a receptive field.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Spontaneous activity with two fundamental frequencies
We studied the spontaneous activity of ERs because its stationarity is a prerequisite for applying analytical approaches from time series analysis and nonlinear dynamics to look for oscillatory processes. Spontaneously active biological oscillators fall within the general class of so-called self-sustained oscillators, a type of dynamical system defined mathematically, exhibiting stable oscillations whose amplitude and frequency depend on internal parameters of the system rather than on initial conditions. Self-sustained oscillators are inherently nonlinear, and so approaches from nonlinear physics are valuable and appropriate for characterizing them (see, e.g., Anishchenko et al. 2002; Strogatz 1994).
Figure 1 B illustrates the spontaneous activity of paddlefish ERs. Spontaneous noisy voltage oscillations at about 25 Hz were always present in recordings made with water-filled glass pipettes inserted partway into receptor canals (Fig. 1B, canal traces), in healthy preparations <16 h old. Such "canal oscillations" had rms amplitudes of 15 ± 6 µV, ranging from 7 to 33 µV, and a mean peak–peak amplitude of about 140 µV (i.e., ±70 µV), ranging from 65 to 350 µV (for 42 canals from 5 fish at about 22°C). The amplitude of oscillations waxed and waned on a time scale of a few seconds, following different time courses in different canals. Their frequency could switch between the fundamental mode at about 25 Hz and harmonics at 2x or 3x higher frequencies (Fig. 1C, bottom canal trace).
The primary afferents from paddlefish electroreceptors fired continuously in the absence of external stimulation (Fig. 1B, afferent trace). The mean firing frequency was 54.1 ± 8.5 Hz (range 27.6–69.1) for 39 afferents from 16 fish at controlled temperature (22.0 ± 0.61°C). The instantaneous firing rate was characteristically irregular in fresh preparations, varying 2- to 3-fold, giving coefficients of variation of the ISIs of 0.19 ± 0.06 (range 0.10–0.38, mode 0.17, for 39 afferents). Spike doublets occurred frequently (Fig. 1C). Fluctuations in an afferent’s firing rate on slower time scales were revealed by computing moving averages using a sliding window. The firing rate fluctuated around a mean, usually with no net trend over the several hours’ duration of a recording. Because data must be stationary for most time series analyses, we applied the criteria that there should be no net trend of an afferent’s firing rate and that, in moving averages with a 10-s sliding window, the firing rate should fluctuate less than ±2% from the mean rate for the data segment.
PROPERTIES OF SPONTANEOUS CANAL OSCILLATIONS. The voltage fluctuations we recorded from a canal appeared to be summed field potentials from a population of similar oscillators in the canal’s sensory epithelium. Power spectra of canal signals (Fig. 2 A) always showed a fundamental peak at a center frequency fc= 25.5 ± 1.6 Hz (range 22.6–27.5, for 25 canals from 4 fish at 21.5–21.9°C). There was always a long series of higher harmonics at integer multiples of fc, which declined in power and increased in width and symmetry at higher frequency, as expected for nonlinear stochastic oscillators. The oscillation frequencies were remarkably similar in simultaneous recordings from pairs of canals (Fig. 2A): the difference in fc was 0.06 ± 0.37 Hz for 18 pairs of canals from 5 fish, not significantly different from zero (t-test). In a few canals, the fundamental fc peak was fractionated into 2 or 3 subpeaks. Sometimes there was an additional broad peak in power spectra of canal signals, in the range of 10–28 Hz.
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We did several control experiments to exclude alternate explanations for the canal oscillations. 1) Lifting the pipette tips into the water >5 mm above the skin abolished the oscillations. 2) The canal oscillations persisted while the ventilatory water flow was stopped briefly. 3) Similar canal oscillations were observed when the water chiller was not installed, or when the recirculation pump was switched off. 4) Pressing the pipette tip to the skin gave only low-frequency noise, having a power spectrum resembling 1/f noise.
Lack of correlation between canal pairs. When the normalized cross-correlation function G(t) (see METHODS) was calculated between signals from pairs of canals of the same cluster (i.e., same receptive field), the cross-correlation was negligible: |G| < 0.015. For comparison, cross-correlations were calculated between canals of different clusters (i.e., different receptive fields), which had similar negligible magnitudes of about ±0.015. The lack of cross-correlation shows that the oscillatory signals in different canals arise independently, even within the same receptive field, despite their remarkable similarity in frequency.
Noisiness of canal oscillations.
Canal oscillations were obviously noisy. Several analyses were carried out to show that their noise (stochasticity) was attributed to fluctuations of both the instantaneous (cycle-by-cycle) frequency as well as the instantaneous amplitude. 1) Instantaneous frequency was derived from the times between zero crossings of canal signals. Some canal recordings showed mainly the fundamental frequency fc, whereas others dwelled in the 2fc mode for extended times (as Fig. 1C, bottom canal trace). In a probability density plot of the instantaneous period (not illustrated), the half-maximum width of the fundamental peak was 2.4 ± 0.6 Hz for n = 6 canal recordings. Hence, within a given recording, the characteristic frequency of canal oscillations did vary about ±5% from the center fc frequency. This was also indicated by the finite width of the fc peak in canal power spectra (Fig. 2A); we measured f50 = 1.8 ± 0.3 Hz for 10 canals from 2 fish, by fitting Lorentzians (see METHODS). 2) The instantaneous peak-to-peak amplitude of canal oscillations was derived using the Hilbert transform (see METHODS; Bendat and Piersol 2000). Such amplitudes conformed well to a Rayleigh distribution (not illustrated), consistent with varying randomly (Bendat and Piersol 2000).
TWO FUNDAMENTAL FREQUENCIES IN POWER SPECTRA OF SPONTANEOUS AFFERENT FIRING. We made extensive use of power spectral analysis of afferent spike trains (see METHODS), because spectra provide detailed information in the frequency domain, are appropriate for studying oscillatory processes, and also reveal variability. Power spectra of long (5–15 min) stationary recordings of spontaneous afferent firing always showed a consistent pattern of peaks (Fig. 3 A, black trace). The peaks are indicative of oscillatory processes because a spectral peak signifies periodicity. The narrow peak labeled "fa" was usually the highest in power; we will present several types of analyses and experimental data indicating that the fa peak arises from a pacemaker mechanism in the afferent terminals. There was another narrow peak at 20–30 Hz, labeled "fe"; we will show that the fe peak corresponds to synaptic input to the afferent from the epithelial (canal) oscillators. Higher harmonics of fa and sometimes fe could be observed. Two minor sideband peaks at frequencies of fa ± fe were usually observed. In general, power spectra of spontaneous afferent firing had the structure expected for a periodically forced nonlinear oscillator. By this model, fa is the natural frequency of the driven oscillator, fe is the forcing frequency coming from a second oscillator, and the sideband peaks at fa ± fe are combination frequencies.
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f50) was 4.7 ± 5.6 Hz (for 45 afferents from 14 fish). The fa peak was usually sharp, as measured by its large quality factor (see METHODS), Qa = 31 ± 34 ranging from Q = 2 to Q = 166. Nevertheless, the finite width and broad base of the fa spectral peak means that the frequency of the underlying process fluctuated around a mean (i.e., was stochastic). The center frequency of the fa peak was always similar to the mean firing rate for that data segment; the mean difference between them was 0.01 ± 0.66 Hz for n = 50 afferents from 14 fish, which is not significantly different from zero (t-test). This close correspondence between fa and suggests that the fa oscillator reflects properties of the afferent terminal and probably resides there, as in certain thermoreceptors (Bade et al. 1979; Braun et al. 2000) because the afferent terminal is where spikes are initiated.
The fe peak was also relatively narrow, 1.7 ± 0.4 Hz in width at half-power, ranging from 0.8 to 2.6 Hz (for n = 48 afferents from 16 fish at 22 ± 1°C), similar to the width of the fc peak in canal spectra. Again, such a sharp peak indicates periodic activity, and so we describe the fe peak as arising from a stochastic oscillator (or a population thereof). The fe peak was typically not symmetrical, and instead was often skewed toward lower frequencies, with tails (inset, Fig. 3A). Examples in which the fe peak had 2 maxima were sometimes seen. The center frequency of the fe peak was always similar to the frequency of canal oscillations, measured from the center frequency of the fundamental peak in canal power spectra (as Fig. 2A). The mean difference between them was –0.06 ± 0.47 Hz for n = 42 canal-afferent pairs from 7 fish, which is not significantly different from zero (t-test). This close correspondence between fc and fe suggests that the fe oscillator(s) resides in the canals, specifically in the sensory epithelia, like the epithelial oscillators reported by Clusin and Bennett (1979a,b) and Lu and Fishman (1995). Our hypothesis is that the fe peak in afferent power spectra reflects summed synaptic input to an afferent from populations of stochastic oscillators of similar frequency in the canal epithelia (the receptive field) converging onto the afferent. The fe peak was always observed in afferent power spectra of fresh preparations, including when no pipette electrodes were applied to any canals.
Two sideband peaks at frequencies of fa ± fe signify coupling or nonlinear mixing of the oscillatory processes, resembling line splitting in the output of a heterodyne electronic circuit. The sidebands were most prominent when the fa and fe peaks were narrow and high-power. The sidebands are consistent with 2 alternate models: serial unidirectional coupling from the epithelial oscillators to the afferent oscillator, or parallel nonlinear mixing of the epithelial and afferent oscillatory processes at a downstream stage (see DISCUSSION).
This characteristic pattern of spectral peaks was lost after repeatedly shuffling the order of ISIs, to create a shuffled surrogate (Dolan et al. 1999) whose ISI histogram was unchanged. A power spectrum of the shuffled data (Fig. 3A, gray trace) still showed a peak at the mean firing rate , supporting our hypothesis that firing in the afferent terminal is basically driven by an oscillatory process. Because the other peaks were lost after shuffling, they reflect correlations in the data between sequences of ISIs.
The overall form of afferent power spectra resembled a ramp, rising with increasing frequency, and leveling off above about 120 Hz. This ramplike shape depends on how the spike time series is represented for purposes of calculating power spectra. We used a series of delta function approximations (see METHODS). Other representations (e.g., as a series of pulses, or as a telegraph waveform) give other global forms to power spectra of time series, while still showing a similar pattern of spectral peaks, characteristic of a given data set. To attempt to factor out the spectrum shape, we calculated a type of SNR ratio by dividing an afferent power spectrum by the power spectrum of the same data after shuffling. This gave an approximately flat baseline (Fig. 3B), with all the same peaks. The fe peak had the highest SNR.
Control experiments. 1) It is important to note that for Fig. 3, the entire rostrum was completely submerged under 5–10 mm of water, and pipette electrodes were not applied to any of the canals, such that there was normal electrical loading on the canals (shunting to the surrounding water). This is important because some authors have regarded ER oscillations as artifacts of reduced canal loading (e.g., attributed to raising the skin into air) and have disputed the normalcy of ER oscillations. 2) Our demonstration of the fe peak in power spectra of spontaneous single-afferent firing demonstrates that the canal oscillations occur normally, given that this approach avoided the use of a pipette to record oscillations from a canal, which could alter its operation. 3) We recorded the background firing of afferents while briefly stopping the flow of ventilatory water to the fish, yet maintaining a constant depth of water (about 5 cm) around the fish, and also switching off the recirculating water pump, chiller, and other nonessential equipment. The spike time series met criteria for stationarity for the initial 1–3 min, on the initial trials. Power spectra from afferents recorded under these conditions (not illustrated), including a pair of afferents recorded simultaneously, still showed all the same peaks as in Fig. 3, as evidence that the peaks are not artifacts of water flow noise, the water chiller, or other instruments. 4) Another type of control experiment was to surround the rostrum in a close-fitting enclosure made of mu metal, to shield the electroreceptors from possible electrical or magnetic fields. The mu metal wall of the shield was coated to insulate it electrically from the water, but a wire connected the mu metal to system ground. After finding an afferent with a receptive field near the tip of a rostrum, the afferent recording was held while sliding the mu metal enclosure horizontally until the receptive field was 7–9 cm inside the enclosure. With the shield in place, long recordings of background afferent firing gave power spectra (not illustrated) resembling those in Fig. 3, with all the same peaks. 5) We were unable to reveal alternating electric currents in the chamber water at frequencies near fe or fa, using recording electrodes in the chamber water, connected to nerve preamplifiers. 6) We also used a LakeShore model 420 Gaussmeter with a probe sensitive to 10–4 G, in different orientations inside the iron-screen Faraday cage, but it failed to reveal any oscillatory magnetic fields in the range of fe or fa. We conclude that the peaks in afferent power spectra are normal features of electroreceptor firing.
Coherence between canal and afferent.
To confirm the close relationship between the natural frequency of canal oscillations (fc) and the fe peak in afferent power spectra, we analyzed the coherence between canal and afferent spontaneous activity (METHODS). At frequencies near fe = fc, we observed high levels of coherence (Fig. 4, asterisk), 
0.8. This supports our model in which the fe peak is attributed to periodic forcing of afferent firing by the canal oscillations, by way of the hair cell-to-afferent synapses.
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). In some recordings, afferent-canal coherence near fe was not present or was small (<0.1), probably because of synaptic input to the afferent from other canals (as many as 30) in the receptive field, whose activities are statistically independent and so act as background noise. This interference was circumvented in experiments of inactivating all but one canal, removing the interference from other canals: then the coherence was 1 between afferent firing and the oscillations in the single canal remaining viable, precisely at fe = fc (Russell and Neiman, unpublished data).
In control studies, the coherence was flat, near zero, when calculated between an afferent’s firing and the oscillations of a canal outside its receptive field (Fig. 4, gray skyline trace). As a computational control, a surrogate times series was generated for the canal signal of Fig. 4, using the software package TISEAN (Hegger et al. 1999), which uses the amplitude-adjusted Fourier transform method proposed by Theiler et al. (1992) and modified by Schreiber and Schmitz (1996) to produce surrogates that preserve the power spectrum of data but randomize its phase information. The surrogate canal signal had a power spectrum identical to that of Fig. 4, canal PS trace (not illustrated). However, randomizing the phase destroyed any coherence between the canal and afferent (Fig. 4, thin black trace): all peaks were eliminated, leaving only small baseline fluctuations. This confirms that the coherence peak near fe = fc in Fig. 4 (asterisk) arises from correlations between afferent and canal activity at this frequency.
Variable and invariant features of afferent power spectra.
To try to estimate the "true" form of afferent power spectra, data from different afferents were compared, limiting the data set to files collected early from healthy fish, all at similar temperatures (21.8 ± 0.6°C), given that ER epithelial oscillations and also afferent firing are known to be temperature-sensitive (Braun et al. 1994; Lu and Fishman 1995). In the examples of Fig. 5 A, the fe peaks were all similar in frequency, about 26 Hz, whereas the fa peaks ranged from 44 to 64 Hz. That is, the fe peak was consistent in frequency for different electroreceptors, even in different fish, whereas the fa frequency could vary 2-fold between different electroreceptors, even in the same fish (all at fixed temperature). In a sample of 22 afferents meeting the above criteria (from 11 fish), fe = 25.4 ± 1.3 Hz (range 22.6–27.3 Hz) and fa = 52.9 ± 9.5 Hz (range 27.8–67 Hz), giving coefficients of variation of 0.053 for fe compared with 0.180 for fa, again illustrating that the afferent frequency was more variable.
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The different shapes of the fa peak in Fig. 5A corresponded to different types of ISI histograms. High-power narrow fa peaks corresponded to symmetrical narrow distributions (Fig. 5Bi), whereas low-power broad fa peaks corresponded to wide highly skewed gamma-like distributions (Fig. 5Biv). ISI histograms contain the same information as in shuffled surrogates (see, e.g., Plesser and Geisel 2001), and so are not capable of revealing correlations between spikes, such as arise from the oscillatory input to afferents from canals.
Quantitative relations of afferent power spectral peaks.
1) The ratio of the fa and fe frequencies (fa/fe) was 2.05 ± 0.31 (range 1.15–2.52, for n = 67 afferents from 19 fish). That is, the fa oscillator ran at about twice the fe frequency. Nevertheless, the 2 oscillators were almost never locked in a rational (integer) relationship of exactly 2, as can be seen from a histogram of the ratio values (Fig. 6 A), which is skewed toward ratios >2, peaking at ratios of 2.3–2.4. 2) The quality factor of the fa peak was inversely related to the coefficient of variation (CV) of ISIs (Fig. 6B). That is, high-power narrow fa peaks corresponded to less variable firing. 3) CV values for different afferents were unimodally distributed (Fig. 6C). This differs from the bimodal distribution observed for vestibular afferents (Goldberg and Fernandez 1971), consistent with the lack of calyx synapses in paddlefish ERs (Jørgensen et al. 1972). 4) We hypothesize that the canal oscillations act as a source of internal noise and are responsible for part of the variability of spontaneous afferent firing. Evidence for this came from comparing the CV of spontaneous afferent firing to the SNR of the fe peak in afferent power spectra. That is, the SNR of the fe peak was used as a measure of the "strength" of canal oscillation input to an afferent. The SNR was calculated as in Fig. 3B, using shuffled surrogates to define the baseline level. As Fig. 6D shows, there was a tendency to develop higher CV values as the SNR of the fe peak increased. That only a partial correlation (coefficient = 0.69) was observed suggests that there are other sources of variability in afferent firing, besides the canal oscillations. Data from afferents with low-frequency (1–10 Hz) spectral peaks attributed to water motion were excluded because water motion also strongly affected afferent firing, acting as external noise, yielding artifactually low-Q shapes of fa peaks.
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; Janson et al. 2001). Blurring of the lines was attributed to noise. This proves that the background firing pattern of ERs is biperiodic, by an independent approach that does not rely on correlation analyses. It also proves that the 2 frequencies need not form exact integer ratios, just as we observed for the canal (fc) and afferent (fa) oscillator frequencies. The fa/fc ratio was 2.5 in Fig. 7, consistent with little tendency toward fixed points. In other data, phase angle maps showed similar lines when the flow of ventilatory water was stopped (not illustrated).
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EXTERNAL ELECTRICAL STIMULATION.
Our aim was not to characterize the responses or sensitivity of paddlefish ERs per se, but rather to demonstrate that the epithelial and afferent oscillators respond differently to perturbations. Electrical stimuli were presented as voltage gradients in the water around the rostrum, applied between plate electrodes at the ends of the experimental chamber, or applied from a local dipole placed over the receptive field of an afferent. The ampullae of Lorenzini of cartilaginous fishes respond best at 1–10 Hz, and are excited by cathodal stimuli (i.e., when an electrode near the skin pore is made negative, relative to the environmental water), and inhibited by anodal stimuli; paddlefish ERs conform to this description (Pei et al. 1998; Wilkens et al. 1997).
Noise.
When computer-generated Gaussian wideband noise was applied, the firing pattern of afferents changed qualitatively, to a bursting mode (Fig. 8 A, afferent trace; Neiman and Russell 2002). The bursts occurred at irregular intervals and had variable durations (i.e., were stochastic). The firing rate during a burst followed a parabolic time course, rising to a maximum and then declining, and could achieve peak firing rates 250 Hz. Bursting became more pronounced as the noise amplitude was increased, seen as increased height of a short-latency peak in autocorrelograms of afferent firing (e.g., at 5–10 ms), attributed to fast intraburst firing (not illustrated; see Gabbiani and Koch 1998). In contrast, the oscillatory activity of canals was scarcely changed during noise stimulation (Fig. 8A, canal trace). The frequency of canal oscillations remained similar over a wide range of noise amplitudes, and there was little effect on the quality factor of the fundamental (fc) peak in power spectra of canal oscillations. However, the canal oscillations could stop briefly after cessation of high-amplitude noise.
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Sine waves. When a weak sine wave stimulus (about 3x threshold) was applied, only the fa peak was affected, which split to show sidebands at fa ± fs, where fs was the stimulus frequency (Fig. 8B2). The fa ± fe combination peaks were also split to develop sidebands at frequencies fa ± fe ± fs (asterisks), suggesting that the combination peaks may provide additional frequency bands for encoding stimulus information. In contrast, the fe peak associated with canal oscillations was unaffected by sine wave stimuli. Its amplitude and frequency did not change, and it did not develop discernible sidebands at fe ± fs. Thus sine wave stimulation affected only the afferent oscillator, not the canal oscillations.
Steps.
As noted by Clusin and Bennett (1979a), canal oscillations transiently become larger in amplitude at the onset of cathodal (excitatory) step stimuli, and smaller at the onset of anodal (inhibitory) steps, as we document here for paddlefish receptors (Fig. 8C1). Although weak- to intermediate-amplitude stimuli had little effect on the frequency or phase of canal oscillations, some effects were detected at the onset of high-amplitude cathodal step stimuli, detected by averaging the instantaneous frequency of canal oscillations over several trials. This revealed a transient fall in frequency at the step onset, from about 25 to about 21 Hz in Fig. 8C2. The decline in frequency decayed with a time constant of about 0.5 s, and thus would not be noticed during higher-frequency stimulation. No such changes in the frequency of canal oscillations were observed during large spontaneous changes in amplitude: instead, their frequency could remain constant, or could switch to 2x or 3x harmonics of the fundamental frequency (Fig. 1, B and C).
THERMAL STIMULATION.
Electroreceptors are known to be temperature-sensitive (Braun et al. 1994; Hensel 1974; Lu and Fishman 1995; Sand 1938). Changing the temperature at ERs was an alternate way to perturb them, leading to different responses of the afferent and canal oscillations, as evidence that they are distinct processes. In response to a long step change in temperature, the static firing rate of paddlefish ERs (labeled "3" in Fig. 9 A) became faster during warming, and slowed during cooling. However, for a brief time just after a step in temperature, the afferent firing rate did the opposite (labeled "2" and "4" in Fig. 9), attributable to thermoelectric properties of the gel in the canals (Brown 2003). Here, we are concerned with only the static response.
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The static temperature sensitivity of the frequency of canal oscillations (fc or fe values) was about 1.5 Hz/°C near 22°C. Data from 54 different canals or afferents could be fit with the power relation fc,e = –3.7 + 9.2 x 100.023T Hz, with r = 0.95 (circles and line 3 in Fig. 9B, including one ER tested over a wide range of temperatures, open circles). This power relation has a slope of 1.5 Hz/°C at 22°C and corresponds to a Q10 of 1.8. Figure 9B indicates that the frequency of canal oscillations should exceed that of afferent firing at temperatures <10°C, where lines 1 and 3 cross, and this was observed in some paired recordings.
In contrast, the static temperature sensitivity of the fa frequency, or afferent oscillator, was 2- to 3-fold larger, about 3.2–3.4 Hz/°C. It could be represented by the line fa = 3.2T – 20 Hz, with a correlation coefficient r = 0.92 (gray triangles and line 1 in Fig. 9B, for 40 different afferents from 13 fish). Data for one afferent tested over a wide range of temperatures gave similar results, fa = 3.4T – 20 Hz (white inverted triangles and line 2 in Fig. 9B; r = 0.99). A linear relation gave a better fit than a power relation because the latter failed badly below 13°C, attributed to the afferents firing more slowly than predicted. The observed temperature sensitivity of about 3.2–3.4 Hz/°C probably overestimates the specific (intrinsic) thermal sensitivity of the fa oscillator, given that the temperature of water flowing onto a receptive field will also exert indirect effects on an afferent resulting from thermal changes in its synaptic excitation by hair cells. The different thermal sensitivities of the fe,c and fa frequencies support our hypothesis that they represent distinct oscillators.
Afferent bursting at low temperature.
We observed spontaneous repetitive bursting of some afferents when their receptive field was chilled to 7–10°C with a focal stream of cold water, indicative of oscillatory processes. The afferent bursting could occur while there were no noticeable changes in canal oscillatory activity (Fig. 9C1), indicating that bursting arises in the afferent terminal. The firing rate during bursts followed a "parabolic" time course (Fig. 9C2). The temperature range at which we observed spontaneous bursting, 7–10°C, is within the range encountered by paddlefish in winter (Rosen and Hales 1981). Paddlefish stop feeding twice during the year, during summer (July–August) and also winter (January–March) (Rosen and Hales 1981). This has been attributed to food scarcity, but an alternate hypothesis is that electroreceptors, their primary means of locating prey, may be nonfunctional at these times because of extremes of water temperature.
Different time courses of temperature effects. Additional evidence that the fe,c and fa oscillators are distinct came from their different behaviors during step shifts in temperature. The frequency of canal oscillations always promptly tracked the change in water temperature, measured at the skin using a miniature sensor. For example, in Fig. 10 A, the fe peak stepped up promptly from 24 Hz at 21.8°C to a maximum of 36.3 Hz during focal warming of the receptive field to 28.1°C. There was little adaptation: fe declined only 8% by the end of this 300-s application of warm water.
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