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1Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, New York; and 2Departamento de Fisiología, Facultad de Medicina and 3Sección Biomatemática, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay
Submitted 22 October 2007; accepted in final form 27 January 2008
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ABSTRACT |
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INTRODUCTION |
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), a pair of large reticulospinal neurons that mediate tail-flip escape responses in fish (Eaton et al. 2001), challenge this perception because their synapses undergo activity-dependent potentiation (Yang et al. 1990; for review see Pereda et al. 2004). That is, discontinuous, "burstlike" stimulation of these afferents with high-frequency trains evokes a long-term potentiation of both components of their mixed—electrical (gap-junction–mediated) and chemical—synaptic response (Yang et al. 1990). The plastic properties of these synapses likely represent a mechanism for input sensitization (Yang et al. 1990) and therefore an unusual specialization for a primary auditory afferent that, in contrast to most auditory afferents that faithfully relay critical timing information for its processing along the auditory pathway, provide a decision-making neuron (Eaton et al. 2001) with relevant sensory information that could be directly translated into a behavioral response that is essential for the survival of the fish.
Although the properties and mechanisms of plasticity of their single synapses have been the subject of detailed analysis (for review see Pereda et al. 2004), little is known regarding the electrophysiological characteristics of these identifiable auditory afferents, in particular their ability to undergo high-frequency repetitive firing, which constitutes an essential requirement for induction of synaptic plastic changes (Pereda and Faber 1996; Smith and Pereda 2003; Yang et al. 1990). The electrophysiological properties of primary auditory afferents have been investigated in several species (Santos-Sacchi 1993), including goldfish saccular afferents (Davis 1996), which constitute the auditory component of the VIIIth cranial nerve organ in fish (Furukawa 1978; Furukawa and Ishii 1967). Detailed biophysical analysis revealed the presence of a variety of sodium (Na+) and potassium (K+) conductances at both goldfish saccular afferents (Davis 1996) and mammalian spiral ganglion cells (Adamson et al. 2002; Davis 2003; Dulon et al. 2006; Hossain et al. 2005; Jagger and Housley 2002; Mo et al. 2002; Santos-Sacchi 1993). Yet, is still unclear how these conductances interact in these neurons to shape their firing pattern under more physiological conditions and how they relate to their function. Repetitive firing is an essential property of auditory afferents because changes in their firing rate are known to encode variations in stimulus intensity (Pickles 1982; Sachs and Abbas 1974). Interestingly, it has been suggested that auditory afferents might not constitute a homogeneous cellular population but rather, like some inner-ear hair cells (Fettiplace and Fuchs 1999), could be electrophysiologically tailored to their functional roles (Adamson et al. 2002; Davis 2003).
Due to unfavorable anatomical characteristics (they span from peripheral receptors to their target in the CNS) the membrane and synaptic properties of primary auditory afferents have been generally investigated in vitro at either their central (Zhang and Trussell 1994) or peripheral ends (Davos 1996; Glowatzki and Fuchs 2002; Santos-Sacchi 1993). Because of their advantageous experimental in vivo accessibility (where anatomical integrity and synaptic connectivity are preserved) and critical role in the initiation of escape response, identifiable auditory afferents terminating as large myelinated club endings on the M-cells provide an ideal opportunity to link cellular biophysical analysis with system-level analysis of information processing. Here we show that these afferents are endowed with electrophysiological properties that allow them to translate their broad auditory frequency sensitivity into patterns of activity that are adapted to the requirements of their highly modifiable synapses. Consistent with their ability to generate bursts of action potentials, these afferents are capable of sustaining high-frequency repetitive firing and exhibit a strong frequency adaptation in response to depolarizing pulses. Our results also indicate that, while their ability to sustain repetitive firing critically relies on the presence of a persistent Na+ current, their frequency adaptation results from the delayed activation of an A-type K+ current (IA). Furthermore, the interplay of these conductances with passive membrane properties endows these specialized afferents with electrical resonance, whose band of frequency preference is consistent with both the goldfish's hearing range and the firing frequencies required for facilitation of their chemical synapses, a requisite for the induction of long-term plastic changes.
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METHODS |
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The experiments were performed in adult goldfish (Carassius auratus), 3 to 5 in. long. The surgical and in vivo recording techniques were similar to those previously described (Curti and Pereda 2004; Lin and Faber 1988a; Pereda et al. 1995). Briefly, auditory afferents establishing mixed synapses on the M-cell known as "Club endings" (n = 90) were intracellularly recorded outside the brain at the posterior branch of the VIIIth nerve, which contains these saccular afferents. Club ending afferents were identified by the presence of electrotonic coupling potentials after M-cell antidromic activation by stimulating the spinal cord (see RESULTS). For most recordings, glass microelectrodes (30–45 M
) were filled with 2.5 M KCl. Only afferents presenting resting potentials more negative than –67 mV and action potentials >70 mV in amplitude were used for this study. Due to the fast membrane time constant of the afferent fibers (estimated as 
200 µs in the present study) the bridge was balanced using the "spike-height method" (Frank and Fourtes 1956). For intracellular recordings of the M-cell, a second electrode (5 M KAc or 2.5 M KCl, 4–12 M) was inserted either 350 or 400 µm lateral to this cell's axon cap into the lateral dendrite or into its axon, placing the electrode more caudally between the vagal lobes. To activate the saccular afferents, a bipolar stimulating electrode was positioned on the posterior VIIIth nerve, distal to the recording site. In the case of acoustic stimulation, sound stimuli consisted of 500-µs broadband noise square pulses delivered by a 2.5-in. speaker (Quam; frequency response 0.2–8 kHz) located about 4 in. from the animal's head, and connected to a Grass AM8 audio monitor. Experimental data were acquired and recorded using software developed in the laboratory and analyzed using Kaleida Graph (Synergy Software), Igor Pro (WaveMetrics), and Superscope II (GW Instruments) software. Student's t-test was used to assess statistical significance of the data. Group data were reported as means ± SE, unless otherwise stated.
Drug application
The fish's brain was continuously superfused (1.5 ml/min) with artificial cerebrospinal fluid [ACSF (in mM): 124 NaCl; 5.1 KCl; 3.0 NaH2PO4·H2O; 0.9 MgSO4; 5.6 dextrose; 1.6 CaCl2·H2O; and 20 HEPES (pH 7.2–7.4)]. Experimental drugs were added either to the intracellular recording solution [50 mM N-(2,6-dimethylphenyl carbamoylmethyl)triethylammonium bromide (QX-314); 0.5–1 M tetraethylammonium chloride (TEA-Cl), 0.075/0.15 M 4-aminopyridine (4-AP); 1–2 M CsCl], applied topically to the surface of the posterior VIIIth nerve [1–10 µM tetrodotoxin (TTX); 1–5 µM 
-dendrotoxin (-DTX)], or included in the superfusing ACSF (5 mM 4-AP). Because of limitations to diffusion in the intact brain, the effective concentration of extracellularly applied drugs is expected to be significantly lower (up to an order of magnitude in some cases; Pereda et al. 1992) than those of the superfusate.
Computer simulations
A first approximation to the characterization of the electrical resonance of Club endings was obtained modeling a combination of low-pass and high-pass linear filters (Oppenheim et al. 1997) implemented in Matlab (The MathWorks, Natick, MA).
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RESULTS |
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; Smith and Pereda 2003).
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) acoustic stimulation. To investigate the mechanisms underlying this firing property we examined the responses of Club ending afferents to depolarizing current pulses. We found that depolarizing pulses of 1.5 their threshold typically evoked an initial high-frequency burst of action potentials, which was immediately followed by a complete absence of activity (Fig. 1C). In contrast, depolarization of the M-cell axon with a depolarization of equivalent (1.5 threshold; Fig. 1D) or stronger magnitude invariably resulted in a single action potential. These results suggest that 1) Club ending afferents are endowed with electrophysiological properties that favor the generation of high-frequency bursts in response to strong depolarizations; and 2) because the M-cells are not capable of repetitive firing (an otherwise inconvenient feature for a cell in which a single action potential initiates an escape response that lasts several hundred milliseconds; Eaton et al. 1988; Korn and Faber 2005), we hypothesize that their ability to generate high-frequency bursts must represent a functional specialization of these afferents with the goal of providing the M-cell with adequate patterns of synaptic activation. Characterization of repetitive responses
A characterization of the firing properties of Club ending afferents using pulses of increasing magnitude revealed the presence of a bilinear relationship between firing frequency and the injected current (Fig. 2A). Whereas a pulse of current at its "threshold" or "rheobasic" intensity (minimum stimulus strength of infinite duration that triggers a response) evokes a single action potential, a current step 1.5-fold the threshold intensity evoked a repetitive response that averaged 6 to 7 spikes (6.8 ± 0.83, n = 11; Fig. 2A, middle). Finally, a current pulse twice its threshold intensity elicited a repetitive response that lasted for the duration of the pulse (Fig. 2A, bottom). To characterize the dependence of repetitive firing on the magnitude of the injected current, we plotted instantaneous frequency versus current injection for the first, second, and third interspike intervals (ISIs; Fig. 2B). The slope of the primary range for the first, second, and third ISIs averaged 516.5 ± 62.4, 596.6 ± 61.5, and 571.5 ± 64.6 Hz/nA, respectively, whereas the slope of the secondary range averaged 165.6 ± 12.8, 232.2 ± 20.5, and 269.8 ± 27.2 Hz/nA (n = 11) for the first, second, and third ISIs, respectively. In all the examined examples, the slope of the primary range was significantly higher than that of the secondary range (P < 0.0005).
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= 18 ± 1.5 ms, n = 12) plus a constant. Depending on the strength of the current pulse, the repetitive discharge decayed from an initial frequency (Fi) of 448.4 ± 45 Hz to a final value (Ff) of 153.5 ± 19 Hz (n = 11); the initial and final frequency values (Fi and Ff) represent the frequency at t = 0 and the value of the constant obtained from the fit, respectively. The degree of adaptation [Fadapt = (Fi – Ff)/Fi] (Liu and Wang 2001) was quantified and expressed as percentage of the initial rate, averaging 64 ± 4% (n = 11). Thus Club ending afferents are endowed with mechanisms that allow them to respond with brief bursts of 200–600 Hz to stimulus of increasing intensity. These electrophysiological properties likely represent those of the ending of the afferent contacted by the hair cell because brief acoustic stimulation was also able to trigger repetitive discharges of characteristics similar to those observed by depolarizing the axon in our recording site (Fig. 1B). This observation is consistent with recent data, based on the ubiquitous distribution of Nav1.6 Na+ channels in primary auditory afferents, which indicates that these neurons generate (and regenerate) action potentials at multiple sites along their anatomy, including the afferent endings, ganglionic initial segments, and nodes of Ranvier (Hossain et al. 2005). Subthreshold Na+ conductance is essential for repetitive firing
Subthreshold Na+ conductances are known to underlie repetitive firing in many neuronal types (Crill 1996; Enomoto 2006). Furthermore, we have previously described the presence in Club ending afferents of a subthreshold conductance with properties similar to those of a persistent Na+ current (Curti and Pereda 2004). To investigate the possible involvement of a persistent Na+ current in repetitive firing at Club ending afferents we tested the effect of intracellularly injected QX-314 (that blocks Na+ channels) on repetitive firing responses evoked by depolarizing current pulses (Fig. 3A). Subthreshold Na+ currents are generally affected earlier than transient Na+ currents to application of blockers (Brumberg et al. 2000; Hu 1991; Staftrom et al. 1985). QX-314 dramatically abolished repetitive firing (Fig. 3A, center, n = 10). These changes occurred within a time window in which the action potentials of the afferents remained largely unaffected (Fig. 3, A, center and B; amplitude averaged 92.5 ± 4.63 and 89.1 ± 3.82 mV for control and QX-314, respectively, n = 7, P = 0.13) and was accompanied by a drastic reduction of the retrograde coupling potential amplitude obtained at depolarized membrane potentials (Fig. 3, A, right and C), a phenomenon that results from the amplification of this retrogradely transmitted coupling by the subthreshold Na+ current (Curti and Pereda 2004). Because QX-314 has been reported to have nonspecific actions on other than Na+ channels we tested the effect of extracellular application of TTX (1–10 µM), which specifically blocks Na+ channels, on the repetitive responses evoked by depolarizing current pulses. As illustrated in Fig. 3D, application of TTX also led to a dramatic suppression of repetitive responses (n = 6). As in the case of QX-314, the observed suppression of repetitive firing took place within a time window in which the action potentials of the afferents remained largely unaffected; amplitude averaged 97.5 ± 4.3 and 95.1 ± 3.8 mV for control and TTX, respectively (n = 6, P = 0.7) (Fig. 3, E and F). Both QX-314 and TTX ultimately led, as previously reported (Curti and Pereda 2004), to the complete blockade of the first action potential (not shown). Finally, consistent with the elimination of a subthreshold amplifying mechanism, the depolarizing prepotentials that usually lead to initiation of the next action potential in repetitive responses (Amir et al. 2002a,b; Lanthorn et al. 1984; MacVicar 1985) were no longer observed after TTX application (Fig. 3G).
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). To investigate whether this slowly decaying TTX-sensitive subthreshold membrane response was the underlying mechanism responsible for the adapting firing pattern observed in Club ending afferents, we compared the time courses of both phenomena. As illustrated in Fig. 4D, the decay of the membrane response to a near-threshold depolarizing pulse closely followed the time course of the instantaneous firing frequency obtained for a suprathreshold current pulse in the same fiber (in which the response lasted for the duration of the pulse; see earlier text), suggesting a primary role of subthreshold mechanisms in shaping the firing patterns at Club ending afferents.
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The results so far indicate that subthreshold mechanisms are largely responsible for the firing pattern of Club ending afferents. However, because subthreshold Na+ currents have a slow process of inactivation with time constants in the order of hundreds to thousands of milliseconds (Crill 1996; French et al. 1990; Ogata and Ohishi 2002), the relatively faster decay of the TTX-sensitive subthreshold responses to depolarizing current pulses (Fig. 4, A–C) suggests the involvement of an opposing repolarizing conductance. The existence and contribution of more than one active membrane mechanism to near-threshold responses were demonstrated by subtracting the response of a 0.2-nA pulse (mostly determined by resistive and capacitive properties of the membrane) multiplied by a factor of 10, from a near-threshold response evoked by a 2-nA depolarizing pulse (Fig. 5A). This subtraction revealed the presence of an initial depolarization (likely corresponding to the activation of a subthreshold Na+ current), which was followed by a sustained hyperpolarization (Fig. 5A, bottom). Because subthreshold Na+ currents are generally opposed by repolarizing K+ conductances (Crill 1996) we tested the effects of intracellular applications of a combination of K+ channel blockers (see METHODS), covering a wide spectrum of these channels, on the membrane responses to depolarizing current steps. We found that blockade of K+ channels prolonged the initial voltage response to a depolarizing pulse (Fig. 5B), suggesting the presence of a persistent Na+ current that was able to reveal, unopposed, its time course. Accordingly, membrane responses, which under these conditions lacked their typical decay, were greatly attenuated by extracellular application of TTX (Fig. 5B), confirming the presence of a noninactivating or very slowly inactivating component with the characteristics of a persistent Na+ current (Crill 1996).
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; Jerng et al. 2004; Rudy 1988), on the membrane responses to depolarizing current steps. As with the intracellular application of K+ channel blockers, extracellular application of 4-AP prolonged the initial voltage response to a depolarizing pulse and lacked its characteristic sag, as illustrated by the modification of the ratio between the late and early amplitudes of pulse responses that became approximately 1 (see Fig. 5C). The off response to depolarizing pulses was followed by a small "tail," which was greatly reduced by TTX (arrows in Figs. 4A and 5B), suggesting that the decay corresponds to the action of some persistent Na+ channels, which deactivate slowly relative to the rapid variations of the membrane potential produced by the injected current step. Consistent with this observation, this tail was enhanced by 4-AP, which by removing IA leaves persistent Na+ channels acting unopposed (arrow in Fig. 5C). Thus near-threshold depolarizing responses at Club ending afferents are dominated by the interplay of two independent active mechanisms that are sequentially activated. Initially, the response is dominated by the rapid activation of an amplifying persistent Na+ current, which is counterbalanced by the relatively slow activation of a subthreshold K+ current, whose activation opposes membrane depolarizations (Fig. 5D).
The sensitivity to 4-AP of subthreshold membrane responses suggested the involvement of an A-type K+ current (IA), which is known to operate within this voltage range (Rudy 1988; Storm 1990). We confirmed this possibility by using a standard protocol to reveal the presence of this current (Storm 1988). More specifically, we measured the delay to the first spike when bringing the cell to threshold from hyperpolarized potentials, which removes IA steady-state inactivation (Fig. 6A). As IA became more activated, it characteristically introduced a delay in the generation of the spike that was inversely proportional to the prepulse membrane potential (Fig. 6B). Finally, and consistent with its pharmacological effects on subthreshold membrane responses, this delay was greatly reduced by extracellular application of 4-AP (Fig. 6, C and D). To further characterize the properties of this subthreshold conductance, we estimated its recovery from inactivation following a similar protocol. For this purpose, a hyperpolarizing prepulse of variable duration and fixed amplitude (adjusted to drive the membrane potential to about –100 mV) was followed by a suprathreshold depolarizing current pulse; the availability of IA channels was inferred from the delay to the first action potential (Fig. 6E). As illustrated in Fig. 6F, this delay increased with the prepulse duration, indicating that the recovery from inactivation followed an exponential time course with a time constant of 56.2 ± 4.73 ms (range: 46.8–61.8 ms, n = 3), a value that is consistent with those found for similar A-type conductances in other cell types (Jerng et al. 2004; Koyama and Appel 2006; Petersen and Nerbonne 1999; Wang and Schreurs 2006), including in the auditory system (Rothman and Manis 2003). In an attempt to determine the identity of the involved K+ channels we tested the effects of -DTX (1–5 µM), which blocks channels of the Kv1 family known to be responsible for low-threshold K+ conductances in the auditory system (Klug and Trussell 2006; Mo et al. 2002; Rathouz and Trusell 1998; Trussell 1999), on subthreshold responses to depolarizing current pulses. In contrast to the effects of 4-AP, we did not detect changes in the decay of near-threshold responses as a result of the application of this toxin (see Fig. 5C), suggesting that channels other than those of the Kv1 family are responsible for this hyperpolarizing conductance. Consistent with a primary role of this subthreshold mechanism and confirming an early report (Davis 1996), we did not observe evidence for the involvement of a Ca2+-dependent K+ current [IK(Ca)] (see Supplementary Fig. S1A and legend).1 In addition, our analysis revealed that the observed firing pattern could not be explained by a progressive decrease in the availability of transient Na+ channels (see Supplementary Fig. S1, B–F, and legend).
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). As illustrated in Fig. 7A, depolarization of the afferent to about –55 mV from resting potential (–75 mV in this case) elicited a single action potential; in contrast, depolarization to the same membrane potential from about –120 mV (held at this potential by DC current injection over a period of 
10 s) elicited instead a high-frequency repetitive response. Furthermore, the frequency adaptation of repetitive responses obtained by depolarizing from hyperpolarized potentials was significantly attenuated (Fig. 7B). These effects were prevented by QX-314 (Fig. 7C), confirming that an increased availability of persistent Na+ channels was responsible for the observed increased firing during repetitive responses overcoming the actions of IA, whose increased availability initially causes the delay to the first spike but later begins to inactivate (such delay is consistent with the time constant of inactivation of IA currents in other cell types; Rothman and Manis 2003). To independently confirm this conclusion, we tested the effects of pharmacological blockade of IA on responses to suprathreshold depolarizing pulses. As illustrated in Fig. 7D (left), whereas depolarization to –65 mV from resting potential (–75 mV) evoked a single action potential, the same depolarization led to a high-frequency response following extracellular application of 4-AP (Fig. 7D, middle). Thus blockade of IA led to the unopposed action of persistent Na+ channels, resulting in an enhancement of the repetitive responses. Supporting this conclusion, both 4-AP and a combination of K+ channel blockers ultimately led to the development of a pronounced plateau potential (Figs. 6C and Fig. 7D, right) that was greatly suppressed by extracellular application of TTX (Fig. 7D, right). Consistent with its lack of effect on subthreshold responses, application of -DTX did not enhance firing responses at Club ending afferents, confirming that -DTX–insensitive channels are responsible for spike–frequency adaptation at Club ending afferents (Fig. 7E, top). In contrast, as previously reported (Nakayama and Oda 2004), -DTX induced repetitive firing in the M-cell during parallel control experiments (Fig. 7E, bottom).
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Membrane oscillations were occasionally observed following the initial burst of action potentials, suggesting that underlying oscillatory membrane mechanisms could be responsible for repetitive firing at Club ending afferents (Fig. 8A). Subthreshold oscillations have been shown to be responsible for repetitive firing in primary sensory neurons (Amir et al. 2002a; Liu et al. 2002; Pedroarena et al. 1999; Wu et al. 2001) and are generally caused by the existence of membrane electrical resonance (Hutcheon and Yarom 2000). Electrical resonance characterizes the frequency at which neurons respond best to depolarization and therefore describes its frequency-dependent properties, in particular how neurons process oscillatory inputs at subthreshold potentials (Hutcheon and Yarom 2000). Subthreshold K+ conductances such as those found at Club ending afferents are responsible for the generation of electrical resonant behavior in various neuronal types (Hutcheon and Yarom 2000; Hutcheon et al. 1996) and produce a characteristic "sag" in the subthreshold membrane response to depolarizing pulses (Fig. 5D). The presence of both subthreshold "sags" and membrane oscillations, which are considered time-domain signatures of electrical resonance (Hutcheon and Yarom 2000), suggests that these auditory afferents are endowed with similar membrane properties.
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; Izhikevich 2007). Thus the approximate resonant properties can be estimated if the values of the activation time constant of the "resonant K+ current" and the membrane time constant are determined experimentally. The membrane time constant (low-pass filter) was measured by fitting a single-exponential function to the decay that followed the cessation of current pulses of different polarities and amplitudes and averaged 0.2 ± 0.01 ms (n = 12; Fig. 8B, top). The time constant representing the activation of the A-type current (high-pass filter) was estimated from the decaying portion of the near-threshold membrane response (Fig. 8B). The decay was best fitted with a double-exponential function (P < 0.001) and the time constants of the first and second exponential averaged 2.9 ± 0.26 and 30.1 ± 2.01 ms (n = 12). The fastest and more prominent time constant dominating the decay of the pulse (10-folds faster and 30-fold the magnitude of the second one) was used for the estimates of resonance (Fig. 8B, top). This measurement proved to be a good approximation to the activation kinetics of IA because the obtained values were consistent with the activation kinetics of A-type currents obtained elsewhere (Huguenard and McCormick 1992; Huguenard et al. 1991; Jerng et al. 2004; Rathouz and Trusell 1998; Rothman and Manis 2003; Rudy 1988; Storm 1990). The second slower time constant might represent a minor contribution of an unidentified, less prominent outward current to the decay and it was not included in the estimates. The filtering properties determined by the obtained IA and membrane time constants are illustrated in the Bode plots of Fig. 8B, determining cutoff frequencies for the high-pass (middle) and low-pass filters (bottom) of 61 ± 6 and 803 ± 45 Hz (n = 12), respectively. When combined (Fig. 8C), these values determined a band-pass filter with a bandwidth (defined as the range contained by the cutoff frequencies) of 742 Hz and a peak value at 220 Hz, suggesting the existence of resonant properties at Club ending afferents.
Independently supporting these measurements, the estimated bandwidth of the electrical resonance matched the frequency range of repetitive firing in Club ending afferents (200 to 600 Hz; see Fig. 2). Furthermore, the estimated peak resonant frequency was also in agreement with that calculated for the "minimum frequency," the instantaneous frequency of a minimal repetitive response consisting of only two spikes triggered by a depolarizing pulse, indicating a propensity of Club ending afferents to generate repetitive responses within this frequency range (Fig. 8E). A second consequence of electrical resonance is that, in addition to allowing neurons to undergo high-frequency repetitive firing within a given frequency range, it can also make them more susceptible to respond to inputs with this particular frequency content. Accordingly, the bandwidth of this resonance matched the effective range of hearing of this species, estimated to be about 100 to 1,000 Hz (Fay 1995). The tuning curves of two fibers, representative of the "high" and "low" frequency types of broadly tuned afferents identified in goldfish (Fay 1978, 1995), are illustrated superimposed to the Bode plot (Fig. 8C; examples taken from Fay 1995).
The estimates of electrical resonance predict that Club ending afferents would be more easily depolarized in response to intracellularly injected currents with a frequency content near to their resonant frequency. Unfortunately, this direct approach proved to be inapplicable to our in vivo recording conditions. Because the band of resonant frequencies found in Club ending afferents is 20- to 40-fold higher (10–15 vs. 200 Hz) than those found in previous studies where resonant behaviors were explored with this method (Hutcheon et al. 1996; Puil et al. 1986; Wu et al. 2005), the filtering properties of our high-resistance electrode (40 M) made it impossible to reliably induce and monitor changes in voltage at the required high frequencies (up to >1,000 Hz, as the band of resonance is 61–803 Hz).
Given these experimental limitations, we sought additional independent support for the resonant properties of IA and the potential participation of the persistent Na+ current by using computer simulations. For this purpose, a Club ending afferent was modeled, following available anatomical and physiological data (Furukawa and Ishii 1967; Rosenbluth and Palay 1961; Sento and Furukawa 1987; see Supplementary METHODS for details). Because of the impossibility of obtaining direct measurements, we ran computer simulations using parameters of A-type currents described in auditory neurons that are similar to those estimated for these afferents. We found that addition of an A-type current with the kinetic properties estimated experimentally for the ventral cochlear nucleus (Rothman and Manis 2003), a clear resonant behavior appeared with a peak at 220 Hz (Fig. 8D). This approach also allowed us to evaluate the role of the persistent Na+ current in this resonant behavior. As previously shown (Hutcheon and Yarom 2000), the addition of a persistent Na+ current produced a strong amplification (35%) of the predicted membrane resonance without modifying the resonant frequency, suggesting that this conductance is likely to play a relevant functional role by allowing the expression of this resonance (Fig. 8D). Thus despite the low stringency of this model, computer simulations adequately reproduced the frequency range of the predicted membrane resonance, suggesting that IA has robust resonant properties in these neurons. In addition, it indicated an essential role for the persistent Na+ current in amplifying these resonant properties.
Properties of synaptic facilitation at synapses between Club endings and Mauthner cells
Stimulation of the posterior VIIIth nerve, where Club ending afferents run, evokes a mixed (electrical and chemical) synaptic potential in the lateral dendrite of the M-cell (Fig. 9A; Furshpan 1964). In contrast to most primary auditory afferent synapses that undergo depression (Zhang and Trusell 1994), high-frequency stimulation of these afferents with trains of two to six pulses (Fig. 9A) was shown to evoke a strong facilitation of the glutamate-mediated chemical component (Lin and Faber 1998b; Pereda and Faber 1996; Wolszon et al. 1997). Synaptic facilitation is essential for the induction of long-term potentiation of both components of the mixed synaptic response because it optimizes the required activation of N-methylD-aspartate (NMDA) receptors (Pereda and Faber 1996; Yang et al. 1990).
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; Wolszon et al. 1997; the changes in the facilitated synaptic potential were measured by subtracting the response to a single pulse; see Wolszon et al. 1997). We found that paired-pulse facilitation decayed following an exponential time course, with a time constant of 4.5 ± 0.81 ms (n = 8). This facilitation took place within a narrow temporal window (Fig. 9C, top) and, remarkably, it did not extend beyond the frequency range determined by the firing properties of Club ending afferents, indicating that bursts of 200–600 Hz are optimal in producing facilitation of the chemical component of synaptic response. Further, the time course of the synaptic facilitation was extremely fast when compared with that of other well-characterized contacts (Fig. 9C, bottom), suggesting that firing characteristics of these auditory afferents are adapted to the requirements of synaptic transmission at Club endings. We found that repetitive firing within the 200- to 600-Hz range was also essential to obtain temporal summation of successive synaptic responses (Fig. 9A). Because of the brief time constant of the M-cell (400 µs; Fukami et al. 1965), temporal summation can take place only during the chemical component of the mixed synaptic response. The duration of the chemical component was found in about 5 ms, an integrating interval that is consistent with the band of frequency preference determined by the electrical resonance of the membrane. |
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DISCUSSION |
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), our results show that the ability of Club ending afferents to respond with high-frequency bursts of action potentials results from the interaction of a subthreshold Na+ current, which is required for repetitive responses, with an A-type K+ conductance. This subthreshold Na+ conductance has all the characteristics of a persistent Na+ current. That is, the voltage sensitivity and membrane potential activation range (10–15 mV above resting potential), susceptibility to TTX and QX-314, and prolonged time course in the presence of K+ channel blockers are typical of persistent Na+ currents described in fish (Berman et al. 2001; Doiron et al. 2003; Watanabe et al. 2000) and mammalian neurons (Crill 1996). The A-type K+ conductance was, in contrast to that of the M-cell, insensitive to DTX and therefore unlikely to represent one of the typical "low-threshold" K+ currents, which act to prevent repetitive firing in the auditory system (Davis 2003; Klug and Trussell 2006; Trusell 1999). Rather, this conductance presented values of kinetics of activation and recovery from inactivation and a pharmacological profile (lack of sensitivity to DTX and sensitivity to 4-AP in the millimolar range) that were comparable to those of another A-type current also found in the auditory system (Rothman and Manis 2003), which possibly involves channels of the Kv4 family (Jerng et al. 2004; Patel and Campbell 2005). Unfortunately, we did not observe changes as a result of bath application of rHeteropodatoxin-2 (which blocks Kv4 channels; not shown), suggesting that either this toxin, unlike DTX, has limited experimental access in our in vivo conditions or that the involved fish isoforms are less sensitive to its actions. Thus although the presence of Kv1 channels is probably beneficial for the M-cell, where a single action potential is sufficient to initiate an escape response that lasts several hundreds of milliseconds, the lack of these channels in Club ending afferents allows these afferents to undergo high-frequency repetitive firing, a pattern that is likely to play an important physiological role by producing a strong dendritic depolarization (see following text). Interaction of membrane and synaptic properties
Our results indicate that the Club ending afferents have the propensity to respond with high-frequency (200–600 Hz) bursts of action potentials to strong depolarizing inputs and that this frequency range is ideally suited to produce facilitation of the chemical component of their mixed synaptic response. Bursts are thought to represent reliable neural codes during information processing (Izhikevich et al. 2003; Krahe and Gabbiani 2004; Lisman 1997) and play special roles for the induction of synaptic plasticity (Lisman 1997). The generation of bursts in response to strong acoustic stimuli seems a particularly advantageous strategy for the M-cell system, and it could constitute an efficient and desirable code of information. That is, a burst of action potentials would generate, as opposed to a single action potential, a prolonged synaptic response that can efficiently depolarize the large and unusually low input resistance M-cell (Faber and Korn 1978). Due to the longer duration of the chemical component, high-frequency bursts also allow temporal summation of the mixed synaptic responses, an otherwise unlikely possibility given the short duration of the electrical component and the brief membrane time constant of the M-cell. Because the firing frequency of the burst was found to be proportional to the strength of the depolarization (see Fig. 2B), the results suggest that louder acoustic stimuli (likely required to trigger the escape response) would produce stronger facilitation of synaptic responses. Thus by producing synaptic facilitation and allowing temporal summation of successive synaptic responses, high-frequency bursts of action potentials can lead to stronger and longer-lasting synaptic activation of the M-cell lateral dendrite.
Equally relevant, brief high-frequency bursts of action potentials are required for the induction of activity-dependent long-term potentiation of the mixed synaptic response (Yang et al. 1990) because they optimize the activation of NMDA receptors by providing enhanced glutamate release at more depolarized potentials, whose involvement is essential for the induction of the plastic changes (Pereda and Faber 1996; Smith and Pereda 2003; Wolszon et al. 1997). Thus both membrane and synaptic properties of Club ending afferents act in a concerted fashion and seem to be adapted to the M-cell system, where the increased synaptic gain of these auditory nerve synapses will sensitize a vital escape response, lowering its threshold to acoustic stimuli (Korn and Faber 2005).
Resonant membrane properties
Bursts of action potentials are often generated by the interaction of synaptic inputs with intrinsic membrane properties (Lisman 1997). Our results also suggest that the propensity to respond with high-frequency (200–600 Hz) bursts of action potentials to strong depolarizing inputs is supported by the existence of electrical resonant properties of the Club ending afferent membrane. Furthermore, the optimal intervals required for the synaptic facilitation of the glutamatergic component of the mixed synaptic potential also matched the estimated frequency preference of this resonance, suggesting that this membrane behavior is essential for the interaction between afferent firing and synaptic properties.
Unfortunately, the estimated band of membrane frequency preference was significantly higher than that found in other preparations (5–10 vs. 100–800 Hz) and thus the filtering properties of our sharp recording microelectrode prevented us from obtaining direct evidence of this membrane behavior while depolarizing the membrane with a sinusoidal current of varying frequency. In contrast to those previous examples in which resonance could be explored directly in in vitro conditions (Hutcheon et al. 1996; Puil et al. 1986; Wu et al. 2005), these properties were estimated in Club ending afferents by obtaining measurements of the filtering characteristics of the membrane passive properties and the activation of the subthreshold, A-type K+ conductance at near-threshold responses in an in vivo (more physiological) situation where anatomical integrity is preserved. Because electrical resonance is a voltage-dependent property, although indirect, this method has the advantage of accurately estimating the impact of this behavior at the membrane potential where it is primarily expressed, that is, about this cell's threshold. As a result of activation kinetics slower than the membrane time constant, subthreshold K+ conductances of this type determine "resonant" behavior in many cells types by opposing membrane depolarizations (Hutcheon and Yarom 2000; Izhikevich 2007). These estimates of resonant behavior were independently supported by: 1) the presence of subthreshold oscillations underlying repetitive responses, 2) the propensity of these afferents to respond within this frequency range, and finally 3) by computer simulations generated using the kinetic values obtained for the A-type current found in auditory neurons (Rothman and Manis 2003) of physiological and pharmacological characteristics similar to those found in Club ending afferents, given the impossibility of obtaining direct measurements under our experimental conditions. Despite their low stringency, computer simulations adequately reproduced the frequency range of the predicted membrane resonance, suggesting that IA has robust resonant properties in Club ending afferents.
Although "resonant" currents can by themselves generate membrane resonance, they are often enhanced by "amplifying" currents (such as persistent Na+ currents) that allow them to manifest their functional impact (Izhikevich 2007). That is, because of their depolarized reversal potential and quick activation properties these currents actively enhance, rather than oppose, voltage depolarizing changes that amplify otherwise weak membrane resonant behaviors (Hutcheon and Yarom 2000). Numerical computer simulations also suggested an essential contribution of the persistent Na+ current to this property in Club ending afferents by providing strong amplification of membrane responses at resonant frequencies (35%). If the interaction between "resonant" and "amplifying" currents is sufficiently strong, it can destabilize the membrane potential allowing the generation of spontaneous oscillatory pacemaker-like activity (Hutcheon and Yarom 2000). Most commonly, this interaction is not very strong, so the frequency preference of a given cell is "latent" and oscillatory activity is revealed only in the presence of its inputs. Such "weak" resonance makes a neuron a "good listener" within a specialized frequency band (Hutcheon and Yarom 2000). This second possibility seems to be the case of Club ending afferents, where oscillatory activity was observed only in response to depolarization and the estimated band of electrical resonance matched that of the effective frequency range of hearing of the goldfish (100–1,000 Hz; Fay 1995), making these afferents more sensitive to a broad range of behaviorally relevant frequencies.
Neurons are excitable because they are near transitions from resting to spiking. From the perspective of dynamic systems this transition corresponds to a bifurcation (Izhikevich 2007). This approach provides an alternative framework in which the excitable properties of neurons can be understood. Regardless of the cellular type and ionic conductances involved, they are only four different types of bifurcation of equilibrium that a system can undergo (Izhikevich 2007). In this context neurons are divided into integrators and resonators with bistable or monostable activity. The presence of resonant properties indicates that the behavior of this neuron corresponds to an Andronov–Hopf-type of bifurcation. The lack of a bistability of this neuron's electrical behavior suggests that it more specifically corresponds to a supercritical Andronov–Hopf bifurcation. Nevertheless, this categorization should be more appropriately explored and confirmed in the future with more adequate stimuli such as current ramps (Izhikevich 2007). Consistent with our results, Andronov–Hopf bifurcations can be reproduced in reduced models that combine a persistent Na+ current with a delayed K+ current ("persistent sodium plus potassium model"; Izhikevich 2007), indicating that the electrophysiological properties of Club ending afferents can be adequately explained by the interaction between these two currents.
Frequency tuning in goldfish primary afferents
Unlike their mammalian counterparts, fish auditory afferents are broadly tuned and exhibit limited frequency selectivity (Fay 1995; Popper and Fay 1998). The anatomical characteristics of the Club ending afferents (large diameter and characteristic myelinization) meet those of S1-type saccular fibers originating from the rostral part of the sacculus (the auditory organ in fish), following the initial characterization of goldfish auditory afferents by Furukawa and Ishii (1967). In contrast with S2, a second type of smaller fibers, S1 afferents were shown to respond to higher frequencies (>500 Hz; Furukawa and Ishii 1967). More rigorous characterization of goldfish afferent responses confirmed the presence of both high-frequency and low-frequency afferent types (Fay 1978, 1995). Although in these studies physiological responses were not correlated with anatomical identification of the afferent fibers, both low and high tuning were observed in afferents lacking spontaneous activity (Fay 1978), a notable characteristic and identification criteria for Club ending afferents and suggesting that these larger afferents can respond to a broader range of frequencies.
Club endings constitute a relatively homogeneous population of about 100 afferents terminating in the lateral dendrite of the M-cell (Bartelmez 1915). Our results suggest that they are also relatively physiologically homogeneous because all of the studied fibers exhibited similar biophysical properties. Mechanisms of frequency selectivity in lower vertebrates, including goldfish (Sugihara and Furukawa 1989), are known to involve the contribution of resonant electrical membrane properties, which allow inner-ear hair cells to be tuned to stimuli of specific frequency content (Fettiplace and Fuchs 1999). The reported tuning curves and characteristic frequencies of both types of afferent response (Fay 1978, 1995) fell within the band of electrical resonance estimated for Club ending afferents (see Fig. 8C; Fay 1978, 1995), indicating that this mechanism is unlikely to underlie their individual frequency tuning. Rather, because most saccular fibers will respond to any frequency within the goldfish's effective range of hearing at sound levels 40 dB above best threshold (see Fig. 8C for the Q10 dB [range of frequency response at 10 dB above threshold] of each afferent; Fay 1995), this resonant mechanism would act to synchronize this population of large afferents to loud acoustic stimuli of behavioral relevance by making them, regardless their characteristic frequency, electrically tuned to the whole hearing range. Accordingly, strong acoustic stimuli are necessary for triggering an escape response in the M-cell system, which has a characteristic high threshold (Fay 1995).
Essential role of a persistent Na+ current
Our data indicate that the properties of the fast and modifiable Club ending mixed synapses are supported by biophysical specializations that allow these afferents to translate the goldfish's effective range of hearing into adequate patterns of afferent activity. Among these properties, a persistent Na+ current plays an essential functional role as is required for the generation of repetitive responses and likely to enhance an otherwise weak electrical resonance. Although persistent Na+ currents represent a small (1%) noninactivating fraction of the total Na+ current they have a significant functional impact because they are activated about 10 mV negative to the transient Na+ current, where few voltage-gated channels are activated and neuron input resistance is high (Crill 1996). As a result of this property, subthreshold Na+ currents play essential cellular roles in amplifying dendritic synaptic potentials, regulating repetitive firing, and producing depolarizing responses (Crill 1996; Ogata and Ohishi 2002). Persistent Na+ currents have been reported to be present in primary afferents (Bowe et al. 1985; Honmou et al. 1994; Kocsis and Waxman 1983; Rush et al. 2007; Wu et al. 2005) where they are thought to mediate important functional and pathological roles (Stys et al. 1992, 1993). Consistent with these observations, Nav1.6 channels, thought to underlie persistent Na+ currents (Ogata and Ohishi 2002; Rush et al. 2007), were reported to be expressed in primary auditory afferents (Hossain et al. 2005). Thus the presence of a relatively small number of Na+ channels lacking fast inactivation is essential for this neuron's function and define its electrophysiological phenotype, allowing these "anatomically simple" afferents to link behaviorally relevant auditory signals into patterns of activity that match the requirements of their fast and highly modifiable synapses (Fig. 9D). In addition, this subthreshold Na+ current was shown to play an essential role in amplifying retrograde synaptic communication via electrical synapses that, by providing a mechanism of lateral excitation, contributes to the synchronization of Club ending afferents (Curti and Pereda 2004; Pereda et al. 1995).
The specialized functional properties of these neurons suggest that primary afferents can be endowed with complex membrane and synaptic properties and be capable of more sophisticated contributions to auditory processing than generally recognized before.
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ACKNOWLEDGMENTS |
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1 The online version of this article contains supplemental data. 
Address for reprint requests and other correspondence: A. E. Pereda, Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, 1300 Morris Park Ave., Bronx, NY 10461 (E-mail: apereda{at}aecom.yu.edu)
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ABSTRACT
INTRODUCTION
V, ordinate)–current (abscissa) relation obtained in another fiber before (Control, filled circles) and after TTX application (TTX, open circles). The voltage responses were measured 5 ms after the onset of the current step. Membrane response characteristically exhibited a nonlinear response to larger depolarizing current pulses in the form of an apparent increase in the slope resistance (Control), which was abolished by application of TTX [TTX; voltage–current (V–I) relation after TTX was fit with a straight-line function]. C: plot illustrates the difference between the V–I relations obtained before (Control) and after TTX application for the experiment shown in B, revealing the active component blocked by TTX. Note that the TTX-sensitive component was activated only by current pulses >0.8 nA. Inset: subtraction of the voltage responses to depolarizing current pulses illustrated in A (obtained before and after TTX application) revealed the time course of the TTX-sensitive membrane component. This component reached its maximum within 5 ms of the onset of the current pulse and slowly decays toward the end of the pulse. D: subthreshold membrane mechanisms are the major determinant of the firing behavior at Club ending afferents. The time course of the spike–frequency adaptation followed that of membrane responses to near-threshold depolarizing current pulses. To illustrate this property, the scaled decay of the membrane response to a near-threshold current pulse is illustrated superimposed to the plot of instantaneous frequency vs. time of a repetitive discharge induced in the same fiber by a suprathreshold depolarizing current pulse (filled circles; same data shown in 
x 