Subthreshold Sodium Current Underlies Essential Functional Specializations at Primary Auditory...

Subthreshold Sodium Current Underlies Essential Functional Specializationsat Primary Auditory Afferents

Sebastián Curti,1,2 Leonel Gómez,3 Ruben Budelli,3 and Alberto E. Pereda1

1Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, New York; and 2Departamento deFisiologıa, Facultad de Medicina and 3Seccion Biomatematica, Facultad de Ciencias, Universidad de la Republica, Montevideo, Uruguay

Submitted 22 October 2007; accepted in final form 27 January 2008

Curti S, Gómez L, Budelli R, Pereda AE. Subthreshold sodiumcurrent underlies essential functional specializations at primary audi-tory afferents. J Neurophysiol 99: 1683–1699, 2008. First publishedJanuary 30, 2008; doi:10.1152/jn.01173.2007. Primary auditory affer-ents are generally perceived as passive, timing-preserving lines ofcommunication. Contrasting this view, identifiable auditory afferentsto the goldfish Mauthner cell undergo potentiation of their mixed—electrical and chemical—synapses in response to high-frequencybursts of activity. This property likely represents a mechanism ofinput sensitization because they provide the Mauthner cell withessential information for the initiation of an escape response. Consis-tent with this synaptic specialization, we show here that these affer-ents exhibit an intrinsic ability to respond with bursts of 200–600 Hzand this property critically relies on the activation of a persistentsodium current, which is counterbalanced by the delayed activation ofan A-type potassium current. Furthermore, the interaction betweenthese conductances with the membrane passive properties supports thepresence of electrical resonance, whose frequency preference is con-sistent with both the effective range of hearing in goldfish and thefiring frequencies required for synaptic facilitation, an obligatoryrequisite for the induction of activity-dependent changes. Thus ourdata show that the presence of a persistent sodium current is func-tionally essential and allows these afferents to translate behaviorallyrelevant auditory signals into patterns of activity that match therequirements of their fast and highly modifiable synapses. The func-tional specializations of these neurons suggest that auditory afferentsmight be capable of more sophisticated contributions to auditoryprocessing than has been generally recognized.

I N T R O D U C T I O N

Primary afferents are generally perceived as canonical pas-sive lines of communication between peripheral receptors andsecond-order sensory neurons located in the CNS. A specialclass of auditory afferents terminating as single, “large myelin-ated club endings” on the goldfish Mauthner (M-) cells (Bar-telmez 1915), a pair of large reticulospinal neurons that medi-ate tail-flip escape responses in fish (Eaton et al. 2001),challenge this perception because their synapses undergo ac-tivity-dependent potentiation (Yang et al. 1990; for review seePereda et al. 2004). That is, discontinuous, “burstlike” stimu-lation of these afferents with high-frequency trains evokes along-term potentiation of both components of their mixed—electrical (gap-junction–mediated) and chemical—synaptic re-sponse (Yang et al. 1990). The plastic properties of thesesynapses likely represent a mechanism for input sensitization

(Yang et al. 1990) and therefore an unusual specialization fora primary auditory afferent that, in contrast to most auditoryafferents that faithfully relay critical timing information for itsprocessing along the auditory pathway, provide a decision-making neuron (Eaton et al. 2001) with relevant sensoryinformation that could be directly translated into a behavioralresponse that is essential for the survival of the fish.

Although the properties and mechanisms of plasticity oftheir single synapses have been the subject of detailed analysis(for review see Pereda et al. 2004), little is known regarding theelectrophysiological characteristics of these identifiable audi-tory afferents, in particular their ability to undergo high-frequency repetitive firing, which constitutes an essential re-quirement for induction of synaptic plastic changes (Peredaand Faber 1996; Smith and Pereda 2003; Yang et al. 1990).The electrophysiological properties of primary auditory affer-ents have been investigated in several species (Santos-Sacchi1993), including goldfish saccular afferents (Davis 1996),which constitute the auditory component of the VIIIth cranialnerve organ in fish (Furukawa 1978; Furukawa and Ishii 1967).Detailed biophysical analysis revealed the presence of a varietyof sodium (Na�) and potassium (K�) conductances at bothgoldfish saccular afferents (Davis 1996) and mammalian spiralganglion 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 theseconductances interact in these neurons to shape their firingpattern under more physiological conditions and how theyrelate to their function. Repetitive firing is an essential propertyof auditory afferents because changes in their firing rate areknown to encode variations in stimulus intensity (Pickles 1982;Sachs and Abbas 1974). Interestingly, it has been suggestedthat auditory afferents might not constitute a homogeneouscellular population but rather, like some inner-ear hair cells(Fettiplace and Fuchs 1999), could be electrophysiologicallytailored to their functional roles (Adamson et al. 2002; Davis2003).

Due to unfavorable anatomical characteristics (they spanfrom peripheral receptors to their target in the CNS) themembrane and synaptic properties of primary auditory affer-ents have been generally investigated in vitro at either theircentral (Zhang and Trussell 1994) or peripheral ends (Davos1996; Glowatzki and Fuchs 2002; Santos-Sacchi 1993). Be-cause of their advantageous experimental in vivo accessibility(where anatomical integrity and synaptic connectivity are pre-

Address for reprint requests and other correspondence: A. E. Pereda,Dominick P. Purpura Department of Neuroscience, Albert Einstein College ofMedicine, 1300 Morris Park Ave., Bronx, NY 10461 (E-mail: [email protected]).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

J Neurophysiol 99: 1683–1699, 2008.First published January 30, 2008; doi:10.1152/jn.01173.2007.

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served) and critical role in the initiation of escape response,identifiable auditory afferents terminating as large myelinatedclub endings on the M-cells provide an ideal opportunity tolink cellular biophysical analysis with system-level analysis ofinformation processing. Here we show that these afferents areendowed with electrophysiological properties that allow themto translate their broad auditory frequency sensitivity intopatterns of activity that are adapted to the requirements of theirhighly modifiable synapses. Consistent with their ability togenerate bursts of action potentials, these afferents are capableof sustaining high-frequency repetitive firing and exhibit astrong frequency adaptation in response to depolarizing pulses.Our results also indicate that, while their ability to sustainrepetitive firing critically relies on the presence of a persistentNa� current, their frequency adaptation results from the de-layed activation of an A-type K� current (IA). Furthermore,the interplay of these conductances with passive membraneproperties endows these specialized afferents with electricalresonance, whose band of frequency preference is consistentwith both the goldfish’s hearing range and the firing frequen-cies required for facilitation of their chemical synapses, arequisite for the induction of long-term plastic changes.

M E T H O D S

Electrophysiological procedures

The experiments were performed in adult goldfish (Carassiusauratus), 3 to 5 in. long. The surgical and in vivo recording techniqueswere similar to those previously described (Curti and Pereda 2004;Lin and Faber 1988a; Pereda et al. 1995). Briefly, auditory afferentsestablishing mixed synapses on the M-cell known as “Club endings”(n � 90) were intracellularly recorded outside the brain at theposterior branch of the VIIIth nerve, which contains these saccularafferents. Club ending afferents were identified by the presence ofelectrotonic coupling potentials after M-cell antidromic activation bystimulating the spinal cord (see RESULTS). For most recordings, glassmicroelectrodes (30–45 M�) were filled with 2.5 M KCl. Onlyafferents presenting resting potentials more negative than �67 mVand action potentials �70 mV in amplitude were used for this study.Due to the fast membrane time constant of the afferent fibers (esti-mated as �200 �s in the present study) the bridge was balanced usingthe “spike-height method” (Frank and Fourtes 1956). For intracellularrecordings of the M-cell, a second electrode (5 M KAc or 2.5 M KCl,4–12 M�) was inserted either 350 or 400 �m lateral to this cell’saxon cap into the lateral dendrite or into its axon, placing the electrodemore caudally between the vagal lobes. To activate the saccularafferents, a bipolar stimulating electrode was positioned on the pos-terior VIIIth nerve, distal to the recording site. In the case of acousticstimulation, sound stimuli consisted of 500-�s broadband noisesquare pulses delivered by a 2.5-in. speaker (Quam; frequency re-sponse 0.2–8 kHz) located about 4 in. from the animal’s head, andconnected to a Grass AM8 audio monitor. Experimental data wereacquired and recorded using software developed in the laboratory andanalyzed using Kaleida Graph (Synergy Software), Igor Pro (Wave-Metrics), and Superscope II (GW Instruments) software. Student’st-test was used to assess statistical significance of the data. Group datawere reported as means � SE, unless otherwise stated.

Drug application

The fish’s brain was continuously superfused (1.5 ml/min) withartificial cerebrospinal fluid [ACSF (in mM): 124 NaCl; 5.1 KCl; 3.0NaH2PO4�H2O; 0.9 MgSO4; 5.6 dextrose; 1.6 CaCl2�H2O; and 20HEPES (pH 7.2–7.4)]. Experimental drugs were added either to the

intracellular recording solution [50 mM N-(2,6-dimethylphenyl car-bamoylmethyl)triethylammonium bromide (QX-314); 0.5–1 M tetra-ethylammonium chloride (TEA-Cl), 0.075/0.15 M 4-aminopyridine(4-AP); 1–2 M CsCl], applied topically to the surface of the posteriorVIIIth nerve [1–10 �M tetrodotoxin (TTX); 1–5 �M �-dendrotoxin(�-DTX)], or included in the superfusing ACSF (5 mM 4-AP).Because of limitations to diffusion in the intact brain, the effectiveconcentration of extracellularly applied drugs is expected to be sig-nificantly lower (up to an order of magnitude in some cases; Peredaet al. 1992) than those of the superfusate.

Computer simulations

A first approximation to the characterization of the electrical reso-nance of Club endings was obtained modeling a combination oflow-pass and high-pass linear filters (Oppenheim et al. 1997) imple-mented in Matlab (The MathWorks, Natick, MA).

R E S U L T S

Identifiable saccular afferents terminate as single mixed(electrical and chemical) “large myelinated club endings,”henceforth referred to as Club ending afferents, on the distalportion of the lateral dendrite of the M-cell (Fig. 1A). Theafferents were intracellularly recorded in vivo in the posteriorroot of the VIIIth nerve and identified by the presence of theantidromic coupling potential (AD coupling), the electrotoniccoupling potential due to the passive dendritic depolarizationproduced by the antidromically evoked M-cell action potential(Fig. 1B, inset), and characteristic lack of spontaneous activityand high threshold for acoustic stimulation. Previous studiesshowed that intracellular labeling of fibers exhibiting theseproperties invariably resulted in fibers that, because of theirsize, prominent myelinization, dendritic distribution, and sac-cular origin, unambiguously corresponded to Club endingafferents (Lin and Faber 1988a; Smith and Pereda 2003).

In addition to being phase-locked to higher frequencies,these afferents characteristically respond with multiple actionpotentials to brief (Fig. 1B) or low-frequency (Furukawa andIshii 1967) acoustic stimulation. To investigate the mecha-nisms underlying this firing property we examined the re-sponses of Club ending afferents to depolarizing currentpulses. We found that depolarizing pulses of 1.5 their thresholdtypically evoked an initial high-frequency burst of actionpotentials, which was immediately followed by a completeabsence of activity (Fig. 1C). In contrast, depolarization of theM-cell axon with a depolarization of equivalent (1.5 threshold;Fig. 1D) or stronger magnitude invariably resulted in a singleaction potential. These results suggest that 1) Club endingafferents are endowed with electrophysiological properties thatfavor the generation of high-frequency bursts in response tostrong depolarizations; and 2) because the M-cells are notcapable of repetitive firing (an otherwise inconvenient featurefor a cell in which a single action potential initiates an escaperesponse that lasts several hundred milliseconds; Eaton et al.1988; Korn and Faber 2005), we hypothesize that their abilityto generate high-frequency bursts must represent a functionalspecialization of these afferents with the goal of providing theM-cell with adequate patterns of synaptic activation.

Characterization of repetitive responses

A characterization of the firing properties of Club endingafferents using pulses of increasing magnitude revealed the

1684 S. CURTI, L. GOMEZ, R. BUDELLI, AND A. E. PEREDA

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presence of a bilinear relationship between firing frequencyand the injected current (Fig. 2A). Whereas a pulse of currentat its “threshold” or “rheobasic” intensity (minimum stimulusstrength of infinite duration that triggers a response) evokes asingle action potential, a current step 1.5-fold the thresholdintensity evoked a repetitive response that averaged 6 to 7spikes (6.8 � 0.83, n � 11; Fig. 2A, middle). Finally, a currentpulse twice its threshold intensity elicited a repetitive responsethat lasted for the duration of the pulse (Fig. 2A, bottom). Tocharacterize the dependence of repetitive firing on the mag-nitude of the injected current, we plotted instantaneousfrequency versus current injection for the first, second, andthird interspike intervals (ISIs; Fig. 2B). The slope of theprimary range for the first, second, and third ISIs averaged516.5 � 62.4, 596.6 � 61.5, and 571.5 � 64.6 Hz/nA,respectively, whereas the slope of the secondary rangeaveraged 165.6 � 12.8, 232.2 � 20.5, and 269.8 � 27.2Hz/nA (n � 11) for the first, second, and third ISIs,respectively. In all the examined examples, the slope of theprimary range was significantly higher than that of thesecondary range (P � 0.0005).

Repetitive responses at Club ending afferents showed thepresence of a strong frequency adaptation, a property thatallows these afferents to respond with an initial brief burstof action potentials to depolarizing stimuli (Fig. 2). The timecourse of this progressive decrease in firing rate in responseto a constant current step (Fig. 2A, bottom) can be better

appreciated during stronger stimulation (Fig. 2C), in whichthe response lasted for the duration of the pulse. The timecourse of this phenomenon could be described by a single-exponential function (� � 18 � 1.5 ms, n � 12) plus aconstant. Depending on the strength of the current pulse, therepetitive 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 theconstant obtained from the fit, respectively. The degree ofadaptation [Fadapt � (Fi � Ff)/Fi] (Liu and Wang 2001)was quantified and expressed as percentage of the initialrate, averaging 64 � 4% (n � 11). Thus Club endingafferents are endowed with mechanisms that allow them torespond with brief bursts of 200 – 600 Hz to stimulus ofincreasing intensity. These electrophysiological propertieslikely represent those of the ending of the afferent contactedby the hair cell because brief acoustic stimulation was alsoable to trigger repetitive discharges of characteristics similarto those observed by depolarizing the axon in our recordingsite (Fig. 1B). This observation is consistent with recentdata, based on the ubiquitous distribution of Nav1.6 Na�

channels in primary auditory afferents, which indicates thatthese neurons generate (and regenerate) action potentials atmultiple sites along their anatomy, including the afferentendings, ganglionic initial segments, and nodes of Ranvier(Hossain et al. 2005).

FIG. 1. Club endings undergo high-frequency repetitive firing. A: experimental arrangement. Large identifiable auditory afferents innervate the rostral portionof the saccular macula (Sacculus), the auditory component of the goldfish ear, and terminate as mixed (electrical and chemical) synapses known as largemyelinated club endings (“Club endings”) on the lateral dendrite of the Mauthner (M-) cell. Intracellular recordings were obtained in the posterior branch of theVIIIth nerve, where Club ending afferents run. In some occasions, intradendritic recordings were also obtained to monitor changes produced by the activationof these afferents. B: traces illustrate electrophysiological responses obtained sequentially from the M-cell lateral dendrite and a Club ending in response to briefacoustic stimulation (500-�s duration sound click, bottom trace). Brief acoustic stimulation evokes a high-frequency burst of action potentials in the recordedClub ending (top trace) that temporally correlates with the sound-evoked synaptic potential (PSP) recorded in the M-cell lateral dendrite (middle trace), producedby the activity of this and an undetermined number of these afferents. Inset: Club ending afferents were routinely identified by the presence of the couplingpotential of the M-cell antidromic spike (AD coupling) evoked by stimulation of the spinal cord. C: direct intracellular activation of Club ending afferents withdepolarizing current pulses (50-ms duration, bottom trace) at 1.5 its rheobasic strength or threshold (1.5 T) evokes a repetitive discharge consisting in a trainof 7 action potentials that exhibits marked frequency adaptation. D: in contrast, direct intracellular activation of the M-cell axon with a depolarizing current pulseof equivalent magnitude (1.5 T) evokes a single action potential.

1685REPETITIVE FIRING IN PRIMARY AUDITORY AFFERENTS


Subthreshold Na� conductance is essentialfor repetitive firing

Subthreshold Na� conductances are known to underlie repeti-tive firing in many neuronal types (Crill 1996; Enomoto 2006).Furthermore, we have previously described the presence in Clubending afferents of a subthreshold conductance with propertiessimilar to those of a persistent Na� current (Curti and Pereda2004). To investigate the possible involvement of a persistent Na�

current in repetitive firing at Club ending afferents we tested theeffect of intracellularly injected QX-314 (that blocks Na� chan-nels) on repetitive firing responses evoked by depolarizing currentpulses (Fig. 3A). Subthreshold Na� currents are generally affectedearlier than transient Na� currents to application of blockers(Brumberg et al. 2000; Hu 1991; Staftrom et al. 1985). QX-314dramatically abolished repetitive firing (Fig. 3A, center, n � 10).These changes occurred within a time window in which the actionpotentials of the afferents remained largely unaffected (Fig. 3, A,center and B; amplitude averaged 92.5 � 4.63 and 89.1 � 3.82mV for control and QX-314, respectively, n � 7, P � 0.13) andwas accompanied by a drastic reduction of the retrograde couplingpotential amplitude obtained at depolarized membrane potentials(Fig. 3, A, right and C), a phenomenon that results from theamplification of this retrogradely transmitted coupling by thesubthreshold Na� current (Curti and Pereda 2004). Because QX-314 has been reported to have nonspecific actions on other thanNa� channels we tested the effect of extracellular application of

TTX (1–10 �M), which specifically blocks Na� channels, onthe repetitive responses evoked by depolarizing current pulses.As illustrated in Fig. 3D, application of TTX also led to adramatic suppression of repetitive responses (n � 6). As in thecase of QX-314, the observed suppression of repetitive firingtook place within a time window in which the action potentialsof the afferents remained largely unaffected; amplitude aver-aged 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-314and TTX ultimately led, as previously reported (Curti andPereda 2004), to the complete blockade of the first actionpotential (not shown). Finally, consistent with the eliminationof a subthreshold amplifying mechanism, the depolarizingprepotentials that usually lead to initiation of the next actionpotential in repetitive responses (Amir et al. 2002a,b; Lan-thorn et al. 1984; MacVicar 1985) were no longer observedafter TTX application (Fig. 3G).

To directly demonstrate the presence of a subthresholdvoltage-sensitive Na� conductance, the membrane propertiesof the afferents were examined by measuring their voltage–current (V–I) relations (Fig. 4A). For a given depolarizingcurrent pulse, we found a nonlinear voltage response that wasmaximal within approximately 2–5 ms of the pulse onset andthen rapidly decayed to a steady-state value. The magnitude ofthis initial response was not linearly correlated to the injectedcurrent and was more obvious for “near-threshold” depolariza-

FIG. 2. Characterization of repetitive firing at Club ending afferents. A: responses of a Club ending to intracellular depolarizing current pulses of increasingmagnitude. A 1.7-nA current step (rheobasic intensity) evokes a single action potential at the beginning of the pulse (top trace). In contrast, a 2.3-nA depolarizingpulse (1.5 its rheobasic intensity) evokes an initial burst of 7 action potentials (middle trace). Finally, a current step almost twice the rheobasic intensity (3.0nA, bottom trace) evokes repetitive firing throughout the duration of the current pulse (note the strong frequency adaptation). B: frequency (ordinate)–current(abscissa) plot obtained in the same afferent shown in A for the first (1st ISI, open circles), second (2nd ISI, filled circles), and third (3rd ISI, open triangles)interspike intervals, indicating the presence of primary and secondary firing ranges. The experimental data were fitted with straight lines to the primary andsecondary ranges (solid and dashed lines, respectively). The slopes of the 2 ranges for the 1st ISI are indicated. C: plot of instantaneous firing frequency vs. timefor a repetitive discharge evoked by a depolarizing current pulse of 3 nA and 50-ms duration illustrating the time course of the spike–frequency adaptation (sameexample shown in A, bottom trace; each point represents the average of 15 individual single responses). The data were fitted to a single-exponential functionwith a time constant (�) of 15 ms and the estimated initial (Fi) and final (Ff) frequencies are indicated.



tions, defined as the membrane potential in which a given pulseelicits an action potential in about 50% of the trials (Fig. 4, Aand B; only the responses lacking action potentials wereaveraged). We found that this initial nonlinear component wasabolished by TTX. Voltage responses to near-threshold depo-larizing current pulses averaged 62.5 � 3.5% (range: 56.5–68.7%, n � 3) of its control amplitude (Fig. 4A) followingTTX application, and the V–I relationship became linear (Fig.4B). The nonlinear nature and time course of the TTX-sensitivesubthreshold component were also revealed by subtracting theV–I relationship obtained in TTX from that obtained in controlconditions (Fig. 4C). The membrane responses to current steps

were similar in all studied fibers (see also Curti and Pereda2004). To investigate whether this slowly decaying TTX-sensitive subthreshold membrane response was the underlyingmechanism responsible for the adapting firing pattern observedin Club ending afferents, we compared the time courses of bothphenomena. As illustrated in Fig. 4D, the decay of the mem-brane response to a near-threshold depolarizing pulse closelyfollowed the time course of the instantaneous firing frequencyobtained for a suprathreshold current pulse in the same fiber (inwhich the response lasted for the duration of the pulse; seeearlier text), suggesting a primary role of subthreshold mech-anisms in shaping the firing patterns at Club ending afferents.

FIG. 3. Repetitive firing is abolished by application of QX-314and tetrodotoxin (TTX). A: repetitive discharges evoked by anintracellular depolarizing current pulse (1.8 nA, 50-ms duration) 2min (Control, left) and 11 min after the penetration of the cell withan electrode containing 50 mM QX-314 (QX-314, middle). Right:intracellular application of QX-314 simultaneously produced amarked reduction of the amplitude AD coupling potential at depo-larized potentials (AD coupling). Superimposed traces of ADcoupling recorded 2 min (control) and 11 min after penetration ofthe cell with the QX-314 (QX-314) containing electrode (each tracerepresents the average of 10–12 single recordings). B: the effects ofQX-314 were observed within the time window in which the actionpotential of the afferents remained largely unaffected by the drug,suggesting that only persistent sodium channels were affected.Graph plots both, the number of action potentials per train (leftordinate, filled circles) and the amplitude of the first action poten-tial (right ordinate, open circles), as a function of time after QX-314application (abscissa). C: correlation between the decrease in spikenumber and the amplification of the AD coupling after QX-314application. Error bars represent SD. D: repetitive firing evoked bya depolarizing current pulse (3.3 nA, 50-ms duration) before(Control, left) and 30 min after extracellular application of 1 �MTTX (TTX, right). E: as with QX-314, the effects of TTX wereobserved within the time window in which the action potential ofthe afferents remained largely unaffected by the drug, suggestingthat only persistent sodium channels were affected. Graph plotsboth, the number of action potentials per train (left ordinate, filledcircles) and the amplitude of the first action potential (right ordi-nate, open circles), as a function of time after TTX application(abscissa). Although repetitive firing was quickly abolished afterTTX application (action potentials per train were reduced from 11to 1 within a few minutes), the amplitude of the first actionpotential remained largely unchanged. F: summary of the effects ofTTX on the number of action potentials per train and actionpotential amplitude in 6 fish. The mean amplitude of the first actionpotential (First spike; ordinates) is plotted against the mean numberof action potentials per train (Spikes number; abscissa), before(control, filled square) and after TTX application (TTX, opencircle). Error bars represent SD. G: traces shown in D (Control andTTX) are illustrated superimposed and aligned by the first actionpotential. Note the marked reduction of the depolarizing prepoten-tial that generally precedes repetitive firing (arrow after TTXapplication).



Subthreshold K� conductance underlinesspike-frequency adaptation

The results so far indicate that subthreshold mechanisms arelargely responsible for the firing pattern of Club ending affer-ents. However, because subthreshold Na� currents have a slowprocess of inactivation with time constants in the order ofhundreds to thousands of milliseconds (Crill 1996; Frenchet al. 1990; Ogata and Ohishi 2002), the relatively faster decayof the TTX-sensitive subthreshold responses to depolarizingcurrent pulses (Fig. 4, A–C) suggests the involvement of anopposing repolarizing conductance. The existence and contri-bution of more than one active membrane mechanism tonear-threshold responses were demonstrated by subtracting theresponse of a 0.2-nA pulse (mostly determined by resistive andcapacitive properties of the membrane) multiplied by a factorof 10, from a near-threshold response evoked by a 2-nAdepolarizing pulse (Fig. 5A). This subtraction revealed thepresence of an initial depolarization (likely corresponding tothe activation of a subthreshold Na� current), which wasfollowed by a sustained hyperpolarization (Fig. 5A, bottom).Because subthreshold Na� currents are generally opposed byrepolarizing K� conductances (Crill 1996) we tested the ef-fects of intracellular applications of a combination of K�

channel blockers (see METHODS), covering a wide spectrum ofthese channels, on the membrane responses to depolarizingcurrent steps. We found that blockade of K� channels pro-longed the initial voltage response to a depolarizing pulse (Fig.5B), suggesting the presence of a persistent Na� current thatwas able to reveal, unopposed, its time course. Accordingly,membrane responses, which under these conditions lackedtheir typical decay, were greatly attenuated by extracellularapplication of TTX (Fig. 5B), confirming the presence of anoninactivating or very slowly inactivating component with thecharacteristics of a persistent Na� current (Crill 1996).

By opposing the action of a persistent Na� current, thedelayed activation of a subthreshold K� conductance is re-sponsible for the decay observed at near-threshold membraneresponses and therefore responsible for the frequency adapta-tion observed during repetitive responses at Club ending affer-ents. To investigate the identity of the involved K� conduc-tance we tested the effects of extracellularly applied 4-AP (5mM, bath applied; see METHODS), known to affect some sub-threshold K� conductances (Faber and Sah 2003; Jerng et al.2004; Rudy 1988), on the membrane responses to depolarizingcurrent steps. As with the intracellular application of K�

channel blockers, extracellular application of 4-AP prolongedthe initial voltage response to a depolarizing pulse and lackedits characteristic sag, as illustrated by the modification of theratio between the late and early amplitudes of pulse responsesthat became approximately 1 (see Fig. 5C). The off response todepolarizing pulses was followed by a small “tail,” which wasgreatly reduced by TTX (arrows in Figs. 4A and 5B), suggest-ing that the decay corresponds to the action of some persistentNa� channels, which deactivate slowly relative to the rapidvariations of the membrane potential produced by the injectedcurrent step. Consistent with this observation, this tail wasenhanced by 4-AP, which by removing IA leaves persistentNa� channels acting unopposed (arrow in Fig. 5C). Thusnear-threshold depolarizing responses at Club ending afferentsare dominated by the interplay of two independent active

FIG. 4. Membrane responses to current steps reveal the presence of asubthreshold Na� current. A: superimposed voltage responses to currentpulses of both polarities (50-ms duration, �2.0 and �0.5 nA, bottom)before (Control) and 10 min after extracellular application of 10 �M TTX(TTX, thicker trace). Note the larger response at the beginning of depo-larizing current pulses obtained in control conditions. Each trace representsthe average of �10 single responses. B: voltage (V, ordinate)– current(abscissa) relation obtained in another fiber before (Control, filled circles)and after TTX application (TTX, open circles). The voltage responses weremeasured 5 ms after the onset of the current step. Membrane responsecharacteristically exhibited a nonlinear response to larger depolarizingcurrent 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 illus-trated in A (obtained before and after TTX application) revealed the timecourse of the TTX-sensitive membrane component. This componentreached its maximum within 5 ms of the onset of the current pulse andslowly decays toward the end of the pulse. D: subthreshold membranemechanisms are the major determinant of the firing behavior at Club endingafferents. The time course of the spike–frequency adaptation followed thatof membrane responses to near-threshold depolarizing current pulses. Toillustrate this property, the scaled decay of the membrane response to anear-threshold current pulse is illustrated superimposed to the plot ofinstantaneous frequency vs. time of a repetitive discharge induced in thesame fiber by a suprathreshold depolarizing current pulse (filled circles;same data shown in Fig. 2C).



mechanisms that are sequentially activated. Initially, the re-sponse is dominated by the rapid activation of an amplifyingpersistent Na� current, which is counterbalanced by the rela-tively slow activation of a subthreshold K� current, whoseactivation opposes membrane depolarizations (Fig. 5D).

The sensitivity to 4-AP of subthreshold membrane responsessuggested the involvement of an A-type K� current (IA),which is known to operate within this voltage range (Rudy1988; Storm 1990). We confirmed this possibility by using astandard protocol to reveal the presence of this current (Storm1988). More specifically, we measured the delay to the firstspike when bringing the cell to threshold from hyperpolarizedpotentials, which removes IA steady-state inactivation (Fig. 6A).As IA became more activated, it characteristically introduced adelay in the generation of the spike that was inversely propor-tional to the prepulse membrane potential (Fig. 6B). Finally,and consistent with its pharmacological effects on subthresholdmembrane responses, this delay was greatly reduced by extra-cellular 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 similarprotocol. For this purpose, a hyperpolarizing prepulse of vari-able duration and fixed amplitude (adjusted to drive the mem-brane potential to about �100 mV) was followed by a suprath-reshold depolarizing current pulse; the availability of IA chan-nels was inferred from the delay to the first action potential(Fig. 6E). As illustrated in Fig. 6F, this delay increased withthe prepulse duration, indicating that the recovery from inac-tivation followed an exponential time course with a timeconstant of 56.2 � 4.73 ms (range: 46.8–61.8 ms, n � 3), avalue that is consistent with those found for similar A-typeconductances in other cell types (Jerng et al. 2004; Koyamaand Appel 2006; Petersen and Nerbonne 1999; Wang andSchreurs 2006), including in the auditory system (Rothman andManis 2003). In an attempt to determine the identity of theinvolved K� channels we tested the effects of �-DTX (1–5�M), which blocks channels of the Kv1 family known to beresponsible for low-threshold K� conductances in the auditorysystem (Klug and Trussell 2006; Mo et al. 2002; Rathouz andTrusell 1998; Trussell 1999), on subthreshold responses todepolarizing current pulses. In contrast to the effects of 4-AP,we did not detect changes in the decay of near-thresholdresponses as a result of the application of this toxin (see Fig.

FIG. 5. Time course of membrane responses to depolarizing current steps isdetermined by the interplay between a persistent Na� current and a subthresh-old K� current. A: kinetics of membrane responses to near-threshold depolar-izing current pulses (50 ms) suggests the interplay between depolarizing andhyperpolarizing active conductances. Top: average voltage responses to �2.0and �0.2 nA (thicker trace) current pulses are represented superimposed (n �15). Also superimposed, is the response to the �0.2-nA current pulse multi-plied by a factor of 10 [(�0.2 nA) 10; gray thick trace]. Note the differencebetween the waveforms of the scaled response, mostly determined by resistiveand capacitive properties of the membrane, and that obtained in response to acurrent pulse 10-fold stronger, indicating the contribution of active membranemechanisms to near-threshold responses. Bottom: trace corresponds to thedifference between the response to a �2.0-nA current pulse and the responseto a �0.2-nA current pulse scaled by a factor of 10 {(�2.0 nA) � [(�0.2nA) 10]}; dashed line indicates the 0-mV level and the area above this levelis represented in gray for clarity. Consistent with the presence of a TTX-sensitive subthreshold Na� inward current, near-threshold responses are ini-tially supralinear (gray area). This response gradually attenuates to becomesublinear (arrow), suggesting the slower and delayed activation of a subthresh-old outward current. B: sustained depolarizing responses observed in thepresence of K� channel blockers are abolished by extracellular application ofTTX, revealing the presence of a persistent Na� current. Traces illustratevoltage responses to depolarizing current pulses (�1.0 nA, 50-ms duration)obtained after intracellular application of a combination of K� channelblockers in the absence (K� blockers) and presence of 10 �M TTX (K�

blockers � TTX, thicker trace; traces illustrate the average of 15 individualresponses). The gray area represents the magnitude and time course of theTTX-sensitive component evoked by membrane depolarization. C: extracellu-lar application of 4-aminopyridine (4-AP, 5 mM), known to block A-type K�

conductances, prolongs the duration of the depolarizing active responses. Top:voltage responses to a �0.8-nA current pulse (50-ms duration) are illustratedsuperimposed before (control, thin trace) and after (4-AP, thick trace) extra-cellular application of 4-AP (traces illustrate the average of 10 individualresponses). Bottom: graph represents the mean values of the percentagechanges in the ratio between the amplitudes of the voltage responses measuredat 5 ms (open circle in top) and 45 ms after the onset of the pulse (filled circlein top), obtained after application of 4-AP and �-dendrotoxin (�-DTX; errorbars indicate SE). D: participation of active mechanisms in near-thresholdmembrane responses. The figure shows a representative response of a Clubending to a depolarizing current pulse. At the beginning of the pulse theresponse is dominated by the activation of a persistent Na� current (Na�p).The amplifying action of this Na� current is counterbalanced by the delayedactivation of an A-type K� current (K�).



5C), suggesting that channels other than those of the Kv1family are responsible for this hyperpolarizing conductance.Consistent with a primary role of this subthreshold mechanismand confirming an early report (Davis 1996), we did notobserve evidence for the involvement of a Ca2�-dependent K�

current [IK(Ca)] (see Supplementary Fig. S1A and legend).1 Inaddition, our analysis revealed that the observed firing patterncould not be explained by a progressive decrease in theavailability of transient Na� channels (see Supplementary Fig.S1, B–F, and legend).

Our data are consistent with the notion that a balancebetween a persistent Na� and a IA currents dominate near-threshold responses to depolarizing current pulses and arelikely responsible for determining the observed firing pattern atClub ending afferents (Fig. 4D). To confirm the primaryfunctional role of this interaction, we investigated how therelative availability of these channels affects the firing patternof Club ending afferents by modifying the balance betweenthese two conductances (Fig. 7). For this purpose, we increasedthe contribution of persistent Na� current by bringing the cell

to threshold from more hyperpolarized membrane potentials,which is expected to increase the availability of these channelsby removing their inactivation (they also present inactivationbut of slower time course; Fleidervish et al. 1996). As illus-trated in Fig. 7A, depolarization of the afferent to about �55mV from resting potential (�75 mV in this case) elicited asingle action potential; in contrast, depolarization to the samemembrane potential from about �120 mV (held at this poten-tial by DC current injection over a period of �10 s) elicitedinstead a high-frequency repetitive response. Furthermore, thefrequency adaptation of repetitive responses obtained by de-polarizing from hyperpolarized potentials was significantlyattenuated (Fig. 7B). These effects were prevented by QX-314(Fig. 7C), confirming that an increased availability of persistentNa� channels was responsible for the observed increased firingduring repetitive responses overcoming the actions of IA,whose increased availability initially causes the delay to thefirst spike but later begins to inactivate (such delay is consistentwith the time constant of inactivation of IA currents in othercell types; Rothman and Manis 2003). To independently con-firm this conclusion, we tested the effects of pharmacological1 The online version of this article contains supplemental data.

FIG. 6. Electrophysiological and pharmacological evidenceconfirm the presence of an A-type K� current (IA). A: intra-cellular activation of Club ending afferents from hyperpolar-ized membrane potentials induces a marked increase on thetime to the first action potential. Superimposed traces illustratemembrane responses to suprathreshold current pulses (50-msduration) delivered at resting (�73 mV; pulse: �0.9 nA) and ata more hyperpolarized membrane potential (�113 mV; pulse:�2.5 nA; membrane potential held by DC current application;�1.7 nA). Note that regardless of their different initial mem-brane potentials, both current pulses reach the same level ofdepolarization. B: graph plots the time to the first actionpotential (Time to first spike; ordinate) as a function of themembrane potential (held by DC current application; abscissa)for the same fiber as shown in A. C: the time to the first actionpotential observed at hyperpolarized membrane potentials isreduced by extracellular application of 4-AP (5 mM). Super-imposed traces illustrate membrane responses to depolarizingcurrent pulses delivered at hyperpolarized potentials (�100mV; pulse: �2.7 nA; DC current: �1.7 nA), before (Control)and after 4-AP application (thicker trace). 4-AP ultimatelyleads to the unmasking of a prominent depolarizing plateaupotential (see RESULTS and Supplementary Fig. S2). D: graphsummarizes the effect of 4-AP. Plot illustrates the mean time tothe first action potential (time to first spike) obtained fordepolarizing current pulses delivered at resting potential (Con-trol) and at a hyperpolarized potential, in the absence (Hyper-polarization) and presence of 4-AP (Hyperpol. � 4-AP). Errorsbars represent SE (P � 0.05). E: estimate of the A-type currentrecovery from inactivation. The availability of IA channels wasinferred from the delay to the first action potential. Superim-posed traces illustrate membrane responses to suprathresholddepolarizing current pulses (�64 mV; �5.8 nA). The pulseswere preceded by hyperpolarizing prepulses of variable dura-tion (5 to 500 ms) but fixed magnitude (�3.6 nA) that bring themembrane potential to about �100 mV. F: graph plots the timeto the first action potential (time to first spike; ordinate) as afunction of the hyperpolarizing prepulse duration (abscissa) forthe same fiber as shown in E. The data were fitted to asingle-exponential function with a time constant (�) of 60 ms.



blockade of IA on responses to suprathreshold depolarizingpulses. As illustrated in Fig. 7D (left), whereas depolarizationto �65 mV from resting potential (�75 mV) evoked a singleaction potential, the same depolarization led to a high-fre-quency response following extracellular application of 4-AP(Fig. 7D, middle). Thus blockade of IA led to the unopposedaction of persistent Na� channels, resulting in an enhancementof the repetitive responses. Supporting this conclusion, both4-AP and a combination of K� channel blockers ultimately ledto the development of a pronounced plateau potential (Figs. 6Cand Fig. 7D, right) that was greatly suppressed by extracellularapplication of TTX (Fig. 7D, right). Consistent with its lack ofeffect on subthreshold responses, application of �-DTX did notenhance firing responses at Club ending afferents, confirmingthat �-DTX–insensitive channels are responsible for spike–frequency adaptation at Club ending afferents (Fig. 7E, top). Incontrast, as previously reported (Nakayama and Oda 2004),

�-DTX induced repetitive firing in the M-cell during parallelcontrol experiments (Fig. 7E, bottom).

Club ending afferents exhibit electrical resonance

Membrane oscillations were occasionally observed follow-ing the initial burst of action potentials, suggesting that under-lying oscillatory membrane mechanisms could be responsiblefor repetitive firing at Club ending afferents (Fig. 8A). Sub-threshold oscillations have been shown to be responsible forrepetitive firing in primary sensory neurons (Amir et al. 2002a;Liu et al. 2002; Pedroarena et al. 1999; Wu et al. 2001) and aregenerally caused by the existence of membrane electricalresonance (Hutcheon and Yarom 2000). Electrical resonancecharacterizes the frequency at which neurons respond best todepolarization and therefore describes its frequency-dependentproperties, in particular how neurons process oscillatory inputsat subthreshold potentials (Hutcheon and Yarom 2000). Sub-threshold K� conductances such as those found at Club endingafferents are responsible for the generation of electrical reso-nant behavior in various neuronal types (Hutcheon and Yarom2000; 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” andmembrane oscillations, which are considered time-domain sig-natures of electrical resonance (Hutcheon and Yarom 2000),suggests that these auditory afferents are endowed with similarmembrane properties.

FIG. 7. Balance between persistent Na� and A-type K� currents determinesthe patterns of repetitive responses at Club ending afferents. A: superimposedtraces illustrate membrane responses to suprathreshold current pulses delivered atresting (�75 mV; pulse: �0.5 nA) and at a more hyperpolarized membranepotential (�119 mV; pulse: �2.5 nA; DC current membrane potential held byDC current application; �2.0 nA). Both depolarizing current pulses reach thesame final membrane potential. Whereas the pulse applied at resting potentialinduces just a single spike, that applied from a hyperpolarized membrane leveltriggers a delayed and sustained repetitive discharge, likely due to an increasedavailability of both A-type (delay) and persistent sodium (repetitive firing)channels. B: plot of instantaneous frequency (Frequency) vs. time duringrepetitive discharge (Time) evoked by current pulses applied at these 2membrane potentials (open circles: �75 mV; filled circles: �119 mV) in thesame fiber. The intensity of the current pulse applied at resting potential wasadjusted to give rise to a repetitive response, and its time course fitted to asingle-exponential function (solid line). Again, note the increased firing re-sponse of the Club ending when activated at a hyperpolarized membranepotential. C: membrane responses to suprathreshold current pulses delivered ata hyperpolarized level (�100 mV; pulse: �2.9 nA, DC current: �1.5 nA)recorded 2 min (Control, left) and 13 min after penetrating the cell with anelectrode containing QX-314 (QX-314; 50 mM; right). Intracellular QX-314application induced a marked reduction in the number of spikes. D: membraneresponses to current pulses obtained before (Control, left) and 5 min afterextracellular application of 5 mM 4-AP (4-AP; middle). The current pulse thatin control conditions was just sufficient to evoke a single action potential wascapable of inducing a vigorous repetitive discharge 5 min after 4-AP applica-tion. Right: intracellular application of a combination of K� channel blockersultimately leads to the development of a prominent plateau potential, whichfollows the initial fast action potential (triggered by a pulse of 5-ms duration,and 1.3 nA in control and 2.0 nA after TTX). Superimposed is the responseobtained 7 min after extracellular application of TTX (10 �M). Both theamplitude and duration of this plateau potential were greatly suppressed byextracellular application of TTX. E, top: membrane responses to current pulsesof the same amplitude obtained before (Control, left) and 11 min afterextracellular application of �-DTX (�-DTX; middle). No changes in the firingbehavior of the afferent were observed after the application of this toxin.Bottom: responses to current pulses of 1.5 its rheobasic strength (threshold)obtained in the M-cell axon before (Control, left) and 10 min after extracellularapplication of �-DTX.



The frequency preference of Club ending afferents wasestimated by determining the underlying resonant mechanismsfrom near-threshold membrane responses (“sag”). Althoughindirect, this approach has the advantage of accurately estimat-ing the impact of this voltage-dependent behavior at the mem-brane potential where it is primarily expressed, the threshold of

the cell. Electrical membrane resonance is known to resultfrom the interaction of two mechanisms with specific frequency-dependent properties: a low-pass filter determined by the mem-brane passive properties (membrane time constant) that atten-uate responses to inputs with high-frequency content, and ahigh-pass filter, which is set by slowly activating voltage-

FIG. 8. Club endings exhibit resonant membrane properties. A: electrophysiological recordings revealed the presence of subthreshold membrane oscillations.Trace illustrates the membrane response to a depolarizing current pulse, consisting of 4 action potentials followed by a damped oscillation of the membranepotential (trace represents the average of 5 single responses centered in the oscillation; action potentials appear truncated). The frequency of this subthresholdoscillation was estimated fitting a function consisting in the sum of a sinusoidal and an exponential function (143 Hz, thicker trace). B: combination of activeand passive membrane properties determines electrical resonance. Indirect estimates of electrical resonance were obtained by measuring cutoff frequencies ofthe low-pass and high-pass filtering properties of the membrane from subthreshold membrane responses. Top: representative membrane response to anear-threshold depolarizing current pulse (50-ms duration). The time constant of a high-pass filter representing the activation of the A-type current (�k), wasestimated by fitting a double-exponential function to the decaying portion of the response about 5 ms after the pulse onset. Only the faster and most prominentconstant (30-fold the magnitude and 10-fold faster than the second one), which likely represents the activation of the A-type current, is represented here and itsvalue used for the estimates of electrical resonance. The time constant of a low-pass filter, representing membrane passive properties (�m), was accuratelyestimated by fitting a single-exponential function to the decay that followed the cessation of current pulses of different polarities and amplitudes (only one ofthese pulses is illustrated in this example and indicated as �m). The time constants were estimated in 2.6 and 0.2 ms, respectively, for the illustrated example.Bode plots (magnitude vs. frequency) were constructed with a model of linear filters (LTI system) using the mean values of �k and �m for the high- (middle)and low-pass (bottom) filters, respectively. Cutoff frequencies of the high-pass (1/2� �k) and low-pass (1/2� �m) filters averaged 61 � 6 and 803 � 45Hz, respectively (vertical dashed lines, n � 12). C: Bode plot (magnitude vs. frequency) constructed using a model of linear filters (LTI system) combining high-and low-pass filter properties of the membrane. The combination of membrane mechanisms with high-pass and low-pass filtering properties determines aband-pass filter with a bandwidth of 742 Hz and a maximum at 220 Hz, suggesting the existence of resonant membrane properties. For comparison, the tuningcurves of 2 representative saccular afferents are also illustrated in the same graph [gray traces; curves originally illustrated in Fay (1995)]. Threshold in dB(right-side ordinates) is plotted against sound frequency. Note that the characteristic frequencies and Q10 dB responses (horizontal lines) of both tuning curves(corresponding to the responses of the 2 types of afferents found in goldfish) matched the estimated bandwidth of the electrical resonance at Club endings.D: computer simulations with NEURON revealed the relative contributions of A-type (IA) and persistent Na� (INap) currents to membrane resonance. Plotillustrates the computed input impedance (ordinates, normalized to the magnitude of the membrane response at DC in the absence of any active mechanism) vs.frequency (abscissa). An ideal Club ending afferent fiber was modeled as a section consisting in a cylindrical process with passive properties (see SupplementaryMETHODS). When a delayed rectifier and an A-type current with the kinetics estimated experimentally for the ventral cochlear nucleus (Rothman and Manis 2003)were added to the model, a clear resonant behavior appeared centered at 220 Hz (K � IA, gray trace). The addition of a persistent Na� current produced asignificant amplification of the membrane resonance (K � IA � INap, black trace), without modifying the resonant frequency. E: summary plots of the estimatedresonant frequency (left; estimated following the procedure illustrated in B), and minimum frequency (right; defined as the instantaneous frequency of a trainconsisting of only 2 spikes). Individual experiments (open circles) and mean (filled circles) and SD of the population are illustrated superimposed (n � 11).



dependent K� currents that by opposing membrane depolar-ization attenuates voltage responses to inputs with low-fre-quency content (“resonant currents”; Hutcheon and Yarom2000; Izhikevich 2007). Thus the approximate resonant proper-ties can be estimated if the values of the activation time constantof the “resonant K� current” and the membrane time constant aredetermined experimentally. The membrane time constant (low-pass filter) was measured by fitting a single-exponential func-tion to the decay that followed the cessation of current pulsesof different polarities and amplitudes and averaged 0.2 � 0.01ms (n � 12; Fig. 8B, top). The time constant representing theactivation of the A-type current (high-pass filter) was estimatedfrom the decaying portion of the near-threshold membraneresponse (Fig. 8B). The decay was best fitted with a double-exponential function (P � 0.001) and the time constants of thefirst and second exponential averaged 2.9 � 0.26 and 30.1 �2.01 ms (n � 12). The fastest and more prominent timeconstant dominating the decay of the pulse (10-folds faster and30-fold the magnitude of the second one) was used for theestimates of resonance (Fig. 8B, top). This measurementproved to be a good approximation to the activation kinetics ofIA because the obtained values were consistent with the acti-vation kinetics of A-type currents obtained elsewhere (Hugue-nard 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 constantmight represent a minor contribution of an unidentified, lessprominent outward current to the decay and it was notincluded in the estimates. The filtering properties deter-mined by the obtained IA and membrane time constants areillustrated in the Bode plots of Fig. 8B, determining cutofffrequencies 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 containedby the cutoff frequencies) of 742 Hz and a peak value at 220Hz, suggesting the existence of resonant properties at Clubending afferents.

Independently supporting these measurements, the estimatedbandwidth of the electrical resonance matched the frequencyrange of repetitive firing in Club ending afferents (200 to 600Hz; see Fig. 2). Furthermore, the estimated peak resonantfrequency was also in agreement with that calculated for the“minimum frequency,” the instantaneous frequency of a min-imal repetitive response consisting of only two spikes triggeredby a depolarizing pulse, indicating a propensity of Club endingafferents to generate repetitive responses within this frequencyrange (Fig. 8E). A second consequence of electrical reso-nance is that, in addition to allowing neurons to undergohigh-frequency repetitive firing within a given frequencyrange, it can also make them more susceptible to respond toinputs with this particular frequency content. Accordingly,the bandwidth of this resonance matched the effective rangeof hearing of this species, estimated to be about 100 to 1,000Hz (Fay 1995). The tuning curves of two fibers, represen-tative of the “high” and “low” frequency types of broadlytuned afferents identified in goldfish (Fay 1978, 1995), areillustrated superimposed to the Bode plot (Fig. 8C; exam-ples taken from Fay 1995).

The estimates of electrical resonance predict that Club end-ing afferents would be more easily depolarized in response to

intracellularly injected currents with a frequency content nearto their resonant frequency. Unfortunately, this direct approachproved to be inapplicable to our in vivo recording conditions.Because the band of resonant frequencies found in Club endingafferents is 20- to 40-fold higher (10–15 vs. 200 Hz) than thosefound in previous studies where resonant behaviors were ex-plored with this method (Hutcheon et al. 1996; Puil et al. 1986;Wu et al. 2005), the filtering properties of our high-resistanceelectrode (�40 M�) made it impossible to reliably induce andmonitor changes in voltage at the required high frequencies (upto �1,000 Hz, as the band of resonance is 61–803 Hz).

Given these experimental limitations, we sought additionalindependent support for the resonant properties of IA and thepotential participation of the persistent Na� current by usingcomputer simulations. For this purpose, a Club ending afferentwas modeled, following available anatomical and physiologi-cal data (Furukawa and Ishii 1967; Rosenbluth and Palay 1961;Sento and Furukawa 1987; see Supplementary METHODS fordetails). Because of the impossibility of obtaining direct mea-surements, we ran computer simulations using parameters ofA-type currents described in auditory neurons that are similarto those estimated for these afferents. We found that additionof an A-type current with the kinetic properties estimatedexperimentally for the ventral cochlear nucleus (Rothman andManis 2003), a clear resonant behavior appeared with a peak at220 Hz (Fig. 8D). This approach also allowed us to evaluatethe role of the persistent Na� current in this resonant behavior.As previously shown (Hutcheon and Yarom 2000), the addi-tion of a persistent Na� current produced a strong amplifica-tion (�35%) of the predicted membrane resonance withoutmodifying the resonant frequency, suggesting that this conduc-tance is likely to play a relevant functional role by allowing theexpression of this resonance (Fig. 8D). Thus despite the lowstringency of this model, computer simulations adequatelyreproduced the frequency range of the predicted membraneresonance, suggesting that IA has robust resonant propertiesin these neurons. In addition, it indicated an essential rolefor the persistent Na� current in amplifying these resonantproperties.

Properties of synaptic facilitation at synapses between Clubendings and Mauthner cells

Stimulation of the posterior VIIIth nerve, where Club endingafferents run, evokes a mixed (electrical and chemical) synap-tic potential in the lateral dendrite of the M-cell (Fig. 9A;Furshpan 1964). In contrast to most primary auditory afferentsynapses that undergo depression (Zhang and Trusell 1994),high-frequency stimulation of these afferents with trains of twoto six pulses (Fig. 9A) was shown to evoke a strong facilitationof the glutamate-mediated chemical component (Lin and Faber1998b; Pereda and Faber 1996; Wolszon et al. 1997). Synapticfacilitation is essential for the induction of long-term potenti-ation of both components of the mixed synaptic responsebecause it optimizes the required activation of N-methyl-D-aspartate (NMDA) receptors (Pereda and Faber 1996; Yanget al. 1990).

Given the firing properties of Club ending afferents, weexplored the impact of various frequencies on the time courseof paired-pulse facilitation of the chemical component of themixed synaptic potential (Fig. 9B). Paired pulses were used



instead of trains to minimize the postsynaptic contribution ofNMDA receptors to the facilitated responses, which wasshown to be prominent during the last pulses of a short train(Pereda and Faber 1996; Wolszon et al. 1997; the changes inthe facilitated synaptic potential were measured by subtractingthe response to a single pulse; see Wolszon et al. 1997). Wefound that paired-pulse facilitation decayed following an ex-ponential time course, with a time constant of 4.5 � 0.81 ms(n � 8). This facilitation took place within a narrow temporalwindow (Fig. 9C, top) and, remarkably, it did not extendbeyond the frequency range determined by the firing propertiesof Club ending afferents, indicating that bursts of 200–600 Hzare optimal in producing facilitation of the chemical compo-

nent of synaptic response. Further, the time course of thesynaptic facilitation was extremely fast when compared withthat of other well-characterized contacts (Fig. 9C, bottom),suggesting that firing characteristics of these auditory affer-ents are adapted to the requirements of synaptic transmis-sion at Club endings. We found that repetitive firing withinthe 200- to 600-Hz range was also essential to obtaintemporal summation of successive synaptic responses (Fig.9A). Because of the brief time constant of the M-cell (�400�s; Fukami et al. 1965), temporal summation can take placeonly during the chemical component of the mixed synapticresponse. The duration of the chemical component wasfound in about 5 ms, an integrating interval that is consistent

FIG. 9. Time course of synaptic facilitation at Club ending afferents. A: synaptic responses evoked by a train of 4 VIIIth nerve stimuli at 5-ms interval (200Hz). Stimulation of the posterior VIIIth nerve evokes a mixed synaptic response consisting of a fast electrical, gap junction–mediated coupling potential(electrical; the fast time course reflects the duration of the presynaptic action potentials) followed by a delayed chemically mediated excitatory postsynapticpotential (EPSP) (chemical). Note the progressive facilitation of the chemical synaptic response with the increasing number of pulses (illustrated traces represent,here and below, the average of 10 single responses). B: characterization of the frequency-dependent facilitation of the chemical component with a 2-stimuliprotocol (paired -pulse facilitation). The stimuli were delivered at different intervals (2, 5, and 10 ms are illustrated; the electrical components of the synapticresponses appear truncated). C, top: facilitation of the chemical component, estimated as [(second EPSP amplitude � first EPSP amplitude)/first EPSP amplitude] 100, is plotted as a function of the paired-pulse protocol interval in a representative experiment. The data were fitted to a single-exponential function (solid line)with a time constant in this case of 6.9 ms. The vertical dashed line and the gray rectangular area approximately indicate the peak value and bandwidth of theestimated electrical resonance, respectively. Bottom: for comparison, the time constant of paired-pulse facilitation of chemical EPSP at Club endings is illustratedtogether with those obtained for the neuromuscular junction (NMJ; Magleby 1987) and Granule to Purkinje cell synapse (Granule cell; Atluri and Regehr 1996).D: club ending afferents are endowed with electrophysiological properties that allow these afferents to translate behaviorally relevant acoustic signals into patternsof activity that match the requirements of their fast and highly modifiable synapses.



with the band of frequency preference determined by theelectrical resonance of the membrane.

D I S C U S S I O N

In contrast to the M-cells, Club ending afferents undergorepetitive firing as a result of intracellular depolarization.Although the lack of repetitive firing on M-cells is thought tobe due to the presence of DTX-sensitive K� channels of theKv1 family (Nakayama and Oda 2004), our results show thatthe ability of Club ending afferents to respond with high-frequency bursts of action potentials results from the interac-tion of a subthreshold Na� current, which is required forrepetitive responses, with an A-type K� conductance. Thissubthreshold Na� conductance has all the characteristics of apersistent Na� current. That is, the voltage sensitivity andmembrane potential activation range (10–15 mV above restingpotential), susceptibility to TTX and QX-314, and prolongedtime course in the presence of K� channel blockers are typicalof persistent Na� currents described in fish (Berman et al.2001; Doiron et al. 2003; Watanabe et al. 2000) and mamma-lian neurons (Crill 1996). The A-type K� conductance was, incontrast to that of the M-cell, insensitive to DTX and thereforeunlikely to represent one of the typical “low-threshold” K�

currents, which act to prevent repetitive firing in the auditorysystem (Davis 2003; Klug and Trussell 2006; Trusell 1999).Rather, this conductance presented values of kinetics of acti-vation and recovery from inactivation and a pharmacologicalprofile (lack of sensitivity to DTX and sensitivity to 4-AP inthe millimolar range) that were comparable to those of anotherA-type current also found in the auditory system (Rothman andManis 2003), which possibly involves channels of the Kv4family (Jerng et al. 2004; Patel and Campbell 2005). Unfortu-nately, we did not observe changes as a result of bath appli-cation of rHeteropodatoxin-2 (which blocks Kv4 channels; notshown), suggesting that either this toxin, unlike DTX, haslimited experimental access in our in vivo conditions or that theinvolved fish isoforms are less sensitive to its actions. Thusalthough the presence of Kv1 channels is probably beneficialfor the M-cell, where a single action potential is sufficient toinitiate an escape response that lasts several hundreds ofmilliseconds, the lack of these channels in Club ending affer-ents allows these afferents to undergo high-frequency repeti-tive firing, a pattern that is likely to play an important physi-ological 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 thepropensity to respond with high-frequency (200–600 Hz)bursts of action potentials to strong depolarizing inputs and thatthis frequency range is ideally suited to produce facilitation ofthe chemical component of their mixed synaptic response.Bursts are thought to represent reliable neural codes duringinformation processing (Izhikevich et al. 2003; Krahe andGabbiani 2004; Lisman 1997) and play special roles for theinduction of synaptic plasticity (Lisman 1997). The generationof bursts in response to strong acoustic stimuli seems a partic-ularly advantageous strategy for the M-cell system, and itcould constitute an efficient and desirable code of information.

That is, a burst of action potentials would generate, as opposedto a single action potential, a prolonged synaptic response thatcan efficiently depolarize the large and unusually low inputresistance M-cell (Faber and Korn 1978). Due to the longerduration of the chemical component, high-frequency burstsalso allow temporal summation of the mixed synaptic re-sponses, an otherwise unlikely possibility given the shortduration of the electrical component and the brief membranetime constant of the M-cell. Because the firing frequency of theburst was found to be proportional to the strength of thedepolarization (see Fig. 2B), the results suggest that louderacoustic stimuli (likely required to trigger the escape response)would produce stronger facilitation of synaptic responses. Thusby producing synaptic facilitation and allowing temporal sum-mation of successive synaptic responses, high-frequency burstsof action potentials can lead to stronger and longer-lastingsynaptic activation of the M-cell lateral dendrite.

Equally relevant, brief high-frequency bursts of action po-tentials are required for the induction of activity-dependentlong-term potentiation of the mixed synaptic response (Yanget al. 1990) because they optimize the activation of NMDAreceptors by providing enhanced glutamate release at moredepolarized potentials, whose involvement is essential for theinduction of the plastic changes (Pereda and Faber 1996; Smithand Pereda 2003; Wolszon et al. 1997). Thus both membraneand synaptic properties of Club ending afferents act in aconcerted fashion and seem to be adapted to the M-cell system,where the increased synaptic gain of these auditory nervesynapses will sensitize a vital escape response, lowering itsthreshold to acoustic stimuli (Korn and Faber 2005).

Resonant membrane properties

Bursts of action potentials are often generated by the inter-action of synaptic inputs with intrinsic membrane properties(Lisman 1997). Our results also suggest that the propensity torespond with high-frequency (200–600 Hz) bursts of actionpotentials to strong depolarizing inputs is supported by theexistence of electrical resonant properties of the Club endingafferent membrane. Furthermore, the optimal intervals requiredfor the synaptic facilitation of the glutamatergic component ofthe mixed synaptic potential also matched the estimated fre-quency preference of this resonance, suggesting that this mem-brane behavior is essential for the interaction between afferentfiring and synaptic properties.

Unfortunately, the estimated band of membrane frequencypreference was significantly higher than that found in otherpreparations (5–10 vs. 100–800 Hz) and thus the filteringproperties of our sharp recording microelectrode prevented usfrom obtaining direct evidence of this membrane behaviorwhile depolarizing the membrane with a sinusoidal current ofvarying frequency. In contrast to those previous examples inwhich resonance could be explored directly in in vitro condi-tions (Hutcheon et al. 1996; Puil et al. 1986; Wu et al. 2005),these properties were estimated in Club ending afferents byobtaining measurements of the filtering characteristics of themembrane passive properties and the activation of the sub-threshold, A-type K� conductance at near-threshold responsesin an in vivo (more physiological) situation where anatomicalintegrity is preserved. Because electrical resonance is a volt-age-dependent property, although indirect, this method has the



advantage of accurately estimating the impact of this behaviorat the membrane potential where it is primarily expressed, thatis, about this cell’s threshold. As a result of activation kineticsslower than the membrane time constant, subthreshold K�

conductances of this type determine “resonant” behavior inmany cells types by opposing membrane depolarizations(Hutcheon and Yarom 2000; Izhikevich 2007). These estimatesof resonant behavior were independently supported by: 1) thepresence of subthreshold oscillations underlying repetitive re-sponses, 2) the propensity of these afferents to respond withinthis frequency range, and finally 3) by computer simulationsgenerated using the kinetic values obtained for the A-typecurrent found in auditory neurons (Rothman and Manis 2003)of physiological and pharmacological characteristics similar tothose found in Club ending afferents, given the impossibility ofobtaining direct measurements under our experimental condi-tions. Despite their low stringency, computer simulations ad-equately reproduced the frequency range of the predictedmembrane resonance, suggesting that IA has robust resonantproperties in Club ending afferents.

Although “resonant” currents can by themselves generatemembrane resonance, they are often enhanced by “amplifying”currents (such as persistent Na� currents) that allow them tomanifest their functional impact (Izhikevich 2007). That is,because of their depolarized reversal potential and quick acti-vation properties these currents actively enhance, rather thanoppose, voltage depolarizing changes that amplify otherwiseweak membrane resonant behaviors (Hutcheon and Yarom2000). Numerical computer simulations also suggested anessential contribution of the persistent Na� current to thisproperty in Club ending afferents by providing strong ampli-fication of membrane responses at resonant frequencies(�35%). If the interaction between “resonant” and “amplify-ing” currents is sufficiently strong, it can destabilize the mem-brane potential allowing the generation of spontaneous oscil-latory pacemaker-like activity (Hutcheon and Yarom 2000).Most commonly, this interaction is not very strong, so thefrequency preference of a given cell is “latent” and oscillatoryactivity is revealed only in the presence of its inputs. Such“weak” resonance makes a neuron a “good listener” within aspecialized frequency band (Hutcheon and Yarom 2000). Thissecond possibility seems to be the case of Club ending affer-ents, where oscillatory activity was observed only in responseto depolarization and the estimated band of electrical resonancematched that of the effective frequency range of hearing of thegoldfish (�100–1,000 Hz; Fay 1995), making these afferentsmore sensitive to a broad range of behaviorally relevant fre-quencies.

Neurons are excitable because they are near transitions fromresting to spiking. From the perspective of dynamic systemsthis transition corresponds to a bifurcation (Izhikevich 2007).This approach provides an alternative framework in which theexcitable properties of neurons can be understood. Regardlessof the cellular type and ionic conductances involved, they areonly four different types of bifurcation of equilibrium that asystem can undergo (Izhikevich 2007). In this context neuronsare divided into integrators and resonators with bistable ormonostable activity. The presence of resonant properties indi-cates that the behavior of this neuron corresponds to anAndronov–Hopf-type of bifurcation. The lack of a bistabilityof this neuron’s electrical behavior suggests that it more

specifically corresponds to a supercritical Andronov–Hopf bi-furcation. Nevertheless, this categorization should be moreappropriately explored and confirmed in the future with moreadequate stimuli such as current ramps (Izhikevich 2007).Consistent with our results, Andronov–Hopf bifurcations canbe reproduced in reduced models that combine a persistentNa� current with a delayed K� current (“persistent sodiumplus potassium model”; Izhikevich 2007), indicating that theelectrophysiological properties of Club ending afferents can beadequately explained by the interaction between these twocurrents.

Frequency tuning in goldfish primary afferents

Unlike their mammalian counterparts, fish auditory afferentsare broadly tuned and exhibit limited frequency selectivity(Fay 1995; Popper and Fay 1998). The anatomical character-istics of the Club ending afferents (large diameter and charac-teristic myelinization) meet those of S1-type saccular fibersoriginating from the rostral part of the sacculus (the auditoryorgan in fish), following the initial characterization of goldfishauditory afferents by Furukawa and Ishii (1967). In contrastwith S2, a second type of smaller fibers, S1 afferents wereshown to respond to higher frequencies (�500 Hz; Furukawaand Ishii 1967). More rigorous characterization of goldfishafferent responses confirmed the presence of both high-fre-quency and low-frequency afferent types (Fay 1978, 1995).Although in these studies physiological responses were notcorrelated with anatomical identification of the afferent fibers,both low and high tuning were observed in afferents lackingspontaneous activity (Fay 1978), a notable characteristic andidentification criteria for Club ending afferents and suggestingthat these larger afferents can respond to a broader range offrequencies.

Club endings constitute a relatively homogeneous popula-tion of about 100 afferents terminating in the lateral dendrite ofthe M-cell (Bartelmez 1915). Our results suggest that they arealso relatively physiologically homogeneous because all of thestudied fibers exhibited similar biophysical properties. Mech-anisms of frequency selectivity in lower vertebrates, includinggoldfish (Sugihara and Furukawa 1989), are known to involvethe contribution of resonant electrical membrane properties,which allow inner-ear hair cells to be tuned to stimuli ofspecific frequency content (Fettiplace and Fuchs 1999). Thereported tuning curves and characteristic frequencies of bothtypes of afferent response (Fay 1978, 1995) fell within theband of electrical resonance estimated for Club ending affer-ents (see Fig. 8C; Fay 1978, 1995), indicating that this mech-anism is unlikely to underlie their individual frequency tuning.Rather, because most saccular fibers will respond to anyfrequency within the goldfish’s effective range of hearing atsound levels �40 dB above best threshold (see Fig. 8C for theQ10 dB [range of frequency response at 10 dB above threshold]of each afferent; Fay 1995), this resonant mechanism would actto synchronize this population of large afferents to loud acous-tic stimuli of behavioral relevance by making them, regardlesstheir characteristic frequency, electrically tuned to the wholehearing range. Accordingly, strong acoustic stimuli are neces-sary 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 modifi-able Club ending mixed synapses are supported by biophysicalspecializations that allow these afferents to translate the gold-fish’s effective range of hearing into adequate patterns ofafferent activity. Among these properties, a persistent Na�

current plays an essential functional role as is required for thegeneration of repetitive responses and likely to enhance anotherwise weak electrical resonance. Although persistent Na�

currents represent a small (�1%) noninactivating fraction ofthe total Na� current they have a significant functional impactbecause they are activated about 10 mV negative to thetransient Na� current, where few voltage-gated channels areactivated and neuron input resistance is high (Crill 1996). As aresult of this property, subthreshold Na� currents play essentialcellular roles in amplifying dendritic synaptic potentials, reg-ulating repetitive firing, and producing depolarizing responses(Crill 1996; Ogata and Ohishi 2002). Persistent Na� currentshave been reported to be present in primary afferents (Boweet al. 1985; Honmou et al. 1994; Kocsis and Waxman 1983;Rush et al. 2007; Wu et al. 2005) where they are thought tomediate important functional and pathological roles (Stys et al.1992, 1993). Consistent with these observations, Nav1.6 chan-nels, thought to underlie persistent Na� currents (Ogata andOhishi 2002; Rush et al. 2007), were reported to be expressedin primary auditory afferents (Hossain et al. 2005). Thus thepresence of a relatively small number of Na� channels lackingfast inactivation is essential for this neuron’s function anddefine its electrophysiological phenotype, allowing these “an-atomically simple” afferents to link behaviorally relevant au-ditory signals into patterns of activity that match the require-ments of their fast and highly modifiable synapses (Fig. 9D). Inaddition, this subthreshold Na� current was shown to play anessential role in amplifying retrograde synaptic communicationvia electrical synapses that, by providing a mechanism oflateral excitation, contributes to the synchronization of Clubending afferents (Curti and Pereda 2004; Pereda et al. 1995).

The specialized functional properties of these neurons sug-gest that primary afferents can be endowed with complexmembrane and synaptic properties and be capable of moresophisticated contributions to auditory processing than gener-ally recognized before.

A C K N O W L E D G M E N T S

We thank K. Khodakhah, J. L. Pena, and M. Borde for useful discussionsand comments on the manuscript.

G R A N T S

This work was supported by National Institute on Deafness and OtherCommunication Disorders Grant DC-03186 to A. Pereda. S. Curti was partiallysupported by Comisión Sectorial de Investigación Cientıfica (Uruguay) andInternational Brain Research Organization fellowships.

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