Intracellular Response Properties of Units in the Dorsal Cochlear Nucleus of Unanesthetized Decerebrate Gerbil
Jiang Ding1 and
Herbert F. Voigt1, 2
1 Department of Biomedical Engineering, 2 Department of Otolaryngology, and Hearing Research Center, Boston University, Boston Massachusetts 02215-2407
 |
ABSTRACT |
Ding, Jiang and Herbert F. Voigt. Intracellular response properties of units in the dorsal cochlear nucleus of unanesthetized decerebrate gerbil. J. Neurophysiol. 77: 2549-2572, 1997. Intracellular recording experiments on the dorsal cochlear nuclei of unanesthetized decerebrate gerbils were conducted. Acceptable recordings were those in which resting potentials were
50 mV or less and action potentials (APs) were
40 mV. Responses to short-duration tones and noise, and to current pulses delivered via recording electrodes, were acquired. Units were classified according to the response map scheme (types I-IV). Ninety-two acceptable recordings were made. Most units had simple APs (simple-spiking units); nine units had both simple and complex APs, which are bursts of spikes embedded on slow, transient depolarizations (complex-spiking units). Of 83 simple-spiking units, 46 were classified as follows: type I/III (9 units), type II (9 units), type III (25 units), type IV (2 units), and type IV-T (1 unit). One complex-spiking unit was classifiable (a type III unit); six were unclassifiable because of weak acoustic responses. Classifying 39 other simple-spiking units and 2 complex-spiking units was impossible, because they were either injured or lost before sufficient data were acquired. Many simple-spiking units showed depolarization or hyperpolarization (~5-10 mV) during acoustic stimulation; some were hyperpolarized during the stimulus-off period. Type I/III units were not hyperpolarized during off-best-frequency (off-BF) stimulation. In contrast, many type II units were hyperpolarized by off-BF frequencies, suggesting that they received strong inhibitory sideband inputs. When inhibited, some type III units were hyperpolarized. Type IV units were hyperpolarized during inhibition even at low levels (<60 dB SPL); sustained depolarizations occurred only at higher levels, suggesting that they receive strong inhibitory and weak excitatory inputs. Several intracellular response properties were statistically different from those of extracellularly recorded units. Intracellularly recorded type II units had higher thresholds and lower maximum BF-driven and noise-driven rates than their extracellularly recorded counterparts. Type I/III units recorded intracellularly had lower maximum BF-driven rates. Type III units recorded intracellularly had higher maximum noise rates compared with those recorded extracellularly. Weaker acoustic responses most likely result from membrane disruption, but heightened responses may be related to weakened chloride-channel-dependent inhibition due to altered driving forces resulting from KCl leakage. Firing rates of simple-spiking units increased monotonically with increasing levels of depolarizing current pulses. In contrast, many complex-spiking units responded nonmonotonically to depolarizing current injection. The monotonic rate-versus-current curves and the nonmonotonic rate-versus-sound level curves of type IV and III units suggest that the acoustic behavior is the result of extrinsic inhibitory inputs and not due solely to intrinsic membrane properties.
 |
INTRODUCTION |
The cochlear nucleus (CN) is the first nucleus in the central auditory pathway to process information about the auditory environment transduced and encoded within the cochlea and conveyed by the auditory nerve. The CN is subdivided into dorsal (DCN), anteroventral, and posteroventral subnuclei on the basis of anatomic and cytoarchitectural differences (Lorente de Nó 1981; Osen 1969
; Ramón y Cajal 1909
). Each subnucleus receives similar tonotopically arranged auditory nerve input (Brown and Ledwith 1990
; Osen 1969
; Rose et al. 1960
) and projects to higher auditory centers via different pathways (Adams 1979
; Adams and Warr 1976
; Cant and Gaston 1982
; Osen 1972
; Ryugo and Willard 1985
).
The DCN is distinguished from other cochlear subnuclei by its layered structure, variety of morphologically different neurons, intrinsic neural circuitry, and diverse physiology. Neurons in the DCN include large projection neurons (fusiform/pyramidal and giant cells) and a group of small interneurons (cartwheel, granule, Golgi, stellate, and corn or vertical cells) (Benson and Voigt 1995
; Brawer et al. 1974
; Kane 1974
; Lorente de Nó 1981; Mugnaini et al. 1980a
,b
; Osen 1969
; Osen and Mugnaini 1981
; Wickesberg and Oertel 1988
; Wouterlood and Mugnaini 1984
; Wouterlood et al. 1984
; Zhang and Oertel 1993a
-c
, 1994). Extensive electrophysiological studies have revealed that DCN neurons display a variety of responses to acoustic stimulation. These responses have been classified with the use of discharge patterns (peristimulus time histograms, regularity analysis) (Gdowski 1995
; Pfeiffer 1966
; Pfeiffer and Kiang 1965
; Rhode and Smith 1986a
,b
; Young et al. 1988
) and/or response maps (types I-V) (Davis et al. 1996a
; Evans and Nelson 1973
; Young and Brownell 1976
; Young and Voigt 1982
). How these response properties are related to auditory information processing and perception remains largely unknown. In the past, most in vivo electrophysiological studies of CN physiology have been extracellular recording studies (e.g., Davis et al. 1996a
; Evans and Nelson 1973
; Nelken and Young 1994
; Rhode and Smith 1986a
,b
; Shofner and Young 1985
; Young and Brownell 1976
; Young and Voigt 1982
). The few in vivo intracellular recording studies conducted (e.g., Rhode et al. 1983a
,b
; Romand 1978
; Rouiller and Ryugo 1984
; Smith and Rhode 1985
, 1989
), have all been performed on anesthetized animals, and units were classified on the basis of temporal discharge patterns. Electrophysiological properties were not investigated in these studies. Ostapoff et al. (1994)
reported that a cartwheel cell recorded in an anesthetized gerbil DCN was a chopper.
Recently, in vitro slice studies in mice and guinea pigs described responses of some CN neurons to current pulse injection, to stimulation of various axon pathways, and to various pharmacological manipulations (Hirsch and Oertel 1988a
,b
; Manis 1990
; Manis et al. 1994
; Oertel and Wu 1989
; Oertel et al. 1990
; Zhang and Oertel 1993a
-c
, 1994). Although the electrophysiology of these neurons, such as action potential features and membrane properties [current-voltage (I-V) relationship, input resistances, etc.] can be well studied with this approach, assessing the cells' acoustic response properties directly is impossible.
This study aims at a comprehensive physiological investigation of DCN neurons by conducting intracellular in vivo single-unit recording experiments. Mongolian gerbils (Meriones unguiculatus) were chosen as subjects because they have a well-developed auditory system capable of low-frequency hearing (Ryan 1976
), neuronal organization and cell types similar to those of cats (Benson and Voigt 1995
; Schwartz et al. 1987
), large bullae enabling easy access to the DCN (Frisina et al. 1982
; Lay 1972
; Plassmann et al. 1987
), and a stable preparation for in vivo intracellular studies. Our goal was to record intracellular responses to both acoustic and electrical stimuli, classify the units according to the response map scheme, and then mark the neurons so that associations could be made between neuron type and unit response type. In this paper, we report on the intracellular responses obtained from neurons not marked or recovered. The response properties of identified DCN neurons will be reported in a subsequent paper. Some of this work has been reported before in abstract form (Ding et al. 1996
).
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METHODS |
Surgical preparation
An unanesthetized, decerebrate preparation was selected to eliminate the influence of barbiturates on neuronal response properties (Evans and Nelson 1973
; Young and Brownell 1976
). All experiments were performed in a sound-attenuating chamber (IAC, model 1202A) with the use of institutionally approved protocols. Detailed surgical procedures can be found in a separate paper (Davis et al. 1996a
). Briefly, young (~3 mo old) gerbils were first administered atropine (0.04 mg/kg im) to reduce respiratory mucus buildup. The animals were then anesthetized by an intraperitoneal injection of brevital sodium (methohexital sodium, 65 mg/kg), an ultrashort-acting barbiturate anesthetic. Supplemental doses of brevital sodium (32 mg/kg) were administered as needed during surgery. Body temperature was monitored and maintained at ~39°C with the use of a Harvard Apparatus heating blanket and controller. After an incision in the throat, a small slit was made on the ventral surface of the trachea, and the common carotid arteries were ligated with silk. The animal was placed in a stereotaxic device (KOPF, model 1730) after the pinnae were removed. A hole was made in the skull and a supracollicular decerebration was performed by aspirating all the brain tissue rostral to the superior colliculus. This complete aspiration precludes the return of motoric activity when the anesthetic wears off (Newlands and Perachio 1990
). The empty portion of the skull was gently packed with gelfoam to encourage blood clotting and to provide mechanical support for the remaining brain tissue. The DCN was accessed with the use of a transbullar approach (Frisina et al. 1982
). The anesthetic was discontinued and the animal was allowed to stabilize for ~30 min.
Acoustic system
Acoustic stimuli were delivered monaurally in a closed system to the left ear by an earphone (Beyer Dynamic DT48A, 200
) that was coupled to a hollow earbar. A probe-tube microphone (0.5 in. Bruel & Kjaer, model 4134) was placed near the tympanic membrane to measure the sound pressure level during acoustic calibration procedures. Pure tone stimuli were generated by a programmable (Wavetek, model 5100) or manual (Wavetek, model 188) oscillator with low harmonic distortion (less than
60 dB). Broadband noise stimuli were digitally generated on a personal computer (Gateway 2000, 486DX) and output through a D/A converter (Tucker-Davis) at a sampling frequency of 100 kHz (Davis et al. 1996a
). Bursting stimuli were gated on and off with 5-ms rise/fall times by the use of an electronic cosine switch (Wilsonics, model BSIT). The signals were attenuated by a programmable attenuator (Wilsonics, model PATT) to achieve the desired stimulation levels. For tones, this attenuation was relative to the acoustic ceiling; for noise, the attenuation was relative to the maximum level of noise without attenuation (~95 dB SPL; bandwidth 0-25 kHz). The acoustic system used is more completely described in Davis et al. (1996a)
, which contains a representative calibration curve (see their Fig. 1). A DEC LSI 11/73 computer system was used to control stimulus presentation and data acquisition.

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| FIG. 1.
Intracellular responses (A), driven discharge rate-vs.-sound level curves (B), and discharge rate-vs.-current level curves (C) from 3 type I/III units, J72293-6-1 (left), J73195-1-1 (middle), and J82593-12-1 (right, localized to the fusiform cell layer). A: 3 intracellular responses from each unit to 50- or 100-ms, best frequency (BF) tone bursts at 70, 60, and 60 dB SPL, respectively. Responses are displaced from each other to aid visualization. Bar along time axis: stimulation interval. B: driven discharge rate-vs.-sound level curves for each unit derived from responses to 50- or 100-ms BF tones and noise bursts from 0 to 80 dB SPL in 5-dB steps. Data were smoothed with a 3-point filter. BF is indicated on each plot. C: nonfiltered discharge rate-vs.-current level curves for each unit derived from responses to 16 or 17 trials of 50-ms current pulses from 1.0 to 1.0 nA in equal steps. Hyperpolarizing currents had negative values. Insets: estimated current-voltage (I-V) curves. Input resistance estimates for these 3 units are 26, 62, and 63 M (left to right). SpAc, spontaneous activity. V, change in transmembrane potential.
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Calibration
The acoustic system was calibrated in each experiment before data collection to find the maximum deliverable sound pressure level (dB SPL) for pure tones over a range of 0-25 kHz. This was done by delivering an acoustic click (5V, 20 µs) and measuring the resulting sound pressure (impulse response) near the tympanic membrane. The system's frequency response was computed by performing a fast Fourier transform of the impulse response. A10-band equalizer (BSR, model EQ-3000) was used to achieve the flattest frequency response by modifying the frequency content of the click before delivery to the ear. To compensate for the nonflat frequency response, the digital noise was created to have a spectrum whose magnitude was the inverse of the magnitude of the system frequency response (up to 25 kHz), and the phase was randomized between ±
radians.
Electrodes
Glass microelectrodes were pulled with the use of a Flaming-Brown micropipette puller (Sutter Instrument, model P80/PC), and filled with 0.5 M KCl, 0.05 M tris(hydroxymethyl)aminomethane buffer, and 4% horseradish peroxidase. The tips were usually <0.5 µm and the initial resistances were >100 M
, measured at 1 kHz with the use of a microelectrode impedance meter (Winston Electronics, model BL-1000). The electrodes werebeveled in a saline-silicon carbide (Buehler) slurry to reduce the resistance to ~40 M
before use.
The electrode was advanced into the DCN through the paraflocculus by a stepper motor microdrive (Kopf Instruments, model 660). A silver-silver chloride wire was used to connect the electrode to the head stage of an Axoclamp 2-A (X1) amplifier (Axon Instruments). Another such wire was placed in the neck musculature as a reference electrode. The electric activity recorded by the Axoclamp was further amplified by a DC amplifier (Tektronix, model AM502), digitized by an A/D converter, and stored on the LSI 11/73 computer system. The signals were sometimes also recorded on videotape by a VCR (Sony, model SL-HF 900) after being processed by a modified pulse-code module (Sony, model PCM-501ES) (Bezanilla 1985
).
Brain stem auditory evoked responses
The click-induced brain stem auditory evoked response (BAER) was measured in each animal before placement of a glass microelectrode into the DCN, to gauge the integrity of the auditory brain stem pathways. Platinum needle electrodes were placed subdermally at skull midline (noninverting), posterior to the ear of stimulation (inverting), and at the midline 2-cm posterior to the base of the neck (common). Amplification gain was set to 105 by coupling a Grass P15d bioamplifier to a Tektronix AM502 differential amplifier. The resulting signal was filtered from 0.1 to 10 kHz and sampled at 25 kHz for 10.2 ms with the LSI 11/73 computer system. Each BAER was the average of 350 click responses. Clicks were produced by routing a 4-V, 50-µs pulse through a PATT attenuator to the DT 48A earphone. Click level was manually adjusted in 5- to 10-dB steps to determine click-evoked BAER threshold approximately. The experiment would continue if click-evoked BAER threshold was within normal range (Burkard and Voigt 1989
). Click-evoked BAER thresholds were checked during the experiment if unit thresholds appeared to increase; experiments were ended if BAER thresholds increased by 30 dB.
Unit recording
As a microelectrode was advanced through the cerebellum's paraflocculus into the DCN, broadband noise bursts were used to detect background driving. Once background responses to the noise stimuli were observed, tone bursts were used as search stimuli. A recording was considered intracellular and acceptable if the resting membrane potential was
50 mV or less and the maximum action potential size was
40 mV. After an acceptable neuron penetration, the unit's best frequency (BF) and threshold (
) were estimated audiovisually. Three trials of 50- or 100-ms tone bursts (250-ms or 1-s interstimulus interval, stimuli began 10 ms after the start of a trial) were presented at three frequencies (BF and BF ± 1 octave or BF ± 0.7 octaves) and 17 sound pressure levels each (0-80 dB SPL, 5-dB steps). This was followed by three trials of 50- or 100-ms broadband noise bursts (250-ms or 1-s interstimulus interval, stimuli began 10 ms after the start of a trial) at each of 17 levels (0-80 dB SPL, 5-dB steps). Occasionally, longer-duration tone and/or noise bursts (duration 200 ms, interstimulus interval 1,000 ms) were also used and the unit's spike times were recorded. To assess the unit's response to current stimulation, 50-ms electric current pulse bursts (250-ms interstimulus interval, stimuli began 10 ms after the start of a trial) were delivered through the electrode (16 trials, from
1.0 to 1.0 nA in equal steps). Sometimes this DC paradigm was repeated for the same current levels and/or for current levels ranging from
2.0 to 2.0 nA in equal steps.
Data processing
In classifying a unit physiologically, deviations from spontaneous activity (SpAc) were used to determine excitation or inhibition (Davis et al. 1995
). A driven rate that is larger (smaller) than SpAc by >2 SD of the SpAc was regarded as reflecting excitation (inhibition). For intracellular data obtained with 50-ms (or100-ms) stimuli, driven rate was estimated over a 40-ms (or80-ms) period starting 10 ms after stimulus onset. SpAc was estimated during a no-stimulus condition, or if this was not available over a 100-ms interval, at the 0 dB SPL condition. For extracellularly recorded spike time data obtained with 200-ms stimuli, driven rate was computed over the last 80% of the stimulus duration (160 ms) and SpAc was computed over the last 160 ms of the 1,000 s trial. Rate-versus-sound pressure level (RSL) curves were constructed from these data. Unless stated otherwise, these curves were smoothed with the use of a three-point filter (Eq. 1) to reduce rate variations
|
(1)
|
where R(k) and RF(k) are the kth rate in the data array before and after filtering, respectively. As a measure of nonmonotonicity, a straight-line (least-squares) fit was applied to the portion of the RSL curve between the maximum (the 1st sharp change in the slope) or the transition to negative slope and the next minimum or sudden change in slope. This estimate of slope was normalized by dividing it by the maximum discharge rate (Young and Voigt 1982
) and is called the normalized tone slope. The relative noise response,
, which is the ratio of the maximum response to noise minus SpAc to the maximum response to BF tones minus SpAc, was also measured (Young and Voigt 1982
).
Responses to 50-ms current pulses were examined for signs of postcurrent hyperpolarizations, anode break excitation, and sags, and were used to construct rate-versus-current level (RCL) curves. For current values that did not give rise to action potentials, estimates of the I-V curves were made. In all cases, the cells' steady-state voltage responses were measured near the end of the current pulse injection. Estimates of the cell's input resistance were made from these I-V curves. In cases in which the amplifier bridge was not balanced (normal case), estimates of the electrode's contribution to the voltage response to current injection were made by fitting the voltage response to the sum of three decaying exponentials. The coefficient of the fastest-decaying exponential was taken to represent the resistance of the electrode, and this component was subtracted from the voltage response to yield the cell's response to the current pulse (
V in Figure insets).
Analysis of membrane voltage drops in response to step hyperpolarizing current injection
It has been shown, under appropriate constraints, that a neuron's transmembrane voltage change in response to a step hyperpolarizing current can be described by the sum of an infinite number of exponential decays (Rall 1969
, 1977
). The equalizing time constants and the corresponding coefficients in this series reflect the passive properties of the neuron's membrane. Under shunt-free conditions, the largest time constant is the membrane time constant (Durand 1984
; Rose and Dagum 1988
).
In the present study, a three-term exponential model was used to fit the data recorded from DCN intracellular units. Higher orders of exponentials cannot be reliably estimated because of practical limitations (e.g., bandwidth, sampling rate). Because the fastest change occurs at the beginning of voltage drop, the first sample of data can have large errors if it is not sampled exactly at the stimulus onset (t = 0). To avoid such error, a delay parameter was added to the model and fitted to the data after skipping the first one or two data points. The mathematical description of the model is
|
(2)
|
where V(t) is the observed voltage response, DC is the known resting membrane potential before the current injection,
i and Ci (i = 1,2,3) are equalizing time constants and coefficients (
3 >
2 >
1), and d is the delay.
Estimates of Ci,
i, and d were based on a modified Levenberg-Marquardt algorithm (Moré et al. 1980) and executed on a DEC 3000 AXP workstation. To assess the quality of the results, a 95% marginal confidence interval was approximated for each estimate with the use of the following method (Bates and Watts 1988
): let the parameter vector be
= [d
1
2
3 C1 C2 C3]T, then
|
(3)
|
where
* is the optimal estimate of
,
*i is the ith element of
*, J(
) is the Jacobian matrix whose elements are the values of the derivatives of the voltage drop with respective to individual parameters at different time lags, [J(
*)TJ(
*)]ii is the ith diagonal element of J(
*)TJ(
*), N is the number of data points used, P is the number of parameters (P = 7),
is the square root of variance estimate based on N
P degrees of freedom, and t(N
P,
/2) is the
/2 quartile for Student's t-distribution with N
P degrees of freedom.
Unit typing
Units were classified physiologically according to the response map scheme established for cats (Evans and Nelson 1973
) as modified by others (Shofner and Young 1985
; Young and Brownell 1976
; Young and Voigt 1982
) and adapted for gerbils (Davis et al. 1996a
). Type I/III units have a SpAc rate
2.5 spikes/s, an excitatory response to BF tones and noise, and no detectable sideband inhibition. Type II units have little or no SpAc (
2.5 spikes/s),an excitatory response to BF tones, and little to no noise response. Type III units have SpAc rates >2.5 spikes/s, excitatory responses to BF tones and noise, and sideband inhibition. Type IV units have an island of excitation near BF, inhibition at higher levels, and inhibitory sidebands, and respond to noise; type IV-T units have BF-tone-driven rates that drop below half of the sum of the maximum driven rate and the SpAc within 35 dB SPL of the peak. Two unit subclasses have been identified recently (Davis et al. 1996a
): type III-i units, which have type III features, except that they are inhibited by noise at low levels and excited at higher levels, and type IV-i units, which have type IV properties, except that they are inhibited by noise at high levels.
 |
RESULTS |
During these experiments, many units were recorded extracellularly to establish a normative data base for the DCN in the decerebrate gerbil. These data were presented in a separate paper (Davis et al. 1996a
). A major goal of our intracellular studies was to record units intracellularly and then mark them to find the neurons' structure. All successfully labeled units (i.e., cells recovered and associated with recorded physiology with high confidence) will be reported in a subsequent paper. Presented in this paper are results from 92 acceptably impaled spiking units (see criteria for acceptability in METHODS) from 69 gerbils for which marking was unsuccessful. Most of these units (83) had simple action potentials (simple-spiking units); 9 units had both simple and complex action potentials (complex-spiking units). Complex action potentials consist of bursts of spikes superimposed on slow and transient depolarization lasting ~10-40 ms; examples may be seen in Fig. 10. Table 1 shows the distribution of unit response types for simple- and complex-spiking units. Type III units are the most commonly encountered, whereas type IV and IV-T units are the least common. Only one complex-spiking unit could be classified; it was a type III unit. The other complex-spiking units were unclassifiable because of their high acoustic thresholds, weak responses, and broad tuning. An additional 39 simple-spiking units and 2 complex-spiking units could not be classified because of incomplete data acquisition (units were either lost or injured during the recording). Intracellularly recorded nonspiking and nonresponsive (to either acoustic or electrical stimulation) units were frequently impaled; presumably these were glial cells.

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| FIG. 10.
Intracellular responses (A), rate-vs.-sound level curves (B), and rate-vs.-current level curves (C) of 3 complex-spiking units, J41194-14-1 (left, localized to the DCN molecular layer), J61793-8-1 (middle, localized to the DCN molecular layer), and J41394-4-1 (right). A: 3 intracellular responses for each unit to 50-ms BF tone, at 60 dB SPL for unit J41194-14-1, 30 dB SPL for unit J61793-8-1, and 40 dB SPL for unit J41394-4-1, displaced from each other to aid visualization. Bar along time axis: stimulation interval. B: discharge rate-vs.-sound level curves for each unit derived from responses to 50-ms BF tones and noise bursts from 0 to 80 dB SPL in 5-dB steps. Data were smoothed with a 3-point filter. BF is indicated on each plot. C: discharge rate-vs.-current level curves for each unit derived from responses to 16 trials of 50-ms current pulse from 1.0 to 1.0 nA in equal step size. Hyperpolarizing currents had negative values. Insets: estimated I-V curves. Input resistance estimates for these 3 units are 48, 43, and 55 M (left to right).
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Precise localization of the units included in Table 1 is problematic because these units are those for which intracellular marking was either not attempted or unsuccessful. Estimates of unit localization can be inferred in some cases by referencing the locations of unlabeled cells to those of labeled units. Of the 53 units in Table 1, 17 units could be located to a specific DCN layer because a deposit of horseradish peroxidase was found at the sight of the recording (although no neuron was recovered). An additional 19 units were recorded along an electrode track <200 µm away from a track where a deposit of horseradish peroxidase was found within the DCN. The difference in recording depth (roughly dorsal laterally and ventral medially) between these units and the neighboring deposits was <200 µm. Considering that the gerbil DCN spans ~1 mm rostrocaudally, 1.2 mm in the dorsomedial to ventrolateral direction, and 0.5 mm in the dorsolateral to ventromedial direction (unpublished results), it is likely that most of these units were recorded in DCN.
Presented next are three detailed examples from each unit class (Figs. 1, 2, 5, 7, 9, and 10). These examples were selected to represent typical units from different BF regions. Because the response map scheme was not applicable to most complex-spiking units, these units were grouped separately from simple-spiking units. Tabular summaries of several physiological parameters are provided for all classified units (Tables 2-6).

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| FIG. 2.
Intracellular responses (A), rate-vs.-sound level curves (B), and rate-vs.-current level curves (C) of 3 type II units, J60393-2-2 (left, localized to the intermediate acoustic stria), JD2193-13-1 (middle), and JD0293-5-2 (right). A: 3 intracellular responses of each unit to 50-ms, 60-dB SPL BF tone bursts displaced from each other to aid data visualization. Bar along time axis: stimulation interval. B: discharge rate-vs.-sound level curves for each unit derived from responses to 50-ms BF tones and noise bursts from 0 to 80 dB SPL in 5-dB steps. Data were smoothed with a 3-point filter. BF is indicated on each plot. C: nonfiltered discharge rate-vs.-current level curves for each unit derived from responses to 16 trials of 50-ms current pulse from 2.0 to 2.0 nA in equal step size. Hyperpolarizing currents had negative values. Insets: estimated I-V curves. Input resistance estimates for these 3 units are 11, 9, and 14 M (left to right).
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| FIG. 5.
Intracellular responses (A), rate-vs.-sound level curves (B), and rate-vs.-current level curves (C) of 3 type III units, J52793-5-1 (left, localized to the fusiform cell layer, JN2393-11-1 (middle), and J80295-11-1 (right).A: 3 intracellular responses for each unit to 50- or 100-ms, 60-dB SPL BF tone bursts displaced from each other to aid visualization. Bar along time axis: stimulation interval. B: discharge rate-vs.-sound level curves for each unit derived from responses to 50- or 100-ms BF tones and noise bursts from 0 to 80 dB SPL in 5-dB steps. Data were smoothed with a 3-point filter. BF is indicated on each plot. C: nonfiltered discharge rate-vs.-current level curves for each unit derived from responses to 16 or 17 trials of 50-ms current pulse from 1.0 to 1.0 nA in equal step size. Hyperpolarizing currents had negative values. Insets: estimated I-V curves. Input resistance estimates for these 3 units are 22, 15, and 28 M (left to right).
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| FIG. 7.
Intracellular responses (A), rate-vs.-sound level curves (B), and rate-vs.-current level curves (C) of 2 type IV units, JD2193-4-1 (left) and J71593-10-1 [right, localized to the dorsal cochlear nucleus (DCN) deep layer], and 1 type IV-T unit, J31494-19-1 (middle, localized to the DCN deep layer). A: 3 intracellular responses for each unit to 50-ms, 60-dB SPL BF tone bursts displaced from each other to aid visualization. Bar along time axis: stimulation interval. B: discharge rate-vs.-sound level curves for each unit derived from responses to 50-ms BF tones and noise bursts from 0 to 80 dB SPL in 5-dB steps. Data were smoothed by a 3-point filter. BF is indicated on each plot. C: nonfiltered rate-vs.-current level curves of each unit were derived from responses to 16 trials of 50-ms current pulse from 1.0 to 1.0 nA in equal step size. Hyperpolarizing currents had negative values. Insets: estimated I-V curves. Input resistance estimates for these 3 units are 14, 30, and 30 M (left to right).
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| FIG. 9.
A: intracellular responses of the type IV unit (J71593-10-1, localized to the DCN deep layer) as a function of sound pressure level (from 0 to 70 dB SPL in 10-dB steps) for 3 frequencies [2.89, 4.70 (BF), and 7.64 kHz] and noise (50 ms in duration). At each frequency and level, 3 responses were collected and are displaced from each other to aid data visualization. B: 4 intracellular responses from A, enlarged for clarity: Ba, 2.89 kHz, 70 dB SPL; Bb, 4.70 kHz, 70 dB SPL; Bc, 4.70 kHz, 30 dB SPL; Bd, 4.70 kHz, 40 dB SPL. C: same unit's response to 16 trials of 50-ms current pulses from 1.0 to 1.0 nA in equal steps. Traces are overplotted such that response to larger current is placed higher. Sudden shift in voltage was due mainly to voltage drop across the recording electrode. Bar along time axis: stimulation interval.
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Type I/III units
Type I/III units (Table 2, Fig. 1) had resting membrane potentials that ranged from
56 to
72 mV (average:
63.8 ± 5.9 mV, mean ± SD) and action potential sizes that averaged 57.6 ± 9.4 mV. Most type I/III units (7 of 9) exhibited some sustained depolarization during BF stimuli, although in only four cases did this exceed 10 mV. These same seven units also showed sustained depolarization for the below-BF stimuli, but only three of the units had this feature for the above-BF stimulus. In addition, five of nine units had sustained depolarizations of about the same size when noise was presented. None of the type I/III units showed any sign of hyperpolarization during either tone or noise stimulation; however, small (
5 mV) hyperpolarizations were seen in five of nine units after BF stimuli [as seen in the responses of one of the units shown in Fig. 1A (unit J72293-6-1)], in four of nine units after either the below-BF tone or noise stimuli, and in two of nine unitsafter the above-BF tones. Action potentials with undershootswere seen in all but two type I/III units (e.g., unitJ72293-6-1).
All type I/III units had low rates of SpAc (<7 spikes/s). Their average BF tone threshold was 26 dB SPL. Discharge rates increased monotonically in response to BF tone and broadband noise bursts (Fig. 1B), and the RSL curves either saturated (e.g., unit J82593-12-1) or showed sloping saturation (e.g., unit J72293-6-1). Maximum BF-driven rates averaged 176 spikes/s. Noise responses were comparable with tonal responses, but noise thresholds could be 25-35 dB higher than BF tone thresholds. Unit J82593-12-1 is the only type I/III unit with an exceptionally high driven rate (373 spikes/s; highest of all the response types) and had equal thresholds for both BF tones and noise. All type I/III units responded monotonically to increasing levels of 50-ms depolarizing current injection. The RCL curves usually did not saturate at 1.0 nA, as seen in Fig. 1C, and the initial slope of the RCL curve averaged 312 Hz/nA. Figure 1C, insets, are estimates of the units' I-V curves. Estimates of the cells' input resistance, ranged from 13 to 63 M
, with an average of 32 ± 22 M
. Estimates of the largest equalizing time constants ranged from 2.4 to 11.2 ms, with an average of 6.3 ± 4.0 ms. The 95% marginal confidence bounds on these time constant estimates were never >16% of the estimated value. One type I/III unit was localized in the fusiform cell layer.
Type II units
Type II units (Table 3, Figs. 2-4) typically had large, over- and undershooting action potentials (action potential size: 71.3 ± 13.1 mV), whereas their resting membrane potentials were nearly identical to those of type I/III units (resting membrane potential:
63.7 ± 6.9 mV). Sustained depolarization was seen in eight of nine type II units during BF tone stimuli, and in all type II units responding to the below-BF and noise stimuli, but for only one of nine units presented with the above-BF tones. For many type II units, such as J60393-2-2 and Jd0293-5-2 (Fig. 2A), the depolarization was
10 mV at 60 dB SPL. The membrane potential of one type II unit (not shown) responded to below-BF tones of increasing level by changing from no response below threshold to hyperpolarized responses and finally to depolarized responses, although no action potentials were produced. Hyperpolarized responses were never seen for BF stimuli and only rarely seen for either the below-BF (1 of 9) or above-BF (3 of 9) tones. Hyperpolarizations were more common after acoustic stimuli. Eight of nine type II units were hyperpolarized after noise presentations, whereas only five of nine type II units were hyperpolarized after either the BF or below-BF tones.
Most type II units had no SpAc and a majority had high BF tone thresholds (
35 dB SPL). Type II units' discharge rates increased monotonically to increasing levels of BF tones, noise (Fig. 2B), and current injection (Fig. 2C). The maximum BF-driven rates, however, were consistently low (<150 spikes/s for 8 of 9 units) compared with maximum discharge rates measured in extracellularly recorded type II units. Only one unit (Jd0293-5-2) had a maximum discharge rate >200 spikes/s, resulting in an average for the group of 112 ± 52 spikes/s. Although type II units generally gave poor responses to noise bursts, their membrane potential showed clear signs that it was weakly depolarized at suprathreshold levels (Fig. 3, Ad and Bd). Similarly, all type II units were poorly excited by depolarizing current injection and required higher levels of current to reach action potential threshold than other unit classes (average current threshold: 0.84 ± 0.19 nA). The slopes of the RCL curves of type II units were the smallest of all unit classes (average: 113 ± 85 Hz/nA). Figure 2C, insets, are estimates of the units'I-V curves. Estimates of the input resistance for type II units were also lower than those for other unit types (15 ± 4.7 M
). The estimates of the largest equalizing time constant were also very low, averaging 2.9 ± 2.1 ms. This is consistent with an electrode-induced shunt compromising the integrity of the cell's membrane, and is discussed furtherbelow.

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| FIG. 3.
A: intracellular responses of a type II unit (J60393-2-2) as a function of sound pressure level (from 0 to 70 dB SPL in 10-dB steps) for 3 frequencies [1.40, 2.80 (BF), and 5.60 kHz] and noise (50 ms in duration). At each frequency and level, 3 responses were collected and are displaced from each other to aid data visualization. B: 4 intracellular responses from A, enlarged for clarity: Ba, 1.40 kHz, 70 dB SPL; Bb, 2.80 kHz, 30 dB SPL; Bc, 5.60 kHz, 70 dB SPL; Bd, noise, 70 dB SPL. C: unit's responses to 16 trials of 50-ms current pulses from 1.0 to 1.0 nA in equal steps. Traces are overplotted such that response to larger current is placed higher. Sudden shift in voltage was due mainly to voltage drop across the recording electrode. Bar along time axis: stimulation interval. This unit was localized to the intermediate acoustic stria.
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Figure 3 shows more intracellular responses to tones, noise bursts, and current pulses from unit J60393-2-2. Data in Fig. 3A were acquired for three frequencies [1.4, 2.8 (BF), and 5.6 kHz] and noise, each at eight levels from 0 to 70 dB SPL. There were no action potential responses at 5.6 kHz (an octave above BF) up to 70 dB SPL and few responses at 1.4 kHz (an octave below BF). Notice, however, the depolarization during the acoustic stimuli and the slow hyperpolarization during the stimulus-off period for two frequencies (1.4 and 2.8 kHz; Fig. 3, Ba and Bb) and noise (Fig. 3Bd), although in the latter case there were no action potential responses at all. The deviations in membrane potential began at sound levels well below those required for action potential generation. The membrane behavior at the higher frequency, however, was quite different. Instead of depolarizing, the cell remained at its resting position until 60 dB SPL; at higher levels the neuron was hyperpolarized during the stimuli (Fig. 3Bc).
Figure 3C shows this unit's responses to 16 trials of50-ms current pulse injections ranging from
2 to 2 nA in equal steps. The responses are overplotted to aid comparisons. The sudden shift of the recorded potential in each trial was due to the voltage drop across the electrode (the bridge was not balanced before delivery of the current pulses through the electrode). The unit responded with action potentials for depolarizing currents
1.2 nA. Some action potentials had strong overshoots, and the neuron became more depolarized during high-level current injection.
(Young and Voigt 1982
) is the ratio of a unit's maximum response to noise less SpAc to its maximum response to BF tones less SpAc, and can be used to distinguish type I/III units from type II units in decerebrate cats and gerbils (Davis et al. 1996a
). Figure 4A shows
plotted against normalized tone slope for type I/III and type II units. The
values ranged from 0.3 to 1.39 for type I/III units and from 0 to 0.29 for type II units. The normalized slope values for the type I/III units are within the range of values seen with extracellularly recorded type I/III units, but this is not so for the type II units. These differences between extracellularly recorded units and intracellularly recorded units are discussed below.

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| FIG. 4.
Relative noise response vs. normalized tone slopes for intracellularly recorded type I/III ( ) and II ( ) units (A) and intracellularly ( ) and extracellularly ( ) recorded type III units (B). See text for definitions.
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Three type II units were localized. One was found in the fusiform cell layer and the other two were found deep in the DCN bordering the intermediate acoustic stria.
Type III units
Type III units (Table 4, Figs. 5 and 6) make up more than half the classifiable unit population. The resting membrane potentials for the 25 type III units ranged from
51 to
74 mV (average:
60.6 ± 5.3 mV) and their action potential sizes ranged from 42 to 79 mV (average: 61.0 ± 9.2 mV). Most type III units (16 of 25) had undershooting action potentials. Sustained depolarizations or hyperpolarizations were observed in 20 of 25 type III units for some stimulus condition. Sustained depolarizations during BF tone stimuli typically increased as a function of level from a few millivolts at threshold to a maximum of 5-10 mV in 14 of 25 units. Although hyperpolarizations were never seen during BF stimuli, poststimulus hyperpolarizations were seen in 9 of 25 units. Two of these type III units had poststimulus hyperpolarization but no obvious depolarization during the BF tone stimuli. The examples in Fig. 5A show both sustained depolarizations and poststimulus hyperpolarizations.

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| FIG. 6.
A: intracellular responses of the type III unit (J80295-11-1) as a function of sound pressure level (from 0 to 70 dB SPL in 10-dB steps) for 3 frequencies [7.52, 12.22 (BF), and 19.85 kHz] and noise (100 ms in duration). At each frequency and level, 3 responses were collected and are displaced from each other to aid data visualization. B: 4 intracellular responses from A, enlarged for clarity: Ba, 7.52 kHz, 70 dB SPL; Bb, 7.52 kHz, 40 dB SPL; Bc, 19.85 kHz, 70 dB SPL; Bd, noise, 70 dB SPL. C: same unit's response to 16 trials of 50-ms current pulses from 1.0 to 1.0 nA in equal steps. Traces are overplotted such that response to larger current is placed higher. Sudden shift in voltage was due mainly to voltage drop across the recording electrode. Bar along time axis: stimulation interval.
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Type III units had a wide range of SpAc (50 ± 31 spikes/s)and sound thresholds (15 ± 15 dB SPL). In response to BF tone bursts, most of the type III units (20 of 25) increased their discharge rate monotonically with increasing sound levels, saturating at high levels with high maximum rates (220 ± 62 spike/s; e.g., units J52793-5-1 and JN2393-11-1 in Fig. 5B). Unit J80295-11-1 is an example of a type III unit with a nonmonotonic rate-versus-level curve (Fig. 5). Its RSL curve shows a negative slope at middle levels. Like type I/III units, type III units showed excitatory responses to noise at all levels with thresholds ~15-25 dB higher than their BF tone thresholds.
Type III units discharge monotonically in response to increasing levels of current pulse injection. Note in the three examples in Fig. 5C that the units were inhibited by hyperpolarizing current injection and excited by depolarizing current injection (SpAc is shown in the plot as the rate at 0-current level). The threshold to current was <0.3 nA for all type III units. The slopes of the type III RCL curves averaged 235 ± 85 Hz/nA. Figure 5C, insets, are the units' I-V curves. The input resistances for this unit class ranged from 7 to 50 M
with an average of 24 ± 10.3 M
. Estimates of the units' largest equalizing time constants ranged from 1.9 to 6.6 ms with an average of 3.9 ± 1.6 ms.
Shown in Fig. 6 are additional intracellular responses of unit J80295-11-1 to tones and noise bursts (A and B) and current pulse injections (C). Data are presented in the same format used in Fig. 3. This is a typical type III unit, with a high driven rate and a very regular firing pattern. Note that the responses at BF (12.22 kHz) decreased as sound levels rose from 20 to 50 dB SPL, thus resulting in a nonmonotonic RSL curve (also see Fig. 5B, right). The cell was depolarized during suprathreshold stimuli and strongly hyperpolarized when the stimulus was turned off, especially at high levels. Inhibitory responses are seen at both below-BF (7.52 kHz) and above-BF (19.85 kHz) tones, with sustained hyperpolarizations evident during the stimulus at 40 dB SPL for the lower tone (Fig. 6Bb) and at >50 dB SPL for the higher tone (Fig. 6Bc). The responses to 7.52-kHz tones became excitatory as sound levels exceeded 50 dB SPL. These excitatory responses were followed by strong downward shifts in membrane potential that exceeded 10 mV at 70 dB SPL (Fig. 6Ba).
In response to the above-BF stimuli, none of the type III units showed sustained depolarizations. About half of the units (13 of 25) had sustained hyperpolarizations between 5 and 15 mV. For the below-BF stimuli, however, only three of the type III units showed sustained hyperpolarizations. After the below-BF stimuli, hyperpolarizations were seen more frequently (9 of 25). These would often occur without preceding sustained depolarizations (5 of 9), but when they did follow a stimulus-evoked depolarization, they were typically larger than the depolarizations by ~5 mV (8 of 9). Type III units never had poststimulus hyperpolarizations following the above-BF stimuli.
The responses to noise were similar to the responses to BF tones. These included sustained depolarizations of 5-10 mV (8 of 25) and larger (5-15 mV) afterhyperpolarizations (Fig. 6, A and Bd). Hyperpolarizations were never observed during the noise.
Figure 6C shows a type III unit's responses to 16 trials of current pulse injections ranging from
1 to 1 nA in equal steps. The unit fired regularly in response to depolarizing currents (similar to its responses to acoustic stimuli) and it was inhibited by hyperpolarizing current pulses.
Seven of the nine localized type III units were found in the fusiform cell layer; the other two were in the deep DCN.
Type IV and type IV-T units
Type IV and type IV-T units (Table 5, Figs. 7-9) make up only ~6% of the classifiable simple-spiking unit population. The two type IV units and the type IV-T unit recorded in this study had undershooting action potentials; one type IV unit (Jd2193-4-1) also had overshooting action potentials (Fig. 7A). Although depolarizations were not observed during tonal stimulation for either type IV unit, hyperpolarizations were seen during tonal stimuli in all three units and during the stimulus-off period in one unit (Jd2193-4-1). In contrast, the type IV-T unit (Fig. 7, J31494-19-1) had sustained depolarization during tonal stimulation (Fig. 8Bd). Unlike most other units, the depolarization for the type IV-T unit took an abrupt course: ~10 ms after stimulus onset, the cell was quickly depolarized (within 5 ms) and remained so until the stimulus was turned off. The cell then gradually returned to the resting potential without hyperpolarization.

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| FIG. 8.
A: intracellular responses of the type IV-T unit (J31494-19-1) as a function of sound pressure level (from 0 to 70 dB SPL in 10-dB steps) for 3 frequencies [1.85, 3.00 (BF), and 4.87 kHz] and noise (50 ms in duration). At each frequency and level, 3 responses were collected and are displaced from each other to aid data visualization. B: 4 intracellular responses from A, enlarged for clarity: Ba, 1.85 kHz, 70 dB SPL; Bb, 3.00 kHz, 70 dB SPL; Bc, 4.87 kHz, 70 dB SPL; Bd, noise, 70 dB SPL. C: same unit's response to 16 trials of 50-ms current pulses from 1.0 to 1.0 nA in equal steps. Traces are overplotted such that response to larger current is placed higher. Sudden shift in voltage was due mainly to voltage drop across the recording electrode. Bar along time axis: stimulation interval. Arrow: PSP.
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The type IV units had high SpAc (57 and 60 spikes/s). At BF, both units were excited at low sound levels (beginning at 10 dB SPL) and then were inhibited at higher levels (Fig. 7B). One unit (J71593-10-1) could be further excited at levels >60 dB SPL. The type IV-T unit had similar discharge rate characteristics; however, its rate did not fall below SpAc, which was very low. Although the type IV-T unit responded to noise monotonically, the two type IV units responded nonmonotonically. Noise thresholds were ~5-10 dB higher than BF tone thresholds. Unlike the nonmonotonic RSL curves obtained with BF tones, all type IV and IV-T units responded to current pulse injection of increasing levels with increased discharge rates (Fig. 7C). The minimum current level required to reach threshold was very low (~0.07 nA) for both type IV units but high (~0.5 nA) for the type IV-T unit. The discharge rates obtained with 1-nA current pulses exceeded the maximum tone responses by a factor of 2 or 3, and the slopes of the RCL curves were 191 and 166 Hz/nA for the type IV units and 520 Hz/nA for the type IV-T unit. Figure 7C, insets, are I-V curves for the three units. The input resistances for these units are 14, 30, and 30 M
(left to right) and the largest equalizing time constants are 2.6, 10.6, and 12.9 ms, respectively.
Additional data from the type IV-T unit are shown in Fig. 8. Figure 8A shows intracellular responses to tones of three frequencies and noise at eight sound pressure levels. At BF (3.0 kHz) there were fewer spikes at 60 dB SPL than at 40 and 50 dB SPL. Responses below BF (1.85 kHz) were much stronger than those at BF, although the threshold was 20 dB higher. Sustained depolarization is clearly seen during the stimuli at and below BF, at 70 dB SPL for the above-BF tones, and for noise (Fig. 8B). Figure 8C shows this unit's responses to 16 trials of 50-ms current pulses ranging from
1 to 1 nA in equal steps. In this case, the unit did not produce action potentials until the current level reached 0.5 nA. Postsynaptic potentials (PSPs) are clearly seen in this figure (arrow).
Figure 9 shows a set of intracellular responses from one of the type IV units (J71593-10-1) to tones and noise bursts and current pulses. At BF (4.7 kHz), the unit was excited at 10 and 20 dB SPL and then was strongly inhibited from 30 to 50 dB SPL. At higher levels it was excited again. Excitatory responses are observed at the below-BF (2.89 kHz) tone condition at levels of
40 dB SPL. Signs of depolarization during tonal stimuli at levels <60 dB SPL were not obvious (Fig. 9, Ba and Bb). Hyperpolarizations, however, are seen at BF where the unit was inhibited (Fig. 9, Bc and Bd). Note that there was more significant depolarization during high-level noise bursts, but the unit's action potentials decreased in size and got wider, taking on an injured appearance. Figure 9C shows this unit's responses to 16 trials of 50-ms current pulses ranging in amplitude from
1 to 1 nA in equal steps. Notice the regular firing pattern. Current pulses >0.07 nA would cause the unit's discharge rate to exceed the SpAc rate. This type IV unit and the type IV-T unit were found in the deep DCN.
Complex-spiking units
Complex-spiking units (Table 6, Fig. 10) made up 14% of the spiking units encountered in this study; however, only one of these units could be classified by its responses to sound. Figure 10 shows data from three complex-spiking units; unit J61793-8-1 (middle) was classified as a type III unit. All complex-spiking units produced both complex action potentials and simple action potentials. Complex action potentials are composed of bursts of simple spikes superimposed on a slow, transient depolarization that lasts ~10-40 ms (see the examples in Fig. 10A). The resting membrane potential (
67.2 ± 4.1 mV) of complex-spiking units did not vary as much as their action potential sizes measured from simple spikes (58 ± 14 mV). Simple action potentials from most units (6 of 7) had a slow rising and falling phase without undershoots. The complex-spiking type III unit, however, had undershooting action potentials.
Complex-spiking units had some SpAc (23 ± 14 spikes/s).Unclassifiable units were poorly tuned to tonal stimuli and had high BF thresholds (>30 dB SPL) and low maximum driven rates (<100 spikes/s) (e.g., J41194-14-1 and J41394-4-1 in Fig. 10B). Noise responses were even weaker than tonal responses. These units usually responded to acoustic stimuli with simple action potentials. Complex action potentials occurred less frequently and did not appear to be acoustically driven. Type III unit J61793-8-1 was the only one with a relatively low threshold to BF tones (15 dB SPL) and a maximum driven rate >120 spikes/s. It was also the only unit that responded to tone and noise bursts with complex action potentials at all suprathreshold levels.
Unlike the monotonic responses to current pulse injections for all simple-spiking units, many complex-spiking units responded nonmonotonically to depolarizing current pulses (see examples in Fig. 10C). Some of this nonmonotonicity was because the simple action potentials would decrease in size with the larger depolarizing currents, making them difficult to detect. Most units, however, tended to fire complex action potentials at the onset of high-current-level stimuli. Figure 10C, insets, are the estimates of the I-V curves for these units. The input resistance for the complex spiking units averaged 40 ± 18.2 M
, and the largest equalizing time constants averaged 5.0 ± 1.5 ms. Two complex-spiking units were localized to the molecular layer.
Additional features of current pulse responses
Occasionally, a unit's response to current pulse injection would contain features, such as afterhyperpolarization, anode break excitation, or "sag," that warrant mention. Examples of these three features may be seen in Fig. 11. Figure 11A shows unit J82593-12-01, a type I/III unit, responding to a 1-nA current pulse with a steady rate of action potentials throughout the stimulus. After the current pulse stops, the cell's membrane potential drops ~10 mV below resting potential and reaches resting potential again after nearly 40 ms. Afterhyperpolarization following current injection occurred in 13 of 39 units tested, with the majority appearing in the responses of type III units. This feature is seen in about half the type III population. Table 7 summarizes these and other features seen in the current pulse responses.

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| FIG. 11.
Examples of poststimulus hyperpolarization (A), anodal break spikes (B), and sags (C and D) for 4 units in response to current pulse injection. Arrows in each plot: corresponding feature. Current levels are indicated in the plots. Bar along time axis: stimulation interval.
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When the initial voltage response to a current pulse is greater than the unit's steady-state voltage response, there is a sag in the voltage response waveform. Examples of such sags from a type II unit and a type III unit may be seen in Fig. 11, C and D. Sags are seen in about one third of the type III population and in three of seven type II units; they were not seen in type I/III units (Table 7).
Anode break excitation was observed in only 3 of 39 units. An example from a type III unit is seen in Fig. 11B.
 |
DISCUSSION |
Comparison with other intracellular studies: in vivo preparations
All previous in vivo intracellular recording studies of the DCN have been done on anesthetized animals (Britt and Starr 1976
; Gerstein et al. 1968
; Rhode et al. 1983a
,b
; Romand 1978
; Smith and Rhode 1985
, 1989
). Comparing the results of this study with those of previous studies is thus difficult. Another confounding problem is that units in the earlier studies relied primarily on the temporal-response-based (peristimulus time histogram) classification scheme introduced by Pfeiffer (1966)
. Units in the current study are classified according to the response map scheme introduced by Evans and Nelson (1973)
. The response map scheme was recently shown not to be very useful in the barbiturate-anesthetized gerbil, where up to 80% of DCN neurons have almost no SpAc (Gdowski 1995
; Gdowski and Voigt 1997a
,b
). So, in fact, the earlier investigators may have had no choice but to use the peristimulus time histogram scheme.
Gerstein et al. (1968)
were the first to study the intracellular membrane potentials of DCN neurons. They described sound-evoked depolarizations that were usually accompanied by increased discharge rate. More often, however, increases in sound-evoked firing rates occurred without any accompanying depolarizations. Romand (1978)
also reported that DCN units respond to BF tones either with or without sustained depolarizations. Romand suggested that perhaps the recordings with sustained depolarizations were from cell bodies and those without were from cell processes. With better resting potentials, Rhode et al. (1983b)
reported that fusiform cells with resting potentials between
50 and
65 mV, responded to tone pips with depolarizations of ~10 mV that lasted the duration of the stimulus and long-lasting hyperpolarizations of similar size following the stimuli. Many of our units show sustained depolarizations during the acoustic stimuli and long-lasting hyperpolarizations afterward (20 of 46). In fact, only seven of our classified units did not exhibit a stimulus-evoked membrane response other than firing action potentials. It is likely that the use of 3 M KCl in the recording electrodes in some early studies made it difficult to observe hyperpolarizations. Although the electrodes used in the current study were filled with 0.5 M KCl, it is likely that even this concentration affected intracellular responses.
Gerstein et al. (1968)
also described a situation in which a neuron, when presented a tone stimulus, depolarized for the duration of the stimulus, but action potentials were generated only after a delay. Rhode et al. (1983)
reported a similar finding. Examples of this are also seen in our recordings of type II units (Figs. 2, left and middle, and 3A).
Unit incidence
Intracellularly recorded type III units make up nearly half (49%) of the recorded population. Type IV and IV-T units, on the other hand, are only 6% of the population, whereas type I/III and type II units provided ~17% each (see Table 1). About 11% of the units recorded had weak acoustic responses, were broadly tuned, and had complex spikes. Extracellular data from the same lab and preparation (Daviset al. 1996a) had a similar unit distribution of type III and III-i units (62%), type IV and IV-T units (16%), type I/III units (14%), and type II units (8%), on the basis of a total of 133 units (see Table 8). Missing from this group, however, are complex-spiking units, which are difficult to identify reliably in extracellular records. The low numbers of type II units in the present study suggest that neurons with type II unit properties are particularly susceptible to injury by electrode impalement. Another difference between these results and those of Davis et al. (1996a)
concerns type III-i units. Although this is a sizable population in the gerbil, few type III-i units were identified in this study. This was probably due to an inadequate protocol for distinguishing type III-i units from type III units. These two unit types are similar to each other except for their broadband noise responses. Type III units are excited by noise at all levels above threshold, whereas type III-i units are excited by high-level noise stimuli, and are inhibited by low-level noise (Davis et al. 1996a
). Type III-i units are more reliably identified when their rate-versus-level curves are constructed from responses to long-duration (200-ms) stimuli that are presented with the use of a small sound level step size, because usually the inhibition occurs within a narrow range of noise levels (Davis et al. 1996a
). Because intracellular contact times were expected to be short, shorter-duration stimuli and larger sound level step sizes were used in this study. Therefore it is very likely that some type III units in this study are really type III-i units.
Type IV units are more plentiful and type III units less so in the extracellular recordings from the DCN in decerebrate cats. For example, Shofner and Young (1985)
reported 31% type IV units, 23% type III units, and 19% type II units. On the basis of inhibitory interactions between type II units and type IV units in cat (Voigt and Young 1980
, 1990
), the paucity of type IV units in the gerbil has been hypothesized as being due to a paucity of type II units or weak inhibitory properties of existing type II units (Davis et al. 1996
). Simulations showing the effects of a reduced population of inhibitory interneurons on the response properties of DCN projection units are consistent with this hypothesis (Davis and Voigt 1996
a).
Complex-spiking units were generally unclassifiable with the use of the standard response map scheme. Only one unit (a type III unit) was classified. If recorded extracellularly, complex-spiking units would only be reflected by their bursting firing patterns. Recording from bursting units, however, does not necessarily imply recording from complex-spiking units. In fact, a few bursting units (~7%) were noted in the experimental log and placed in the extracellular data base, but all these units were classified as type III or type IV units. Because we only included classifiable units in our extracellular data base, some bursting units with poor acoustic response might have been overlooked.
Sound-evoked and spontaneous intracellular membrane potentials
Individual excitatory PSPs (EPSPs) and inhibitory PSPs (IPSPs) were rarely seen in these intracellular records. This is similar to the in vivo recordings of Rhode et al. (1983)
but in contrast to the in vitro recordings of Oertel and coworkers. Integrated EPSPs and IPSPs evoked by sound stimuli, however, were frequently encountered.
Type I/III units
In general, type I/III units respond to tones and noise with sustained depolarizations that may or may not be followed by afterhyperpolarizations. Rhode et al. (1983)
recorded from fusiform cells in cat and presented examples of hyperpolarizations following sustained depolarizations, some of which extended for hundreds of milliseconds after the stimulus ended. Rhode et al. also showed examples in which the hyperpolarization begins before the stimulus ended. In these cases the tones were far from BF, and the hyperpolarizations were clearly the result of inhibitory processes. It is not clear, however, whether the afterhyperpolarizations are the result of active inhibitory processes or are due to some internal regulatory activity of the neurons themselves that compensates for the preceding sustained depolarization. It seems more likely that it is due to internal regulatory activity of the neurons, because they always appear with sustained depolarization. In addition, two of nine type I/III units showed hyperpolarizations after the offset of depolarizing current pulse injection (Fig. 11A).
Because type I/III units have little, if any, SpAc, inhibition cannot be detected simply by counting spikes. Inhibitory responses during acoustic stimulation can be detected, however, by observing hyperpolarizations. Only one type I/III unit responded to sound with hyperpolarization, and this was to a tone whose frequency was an octave above BF. It appears then that the typical type I/III units receive few, if any, inhibitory inputs that cause the cell to hyperpolarize. That is, if there are inhibitory inputs to type I/III units, their influence rarely overcomes the more prominent excitatory input and they would probably be mediated by clamping the membrane at its resting potential.
Type II units
Most of the type II units exhibited strong sustained depolarizations in response to tones. Many of these also had afterhyperpolarizations with the depolarizations. Type II units, like type I/III units, lack enough SpAc to detect sideband inhibition. The fact that they respond weakly to broadband noise implies that they receive inhibition strong enough to overcome the excitatory input from near BF energy. In fact, type II units depolarize slightly when broadband noise is presented, just not enough to elicit action potentials. Shofner and Young (1985)
showed that type II units were inhibited by shocks to the VIIIth nerve. Spirou and Young (1991)
have shown that this inhibitory input can be observed if one first activates the type II unit with a low-level BF tone before presenting a second tone whose frequency and level falls within the inhibitory sideband. The intracellular data of the present study confirm hyperpolarization of many type II units during off-BF stimuli, providing strong evidence of the existence of inhibitory sideband inputs.
It is widely thought that type II units, which in cat may be antidromically activated from the anteroventral CN (Young 1980
), are tuberculoventral neurons of Oertel (also called corn cells or vertical cells).
Type III units
Type III units have enough SpAc so that sideband inhibition can be seen for both intracellular and extracellular recording situations. When inhibited, many type III units exhibited noticeable hyperpolarizations. Some units, however, lacked such hyperpolarizations.
Preliminary results from our intracellular recording and marking study have shown that many type III units are fusiform cells.
Type IV and type IV-T units
Gerbil type IV and IV-T units are the rarest units in both the intracellular and extracellular unit groups. Unlike most other units (including type IV-T units), the type IV units did not exhibit sustained depolarization during tonal stimulation at levels <60 dB SPL. Hyperpolarizations, on the other hand, were seen in the type IV units at lower levels at which the units were inhibited. Such membrane behavior suggests either a weak excitatory input or a relatively strong inhibitory input onto type IV units. In contrast, strong onset depolarization during tonal stimulation in one type IV-T unit suggested that it could receive a very strong excitatory input. This cell also showed spontaneous PSPs throughout its record that usually did not result in action potentials. Such PSPs may be EPSPs, but the relatively low resting potential (
77 mV) argues that even IPSPs may cause the membrane potential to drive to an equilibrium potential that is less polarized than this and to appear as positive deflections. Leakage of KCl from the recording electrode may also cause disruption of inhibitory mechanisms, making identification of these small potentials problematic.
Complex-spiking units
Zhang and Oertel (1993a)
identified cartwheel neurons as a source of complex-spiking units in the mouse DCN slice preparation. Manis et al. (1994)
reported the same in the guinea pig DCN slice preparation; however, simple spikes were only found in 3 of 29 complex-spiking units. The complex-spiking units of this study all generated simple spikes as well. Parham and Kim (1995)
reported that 80% of the extracellularly recorded burstinglike units in the cat DCN, which they presumed were from cartwheel cells, responded weakly to sound stimuli. This is true of all but one of our complex-spiking units. In addition, preliminary data from this laboratory support the notion that cartwheel cells are a source of complex-spiking neurons (Ding et al. 1994b
). The weak acoustic responses of most complex-spiking units imply nonauditory functions for these units. In fact, it has been shown that somatosensory stimulation can activate burstinglike units (Davis et al. 1996b
) and inhibit DCN principal cells (Young et al. 1995
). These results suggest that complex-spiking units, presumably cartwheel cells, play a special role in processing multisensory information.
Measurements obtained from intracellular current injections
Unit input resistances in this study are generally small, suggesting the presence of a microelectrode-induced shunt. These resistances, however, are comparable with those measured by Manis in vitro from fusiform cells and cartwheel cells (Manis 1990
; Manis et al. 1994
), but lower than those reported for DCN neurons in vitro by Zhang and Oertel (1993a
-c
, 1994). Oertel has been coating electrode tips with dichlorodimethyl silane, which Oertel claims facilitates sealing of the membrane around the penetrating electrode. This may be the reason for the disparity in reported membrane resistances in DCN units.
The majority of I-V curves (65%) from units in this study appears linear within 10-15 mV below the resting membrane potential. This is similar to results obtained by Zhang and Oertel (1993a
-c
, 1994).
Intracellular versus extracellular data
Neurons impaled with microelectrodes are sometimes injured, and therefore responses from such neurons may be slightly or even dramatically different from their natural responses. Although such damage may occur with extracellular methods as well, it is worth checking for obvious differences in response properties of neurons recorded intracellularly with those recorded extracellularly. Figure 12 shows the intracellularly recorded unit's BF tone threshold plotted against its BF. BFs typically ranged from 2 to 10 kHz and the thresholds ranged from 0 to 55 dB SPL. Except for type II units and the complex-spiking units, most of the other units are within the threshold-BF boundary for auditory nerve fibers (dotted lines, from Schmiedt 1989
) and also overlap with the thresholds of extracellularly recorded units obtained from the same preparation (dash-dot lines, from Davis et al. 1996a
).

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| FIG. 12.
BF threshold vs. BF for all intracellular units. Dotted lines and dash-dot lines: boundaries of the thresholds of auditory nerves (Schmiedt 1989 ) and of the units recorded extracellularly (Davis et al. 1996a ), respectively.
|
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To assess the possible ill effects of intracellular penetration on the response properties of these physiologically identified units, comparisons were made of BF tone threshold, noise threshold, maximum discharge rates to BF tone and noise stimuli,
, normalized slope, and SpAc for units recorded intracellularly against those recorded extracellularly. Differences in these various parameters were tested for significance with the use of a two-tailed t-test; P values <0.05 were taken to be significant. The results of these tests are summarized for type I/III, type II, and type III units in Table 9 and are discussed below.
Type I/III units
BF tone thresholds and SpAc rates of type I/III units recorded intracellularly are similar to those of type I/III units recorded extracellularly (see Table 2, 7, and 9). The average maximum driven rates to noise stimuli are also comparable. The average maximum BF-driven rate, however, was only 176 spikes/s when the type I/III units were impaled compared with 263 spikes/s when the units were recorded extracellularly. This difference is significant at theP < 0.05 level (Table 9) and suggests that the microelectrode penetration of type I/III units affected at least some units' acoustic properties. Because of the decreased response to BF tones, the relative noise index for type I/III units also changed significantly (P < 0.05).
Type II units
The effects of intracellular impalement are even greater on the acoustic response properties of type II units. Intracellularly recorded type II units had on average twice the threshold to BF tones of extracellularly recorded type II units (32 vs. 19 dB SPL). The average maximum BF-driven rate was less than half as much as that of extracellular units (112 vs. 261 spikes/s, see Table 3, 7, and 9). Although
values were within normal range for type II units, the normalized tone slopes were much smaller and, often, positive. The differences in type II units' BF tone thresholds, maximum rates to both BF tones and noise, and the normalized tone slopes are all statistically significant (Table 9). Because most type II units in this study had large, overshooting action potentials (largest average APs of all units types), the penetration of the microelectrode probably did not damage the units' spike initiation mechanism. In addition, the type II units appeared healthy with respect to resting potential and action potential shape. We consider how the electrode may be affecting some acoustic response properties of these units below.
Type III units
Type III units are the largest population in both intracellular and extracellular unit groups. The average BF tone thresholds (15 and 12 dB SPL), maximum BF-driven rates (220 and 226 spikes/s), normalized tone slopes, and spontaneous rates of activity are comparable (see Tables 2 and 3). The maximum rate to noise, however, was significantly greater from type III units recorded intracellularly (Table 9).
is consequently greater for the intracellular population (Fig. 4B). These are unexpected and interesting results that are contrary to the type II unit results, where the driven rates simply decreased. To check whether the significance of this result was simply spurious, the extracellular data set was divided into two equal parts and each set was tested against the intracellular data set again with the use of both thet-test and the Wilcoxon-Mann-Whitney rank-sum test. The latter test is to determine whether these data sets could have come from two populations with the same mean (Diem 1966
; Kanji 1993
). In each case, the null hypothesis that the means are the same for the two populations was rejected at
95% confidence level.
Type IV and IV-T units
There are too few examples of type IV units in this study to say what effect, if any, electrode penetration has on type IV acoustic responses. The average thresholds and maximum BF-driven rates of the type IV units were 11 dB SPL and 125 spikes/s for the intracellular data and 11 dB SPL and 130 spikes/s for the extracellular data. Type IV-T units differed little from type IV units in both threshold and maximum rate (see Tables 2 and 3).
Impact of the intracellular recording electrode
It appears that the effects of the intracellular recording electrode on the acoustic response properties of DCN neurons depend to some extent on the unit type impaled. This is interesting, especially because some differences were not expected (e.g., type III units' maximum responses to noise increases when recorded from intracellularly). To check that the results of Table 9 are not simply due to the inclusion of cells with poor resting potentials, the t-tests were rerun with the use of only those cells with resting potentials of
60 mV or less instead of
50 mV. Except for the type II threshold difference now being insignificant, all other results remained statistically significant. In addition, the resting potentials at the start of data collection were compared with those at the end of data collection and were found not to be different (paired t-test), suggesting that the results are not due to some general cell deterioration.
The stimulus durations for the intracellular recordings were shorter than those for the extracellular recordings (50 vs. 200 ms), and therefore the rate estimates for the two situations were calculated over different intervals. To ensure that the maximum discharge rates to tone and noise were not different simply because of these two different rate estimates, the discharge rates for the extracellular data were recalculated with the use of only the first 50 ms of data. The use of this rate estimate did not alter any of the statistically significance differences reported in Table 9 for type I/III, type II, or type III units.
Staley et al. (1992)
studied the membrane properties of dentate gyrus granule cells with the use of both sharp electrodes and whole cell recordings in hippocampal slice preparations. They estimated the electrotonic length of the equivalent cylinder representing the cell processes to be only 0.49 from the whole cell data instead of 0.79 given by the sharp electrode data. They also calculated from the whole cell data that at rest there is only a 10% decrement in the DC membrane voltage along the length of the dendrite and thus synaptic events at the distal dendrites have a greater impact on the cell than previously thought. Staley et al. (1992)
suggest that the differences resulting from the use of sharp versus patch electrodes are due to a combined local electrode-associated nonspecific leak conductance and a potassium conductance that is distributed over the cell soma and dendritic processes. Both conductances would have reversal potentials near the cell's resting potential (Staley et al. 1992
). It is intriguing to speculate what effects these additional conductances have on DCN unit response properties. Of course, if the damage done by the electrode is too great, the resting potential will dissipate and the cell will die. We are not considering this case, but one in which the resting potential is maintained despite the electrode's presence. If we assume that the behavior of extracellularly recorded neurons is more similar to that of neurons recorded with patch electrodes than with intracellular sharp electrodes, then a smaller value of electrotonic length may be assumed for extracellularly recorded units. This implies that the steady-state voltage decay over the length of the dendrites is smaller for units recorded extracellularly than for those recorded intracellularly. If this is true, then synapses on distal dendrites would have a more profound impact on the somas of neurons that were not impaled. Perhaps this is the reason type II and type I/III units give greater responses to BF tones when they are recorded extracellularly rather than intracellularly. The situation involving type III units, however, is more complex. A larger noise response might occur if the noise threshold were specifically reduced, but this is not so (Table 9). Applying the logic above (i.e., distal dendrites will have less influence on activity near the soma of intracellularly recorded units) to the intracellularly recorded type III units would account for the increased response to noise only if the preponderance of distal synapses were inhibitory. Inhibitory synapses on fusiform cells are thought to arise from at least three sources. Cartwheel cells of the molecular and fusiform cell layer are thought to provide inhibitory synapses to fusiform cells (Berrebi and Mugnaini 1991
). Cartwheel cells are not often strongly activated by auditory stimuli (Parham and Kim 1995
; unpublished results) and are thus unlikely candidates. Vertical cells are thought to have type II unit response properties (Voigt and Young 1990
; Young and Voigt 1982
), to be glycinergic (Saint Marie et al. 1991; Wickesberg and Oertel 1990
), and to provide synapses to the soma and proximal dendrites of fusiform cells, and are not activated strongly by noise stimuli. Thus they are unlikely to play a role in the increased noise responses of intracellularly recorded type III units. One likely possibility is the wideband inhibitor (Nelken and Young 1994
; Winter and Palmer 1995
), which may correspond to the D-stellate cells of the posteroventral CN, whose axons project into the deep DCN (Oertel et al. 1990
). These projections could target both the basal dendrites of the fusiform cells and the dendrites and somata of the vertical cells and giant cells. The properties required of the wideband inhibitor include a weak response to tones and a strong response to noise, which are precisely the response properties of the onset-C units (Winter and Palmer 1995
). Preliminary results from this lab have shown that type III unit properties can arise from gerbil fusiform cells (Ding et al. 1994a
). If these fusiform cells are impaled with a microelectrode and the inhibitory influences of the wideband inhibitors are reduced preferentially to the excitatory, auditory nerve input, then a greater noise response in this cell would result. A problem with this scenario is that the auditory nerve input to fusiform cells is also on the basal dendrites and therefore subject to the same effects caused by the electrode. Thus consideration of the effects of the impaling electrode on the cable properties of neurons may account for the type I/III and type II unit responses, but not those from type III units.
Another possible explanation for the enhanced noise responses from intracellularly recorded type III units is that the 0.5 M KCl within the microelectrode had a more direct impact on the inhibition mediated by chloride conductances. Fromm and Schultz (1981)
concluded that leakage out of microelectrodes filled with 3 M KCl was unnecessarily high and that it could be reduced fivefold by the use of 0.5 M KCl. The reduced salt concentration would also yield electrodes with tip resistances or tip potentials that were not too large. Although this concentration of KCl, which was used in previous DCN studies (Manis et al. 1994
; Rhode et al. 1983
), is better than the 3 M KCl solutions used in the initial DCN studies (Gerstein et al. 1968
; Romand 1978
), it may still have an important impact on Cl
-channel-mediated inhibitory mechanisms functioning in DCN neurons. The impact of Cl
may have been compounded further in these earlier studies by the presence of barbiturates known to affect
-aminobutyric acid receptors (Barker and Ransom 1978
), which have been associated with Cl
channels. Although the presence of barbiturates is not a concern in this study, a reduction in the inhibitory influences on the soma of a fusiform cell might result from KCl leakage from an impaling microelectrode. If the inhibitory action affected is normally activated when noise is presented, as with the case of the wideband inhibitor, then an increased response to the noise would be expected.
Responses to electric current
Despite the diversity in their acoustic responses, all simple-spiking units responded monotonically to current injection. Therefore the nonmonotonic behavior of these cells in response to acoustic stimulation is most likely the result of inhibitory inputs and not due solely to the membrane properties. For units with SpAc (type III and IV units), inhibition could also be seen when hyperpolarizing current was injected. Thresholds to current injection were comparable for all units except the type II units. The high thresholds of type II units are consistent with their high sound thresholds (Davis et al. 1996a
; Young and Voigt 1982
). Data from tuberculoventral cells in the mouse slice preparation show relatively high (~1 nA) current thresholds for action potential generation (Zhang and Oertel 1993c
).
Time- and voltage-dependent sags were seen in the responses to current injection in 9 of 35 simple-spiking units in this study. Manis (1990)
reported such sags in 23 of 53 simple spiking cells in DCN slices from guinea pig.
The slopes of the frequency-current curves varied from a low average of 113 Hz/nA for type II units to a high average of 312 Hz/nA for type I/III units. The simple-spiking units of Manis (1990)
(mostly fusiform cells) had a mean slope of 116 Hz/nA, which is in the same range as type II units; however, it was much smaller than the 235 Hz/nA from type III units, primarily thought to be from fusiform cells, reported here. Zhang and Oertel (1994)
report slopes between 100 and 300 Hz/nA for their population of fusiform cells recorded in the the mouse slice preparation. The tuberculoventral cells of Zhang and Oertel (1993c)
appear to have substantially larger slopes. Because we have argued that the type II units of this study had response properties that were substantially altered by the impaling microelectrode, it is likely that these slopes are only lower bound estimates.
For complex-spiking units, the action potentials were related to the current strength. High current levels were likely to trigger complex action potentials and could induce onset responses, resulting in nonmonotonic current responses for many units. On the basis of this relationship between the spike appearance and current strength, the coexistence of simple and complex action potentials during acoustic stimulation might suggest a difference in the strength of excitatory inputs. Complex action potentials were probably triggered when strong excitatory inputs were integrated and the membrane potential reached well above the threshold, whereas simple action potentials were probably generated when weak excitatory inputs were integrated and slightly exceeded the threshold. The strength of the excitatory input could be related to different synaptic contacts and proportional to the number of the excitatory synaptic inputs as well.
Possible mechanism for controlling a unit's bandwidth
Depolarizations at levels below spike generation in type II units (example in Fig. 3A) and type IV-T units (example in Fig. 8A) indicate that these units are more sensitive than spike threshold reveals. This is intriguing because if there were mechanisms to modify a unit's excitability, controlling the frequency selectivity expressed by the unit would be possible. The granule cell population, with their parallel fibers, makes an interesting candidate for this bandwidth control. Activation of parallel fibers is thought to cause increased excitability in their targets (Manis 1989
; Osen and Mugnaini 1981
). Thus sound levels that evoke spikeless depolarizations in these target cells (principally fusiform cells) might now, with parallel fiber activation, provoke cell discharge. At BF, this would decrease sound-evoked spike threshold. Off BF, it is also likely that stimulus conditions that failed to generate spikes would now become active. Inactivation would lead to increased spike thresholds. This is a possible neural mechanism by which the auditory system can either increase or decrease the bandwidth of DCN neurons. Although the role of such a mechanism in audition is strictly speculative at this time, this might be an important mechanism for the auditory system to use in modifying signal to noise ratios or for selecting various portions of the input stream to analyze.
 |
ACKNOWLEDGEMENTS |
Thanks to P. Patterson and K. Hancock for help in producing the figures. Thanks also to K. Hancock for comments and discussions of earlier drafts of this paper.
This work was seeded by National Science Foundation Grant BNS 8420495 and further supported by National Institute of Deafness and Other Communications Disorders Grant DC-01099 and by the Department of Biomedical Engineering at Boston University.
 |
FOOTNOTES |
Address for reprint requests: H. F. Voigt, Dept. of Biomedical Engineering, Boston University, 44 Cummington St., Boston, MA 02215-2407.
Received 10 June 1996; accepted in final form 21 January 1997.
 |
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