Download Functional Analysis of Whole Cell Currents From Hair Cells of the

J Neurophysiol 88: 3279 –3292, 2002;
10.1152/jn.00771.2001.
Functional Analysis of Whole Cell Currents From Hair Cells of the
Turtle Posterior Crista
JAY M. GOLDBERG1 AND ALAN M. BRICHTA2
Departments of 1Neurobiology, Pharmacology, and Physiology and of 2Otolaryngology-Head and Neck Surgery,
University of Chicago, Chicago, Illinois 60637
Received 17 September 2001; accepted in final form 28 June 2002
Several studies have described voltage-sensitive, outwardly
rectifying K⫹ conductances in vestibular hair cells (Correia et
al. 1989; Marcotti et al. 1999; Masetto et al. 1994; Ohmori
1984; Rennie and Correia 1994; Rüsch and Eatock 1996;
Rüsch et al. 1998). Although voltage responses to injected
currents have also been described (Baird 1994; Correia and
Lang 1990; Correia et al. 1989; Eatock et al. 1998; Griguer et
al. 1993; Rennie et al. 1996; Ricci and Correia 1999; Weng and
Correia 1999), the roles of these conductances in shaping
afferent responses are far from certain.
A possible reason for this lack of certainty is the choice of
testing stimuli, which have been of short duration compared
with many signals involved in vestibular transduction. In addition, controlled currents have been presented in the absence
of background currents so that the resting potential serves as a
baseline. There is reason to believe that hair cells normally
operate around potentials more depolarized than the resting
potential. In particular, afferents have a resting discharge (Fernández and Goldberg 1976a; Goldberg and Fernández 1971;
Lowenstein and Sand 1936), which in turn is the result of
neurotransmitter release from hair cells (Rossi et al. 1994; Xue
et al. 2002). Resting potentials of vestibular hair cells are more
hyperpolarized than the voltages needed to trigger the Ca2⫹
conductances underlying quantal neurotransmission (Bao et al.
1999; Martini et al. 2000; Prigioni et al. 1992). This implies
that transducer currents are active at rest and serve to depolarize the hair cell.
A goal of our research has been to determine how voltagesensitive currents in hair cells are related to the diversity in
response properties of vestibular afferents. In the case of the
turtle posterior crista, bouton fibers innervating the neuroepithelium near the planum and near the nonsensory torus differ in
several of their firing properties, including their discharge
regularity and their rotational gains and phases (Brichta and
Goldberg 2000). Furthermore, the gains and phases of calyxbearing afferents are lower than those of bouton afferents
having a similarly irregular discharge. This and the preceding
paper (Brichta et al. 2002) were designed to answer two
questions. Could the large differences in discharge properties
of bouton afferents located near the planum and torus be
related to differences in the electrophysiology of the hair cells
they innervate? Could differences in the currents of type I and
II hair cells be responsible for differences between calyxbearing and bouton afferents? In the preceding paper, preliminary answers to these questions were provided by voltageclamp experiments.
Here, we used injected currents to continue the analysis. We
first used brief current steps to compare responses of type I hair
cells with those of type II hair cells selectively harvested from
Address for reprint requests: J. M. Goldberg, Dept. of Neurobiology, Pharmacology and Physiology, University of Chicago, 947 E. 58th St., Chicago, IL
60637 (E-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked ‘‘advertisement’’
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
INTRODUCTION
www.jn.org
0022-3077/02 $5.00 Copyright © 2002 The American Physiological Society
3279
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
Goldberg, Jay M. and Alan M. Brichta. Functional analysis of
whole cell currents from hair cells of the turtle posterior crista. J
Neurophysiol 88: 3279 –3292, 2002; 10.1152/jn.00771.2001. Controlled currents were used to study possible functions of voltagesensitive, outwardly rectifying conductances. Results were interpreted
with linearized Hodgkin-Huxley theory. Because of their more hyperpolarized resting potentials and lower impedances, type I hair cells
require larger currents to be depolarized to a given voltage than do
type II hair cells. “Fast” type II cells, so-called because of the fast
activation of their outward currents, show slightly underdamped responses to current steps with resonant (best) frequencies of 40 – 85 Hz,
well above the bandwidth of natural head movements. Reflecting their
slower activation kinetics, type I and “slow” type II cells have best
frequencies of 15–30 Hz and are poorly tuned, being critically damped
or overdamped. Linearized theory identified the factors responsible
for tuning quality. Our fast type II hair cells show only modestly
underdamped responses because their steady-state I-V curves are not
particularly steep. The even poorer tuning of our type I and slow type
II cells can be attributed to their slow activation kinetics and large
conductances. To study how ionic currents shape response dynamics,
we superimposed sinusoidal currents of 0.1–100 Hz on a small depolarizing steady current intended to simulate resting conditions in vivo.
The steady current resulted in a slow inactivation, most pronounced in
fast type II cells and least pronounced in type I cells. Because of
inactivation, fast type II cells have nearly passive response dynamics
with low-frequency gains of 500 –1,000 M⍀. In contrast, type I and
slow type II cells show active components in the vestibular bandwidth
and low-frequency gains of 20 –100 and 100 –500 M⍀, respectively.
As there are no differences in the responses to sinusoidal currents for
fast type II cells from the torus and planum, voltage-sensitive currents
are unlikely to be responsible for the large differences in gains and
response dynamics of afferents innervating these two regions of the
peripheral zone. The low impedances and active components of type
I cells may be related to the low gains and modestly phasic response
dynamics of calyx-bearing afferents.
3280
J. M. GOLDBERG AND A. M. BRICHTA
was done every 5 ms. Once every 500 ms, a 10-mV, 25-ms hyperpolarizing pulse was delivered to measure conductance.
In all cases, voltage was corrected for a junction potential of ⫹7
mV and voltage-current curves were corrected for the uncompensated
series resistances in voltage clamp and for the entire series resistance
in current clamp.
Results are expressed as means ⫾ SE unless otherwise stated.
Theory
The goal of this section is to present a linearized version of the
Hodgkin-Huxley equations for outwardly rectifying K⫹ currents
(Ashmore and Attwell 1985; Detwiler et al. 1980; Mauro et al. 1970).
Let the membrane be at a definite potential (v៮ ) with an associated K⫹
current (ı៮K) and an instantaneous (high-frequency) conductance (g៮ HF).
The three variables are related by
៮ı K共v៮ 兲 ⫽ g៮ HF共v៮ ⫺ vK兲
(1)
⫹
where vK is the K equilibrium potential. For small variations, ⌬iK
and ⌬v, we can ignore second-order terms and
⌬i K ⫽ 关g៮ HF ⫹ g៮ H⬘ F共v៮ ⫺ vK兲兴⌬v
where g៮ ⬘HF ⫽ dg៮ HF /dv at v ⫽ v៮ . The slope (low-frequency) conductance is
g៮ LF ⫽ ⌬iK/⌬v ⫽ g៮ HF ⫹ g៮ H⬘ F共v៮ ⫺ vK兲
METHODS
Preparative methods were identical to those used previously
(Brichta et al. 2002). Briefly, red-eared turtles were decapitated, the
posterior ampulla on one side was excised, the neuroepithelium was
exposed, and an enzymatic dissociation procedure was used to harvest
hair cells from one of three regions (planum, torus, or central zone).
The chamber containing the isolated hair cells was placed on the
sliding stage of an inverted microscope (Zeiss Axiovert 100) and
continually perfused at a rate of 500 ␮l/min with a standard external
solution. Hair cells were examined at ⫻600 with Nomarski optics and
were recorded in the ruptured-patch, whole cell mode with patch
pipettes connected to an Axopatch 200A amplifier (Axon Instruments,
Foster City, CA). All procedures were done at 22°C, and both external
and pipette solutions were identical to the standard solutions described
in the preceding paper.
A cell selected for recording was photographed for later morphological classification. Next, the series resistance (RS) and membrane
capacitances (CM) were determined with 3-ms voltage clamps. A
standard 200-ms voltage-clamp series was then run (see Brichta et al.
2002) with the capacitative transient canceled and the series resistance, which was typically 5–15 M⍀, compensated 70 –90%. Two
controlled-current protocols were run either on the same or separate
cells. Currents were delivered in the “fast” mode of the amplifier as
this minimized undesirable current transients. The first protocol was a
standard current-clamp series. Current was stepped from zero to each
of 10 values (⫺50, ⫺20, ⫺10, 0, 10, 20, 50, 100, 200, and 500 pA)
for 200 ms and then returned to zero. Voltages were filtered at 3 kHz
and were sampled every 0.6 ms. Current traces were similarly sampled to insure that uncontrolled transients were not present.
In the second protocol, sinusoidal currents (0.1–100 Hz) usually of
⫾25-pA amplitude were introduced on a background current (usually
50 pA). Frequencies were spaced 1/2 decade apart. The number of
points per cycle ranged from 1,024 at 0.1 Hz to 64 at 10 –100 Hz.
Currents and voltages were sorted into 32 equally spaced bins, and
values for successive cycles after the first were averaged into a single
cycle. A least-squares analysis was used to determine the best-fitting
sinusoids for the current input and the voltage output, from which gains
and phases were calculated. Gains were expressed in units of mV/pA
(⫽1,000 M⍀), and positive phases indicated that voltage led current.
Long-term inactivation was studied in voltage-clamp mode with
60-s steps to ⫺47 mV from a holding potential of ⫺67 mV. Sampling
J Neurophysiol • VOL
(2)
(3)
For an outwardly rectifying current in the voltage range v៮ ⬎ vK, both
g៮ ⬘HF and (v៮ ⫺ vK), the two terms in the last expression on the right
side of Eq. 3, are positive. Hence, the expression is positive and
g៮ LF ⬎ g៮ HF.
The variation in ⌬i for a voltage step ⌬v can be expressed as
Î共s兲 ⫽ 关g៮ HF ⫹ 共g៮ LF ⫺ g៮ HF兲H共s兲兴V̂共s兲
(4)
where Î(s) and V̂(s) are, respectively, the Laplace transforms of ⌬iK
and ⌬v, and H(s) is a transfer function describing the frequency
dependence of the transition between the low-frequency (g៮ LF) and
high-frequency (g៮ HF) conductances. From the form of Eq. 4, H(s) ⫽
1 when 兩s兩 3 0 and H(s) ⫽ 0 when 兩s兩 3 ⬁. A second-order equation
meeting these conditions is
H共s兲 ⫽
⫽
␣K1␣K2
, ␣K1 ⬍ ␣K2
共s ⫹ ␣K1兲共s ⫹ ␣K2兲
1
,
共1 ⫹ s ␶ K1 兲共1 ⫹ s ␶ K2 兲
␶ K1 ⬎ ␶ K2
(5)
where ␶K1 ⫽ 1/␣K1 and ␶K2 ⫽ 1/␣K2. The suitability of Eq. 5 is seen
from the response, ⌬i(t), to a voltage step, ⌬v. Inverting Eq. 5 gives
⌬i共t兲 ⫽ i⬁ ⫺
i⬁ ⫺ i0
关␶K1 exp共⫺t/␶K1兲 ⫺ ␶K2 exp共⫺t/␶K2兲兴
␶K1 ⫺ ␶K2
(6)
Equation 6 provides a good fit to our activation data (Brichta et al.
2002, Fig. 7).
The conductance of the channel, when expressed as a Laplace
transform, is
Ĝ共s兲 ⫽ Î共s兲/V̂共s兲
⫽ g៮ HF ⫹
⫽
共g៮ LF ⫺ g៮ HF兲␣K1␣K2
共s ⫹ ␣K1兲共s ⫹ ␣K2兲
g៮ HF关s2 ⫹ 共␣K1 ⫹ ␣K2兲s ⫹ K␣K1␣K2兴
共s ⫹ ␣K1兲共s ⫹ ␣K2兲
(7)
៮ (s) 3 g៮ HF, a constant equal to
where K ⫽ g៮ LF /g៮ HF. When K 3 1, G
the instantaneous conductance. Ĝ(s) can be expressed as the sum of
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
different regions of the neuroepithelium. To extend the studies
to lower frequencies and to determine the influence of background depolarizations, we next superimposed sinusoidal currents over a broad frequency range on steady depolarizing
currents. Results differed from those obtained with brief voltage and current steps because background currents resulted in
a slow inactivation of outward K⫹ conductances, similar to that
described in other hair-cell organs (Correia and Lang 1990;
Marcotti et al. 1999; Rennie et al. 2001; Russo et al. 1996). As
had been reported in the pigeon cristae (Correia and Lang
1990) and as we confirmed with long-duration voltage clamps,
inactivation was more prominent in rapidly activating type II
cells than in type I cells.
To provide a theoretical context for our results, we used a
linearized Hodgkin-Huxley theory developed by others (Ashmore and Attwell 1985; Detwiler et al. 1980; Mauro et al.
1970). An advantage of the theory is that it allows a quantitative comparison of the responses to voltage clamps and to
sinusoidal currents. Another benefit is that the theory identifies
those features of outwardly rectifying K⫹ conductances that
determine the tuning quality of the responses to current steps (Art
and Fettiplace 1987; Ashmore and Attwell 1985).
HAIR-CELL CURRENTS IN TURTLE CRISTA. II.
two terms, only one of which is time-invariant. Leak conductances
contribute to the time-invariant term, g៮ HF.
As we are mainly interested in the voltage produced by an injected
current, we consider the impedance, Ẑ(s) ⫽ 1/Ĝ(s) ⫽ V̂(s)/Î(s), as a
complex gain. When the membrane capacitance, CM, is added to the
circuit, the impedance becomes
Ẑ共s兲
共s ⫹ ␣K1兲共s ⫹ ␣K2兲
⫽
CM 关s3 ⫹ 共␣K1 ⫹ ␣K2 ⫹ ␣1兲s2 ⫹ 共␣K1␣K2 ⫹ ␣1␣K1 ⫹ ␣1␣K2兲s ⫹ K␣K1␣K2␣1 兴
(8)
where ␣1 ⫽ g៮ HF /CM is the reciprocal of ␶1, the effective membrane
time constant at the particular voltage, v៮ . Many features of the system
are easier to deduce with first-order channel kinetics where H(s) 3
␣K1/(s ⫹ ␣K1) and
共s ⫹ ␣K1兲
CM关s2 ⫹ 共␣K1 ⫹ ␣1兲s ⫹ K␣K1␣1兴
(9)
Behavior depends on the roots of the characteristic equation, s2 ⫹
(␣Ki ⫹ ␣1)s ⫹ K␣K1␣a. The system is overdamped when the two
roots are real and distinct, critically damped when they are real and
equal, and underdamped when they are a complex conjugate pair.
Damping increases as K decreases toward unity. When the conduc-
tance ratio, K 3 1, Ẑ(s) 3 1/[ CM(s ⫹ ␣1) ], the impedance of a
passive or RC circuit. From Eq. 3, such passive behavior occurs when
g៮ ⬘HF 3 0, which can happen when g៮ HF approaches its upper limit at
large depolarizations or is dominated by a leak (voltage-independent)
conductance. Critical damping occurs when K ⫽ L, where
L ⫽ 共T ⫹ 1兲2/4T
(10)
with T ⫽ ␶K1/␶1 ⫽ ␶K1g៮ HF/CM.
We first consider the second-order model in the absence of CM
(ionic current only). Sinusoidal currents result in a phase lead that
reaches a maximum
␾ ⫽ atan 共K 1/2兲 ⫺ atan 共1/K1/2兲
(11)
at a frequency, fMAX ⫽ (1/2␲␶K)K1/2 (Fig. 1A1, F—F). At lower
frequencies, phase approaches zero because the sinusoidal variation in
current is so slow that the voltage can reach a quasi-steady state
predicted by the slope conductance (g៮ LF). Phase also approaches zero
for very high frequencies because current variations are so much
faster than activation kinetics that the conductance will not vary from
g៮ HF. As frequency increases, gain (impedance) grows from 1/g៮ LF to
1/g៮ HF (Fig. 1A, F—F). Adding CM results in a second pole with a
corner frequency, fC ⫽ 1/2␲␶1 (Fig. 1, A and A1 ■—■). Introducing
the additional pole of the third-order model affects gain and phase
only slightly (Fig. 1, A and A1 䊐—䊐).
FIG. 1. Top: Bode plots— gains (A) and phases (A1) vs.
frequency— calculated from linearized Hodgkin-Huxley
theory with the following parameters: activation rate constants (␣K1 and ␣K2), 62.8 and 628 s⫺1; steady-state (g៮ LF)
and instantaneous (g៮ HF) conductances, 50 and 10 nS; capacitance (C), 10 pF. Four versions of the model are shown (see
key): 2nd- and 3rd-order models with and without capacitance (ionic only). When activation was 1st-order, the rate
constant was 62.8 s⫺1. Middle: effects of varying activation
rate constants on Bode plots— gains (B) and phases (B1) vs.
frequency. In all calculations, g៮ HF ⫽ 10 nS, g៮ LF ⫽ 50 nS,
CM ⫽ 10 pF. Third-order model with ␣K1 of 10, 100, and
1,000 s⫺1 (see key); ␣K2 was set to 10 times ␣K1 in all cases.
Increasing ␣K1 shifts the maximal gains and phase leads to
higher frequencies and narrows the tuning curve. Bottom:
effects of varying the ratio, K ⫽ g៮ LF /g៮ HF, on Bode plots—
gains (C1) and phases (C2) vs. frequency. All parameters
are as in A and A1 except g៮ LF ⫽ 10, 30, and 100 nS with
K ⫽1, 3, and 10 (see key). Tuning becomes sharper as
K increases.
J Neurophysiol • VOL
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
Ẑ共s兲 ⬵
3281
3282
J. M. GOLDBERG AND A. M. BRICHTA
current was deactivated. Activation time constants, ␶K1 and ␶K2, were
determined by fitting equation 6 to activation data (see, for example,
Brichta et al. 2002, Fig. 7, B–D).
RESULTS
Hair cells were classified based on the outwardly rectifying
currents they displayed (Brichta et al. 2002). Cells with a slow,
noninactivating, outward rectifying current active at voltages
more negative than ⫺57 mV were considered to have IK,L. In
all cases, we verified that the current could be deactivated by
hyperpolarizations to ⫺100 mV. If a cell had IK,L, it was
classified as type I. In most, although not in all cases, cells with
IK,L had constricted necks so their morphology was consistent
with their classification as type I. Cells whose outward currents
only activated more positive than ⫺57 mV were considered
type II. In addition to their having a more depolarized activation range than type I cells, almost all peripheral type II cells
had outward currents with faster activation kinetics and relatively small maximal whole cell conductances. Such type II
cells could also be distinguished by the lack of a constricted
neck and by conspicuous inward currents. Although some
central type II cells had slow activation, the other criteria
served to distinguish them from type I cells.
Type II cells were classified by their half-activation (t1/2)
times on being depolarized from a holding potential of ⫺67 to
⫺37 mV. Cells were called fast if t1/2 ⬍ 7.5 ms, intermediate
if t1/2 was between 7.5 and 15 ms, and slow if t1/2 ⬎ 15 ms.
Responses to brief current clamps
We used brief (200-ms) current steps to compare various
hair cells in terms of their steady–state voltage-current (V-I)
and impedance-current (Z-I) curves and their resonant properties as indicated by the presence of ringing in current-clamp
responses.
FIG. 2. Step responses calculated from linearized 2nd-order Hodgkin-Huxley theory. A: influence of K ⫽ g
៮ LF /g៮ HF. Activation
rate constant, ␣K1 ⫽ 200 s–1; K is varied by setting g៮ LF ⫽ 10, 30 and 100 nS, while keeping g៮ HF ⫽ 10 nS. Critical damping occurs
at K ⫽1.8, but even at K ⫽3 there is only a slight undershoot, ⬇2.3% of the steady-state value. Modest oscillations, amounting
to 1 1/2 cycles occur at K ⫽10. B: expected step responses for various kinds of hair cells based on typical parameters obtained from
voltage-clamp responses. Responses are scaled inversely proportional to g៮ LF with steady-state amplitude of fast type II cell being
set to unity. For all cells, CM ⫽ 10 pF. Type I: g៮ LF ⫽ 100 nS, g៮ HF ⫽ 20 nS, ␣K1 ⫽ 20 s–1; slow type II: g៮ LF ⫽ 50 nS, g៮ HF ⫽ 20
nS, ␣K1 ⫽ 50 s–1; fast type II: g៮ LF ⫽ 20 nS, g៮ HF ⫽ 4 nS, ␣K1 ⫽ 200 s–1. C: effects of current amplitude and steady-state voltage
on step responses for a single cell whose instantaneous conductance was calculated from a steady-state Boltzmann activation curve
g៮ HF ⫽ gMAX/{1 ⫹ exp[⫺(V ⫺ V1/2)/VS]} ⫹ gL with gMAX ⫽ 30 nS, gL ⫽ 1 nS, V1/2 ⫽ ⫺35 mV, VS ⫽ 5 mV, and CM ⫽ 14 pF.
Activation time constant, 30, 7.5, and 5 ms for steady-state voltages, V, of ⫺50, ⫺30 and ⫺10 mV, respectively. For graphical
simplicity, all responses are plotted with a steady-state value of unity.
J Neurophysiol • VOL
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
The pole associated with CM can interact with channel kinetics. As
␣K approaches ␣1, the increase in gain (Fig. 1B) and the corresponding phase lead (Fig. 1B1) become progressively restricted along the
frequency axis and tuning becomes sharper. Tuning is characterized
by a best frequency (BF), where the gain is maximum, and a bandwidth (BW) defined by the two points at which gain is attenuated by
3 dB from maximum. A conventional measure of tuning sharpness is
the dimensionless ratio, Q ⫽ BF/BW. In Fig. 1B, as ␣K1 increases
from 10 to 1,000 rad/s while ␣1 is kept at 1,000 rad/s, the best
frequency increases from 14.5 to 340 Hz and Q increases from 0.16 to
1.4. For fixed values of ␶K and ␶1, tuning increases in parallel with the
ratio, K ⫽ g៮ HF /g៮ LF. This is illustrated in Fig. 1, C and C1, where Q
increases from 0 to 1.55 as K increases from 1 to 10; for the particular
parameters used, critical damping occurs at K ⫽ 4.5.
Step responses, S(t), provide a convenient empirical test of damping
(Fig. 2A). Except when K ⫽ 1, the initial part of the response will
overshoot its steady-state value. When the system is overdamped,
which for the parameters of Fig. 2A occurs when K ⬍ 1.8, the voltage
approaches its final value exponentially from above. Slight underdamping at K ⫽ 3 results in only a small (2–3%) undershooting of the
final value. As K is increases to 10, clear oscillations occur. Step
responses are affected by two other variables, channel kinetics and
current-step amplitude. The slower the kinetics, the more overdamped
the response (Fig. 2B). This can be explained by an increase in ␶K1,
leading to increases in T and L. As current-step size is increased, the
response can be underdamped at one step size (Fig. 2C, ⫺30 mV) but
overdamped for either smaller or larger steps (Fig. 2C, ⫺50 and ⫺10
mV). The reasons are as follows. When current (and voltage) decrease
from optimal, there is a decrease in K and an increase in ␶K. The
increase in ␶K usually outweighs any increase in ␶1 and results in an
increase in T and L. Increasing current (and voltage) beyond optimal
lowers K more rapidly than it does T (and L), the decrease in T being
limited by both ␶K and ␶1 reaching near-minimal values.
The following procedures were used to estimate parameters at a
particular voltage, v៮ , from voltage-clamp data. CM was estimated by
fitting exponentials to brief (3-ms) voltage clamps. Conductances
were obtained from steady-state I-V curves. g៮ LF was calculated as a
slope conductance at v៮ , while g៮ HF was obtained as a chord conductance between v៮ and vK ⫽ ⫺87 mV. For both conductances, we
subtracted the corresponding leak conductance obtained when the
HAIR-CELL CURRENTS IN TURTLE CRISTA. II.
VOLTAGE-CURRENT AND IMPEDANCE-CURRENT CURVES. Because of the presence of IK, L, type I hair cells have more
hyperpolarized resting potentials and lower impedances than
do type II hair cells. As a result, more outward current is
needed to depolarize a type I cell to a given voltage. This is
seen in Fig. 3, which compares current-clamp responses for the
two kinds of hair cells. Results for individual hair cells are
shown above (Fig. 3, A and B); population results, below (Fig.
3, C and D).
The type I cell (Fig. 3A) has a resting potential of ⫺81 mV
and a 500-pA current only depolarizes the cell to ⫺65 mV. In
contrast, the resting potential for the type II cell (Fig. 3B) is
⫺64 mV and 500 pA depolarizes the latter cell to ⫺38 mV. For
reasons that will be considered later (see DISCUSSION), hair cells
are likely to operate around a voltage of ⫺50 mV. A useful
benchmark is the depolarizing current needed to reach this
3283
voltage. In the type II cell, a 170-pA current would suffice, but
even 500 pA would be inadequate in the type I cell. Similar
trends were seen in populations (Fig. 3, C and D). Results are
summarized in Table 1. Type I hair cells reach ⫺50 mV only
with currents approaching 1,000-pA currents, whereas fast type
II hair cells require, on average, currents of ⬍50 pA. Slow type
II cells need currents of 200 –500 pA. Impedances, based
on the slopes of V-I curves at 50 pA, are two to three times
smaller for type I and slow type II cells than for fast type II
cells (Table 1).
As can be seen from population data (Fig. 3D), there are no
obvious differences in the results for type II hair cells harvested
near the planum and near the torus. Even the small differences
seen in the curves for central type II hair cells are a result of the
inclusion of slow cells with relatively low impedances (Table
1). On this basis, we suggest that the large differences in gain
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
FIG. 3. Voltage responses to 200-ms current steps ranging from ⫺50 to 500 pA. A and B: voltage-current (V-I) curves for a type
I hair cell (A) and a type II hair cell (B) with individual voltage responses in insets. For the type I cell, depolarization to ⫺50 mV
(3) is not reached with a 500-pA current, whereas for the type II cell a 170-pA current suffices (1). C and D: mean V-I and
impedance-current (Z-I) curves for 20 type I cells (C) and for 19 central, 16 planum, and 6 torus type II cells plotted separately
and collectively (D); error bars are SE. Impedances were measured from the slopes of the V-I curves taken during the last 5 ms
of current steps. Most type I cells have such low impedances that large currents (⬎500 pA) are needed to depolarize the cells to
⫺50 mV from their resting potential; smaller currents (20 –100 pA) will depolarize type II cells to the same level. V-I and Z-I curves
are similar for planum and torus cells.
J Neurophysiol • VOL
88 • DECEMBER 2002 •
www.jn.org
3284
TABLE
J. M. GOLDBERG AND A. M. BRICHTA
1. Electrophysiological properties of type I and II hair cells from turtle posterior crista based on current-clamp responses
Cell type
n
Resting Potential, mV
Current at ⫺50 mV, pA*
Voltage at 50 pA, mV
Impedance at 50 pA, M⍀
Type I
Type II
Fast
Slow
20
41
30
8
⫺70.4 ⫾ 1.7
⫺64.2 ⫾ 1.4
⫺64.3 ⫾ 1.8
⫺64.8 ⫾ 1.7
900 ⫾ 210
67 ⫾ 16
45 ⫾ 12
330 ⫾ 150
⫺65.8 ⫾ 1.6
⫺51.5 ⫾ 1.4
⫺49.2 ⫾ 1.6
⫺58.1 ⫾ 2.0
51 ⫾ 8
114 ⫾ 13
133 ⫾ 15
61 ⫾ 12
Results based on 200-ms current clamps. Fast type II cells from the central zone (n ⫽ 8) and from the peripheral zone near the planum (n ⫽ 16) and near
the torus (n ⫽ 6) were combined because there were no statistically significant differences among the 3 groups. All of the slow type II cells were from the central
zone. Included in the Type II category are 3 hair cells with intermediate activation kinetics. n, number of hair cells; values are means ⫾ SE. * Values were
interpolated (type II) or extrapolated (type I) from average voltage-current relations.
occurred in response to 50- to 100-pA currents. BFs were
40 – 85 Hz and Q ⫽ 1.4 –2.3 (Table 2).
Slow type II cells were close to critically damped. This can
be seen in the individual cell (Fig. 4B), whose responses show
a small undershoot at 100 but not at 20 or 200 pA. Values for
the three slow type II cells studied were BF ⫽ 25–30 Hz with
Q ⫽ 0.3–1.2 (Table 2), bracketing the value, Q ⫽ 0.5, corresponding to critical damping. Type I cells were overdamped
for all depolarizing currents with responses returning to steadystate values from the depolarizing direction (Fig. 4C). For type
I cells, BF ⫽ 15–30 Hz and Q ⫽ 0.05– 0.40 (Table 2).
There was a high correlation between actual values of BF
and Q and values calculated from theory using voltage-clamp
parameters (BF: r ⫽ 0.98; Q: r ⫽ 0.94; n ⫽ 15). Damping is
determined by the relative values of the conductance ratio, K ⫽
g៮ LH/g៮ HF and L ⫽ (T ⫹1)2/4T where T ⫽ ␶K1/␶1. Relevant
values of the variables, based on voltage-clamp data, are presented in Table 2 for type I and for fast and slow type II cells.
Fast type II cells are predicted to show a small amount of
ringing, based on typical K/L ratios of 3.5 to 10. Slow type II
cells are predicted to be slightly overdamped as K/L ⫽ 0.3–
0.5. Finally, type I cells are predicted to be even more overdamped with K/L ratios of 0.05– 0.4. Values of K show only a
modest decline between fast type II and type I cells (Table 2).
The small values of the K/L ratio in slow type II cells and
especially in type I cells are mainly the result of the large
values of L, which in turn are due to slow activation (large ␶K1)
FIG. 4. Responses to 200-ms current steps of 3 hair cells. The first 50 ms of each response is shown. Currents (pA) are stated
to the right of each trace. A: over a limited voltage range of currents (50 –100 pA), a fast type II cell shows an underdamped
response consisting of 1 1/2 cycles. B: in a type II central cell with slow activation kinetics, it is unclear whether the responses are
underdamped or overdamped. C: responses of a type I cell are overdamped. D: recorded voltages (●) for the 3 cells of A–C are fit
by linearized 2nd-order Hodgkin-Huxley theory (—). Currents were 50 (top), 20 (middle), and 100 pA (bottom). Vertical
calibrations, 5 (top and middle) and 10 mV (bottom). Horizontal calibrations, all records, 20 ms.
J Neurophysiol • VOL
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
of bouton afferents located at different longitudinal positions
along each hemicrista (Brichta and Goldberg 2000) are not the
result of variations in voltage-sensitive outward currents of the
corresponding hair cells. Supporting evidence will be considered below.
RESONANT PROPERTIES OF HAIR CELLS. Hair cells from vibratory and auditory organs of nonmammalian vertebrates show
marked oscillatory responses to current steps (for review, see
Fettiplace and Fuchs 1999). In contrast, most vestibular hair
cells show modestly underdamped responses (Baird 1994; Correia and Lang 1990; Eatock et al. 1998; Weng and Correia
1999). The same was true for our hair cells. Typical currentstep responses are shown for three hair cells, a fast type II (Fig.
4A), a slow type II (Fig. 4B), and a type I hair cell (Fig. 4C).
Responses were reasonably well fit by equations from the
third-order linearized Hodgkin-Huxley theory (Eq. 8; Fig. 4D).
Such fits were used to determine the best frequency (BF) and
tuning quality (Q) of individual hair cells.
The fast type II cell shows oscillations at a BF ⫽ 75 Hz for
100-pA currents with Q ⫽ 1.7 (Fig. 4A). When the current is
lowered to 50 pA, oscillation frequency is lowered to BF ⫽ 50
Hz, while the number of oscillations and Q remain almost the
same. Larger (500 pA) or smaller (20 pA) depolarizing currents result in responses with more damping as indicated by the
voltage first overshooting and then only barely undershooting
its steady-state value. For 500 pA, BF ⫽ 120 Hz and Q ⫽ 1.0;
for 20 pA, BF ⫽ 20 Hz and Q ⫽ 0.94. Similar observations
were made in most fast type II cells. Maximal oscillations
HAIR-CELL CURRENTS IN TURTLE CRISTA. II.
TABLE
3285
2. Tuning properties of type I and II hair cells from turtle posterior crista
Class
n
CM, pF
Type I
Type II
Slow
Fast
5
10.6 ⫾ 1.7
3
5
9.5 ⫾ 0.4
9.5 ⫾ 0.5
gHF, nS
gLF, nS
␶K1, ms
␶1, ms
K
L
BF, Hz
Q
⫾ 2.5
40 ⫾ 6.7
68
⫾ 5.1
0.7 ⫾ 0.1
2.7 ⫾ 0.2
31
⫾ 7.3
20 ⫾ 2.7
0.2 ⫾ 0.1
5.6 ⫾ 0.6
3.6 ⫾ 0.9
24 ⫾ 7.2
14 ⫾ 3.3
75 ⫾ 12
6.0 ⫾ 0.4
2.0 ⫾ 0.3
3.4 ⫾ 1.0
3.8 ⫾ 0.9
4.1 ⫾ 0.3
10 ⫾ 2.4
0.7 ⫾ 0.1
27 ⫾ 1.6
67 ⫾ 8.0
0.7 ⫾ 0.2
1.8 ⫾ 0.2
15
Last 2 columns are from current steps leading to maximal ringing. All other columns are from voltage-clamp data over the same voltage range recorded during
the current steps. n, number of cells; values are means ⫾ SE. CM, capacitance, gHF, instantaneous conductance. gLF, slope conductance. ␶K1, activation time
constant. ␶1 ⫽ CM/gHF, effective membrane time constant. K ⫽ gLF/gHF. L ⫽ (T ⫹ 1)2/4T, where T ⫽ ␶K1/␶1. BF, best-frequency. Q, quality of tuning.
being correlated with large values of g៮ HF (Brichta et al. 2002)
and, hence, with small values of ␶1 ⫽ CM/g៮ HF.
As might be expected, BF and ␶K1— estimated, respectively,
from current steps and voltage clamps—are correlated across
the population (r ⫽ 0.83, n ⫽ 15, P ⬍ 0.001).
Type II hair cells harvested from the peripheral zone near the
planum or near the torus have similar responses to 200-ms
current steps. On this basis, we suggested that the large differences in discharge between afferents innervating these two
regions could not be accounted for by their basolateral currents. As a further test of this suggestion, we used sinusoidal
stimuli similar to those used in our afferent studies (Brichta and
Goldberg 2000). A larger than expected difference in the
responses of type I and type II hair cells was observed. Because
the difference can be related to the fact that the sinusoidal
currents were presented on a constant depolarizing current, we
first turn to the need for the latter.
BACKGROUND CURRENT. We have justified the use of a background current by considering the need for Ca2⫹ currents and
neurotransmitter release under resting conditions. Other more
pragmatic reasons also suggested the use of a background
current. One reason had to do with outward rectification. For
most of our hair cells, whether type I or type II, only a fraction
of their outward currents was activated at the resting potential.
As a result, without the presence of a background current,
FIG. 5. Responses to sinusoidal currents with and without background currents. A: a type I cell. Traces with (top) and without
(bottom) a 200-pA depolarizing current step. The current step eliminates much of the response asymmetry (outward rectification)
and leads to a more sinusoidal voltage response. B: a fast type II cell harvested near the planum. A 200-pA current step initially
depolarizes the cell by 23 mV. Over the next 40 s, the depolarization increases by 28 mV, and the sinusoidal gain increases
threefold. C: a fast type II cell was presented with a persistent holding current of 47.5 pA. Both the superimposed sinusoidal current
(top) and the voltage response (bottom) are asymmetric, being smaller in the depolarizing direction. The response (voltage)
asymmetry is more pronounced than the stimulus (current) asymmetry. Sinusoidal currents: 0.5 Hz, ⫾100 pA (A); 0.3 Hz, ⫾100
pA (B); 1.0 Hz, ⫾23.9 pA (C).
J Neurophysiol • VOL
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
Responses to sinusoidal currents
responses to sinusoidal stimuli were asymmetric. An example
is provided by a type I cell (Fig. 5A). In its response to
sinusoidal currents, the cell has a hyperpolarizing response
more than 15 times larger than its depolarizing response. This
may be contrasted with the almost linear behavior of afferents
to rotation sinusoids. In addition, the large nonlinearity would
preclude a linear analysis of the responses. Introduction of a
background current, presented as a step just before the sinusoid, eliminates the problem in type I cells but introduces a
feature in type II cells that is not paralleled in afferent discharge.
If a background depolarizing current is presented just before
the start of the sinusoid, type II cells show a gradual depolarizing drift in their membrane potential and an increase in their
sinusoidal voltage response. The type II cell in Fig. 5B is
typical. A depolarizing current results in an initial 23-mV
depolarization, but as the current is prolonged, there is an
additional time-dependent depolarization of 28 mV and a large
time-dependent increase in sinusoidal gain. These effects,
which are most conspicuous in fast type II cells, can be
explained by a slow inactivation of outward currents.
To eliminate drifts in membrane potential and sinusoidal
gain of fast type II hair cells required that the background
current be initiated well before the start of the trial. In practice,
the background current was kept on as long as sinusoidal
stimuli were being presented. Under these conditions, as exemplified by the cell illustrated in Fig. 5C, responses appear
3286
J. M. GOLDBERG AND A. M. BRICHTA
Traces occurring over several cycles were
averaged into 32-point single-cycle displays. This was done for
both current input and voltage output. By fitting sine waves to
both curves, we were able to calculate gains and phases.
Displays based on responses to 1-Hz sinusoids are shown for
two fast type II cells (Fig. 6, A and B) and a type I cell (Fig.
6C). Several differences can be noted between type I and type
II cells. First, background currents, which were comparable in
Fig. 6, B and C, resulted in more positive voltages in the type
II cells. Second, even though the amplitudes of sinusoidal
currents were similar in all three cases, the type II peak-to-peak
voltage responses were about 40 mV, while the corresponding
type I response was ⬍4 mV. In short, the type II impedances
were ⬎10 times larger than the type I impedance. Third,
GAIN AND PHASE.
voltage was in phase with current for the type II cells, but led
current by 25–30° in the type I cell.
We studied responses over a wide frequency range in several
cells. Gains and phases for a type I cell (Fig. 7, A and B, points)
are fit by three curves, the best (least-squares) fit of the data
points based on Eq. 9 (best fit), the prediction based on substituting voltage-clamp data into the same equation (VC fit),
and the best fit assuming no active conductances (RC fit).
There is a peak in the gain curve between 10 and 30 Hz,
amounting to a 4.3-fold increase from the gain at 0.1 Hz. A
phase lead of 30° is seen between 1 and 3 Hz. Both the gain
enhancement and the phase lead are evidence of an active
conductance. Except for ⬇40% higher gains and slight shifts in
phase toward higher frequencies, data points are satisfactorily
predicted by the voltage-clamp fit.
Quite different results were obtained in fast type II cells,
including the cell illustrated in Fig. 7, C and D. Here there are
no peaks in the gain and phase curves, even though these are
predicted from voltage-clamp data. Rather, points are well fit
as if there were no active conductances (RC fit). Because active
conductances were present during short protocols, it would
appear that the presence of the background current results in a
long-term inactivation of outwardly rectifying currents. Presumably due to the inactivation, the low-frequency conductance (៮gLF) is 10-fold higher than predicted from short voltage
clamps (Fig. 7C). That the inactivation was incomplete is
suggested by the residual outward rectification indicated by an
asymmetry ratio of 2.2 for this particular cell.
Bode plots are presented in Fig. 8 for several type I, slow
type II, and fast type II hair cells. Most type I cells show phase
leads of 15–30° (Fig. 8B). In three cells, the phase peaked
between 1 and 10 Hz, whereas in five cells, phase continued to
grow as frequency was lowered to 0.1 Hz. The difference
FIG. 6. Voltage responses to 1-Hz sinusoidal currents presented on background currents. Voltages and currents over several
cycles (256 points/cycle) are averaged into a single cycle (32 points/cycle). Curves are least-squares sinusoidal fits. A: a fast type
II cell from the planum. Background current of 19.5 pA (dashed horizontal line) gives rise to a background voltage of ⫺43.4 mV
(unbroken horizontal line). The peak depolarization of 23.5 pA leads to a depolarizing response of 14.9 mV; the hyperpolarizing
values are ⫺17.8 pA and ⫺21.4 mV. The average impedance is 870 M⍀, with a depolarizing impedance of 635 M⍀ and a
hyperpolarizing impedance of 1,200 M⍀. B: a fast type II cell from the torus; 950 M⍀ (average), 800 M⍀ (depolarizing), and 1,050
M⍀ (hyperpolarizing impedance). C: a type I hair cell; 69.5 M⍀ (average), 62.2 M⍀ (depolarizing), and 75.2 M⍀ (hyperpolarizing
impedance).
J Neurophysiol • VOL
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
sinusoidal and are stable over the several sine-wave cycles.
There is still a response asymmetry with hyperpolarizing responses being, 2.4 times as large as depolarizing responses.
Some of the response asymmetry can be explained by the fact
that the sinusoidal current itself was asymmetric: the hyperpolarizing current peaks were 1.4 times larger than the depolarizing peaks. Dividing the voltage asymmetry by the current
asymmetry provides the ratio of a hyperpolarizing impedance
to a depolarizing impedance and, as such, is a measure of
outward rectification. Asymmetry was measured with 1-Hz
sinusoids. In the particular cell (Fig. 5C), the asymmetry ratio
is 1.7. Among type II cells, there was evidence for outward
rectification; the mean ratio was 1.52 ⫾ 0.18 (n ⫽ 16). No
consistent asymmetry was seen in type I cells, and their mean
ratio was close to unity (0.97 ⫾ 0.10, n ⫽ 10). The lack of a
consistent asymmetry may reflect the low impedance of type I
hair cells, which results in a peak-to-peak voltage response of
only 2.5 mV for the ⫾25-pA sinusoidal currents typically used.
HAIR-CELL CURRENTS IN TURTLE CRISTA. II.
3287
between the two groups of cells can be explained by the latter
having considerably slower activation kinetics as measured by
voltage clamps. Two type I cells had near-zero phases between
0.1 and 10 Hz. Their behavior is a result of their being almost
fully activated in the voltage range in which they were tested,
in which case they are expected to have passive (RC) response
dynamics. Except for the latter two units, there are frequencydependent increases in gain (Fig. 8A). Based on fits similar to
those in Fig. 7, the average low-frequency impedance (ZLF) for
the type I cells was 36.7 ⫾ 5.4 M⍀ (n ⫽ 10).
All fast type II cells behaved passively (Fig. 8, E and F).
There were no differences in gain or phase among planum,
torus, and central fast type II cells (key, Fig. 8E), reinforcing
the conclusion that voltage-sensitive outward currents are not
responsible for the differences in discharge properties of planum and torus afferents. The mean ZLF for fast type II cells was
732 ⫾ 83 M⍀ (n ⫽ 10), 20 times larger than the value for type
I hair cells. This may be compared with the two- to threefold
difference in ZLF predicted from short current steps (Table 1).
The discrepancy can be explained by long-term inactivation
being much larger in fast type II cells than in type I cells
Slow type II cells show behavior intermediate between that
of type I and of fast type II hair cells. All slow type II cells
showed peaks in their gain (Fig. 8C) and phase curves (Fig.
8D). The gain peaks were near 30 Hz, the phase peaks between
1 and 10 Hz, similar to the frequencies at which peaks were
seen in type I cells. Clearly, the presence of a steady current
has not abolished active currents in slow type II cells. Reflecting this, the mean ZLF for the seven cells is 130 ⫾ 56 M⍀ (n ⫽
6), about five to six times smaller than the mean for fast type
II cells and three to four times larger than that for type I cells.
J Neurophysiol • VOL
Long-term inactivation
One difficulty in interpreting the results of the preceding
section was our inability to depolarize type I hair cells to the
same extent as type II cells (cf. Fig. 6, B and C). To overcome
this difficulty, we sometimes used larger background currents
of 100 or 200 pA in type I cells without affecting the results.
It, nevertheless, seemed important to study long-term inactivation under more controlled conditions.
This was done in voltage clamp by holding each cell at ⫺67
mV and then stepping to ⫺47 mV for 60 s before returning to
⫺67 mV. Throughout the trial, responses to brief hyperpolarizing pulses provided independent estimates of conductance.
Results are shown for three hair cells in Fig. 9 with original
traces to the left and conductance measurements to the right.
The type I cell shows a 20% conductance decrease over the
60-s voltage step, while the conductance of the fast type II cell
is almost completely inactivated. In this respect, the slow type
II cell is intermediate in its behavior. For 13 cells, the conductance curves during the step to ⫺47 mV, excluding the first 1 s
of the step, were fit by a single exponential. There was no
evidence that time constants differed for the three groups. The
average time constant was 10.7 ⫾ 2.3 s for the 13 cells.
Statistics bearing on long-term inactivation are summarized
in Table 3. Type I cells show no inactivation at 1 s and 25%
inactivation at 60 s. In contrast, fast type II cells show, on
average, 78% inactivation, about half of which takes place in
the first second. Slow type II cells resemble type I cells in
showing little inactivation during the first second, but resemble
fast type II cells in showing a ⬎50% conductance decline
between 1 and 60 s. The latter observation is an indication that
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
FIG. 7. Bode plots for 2 hair cells. A and
B: a type I hair cell. Background current, 46
pA; sinusoidal current, ⫾ 23.6 pA. Data (●)
are fit by 3 curves. Best fit: Bode plots predicted from linearized 2nd-order HodgkinHuxley theory (text Eq. 9) with parameters
chosen to give best fit. VC fit: calculated
from same version of linearized theory with
parameters obtained from 200-ms voltage
clamps. RC fit: best fit assuming only a
voltage-independent current. There is a peak
in the gain curve between 10 and 30 Hz and
in the phase curve between 3 and 10 Hz. The
peaks reflect an active conductance. The actual low-frequency gain is 47 M⍀ as compared with a gain of 27 M⍀ predicted from
voltage clamps. C and D: a central fast type
II hair cell. Background current, 19.8 pA;
sinusoidal current, ⫾23.5 pA. Gains and
phases are well fit by passive curve (RC fit).
There are no peaks corresponding to the
predictions from short voltage clamps (VC
fit). Furthermore, the actual impedance is 10
times higher than the impedance predicted
from voltage-clamp data and more than 20
times higher than the actual impedance of
the type I cell (A).
3288
J. M. GOLDBERG AND A. M. BRICHTA
fast and slow inactivation are not tightly coupled. Further
evidence comes from fast type II cells, which show no correlation between the two kinds of inactivation. Overall, the
difference in gains of fast type II and type I cells after a 60-s
depolarization is 25-fold, similar to the 20-fold difference seen
with sinusoids.
DISCUSSION
Operating range of type I and II hair cells
As was shown in previous studies (Brichta et al. 2002;
Correia and Lang 1990; Rüsch et al. 1998), type I and II hair
cells differ in their electrophysiology. Type II hair cells have a
low-conductance zone encompassing their resting potentials
and flanked to either side by zones of higher conductance. One
of the flanking zones, to the hyperpolarized side of the resting
potential, is dominated by inwardly rectifying IK1 and Ih currents. The other zone, to the depolarizing side, is controlled by
J Neurophysiol • VOL
a variety of outwardly rectifying K⫹ currents. Because of the
low-conductance zone, even small depolarizing currents will
cause large voltage shifts from rest, placing the hair cells into
a range where inward Ca2⫹ currents will be activated and
quantal transmission becomes possible.
Type I hair cells behave differently. Their electrophysiology
is dominated by IK,L, a large, slowly activating, outwardly
rectifying current that is activated at more hyperpolarized
potentials than the voltage-sensitive outward currents in type II
cells (Brichta et al. 2002; Correia and Lang 1990; Rennie and
Correia 1994; Rüsch and Eatock 1996). As a results of the
large size and hyperpolarized activation range of IK,L, type I hair
cells can have resting potentials of ⫺80 mV and even large
applied currents will not depolarize the cells to a level where
calcium entry and neurotransmitter release would seem possible.
Despite these considerations, there is evidence that quantal
transmission takes place between type I hair cells and their
calyx endings. Multiple ribbon synapses are present in type I
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
FIG. 8. Bode plots for 10 type I hair cells (A and
B), for 6 slow type II hair cells (C and D), and for 10
fast type II cells (E and F). Gain curves are to the
left and phase curves to the right. A and B: with 2
exceptions, type I cells show peaks in their gain and
phase curves, The exceptions (dashed lines) were
almost fully activated, which implies that the ratio,
K ⫽ g៮ LF /g៮ HF, approached unity. Under these conditions, linearized Hodgkin-Huxley theory predicts
that gain and phase curves should lack peaks. C and
D: all of the gain and phase curves for slow type II
cells show peaks. E and F: fast type II cells have
high-impedances and their gain and phase curves
resemble those of RC filters. Results are similar for
fast type II cells obtained from the central zone (n ⫽
1) or from the peripheral zone near the torus (n ⫽ 4)
or near the planum (n ⫽ 5).
HAIR-CELL CURRENTS IN TURTLE CRISTA. II.
3289
hair cells (Lysakowski 1996; Lysakowski and Goldberg 1997)
and quantal transmission has been observed in calyx-bearing
afferents (Schessel et al. 1991; Xue et al. 2002). In addition,
calyx afferents have an irregular discharge (Baird et al. 1988;
Goldberg et al. 1990; Lysakowski et al. 1995; Schessel et al.
1991), which requires a source of membrane noise (Smith and
Goldberg 1986). Synaptic noise is large enough to account for
the irregular discharge of the afferents, whereas the noise
associated with ion-channel gating is likely to be much too
small (Goldberg 2000).
Several mechanisms may be involved in quantal transmission from type I hair cells. First, the activation range of Ca2⫹
currents in type I cells might be shifted in a hyperpolarizing
direction to match that of IK,L. This possibility received little
J Neurophysiol • VOL
support from a study by Bao et al. (1999), who found that Ca2⫹
currents began activating near ⫺55 mV in both type I and II
hair cells from the cristae of rat pups. Second, the activation
range of IK,L may shift in a depolarizing direction in situ. Type
I hair cells from a single preparation vary in their IK,L activation ranges and individual type I hair cells can vary in their
activation range with time (Brichta et al. 2002; Chen and
Eatock 2000; Hurley and Eatock 1999; Rüsch and Eatock
1996). The lability of IK,L activation suggests that it may be
under physiological control. Possible modulators include nitric
oxide and cGMP (Behrend et al. 1997; Chen and Eatock 2000).
Third, the depolarization produced in type I hair cells by
transducer currents may be supplemented by other means. It is
possible, for example, that K⫹ ions leave the hair cell through
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
FIG. 9. Left: Voltage clamps in which each hair cell was stepped from ⫺67 to ⫺47 mV for 60 s and then returned to ⫺67 mV.
Every 0.5 s a 25-ms hyperpolarizing (⫺10 mV) step was introduced to measure the conductance, which is plotted to the right. The
type I cell (top) shows minimal long-term inactivation. The fast type II cell (bottom) shows almost complete inactivation. The slow
type II cell (middle) shows intermediate behavior. The declines in conductance are fit with exponential functions (smooth curves)
in all three cases; time constants were 14 (top), 9.4 (middle), and 6.9 s (bottom).
3290
TABLE
J. M. GOLDBERG AND A. M. BRICHTA
3. Long-term inactivation, type I and II hair cells from turtle posterior crista
%inact
Class
n
gpeak, nS
g1s, nS
g60s, nS
1s
60s
Type I
Type II
Slow
Fast
9
68.5 ⫾ 12.6
68.5 ⫾ 12.6
50.3 ⫾ 10.1
0.0 ⫾ 0.0
26 ⫾ 3.0
7
6
14.3 ⫾ 2.4
8.0 ⫾ 1.3
14.2 ⫾ 2.5
5.2 ⫾ 1.3
6.7 ⫾ 1.8
1.9 ⫾ 0.7
1.0 ⫾ 0.5
39 ⫾ 7.7
53 ⫾ 7.9
79 ⫾ 4.1
Results based on 60-s voltage step to ⫺47 mV from a holding potential, VH ⫽ ⫺67 mV. n, number of hair cells; values are means ⫾ SE. All hair cells are
from the central zone. g1s and g60s, based on brief, hyperpolarizing voltage steps at the times indicated. gpeak, calculated by assuming that conductance is
proportional to current. %inact, the percentage decline at the stated time from the peak conductance.
Tuning properties of vestibular hair cells as revealed
by short current clamps
BF and Q are of interest because they indicate whether a
particular cell is tuned to a limited band of physiologically
relevant frequencies. Because of its potential functional importance, there have been several studies of the voltage responses
of vestibular hair cells to current steps (Baird 1994; Correia
and Lang 1990; Eatock et al. 1998; Rennie et al. 1996; Weng
and Correia 1999). As exemplified by our results, type II cells
with rapidly activating conductances are slightly underdamped
and have best frequencies much higher than the frequency
range of natural head movements, whose upper limit is 10 Hz
(Grossman et al. 1988; Pozzo et al. 1990). Type I cells, with
their slowly activating outward rectifier, IK,L, show no oscillations whatsoever (Correia and Lang 1990; Eatock et al. 1998;
Rennie et al. 1996; the present study).
Results for both type I and II hair cells can be explained by
linearized Hodgkin-Huxley theory. Two variables, K ⫽
g៮ LF /g៮ HF and L ⬇ ␶K1/4␶1, determine damping in the secondorder version of the model. ␶K1 is the activation time constant
of the outwardly rectifying K⫹ channel and ␶1 ⫽ CM/g៮ HF is the
effective membrane time constant. When L ⬎ K, voltage
responses are overdamped and, when L ⬍ K, responses are
underdamped. Large values of K, which occur when the
steady-state I-V curve is steep, can lead to pronounced ringing.
Hair cells from auditory and vibratory organs in lower vertebrates are characterized by quite underdamped responses. In
these organs, the dominant outward rectifier is a calciumactivated (KCa) current with a steep I-V curve (Art and Fettiplace 1987; Ashmore and Attwell 1983; Fuchs and Evans
1988; Hudspeth and Lewis 1988).
Because of their high Q values, such hair cells can function
as sharply tuned filters and provide a basis for frequency
discrimination. There are several reasons for doubting that a
similar situation occurs in vestibular organs. First, tuning is
much less sharp in vestibular than in auditory hair cells. Moreover, the BFs of fast type II cells, the vestibular cells showing
the best tuning, would seem too high to be of relevance to the
encoding of head movements. Second, while our slow type II
and type I cells have best frequencies approaching the freJ Neurophysiol • VOL
quency spectrum of head movements, tuning is of poor quality.
To understand the relation between BF and tuning quality, we
need to consider the determinants of the lower and upper limits
of the tuning curve. The former is determined by ␶K1; the latter,
by ␶1. By increasing ␶K1, the lower limit can be made to
approach the frequency range of head movements. But as
shown in the previous paper (Brichta et al. 2002) and confirmed here (Table 2), hair cells with an increased ␶K1 also have
a large g៮ HF. The result is a smaller ␶1, a higher upper tuning
limit, and a broader tuning curve.
Afferent recordings are consistent with the notion that there
are no sharply tuned elements in vestibular organs. At most,
afferents show relatively modest frequency-dependent gain enhancements and phase leads (Boyle and Highstein 1990; Brichta
and Goldberg 2000; Fernández and Goldberg 1971, 1976b; Honrubia et al. 1989). A direct comparison of auditory/vibratory
and vestibular (tilt-sensitive) units is possible in the frog lagena
because both kinds of units are found in this organ. Auditory/
vibratory units have much sharper tuning curves than do vestibular units responding to tilts (Cortopassi and Lewis 1998).
Slow inactivation and the gains and response dynamics
of vestibular hair cells
BACKGROUND CURRENT. We used a background depolarizing
current to simulate resting conditions and to prevent the drift in
background potential and response gain attributable to the
development of slow activation. The need for a background
current can be related to the activation of Ca2⫹ channels. In a
variety of hair cells (Art and Fettiplace 1987; RodriguezContreras and Yamoah 2001; Zidanic and Fuchs 1995), including type I (Bao et al. 1999) and type II vestibular hair cells
(Bao et al. 1999; Martini et al. 2000; Prigioni et al. 1992), Ca2⫹
currents begin activating between ⫺45 and ⫺60 mV. Presumably, this is the minimal voltage range that will result in
quantal neurotransmitter release. Because neurotransmitter release (Rossi et al. 1994; Xue et al. 2002) and afferent discharge
(Brichta and Goldberg 2000; Goldberg and Fernández 1971;
Lowenstein and Sand 1936) can be turned off by inhibitory
hair-bundle deflections, hair cells presumably operate around a
larger than minimal voltage. A background voltage near ⫺50
mV seems plausible. But the resting potentials of vestibular
hair cells are seldom this depolarized (Brichta et al. 2002;
Eatock et al. 1998; Weng and Correia 1999); hence, the need
for a background transducer current. As our study shows,
background currents that result in a depolarization to near ⫺50
mV can produce a slow inactivation of fast type II cells. Less
inactivation is shown by slow type II cells and even less by
type I cells.
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
basolateral ion channels and accumulate in the intercellular
cleft between the hair cell and the calyx ending (Goldberg
1996). Such an accumulation could produce depolarizations of
30 mV in both the hair cell and calyx ending. The presynaptic
depolarization could lead to quantal release, which would be
supplemented by a postsynaptic nonquantal depolarization.
HAIR-CELL CURRENTS IN TURTLE CRISTA. II.
J Neurophysiol • VOL
emphasize is the need to study the electrophysiology of hair
cells under conditions that simulate physiological conditions.
Concluding remarks
We began these studies by asking whether basolateral currents could explain the differences in gain and phase of afferents innervating various zones of the turtle posterior crista. In
contrast to the ⬎100-fold variation in gain and 60° variation in
phase of bouton afferents innervating the peripheral zone near
the planum and near the torus (Brichta and Goldberg 2000),
there are only small differences in basolateral currents recorded
from the corresponding hair cells. Our results are consistent
with the suggestion that differences in response dynamics of
bouton afferents arise at an earlier stage of vestibular transduction (Baird 1994; Highstein et al. 1996). On the other hand,
the large, slow currents recorded from type I cells may contribute to the discharge properties of some calyx-bearing afferents, including their low gains and modestly phasic response
dynamics (Baird et al. 1988; Brichta and Goldberg 2000;
Goldberg et al. 1990; Lysakowski et al. 1995).
Drs. Ruth Anne Eatock and Anna Lysakowski provided helpful comments.
This research was supported by Grant DC 02058 from the National Institute
on Deafness and Other Communication Disorders.
Present address of A. M. Brichta: Discipline of Anatomy, Medicine and
Health Sciences, University of Newcastle, Callaghan, NSW 2308, Australia.
REFERENCES
ART JJ AND FETTIPLACE R. Variation of membrane properties in hair cells
isolated from the turtle cochlea. J Physiol (Lond) 385: 207–242, 1987.
ASHMORE JF AND ATTWELL D. Models of electrical tuning in hair cells. Proc
Royal Soc B Biol Sci 226: 325–344, 1985.
BAIRD RA. Comparative transduction mechanisms of hair cells in the bullfrog
utriculus. I. Responses to intracellular current. J Neurophysiol 71: 666 – 684,
1994.
BAIRD RA, DESMADRYL G, FERNÁNDEZ C, AND GOLDBERG JM. The vestibular
nerve of the chinchilla. II. Relation between afferent response properties and
peripheral innervation patterns in the semicircular canals. J Neurophysiol
60: 182–203, 1988.
BAO H, GOLDBERG JM, AND EATOCK RA. Calcium channel and sodium currents
in type I hair cells of the rat crista. In: Abstr 22nd Midwinter Mtg. Assoc Res
Otolaryngol., 1999, p. 23.
BEHREND O, SCHWARK C, KUNIHIRO T, AND STRUPP M. Cyclic GMP inhibits
and shifts the activation curve of the delayed-rectifier (IK1) of type I
mammalian vestibular hair cells. Neuroreport 8: 2687–2690, 1997.
BOYLE R AND HIGHSTEIN SM. Resting discharge and response dynamics of
horizontal semicircular canal afferents of the toadfish Opsanus tau. J Neurosci 10: 1557–1569, 1990.
BRICHTA AM, AUBERT A, EATOCK RA, AND GOLDBERG JM. Regional analysis
of whole cell currents from hair cells of the turtle posterior crista. J Neurophysiol 88: 3259 –3278, 2002.
BRICHTA AM AND GOLDBERG JM. Morphological identification of physiologically characterized afferents innervating the turtle posterior crista. J Neurophysiol 83: 1202–1223, 2000.
CHEN JWY AND EATOCK RA. Major potassium conductance in type I hair cells
from rat semicircular canals: characterization and modulation by nitric
oxide. J Neurophysiol 84: 139 –151, 2000.
CORREIA MJ AND LANG DG. An electrophysiological comparison of solitary
type I and type II vestibular hair cells. Neurosci Lett 116: 106 –111, 1990.
CORREIA MJ, CHRISTENSEN BM, MOORE LE, AND LANG DG. Studies of solitary
semicircular canal hair cells in the adult pigeon. I. Frequency- and timedomain analysis of active and passive membrane properties. J Neurophysiol
62: 924 –934, 1989.
CORTOPASSI KA AND LEWIS ER. A comparison of the linear tuning properties
of two classes of axons in the bullfrog lagena. Brain Behav Evol 51:
331–348, 1998.
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
SLOW INACTIVATION. A decline in conductance with kinetics
measured in seconds is a property of outwardly rectifying K⫹
channels from a variety of tissues (Fedida et al. 1999; Kukuljan
et al. 1995; Rasmusson et al. 1998), including type II vestibular
hair cells from the cristae of pigeons (Correia and Lang 1990;
Rennie et al. 2001), frogs (Marcotti et al. 1999; Russo et al.
1996), gerbils (Rennie et al. 2001), and guinea pigs (Griguer et
al. 1993). In vestibular hair cells from other species, a delayed
rectifier can be separated pharmacologically into two components, only one of which shows slow inactivation (Marcotti et
al. 1999; Rennie et al. 2001). The slowly inactivating component has slow activation kinetics. This last result is different
from our observations in the turtle crista, where slow inactivation is most conspicuous in fast type II cells. The fact that
80% of the outward current in turtle type II cells was inactivated makes it implausible that a slowly activating, slowly
inactivating component was masked by a rapidly activating,
noninactivating component.
There are two consequences of slow inactivation. First, the
calculated impedance to prolonged stimulation is several times
higher than might be inferred from brief stimulation. Because
slow inactivation is greatest in type II cells, it serves to accentuate differences in gain between type I and II hair cells.
Second, in their responses to current sinusoids over a wide
frequency range, inactivating hair cells do not show the phase
leads and gain peaks characteristic of active conductances.
Rather the cells behave like passive (RC) elements. Interestingly, input impedances were high (250 –2,000 M⍀) in a study
of hair cells recorded in the explanted frog utricular macula
with sharp microelectrodes (Baird 1994). Moreover, passive
behavior in response to sinusoidal currents was observed in
type II cells in slices of the pigeon crista (Weng and Correia
1999), as well as in our fast type II cells. The results in the frog
utricle and the pigeon crista suggest that slow inactivation is
not an artifact of enzymatic dissociation.
It might seem strange for the various outwardly rectifying
currents in fast type II cells to be eliminated by slow inactivation. An obvious advantage of inactivation is that it serves to
linearize the hair cell’s response to sinusoidal currents. Three
other comments are appropriate. First, the slow inactivation is
incomplete even in fast type II cells. Conductance measurements taken during 60-s voltage clamps to ⫺47 mV indicate
that 20% of the current remained. In addition, an outward
rectification was evident as an asymmetry in the response to
sinusoidal currents placed on a background current. Second,
slowly inactivating currents may become rapidly deinactivated
when hair cells are hyperpolarized during head rotations in the
inhibitory direction (Correia and Lang 1990). This would suggest that the outwardly rectifying currents of type II hair cells
would be particularly influential, along with the inward rectifiers found in these cells, in shaping the transition from inhibition to excitation. Third, functional studies need to explore
the voltage range in which hair cells are likely to operate. We
believe that the range is depolarized from the cells’ typical
resting potentials. Only when the latter range is studied in a
variety of preparations will we be able to evaluate the extent of
slow inactivation under differing conditions and its potential
impact on signal processing. It is, of course possible that the
inactivation seen in our fast type II cells was exacerbated by
our isolation and recording procedures. The main point to
3291
3292
J. M. GOLDBERG AND A. M. BRICHTA
J Neurophysiol • VOL
cristae ampullares of the squirrel monkey. J Neurophysiol 73: 1270 –1281,
1995.
MARCOTTI W, RUSSO G, AND PRIGIONI I. Inactivating and non-activating
delayed rectifier K⫹ currents in hair cells of frog crista ampullaris. Hear Res
135: 113–123, 1999.
MARTINI M., ROSSI ML, RUBBINI G, AND RISPOLI G. Calcium currents in hair
cells isolated from semicircular canals of the frog. Biophys J 78: 1240 –
1254, 2000.
MASETTO S, RUSSO G, AND PRIGIONI I. Differential expression of potassium
currents by hair cells in thin slices of frog crista ampullaris. J Neurophysiol
72: 443– 455, 1994.
MAURO A, CONTI F, DODGE F, AND SCHOR R. Subthreshold behavior and
phenomenological impedance of the squid giant axon. J Gen Physiol 55:
497–523, 1970.
OHMORI H. Studies of ionic currents in the isolated vestibular hair cell of the
chick. J Physiol (Lond) 350: 561–581, 1984.
POZZO T, BERTHOZ A, AND LEFORT L. Head stabilization during various
locomotor tasks in humans. I. Normal subjects. Exp Brain Res 82: 97–106,
1990.
PRIGIONI I, MASETTO S, RUSSO G, AND TAGLIETTI V. Calcium currents in
solitary hair cells isolated from frog crista ampullaris. J Vestib Res 2: 31–39,
1992.
RASMUSSON R L, MORALES MJ, WANG S, LIU S, CAMPBELL DL, BRAHMAJOTHI
MV, AND STRAUSS HC. Inactivation of voltage-gated cardiac K⫹ channels.
Circ Res 82: 739 –750, 1998.
RENNIE KJ AND CORREIA MJ. Potassium currents in mammalian and avian
isolated type I semicircular canal hair cells. J Neurophysiol 71: 317–329,
1994.
RENNIE KJ, RICCI AJ, AND CORREIA MJ. Electrical filtering in gerbil isolated
type I semicircular canal hair cells. J Neurophysiol 75: 2117–2123, 1996.
RENNIE KJ, WENG T, AND CORREIA MJ. Effects of KCNQ channel blockers on
K⫹ currents in vestibular hair cells. Am J Physiol Cell Physiol 280: C473–
480, 2001.
RICCI AJ AND CORREIA MJ. Electrical response properties of avian lagena type
II hair cells: a model system for vestibular filtering. Am J Physiol Regulatory
Integrative Comp Physiol 276: R943–R953, 1999.
RODRIGUEZ-CONTRERAS A AND YAMOAH EN. Direct measurement of singlechannel Ca2⫹ currents in bullfrog hair cells reveals two distinct channel
subtypes. J Physiol (Lond) 534: 669 – 689, 2001.
ROSSI ML, MARTINI M, PELUCCHI B, AND FESCE R. Quantal nature of synaptic
transmission at the cytoneural junction in the frog labyrinth. J Physiol
(Lond) 478: 17–35, 1994.
RÜSCH A AND EATOCK RA. A delayed rectifier conductance in type I hair cells
of the mouse utricle. J Neurophysiol 76: 995–1004, 1996.
RÜSCH A, LYSAKOWSKI A, AND EATOCK RA. Postnatal development of type I
and type II hair cells in the mouse utricle: acquisition of voltage-gated
conductances and differentiated morphology. J Neurosci 18: 7487–7501,
1998.
RUSSO G, MARCOTTI W, AND PRIGIONI I. Inactivation of delayed rectifier K⫹
current in semicircular canal hair cells. Neuroreport 7: 2143–2146, 1996.
SCHESSEL DA, GINZBERG R, AND HIGHSTEIN SM. Morphophysiology of synaptic transmission between type I hair cells and vestibular primary afferents.
An intracellular study employing horseradish peroxidase in the lizard, Calotes versicolor. Brain Res 544: 1–16, 1991.
SMITH CE AND GOLDBERG JM. A stochastic afterhyperpolarization model of
repetitive activity in vestibular afferents. Biol Cybern 54: 41–51, 1986.
WENG T AND CORREIA MJ. Regional distribution of ionic currents and membrane voltage responses of type II hair cells in the vestibular neuroepithelium. J Neurophysiol 82: 2451–2461, 1999.
XUE J-T, HOLT JC, AND GOLDBERG JM. Differences in junctional transmission
involving calyx-bearing and bouton afferents in the turtle posterior crista.
Abstr 25nd Midwinter Mtg, Assoc Res Otolaryngol., 2002, p. 30.
ZIDANIC M AND FUCHS PA. Kinetic analysis of barium currents in chick
cochlear hair cells. Biophys J 68: 1323–1336, 1995.
88 • DECEMBER 2002 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.32.246 on August 9, 2017
DETWILER PB, HODGKIN AL, AND MCNAUGHTON PA. Temporal and spatial
characteristics of the voltage response of rods in the retina of the snapping
turtle. J Physiol (Lond) 300: 213–250, 1980.
EATOCK RA, RÜSCH A, LYSAKOWSKI A, AND SAEKI M. Hair cells in mammalian
utricles. Otolaryngol Head Neck Surgery 119: 172–181, 1998.
FEDIDA D, MARUOKA ND, AND LIN S. Modulation of slow inactivation in
human cardiac Kv1.5 channels by extra- and intracellularly permeant cations. J Physiol (Lond) 515: 315–329, 1999.
FERNÁNDEZ C AND GOLDBERG JM. Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. II. Response to sinusoidal
stimulation and dynamics of peripheral vestibular system. J Neurophysiol
34: 661– 675, 1971.
FERNÁNDEZ C AND GOLDBERG JM. Physiology of peripheral neurons innervating otolith organs of the squirrel monkey. I. Response to static tilts and to
long-duration centrifugal force. J Neurophysiol 39: 970 –984, 1976a.
FERNÁNDEZ C AND GOLDBERG JM. Physiology of peripheral neurons innervating otolith organs of the squirrel monkey. III. Response dynamics. J Neurophysiol 39: 996 –1008, 1976b.
FETTIPLACE R AND FUCHS PA. Mechanisms of hair cell tuning. Annu Rev
Physiol 61: 809 – 834, 1999.
FUCHS PA AND EVANS MG. Voltage oscillations and ionic conductances in hair
cells isolated from the alligator cochlea. J Comp Physiol [A] 164: 151–163,
1988.
GOLDBERG JM. Afferent diversity and the organization of central vestibular
pathways. Exp Brain Res 130: 277–297, 2000.
GOLDBERG JM. Theoretical analysis of intercellular communication between
the vestibular type I hair cell and its calyx ending. J Neurophysiol 76:
1942–1957, 1996.
GOLDBERG JM, DESMADRYL G, BAIRD RA, AND FERNÁNDEZ C. The vestibular
nerve of the chinchilla. V. Relation between afferent discharge properties
and peripheral innervation patterns in the utricular macula. J Neurophysiol
63: 791– 804, 1990.
GOLDBERG JM AND FERNÁNDEZ C. Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. I. Resting discharge and
response to constant angular accelerations. J Neurophysiol 34: 635– 660, 1971.
GRIGUER C. KROS CJ, SANS A, AND LEHOUELLEUR J. Potassium currents in type
II vestibular hair cells isolated from the guinea-pig’s crista ampullaris.
Pflügers Arch 425: 344 –352, 1993.
GROSSMAN GE, LEIGH RJ, ABEL LA, LANSKA DJ, AND THURSTON SE. Frequency and velocity of rotational head perturbations during locomotion. Exp
Brain Res 70: 470 – 476, 1988.
HIGHSTEIN SM, RABBITT RD, AND BOYLE R. Determinants of semicircular
canal afferent response dynamics in the toadfish, Opsanus tau. J Neurophysiol 75: 575–596, 1996.
HONRUBIA V, HOFFMAN LF, SITKO S, AND SCHWARTZ IR. Anatomic and
physiological correlates in bullfrog vestibular nerve. J Neurophysiol 61:
688 –701, 1989.
HUDSPETH AJ AND LEWIS RS. Kinetic analysis of voltage- and ion-dependent
conductances in saccular hair cells of the bullfrog, Rana catesbeiana.
J Physiol (Lond) 400: 237–274, 1988.
HURLEY KM AND EATOCK RA. Characterization and modulation of a delayed
rectifier in vestibular type I hair cells. Abstracts 22nd Midwinter Meeting.
Assoc. Res. Otolaryngol., 1999, p. 1993.
KUKULJAN M, LABARCA P, AND LATORRE R. Molecular determinants of ion
conduction and inactivation in K⫹ channels. Am J Physiol Cell Physiol 268:
C535–C556, 1995.
LOWENSTEIN OE AND SAND A. The activity of the horizontal semicircular canal
of the dogfish, Scyllium canicula. J Exp Biol 13: 416 – 428, 1936.
LYSAKOWSKI A. Synaptic organization of the crista ampullaris in vertebrates.
Ann NY Acad Sci 781: 164 –182, 1996.
LYSAKOWSKI A AND GOLDBERG JM. A regional ultrastructural analysis of the
cellular and synaptic architecture in the chinchilla cristae ampullares.
J Comp Neurol 389: 419 – 443, 1997.
LYSAKOWSKI A, MINOR LB, FERNÁNDEZ C, AND GOLDBERG JM. Physiological
identification of morphologically distinct afferent classes innervating the