Developmental Auditory Physiology Laboratory, Boys Town National Research Hospital, Omaha, Nebraska 68131
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ABSTRACT |
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Cai, Yidao, JoAnn McGee, and Edward J. Walsh. Contributions of Ion Conductances to the Onset Responses of Octopus Cells in the Ventral Cochlear Nucleus: Simulation Results. J. Neurophysiol. 83: 301-314, 2000. The onset response pattern displayed by octopus cells has been attributed to intrinsic membrane properties, low membrane impedance, and/or synaptic inputs. Although the importance of a low membrane impedance generally is acknowledged as an essential component, views differ on the role that ion channels play in producing the onset response. In this study, we use a computer model to investigate the contributions of ion channels to the responses of octopus cells. Simulations using current ramps indicate that, during the "ramp-up" stage, the membrane depolarizes, activating a low-threshold K+ channel, KLT, which increases membrane conductance and dynamically increases the current required to evoke an action potential. As a result, the model is sensitive to the rate that membrane potential changes when initiating an action potential. Results obtained when experimentally recorded spike trains of auditory-nerve fibers served as model inputs (simulating acoustic stimulation) demonstrate that a model with KLT conductance as the dominant conductance produces realistic onset response patterns. Systematically replacing the KLT conductance by a h-type conductance (which corresponds to a hyperpolarization-activated inward rectifier current, Ih) or by a leakage conductance reduces the model's sensitivity to rate of change in membrane potential, and the model's response to "acoustic stimulation" becomes more chopper-like. Increasing the h-type conductance while maintaining a large KLT conductance causes an increase in threshold to both current steps and acoustic stimulation but does not significantly affect the model's sensitivity to rate of change in membrane potential and the onset response pattern under acoustic stimulation. These findings support the idea that KLT, which is activated during depolarization, is the primary membrane conductance determining the response properties of octopus cells, and its dynamic role cannot be provided by a static membrane conductance. On the other hand, Ih, which is activated during hyperpolarization, does not play a large role in the basic onset response pattern but may regulate response threshold through its contribution to the membrane conductance.
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INTRODUCTION |
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Octopus cells make up one of the unique cell types
in the auditory system. They reside in a restricted area (the octopus
cell area) in the posteroventral cochlear nucleus (PVCN) (Osen
1969). Their large cell bodies and large but sparsely branched
dendrites are matched only by those of large multipolar stellate cells, also residing in the PVCN (Golding et al. 1995
;
Kane 1973
; Oertel et al. 1990
;
Rhode et al. 1983
; Schwartz and Kane
1977
; Smith and Rhode 1989
). Physiologically,
octopus cells usually respond at stimulus onset with a single action
potential followed by a steady-state depolarization under current
stimulation (Feng et al. 1994
; Romand
1978
) or with a major response peak early in the poststimulus
histogram (PSTH) and little or no response during the steady-state
under acoustic (tonal) stimulation in vivo (Godfrey et al.
1975
; Rhode and Smith 1986
; Rouiller and
Ryugo 1984
). Octopus cells have a very low membrane resistance,
with membrane time constants as short as 200 µs (Golding et
al. 1995
, 1999
). As a result, it is difficult to study these
neurons intracellularly, and voltage-clamp data are not available. In
response to acoustic stimuli, octopus cells show remarkable temporal
precision in their spike activity relative to stimulus onset and
therefore may play a role in the processing of pitch information in
complex stimuli (Cai et al. 1998
; Golding et al.
1995
; Oertel 1991
; Rhode 1995
).
The unique response feature of octopus cells (i.e., the onset response
pattern) has been attributed to intrinsic membrane properties, low
membrane impedance, synaptic inputs, or combinations of these
influences (Cai et al. 1997a; Evans 1998
;
Feng et al. 1994
; Golding et al. 1995
;
Levy and Kipke 1997
, 1998
). In the most commonly held
view, the low membrane impedance, coupled with a short membrane time
constant, is emphasized in the production of onset responses, which
require multiple subthreshold inputs that coincide temporally to
produce a suprathreshold response ("coincidence detection")
(Evans 1998
; Golding et al. 1995
). In accordance with this view, a large leakage conductance has been used to
represent the influence of certain identified ion conductances in one
computational model (Levy and Kipke 1997
), whereas other studies have emphasized factors like the effectiveness of synaptic inputs and dynamic spike thresholds as the principal determinants of
onset responses (Kipke and Levy 1997
; Levy and
Kipke 1998
).
Although the role of ion channels in the production of onset responses
has been recognized (Cai et al. 1997a; Feng et
al. 1994
; Ferragamo and Oertel 1998
; M. J. Ferragamo and D. Oertel, unpublished data; Golding et al.
1995
), opinions regarding their exact contributions vary.
Earlier studies emphasized the Na+ channel,
suggesting that its inactivation prevents the initiation of further
spiking events after the initial onset spike ("depolarization block") (Feng et al. 1994
; Ritz and Brownell
1982
). However, results from a brain slice preparation suggest
that action potentials are not initiated in the soma of octopus cells
(Golding et al. 1995
), and computer simulations suggest
that membrane depolarization does not necessarily lead to
depolarization block when a low-threshold K+
channel (KLT) is present (Cai
et al. 1997a
). Recently, two primary types of ion
channels/currents have been identified in octopus cells: a
KLT channel that is sensitive to
4-aminopyridine (4-AP) and
-dendrotoxin, and an inward rectifier
current (Ih) that is activated during
hyperpolarization and is sensitive to Cs+ (the
conductance corresponding to Ih will
be referred to as h-type conductance and denoted by
gIh). Golding et al. (1995
, 1999
)
demonstrated that blocking Ih with
Cs+ sharply increases the membrane resistance and
prolongs the membrane time constant 20-fold. On the other hand, using
computer simulations, Cai et al. (1997a)
demonstrated
the importance of the KLT channel in
the production and regulation of onset responses in octopus cells by
"injecting" current into model cells (which include a large h-type
conductance), confirming an earlier suggestion made by Feng et
al. (1994)
. Recent current-clamp studies also support the role
of KLT in the onset response of octopus cells.
Ferragamo and Oertel (1998)
, Ferragamo and Oertel, unpublished data,
observed a sharp increase in membrane resistance (20-fold) after
blocking KLT with
-dendrotoxin and
4-AP. Their data also revealed that action potential initiation in
octopus cells depends on the rate that membrane potential changes after
current injection (i.e., if the current is ramped, it may not produce
an action potential even if it is suprathreshold when presented as a step).
Thus it seems that two basic questions must be addressed: one is whether active ion channels merely provide a low membrane impedance (i.e., whether a low membrane impedance is sufficient to produce the response features of octopus cells), and the other is what are the contributions of KLT and Ih to the responses of octopus cells.
We address these questions using a computational model of the octopus
cell that allows us to monitor ion conductance changes without
interfering with the responses of the model cell and to simulate both
in vitro intracellular responses and in vivo physiological responses
using the same set of model parameters. In this study, we made the
KLT conductance
(gKLT) the dominant conductance in the
model initially, then gradually replaced
KLT conductance with h-type
conductance or a leakage conductance while maintaining a constant
overall resting membrane conductance or increased
gIh without changing
gKLT. Through these manipulations we
studied the contributions of KLT and
Ih, as well as whether or not the conductance mainly provided by KLT
channels might be replaced by a static (leakage) membrane conductance.
Ramped currents were used to simulate the sensitivity of octopus cells
to the rate of membrane potential change, and spike trains recorded
from auditory-nerve fibers were used to simulate acoustic stimulation.
The sensitivity of action potential initiation to rate of change in
membrane potential (Ferragamo and Oertel 1998;Ferragamo
and Oertel, unpublished data) and the onset PSTH pattern
(Godfrey et al. 1975
; Rhode and Smith 1986
) served as main criteria to evaluate the performance of
the model.
Our results further support the view that
KLT plays an important role in the
octopus cell responses and suggest that it is the most important factor
affecting their temporal response properties. It not only contributes
to the low membrane resistance, but more importantly, it dynamically
adjusts its conductance in response to stimuli. Such dynamic changes in
the KLT conductance (and thus the
overall membrane conductance) are the basis for the dynamic changes in
the effectiveness of synaptic inputs and spike threshold suggested by
Levy and Kipke (1998). In addition, we showed that the
h-type conductance is probably not an important determinant of the
transient response of octopus cells. However, a large
Ih contributes to the low membrane
resistance and may be involved in the regulation of sensitivity of the
neuron in vivo.
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METHODS |
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Model description
The basic structure of the octopus cell model used in this
study, which was based on available anatomic and physiological data
(Golding et al. 1995; Kane 1973
;
Oertel et al. 1990
; Rhode et al. 1983
;
Schwartz and Kane 1977
; ), is the same as in previous studies (Cai et al. 1997a
). However, in this study, the
relative contribution of KLT
conductance was increased and that of h-type conductance was decreased
or gIh was changed without changes to gKLT. In addition, the membrane
resistivity (Rm) was increased. We
briefly describe the model in the following text, emphasizing the
changes incorporated for this study.
As schematized in Fig. 1A, the
soma of the model neuron was 32 µm in diameter, its axon was 3 µm
in diameter and 70 µm in length, and four identical dendrites were
each 5 µm in diameter and 200 µm in length. Dendrites were modeled
as cylinders for simplicity, even though the dendrites of octopus cells
taper slightly (Golding et al. 1995; Kane
1973
; Morest et al. 1973
; Oertel et al.
1990
; Ostapoff et al. 1994
; Rhode et al.
1983
; Schwartz and Kane 1977
). The axon and the
soma were each represented by a single compartment. Each of the four
dendrites were divided into 20 sections of equal length and thus were
represented by the same number of compartments (Fig. 1B).
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The basic electrical parameters of the model were either standard
values or were selected from standard ranges (Jack et al. 1983) and adjusted to fit available physiological data.
Specifically, the membrane capacitance density
(Cm) was set to 1 µF/cm2, and
the axial resistivity (Ri) to 100
cm, as
typically reported in neuronal models (Jack et al.
1983
). In accordance with the new data that octopus cells may
have a membrane time constant as low as 200 µs (Golding et al.
1997
, 1999
) compared with the original estimate of ~1 ms
(Golding et al. 1995
), the passive membrane resistivity
(Rm) was changed from the 1 k
cm2 in the original model to the present 2 k
cm2, resulting in a smaller leakage conductance or a
higher resistance. However, the maximum conductance of the
KLT channel was increased, making it the
major factor contributing to the resting membrane conductance. As a
result, the total resting membrane conductance was increased
(resistance decreased) compared with the original model. The decision
to increase the contribution of gKLT was
based mainly on the observation that although the original model was sensitive to the ramp time during the initiation of an action potential
(Fig. 2A), the model was
not as sensitive as neurons in vitro. Doubling the
KLT conductance increased the model's
sensitivity to the ramp time (Fig. 2B). The use of a
large KLT conductance was also consistent
with previous simulation results (Cai et al. 1997a
) and
with recent experimental data (Ferragamo and Oertel 1998
; Ferragamo and Oertel, unpublished data), both of which
demonstrated that KLT plays a larger role in
shaping the responses of octopus cells than earlier experimental data
suggested (Golding et al. 1995
). The basic electrical
parameters, together with the morphological parameters, determine other
passive electrical parameters used in the model. The resting membrane
potential was set to
62 mV and was based on the range of values
observed in intracellular recordings from octopus cells (Feng et
al. 1994
; Golding et al. 1995
; Romand
1978
; Rouiller and Ryugo 1984
).
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As shown in Fig. 1C, each compartment contained a
capacitor representing membrane capacitance
(cm) and a leakage branch consisting of a
leakage conductance (gleak) and a battery
(Eleak). For passive compartments, the
leakage equilibrium potential Eleak equals
the resting membrane potential. For compartments with ion channels, one
of gleak and
Eleak is fixed, and the other is adjusted to maintain a stable resting membrane potential as in Rothman et al. (1993). As in the original model, the dendritic
compartments are passive while the soma and axon compartments contained
ion channels. For the axon compartment,
Eleak is fixed at
53 mV and gleak is adjusted to be 2.57 nS. For the
soma compartment, gleak is fixed at 16 nS,
and Eleak is adjustable, having a value of 46 mV for the basic parameter set.
The axon compartment contained exclusively Hodgkin-Huxley-type
Na+ and K+ channels, which are responsible for
generating action potentials. The soma compartment also contained these
two channels, but their maximum conductances in the soma compartment
are low, based on the suggestion that action potentials are generated
at the axon hillock in octopus cells (Golding et al.
1995). Two other ion channels (currents) were included in the
soma compartment: a low-threshold K+ channel,
KLT, and a hyperpolarization-activated
inward rectifier current, Ih, which are
known to exist in octopus cells (Ferragamo and Oertel
1998
; Ferragamo and Oertel, unpublished data; Golding et
al. 1995
). To maximize the dynamic role of the
KLT channel, its kinetics were adjusted to a
faster rate than in the original model (Cai et al.
1997a
), the voltage-activation curve was steeper, and a smaller
portion of channels are now open at rest
(gKLTmax = 0.2 S/cm2,
Bfac = 0.25, K
= 8, and
K
= 15). The
Ih kinetics were also faster than in the
original model but remained much slower than those of other channels.
To allow easier manipulation of the parameters defining the kinetics,
the method of Tabata and Ishida (1996)
was adopted to
implement Ih kinetics. The description is as
follows
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Because voltage-clamp data are not available for octopus cells,
characterization of their ion channels remains qualitative. Therefore
the kinetics of the ion channels used in the model are based on data
from other cell types. As described in Cai et al. (1997a), the kinetics of KLT
were modified from those exhibited by type II (bushy) neurons of the
ventral cochlear nucleus (Manis and Marx 1991
), and
those of Ih were based on data
obtained from a variety of other cell types [e.g., Purkinje fibers
(DiFrancesco 1981
), retinal ganglion cells
(Tabata and Ishida 1996
), and neurons of the medial
nucleus of the trapezoid body of the auditory system (Banks et
al. 1993
)]. As stated earlier, the maximum conductance of
KLT was increased considerably in the
new model. We intentionally minimized the contribution of the h-type
conductance to the resting membrane conductance in the new model as a
computational starting point, to isolate the conductance
(gKLT) that we thought to be the most
important. We then increased gradually the maximum h-type conductance
(with or without decreasing the KLT
conductance) to study the contribution of the two conductances to the
responses of octopus cells.
Auditory-nerve data collection
Both current injection (simulating in vitro experimental
conditions) and spike trains recorded from auditory-nerve (AN) fibers (simulating acoustic stimulation experiments) were used as inputs to
the model. Generally, simulated AN spike trains are used as inputs to
neuronal models of cochlear nucleus neurons (e.g., Banks and
Sachs 1991; Levy and Kipke 1997
, 1998
). However,
we chose to use experimentally recorded AN spike trains to avoid the
oversimplification that typically results from modeling the basilar
membrane stage and the inner hair cell synapse stage used to generate
simulated AN spikes.
Spike trains from AN fibers of cats using tone burst stimuli were
collected as part of a larger study involving harmonic complex stimuli
(e.g., Cai et al. 1998), following standard experimental procedures (e.g., Cai and Geisler 1996
;
Fitzakerley et al. 1994
). Briefly, adults cats ranging
from 0.5 to 2 yr of age, born and raised in the animal care facility of
this institution, were anesthetized with pentobarbital (40 mg/kg ip), a
trachea tube was inserted, and the pinna was removed. A small hole was
opened in the skull and cerebellar tissue was aspirated to expose the
auditory-nerve. The acoustic system then was calibrated. A glass
microelectrode, filled with 2 M KCl and having an impedance of ~15
M
was inserted into the nerve under visual guidance. A microdrive
was used to advance the electrode. When an AN fiber was encountered, a
frequency-threshold tuning curve was acquired, and the characteristic
frequency (CF) and spontaneous firing rate were determined. Tone bursts
were presented to the ear through a Beyer DT-48 dynamic phone. Stimuli, with rise/fall times of 5 ms, durations of 50 ms, and 120-ms repetition intervals, were incremented over an intensity range of 30-70 dB SPL in
5-dB steps and were repeated 50 times at each level. The same set of
stimuli and the same stimulus conditions were used for every fiber
encountered. The care and use of animals were approved by the
Institutional Animal Care and Use Committee of the Boys Town National
Research Hospital.
Synaptic model and application of synaptic inputs
Synapses were modeled as a battery-conductance branch (cf. Fig.
1C). Only excitatory inputs were applied to the model cell because there is no strong evidence that octopus cells receive inhibitory inputs. Results from our previous modeling study of responses to current injection showed that inhibitory inputs are not
necessary to generate the basic onset response pattern. The battery
voltage was set at 20 mV, while the dynamics of the synaptic conductance were modeled by an alpha-function (Jack et al.
1983), similar to that used by others (e.g., Banks and
Sachs 1991
; Rothman et al. 1993
)
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Spike trains from six AN fibers, collected from the same animal using
the same stimulus conditions, served as inputs to the model. For
example, if we wish to investigate the responses of the model neuron to
a tone burst of 1,000 Hz at 70 dB SPL, we use spike trains from all six
AN fibers, collected using the 1,000-Hz tone at 70 dB as stimulus. The
selected fibers had CFs between 880 and 2,970 Hz, corresponding to the
relatively wide tuning characteristics of octopus cells (Godfrey
et al. 1975; Rhode and Smith 1986
). Only fibers
having high spontaneous rates were included because octopus cells
receive inputs primarily from AN fibers with high spontaneous rates
(Liberman 1993
).
Octopus cells receive converging inputs from many AN fibers; for
example, Liberman (1993) estimated that each octopus
cell receives 64 somatic inputs. A total of 120 inputs, generated from spike trains of the six fibers (see next paragraph), were applied at
different locations on the model: 30 at the soma, 30 at the 5 proximal
dendritic compartments, and the remaining 60 at more distal dendritic
compartments. The relatively small number of somatic inputs (30)
compared with Liberman's estimate (64) was implemented to promote
computational efficiency. Although inputs from each AN fiber may span
several compartments, a tonotopical distribution is maintained with
inputs from fibers with the highest CFs applied at distal dendritic
compartments (Oertel 1997
).
To increase the total number of inputs to 120, each spike train has to
be applied to multiple (20) locations. However, the temporal order of
spike trains recorded from an AN fiber was varied at different input
locations. Because each stimulus was presented 50 times (producing 50 trials of spike trains) for each fiber, we varied the number of the
starting trial and applied the spike trains in a circular manner (e.g.,
trials 7, 8, ... , 50, 1, ... , 6) to increase the temporal
variability. This procedure ensures that no two inputs were identical
at a given moment in time even though they originate from the spike
trains obtained from the same AN fiber. The rationale for using this
approach is based on the observation that each AN fiber makes synaptic
contact with an octopus cell at multiple locations (e.g., Kane
1973). Also because each inner hair cell is innervated by
multiple afferent synapses (Spoendlin 1969
), spike
generation in all AN fibers contacting the same inner hair cell is
presumably driven by the same generator potential. Consequently spikes
of AN fibers from a common origin are statistically correlated. Our
approach simulates this association and compensates for the small
number of statistically independent inputs.
Simulation and analysis
Simulations were performed on a Pentium-133 PC running a Linux
(a PC-based Unix) operating system, using a simulation program developed in our laboratory (Cai et al. 1997b). The
program uses a text file to specify the parameters of the model,
including the electrical characteristics and the ion channels of each
compartment, as well as the connections between compartments and the
names and locations of synaptic inputs. The model then is constructed automatically during the simulation based on the parameters in the text
file. For each compartment, a partial differential equation is written,
and the program solves a system of equations using a modified
Crank-Nicholson method with a step size of 10 µs. Synaptic inputs are
stored in separate files and are accessed by the program during the
simulation. When AN fiber spike trains are used as inputs, the
repetition interval is 120 ms, the same as that used during the
collection of AN spike train data. Simulations of 50 trials take ~11
min (~0.9% real time). Action potentials were detected at the axon
compartment using a combination of threshold (
20 mV) and slope (local
maxima) criteria. Timing of action potentials, trial-by-trial changes
of membrane potentials and ion conductances were stored for later
analysis. Poststimulus time histograms (PSTHs) and interspike interval
histograms (ISIHs) also were generated as needed.
To quantify the sensitivity of the octopus cell model to changes in membrane potential during a ramped current simulation, we measured the rate of membrane potential change (mV/ms) before the initiation of an action potential (cf. Figs. 2 and 4A). For each stimulus condition, a derivative function of the soma membrane potential is obtained. There are at least two peaks that can be resolved in the derivative function even when the start of the action potential was not apparent in the membrane potential traces. The first peak occurs before the time an action potential would initiate, and the second peak occurs during the upstroke of the action potential (if an action potential is initiated) or during subsequent potential changes (if an action potential is initiated). The value of the first peak in the derivative function is taken as the rate of membrane potential change by the simulation program. We defined slope threshold as the minimum rate of membrane potential change required to initiate an action potential, using a minimum of 0.1 ms step size for the ramp time when obtaining the slope threshold (see footnote 1).
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RESULTS |
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Figure 3A shows the
responses of the model when DC currents were injected into the soma
compartment. The model had a threshold of 2.8 nA when current was
delivered as a step, consistent with the finding that octopus cells
always have a current threshold of 2 nA under whole cell clamp
condition (Golding et al. 1999
). When an above-threshold
depolarizing current was used, the model produced an action potential
at the stimulus onset followed by membrane depolarization during the
steady state. This is typical of responses of octopus cells
(Feng et al. 1994
; Ferragamo and Oertel
1998
; Ferragamo and Oertel, unpublished data; Golding et al. 1995
, 1999
). When the injected current was hyperpolarizing, the model produced an initial hyperpolarization followed by a sag
toward the resting membrane potential and, depending on the current
level, an anode break action potential at the offset of the stimulus.
This behavior is typical of octopus cells (Golding et al. 1995
,
1999
). The current-voltage relationship (Fig. 3B) exhibited strong rectification, that is also similar to findings obtained experimentally (Ferragamo and Oertel 1998
;
Ferragamo and Oertel, unpublished data; Golding et al. 1995
,
1999
). In the depolarizing range, the membrane potential
changed very little as the level of current was increased. In the
hyperpolarizing range, the slope (impedance) was much larger than that
in the depolarizing range but was small compared with those from other types of neurons in the cochlear nucleus (Oertel 1983, 1997
).
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Responses of the model to current ramps
Simulated responses were obtained to ramped currents, which were
injected into the soma compartment. Different levels of current were
used (3.5, 6, and 9 nA), and each was capable of initiating an action
potential when presented as a step. The responses of the model to 6-nA
current ramps are shown in Fig.
4A. The model produced action
potentials to current ramped over the range from 0.5 to 2.0 ms.
However, only subthreshold responses were observed when ramp time was
2.5 ms. Because the current injection initiates action potentials
when presented as a step, this result suggests that the model is
sensitive to the ramp time (or rate of change in membrane potential,
see Fig. 4D). Such sensitivity is characteristic of octopus
cells (Ferragamo and Oertel 1998
; Ferragamo and Oertel, unpublished data). The action potentials, measured at the soma compartment, are brief, measuring only ~0.4 ms at the base. They are
also very small in size, measuring no more than 20-30 mV from the
resting state or ~20 mV above the steady-state depolarization level.
These features are also similar to those observed experimentally (e.g.,
Golding et al. 1999
).
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Changes in KLT conductance that
correspond to changes in membrane potential during the injection of the
ramped current are shown in Fig. 4B. It is clear that the
KLT conductance underwent large
changes for all ramp times tested, similar to previous results obtained
using current steps (Cai et al. 1997a). In particular, for ramp times in which the model failed to produce action potentials, gKLT changed from 120 to ~350 nS,
nearly tripling its contribution to the membrane conductance. Such a
dynamic change in the KLT conductance
increased the overall membrane conductance and thus increased the level
of current required to initiate an action potential. As ramp times were
shortened (current was delivered faster), the
KLT conductance increased at a faster
rate, and, as a result, more current was needed to depolarize the
membrane. When the current delivery was fast enough to outpace the
increase in KLT conductance, an action
potential was generated. For long ramp times, it would appear that the
current was not delivered at an adequately fast rate (i.e., the ramp
was too long) to overcome the dynamic increase in membrane conductance
and to produce an action potential.
In contrast, the h-type conductance changed at a much slower pace, and there was virtually no difference in the dynamics of gIh, whether or not an action potential was initiated (Fig. 4C). Although the h-type conductance was minimized intentionally in the parameter set used to produce the responses shown in Fig. 4, the slow time course of changes in gIh suggests that even when gIh is large, it is unlikely to significantly influence the transient response of the model.
The interaction between the injected current and the dynamically
increased membrane conductance is reflected in the rate that membrane
potential subsequently changes. In Fig. 4D, we show the relationship between the rate of membrane potential change and the peak
membrane potential relative to the resting potential produced by
current injection into the soma compartment. It is clear that a minimum
rate of potential change (slope threshold) must be attained before the
model neuron produces an action potential. When the rate of potential
change is above ~10 mV/ms, an action potential is always evoked, and
for faster or slower rates of potential change, an increase in the rate
of change in membrane potential resulted in only a slight increase in
the peak height of the depolarization or the action potential. As the
level of current was increased, the maximum ramp time that can evoke an action potential increased, but the slope threshold, defined as the
minimum rate of potential change needed to evoke an action potential,
did not change. For all three current levels used (3.5, 6, and 9 nA),
the slope threshold was ~10 mV/ms. Such independence of the slope
threshold on the level of injected current has also been observed in
experimental studies (Ferragamo and Oertel 1998, unpublished data).1
Effects of increasing the h-type conductance
To further study the roles of KLT
and Ih in shaping the octopus cell's
responses and particularly its sensitivity to changes in membrane
potential, the relative proportion of the
KLT and the h-type conductances was
varied. In the first set of manipulations, we replaced part of
KLT conductance with h-type
conductance: the reduction of KLT's
contribution to the resting membrane conductance was balanced by that
of Ih, thus keeping the resting
membrane conductance constant. When the contribution of the h-type
conductance to the resting membrane conductance was increased (and that
of KLT conductance was decreased), the
current threshold (measured using step currents) decreased slightly,
from the original 2.8 to 2.1 nA when 75%
KLT was replaced. More significantly,
the minimum rate of potential change required to initiate action
potentials (slope threshold) decreased, for all current levels (Fig.
5A). When 25% of
KLT was replaced, the slope threshold
began to show dependence on the level of current used, i.e., at higher
levels, a smaller rate of change was required to initiate an action
potential. Such dependence was more obvious when 50% of
KLT was replaced. When 75% of
KLT was replaced and a 9-nA current
injection was simulated, the model neuron produced action potentials
regardless of ramp time (
50 ms). This suggests that spike production
by the modified model was not sensitive to the rate of potential change
induced by the current. Consequently, its slope threshold is near zero
(Fig. 5A).
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Membrane potential changes in the soma compartment following the
injection of 6- and 9-nA currents (4-ms ramp time) are shown in Fig. 5,
B and C, respectively. When 50% of the
KLT conductance was replaced with the
h-type conductance, the model neuron produced a single action potential
with a 6-nA current (Fig. 5B, ) and two action potentials
with a 9-nA current (Fig. 5C,
). However, when 75% of the
KLT conductance was replaced with the
h-type conductance, five action potentials were produced in the first
20-ms time period when stimulated with a 6-nA current (Fig.
5B, - - -), making the responses of the model neuron more
"chopper-like" under these conditions. When the current level was
increased to 9 nA, the model responded with a sustained chopping
pattern (Fig. 5C, - - -). The effect of replacing
gKLT with
gIh also is reflected in the slight
increase in the width of action potentials generated by the model
(Figs. 4, and 5, B and C). It should be noted
that repetitive firing is not observed when
KLT is blocked partially by 4-AP, and
the width of the action potential increases dramatically after the
KLT blockage (Golding et al.
1999
). These differences might be attributed to a
voltage-dependent Ca2+ channel (which was not
included in the model, see DISCUSSION). The much higher
currents used in the simulation might also be partially responsible for
the repetitive firing. Under these conditions, the Hodgkin-Huxley type
Na+ and K+ channels in the
axon and soma compartments become the dominant factor in determining
the model neuron's response, thus generating a chopping pattern
similar to those of stellate cells (Banks and Sachs
1991
). Nonetheless the decreased slope threshold and the increased tendency of firing multiple spikes after
gKLT was replaced by
gIh further support the idea that
KLT is important to the octopus cell's sensitivity to the rate of change in membrane potential and
that Ih contributes little to this
aspect of the octopus cell's response.
Because an increase of h-type conductance always is accompanied by a decrease in KLT conductance in the h-type conductance substitution experiment, it is unclear whether the change in response is due to increased gIh or decreased gKLT, as both are varied simultaneously. To address this question, we examine the model's responses when gIh is increased while maintaining constant gKLT. Note that a side effect of this manipulation is that the overall membrane conductance is increased.
In Fig. 6A, we show the slope
threshold as a function of the ratio of
gIh and
gKLT at rest, when the resting
KLT conductance was 120 () and 60 nS
(- - -). It is clear that the slope threshold only decreased slightly
over a relatively wide range of
gIh/gKLT ratios. In contrast, there was a significant decrease in slope threshold when the resting KLT
conductance was changed from 120 to 60 nS over the same
gIh/gKLT
range. Consistent with results in Fig. 5A, the slope
threshold also showed dependence on current level when the
KLT conductance was decreased
(- - -).
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When the resting KLT conductance was maintained at 120 nS, the single action potential pattern always was maintained regardless of the value of the h-type conductance and the current level (maximum current used was 15 nA). However, when the resting KLT conductance was reduced to 60 nS, multiple action potentials were elicited for currents 9.2-11 nA, depending on the value of h-type conductance. Even though the increased overall membrane conductance was a complicating factor in this manipulation, the relative small change in slope threshold over a relatively wide range of gIh/gKLT ratios as well as the decreased slope thresholds and increased tendency of multiple firing when resting KLT conductance was changed from 120 to 60 nS, support the idea that the decrease in slope threshold and the multiple firing observed in the h-type conductance substitution experiment (Fig. 5A) are mainly due to the decrease in KLT conductance not the increase in h-type conductance. Thus KLT is the key to the octopus cell's sensitivity to changes in membrane potential and its transient responses.
Although a wide range in h-type conductance does not affect the slope
threshold, the h-type conductance does affect the absolute threshold
(when current was injected as a step; Fig. 6B), especially when the KLT conductance is 120 nS at
rest. As the
gIh/gKLT
ratio increases, the current threshold also increases presumably due to
the increase in overall membrane conductance. The value of the h-type
conductance also affects size and width of the action potential. As
gIh increases, reductions in both size
and width of the action potential are observed that are consistent with the increase in size and width observed when
Ih was blocked by Cs+ (Golding et al. 1999). The
exact amounts depend on gIh and
gKLT and kinetics of
KLT and
Ih. For example, when the
KLT conductance is 120 nS at rest and
the resting h-type conductance was increased from ~4 to 120 nS, the
size and the width of the action potential decreased by
and
, respectively. In general, factors that increase the
membrane conductance can reduce the size and the width of the action potential.
Effects of replacing the KLT conductance with a leakage conductance
To address the question whether the
KLT conductance can be replaced with a
static (leakage) conductance, we gradually replaced the
KLT conductance with a membrane
leakage conductance while keeping the resting membrane conductance
constant, again using the slope threshold as the metric of sensitivity.
As shown in Fig. 7, the results are
similar to those observed when KLT
conductance was replaced by the h-type conductance. In fact, they are
almost identical. The current threshold also decreased slightly as the KLT conductance was replaced with a
leakage conductance. In addition, multiple spikes were evoked when
50% of KLT conductance was replaced with a leakage conductance and current levels were
6 nA. Similarities such as these are not surprising when one considers the slow kinetics of the h-type conductance and the short ramp time implemented in these
simulations (usually <10 ms). These results suggest that KLT not only contributes to the low
membrane resistance but, more importantly, dynamically regulates the
cell's response to inputs. Such a dynamic role cannot be provided by a
static leakage conductance.
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Effect of the speeds of KLT and Ih kinetics
Figure 8A shows the slope threshold as a function of Bfac (the scaling factor that controls the KLT kinetics), using the basic parameters described in METHODS. Larger Bfac (corresponding to slower KLT kinetics) yielded lower slope thresholds. As channel kinetics speed up (Bfac smaller), slope thresholds increased. It should be noted that the absolute current threshold also increased as kinetics became faster, changing from 2.1 nA when Bfac = 1 to 2.8 nA when Bfac = 0.25. When Bfac was changed from 0.1 to 0.05, the current threshold jumped from 3.8 to 5.1 nA.
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Contrary to results obtained when KLT kinetics were varied, changes in both the slope threshold and current threshold were minimal when Ih kinetics were made faster or slower by selecting different Ihfac values (Fig. 8B). This was investigated using the basic parameter set (where gIh is minimized, gIh/gKLT = 0.03) as well as under conditions when the resting h-type conductance was increased to 25, 50, 100, and 200% of the KLT conductance (the resting KLT conductance was kept constant at 120 nS). Simulation results with selected conditions are presented in Fig. 8B, for a current level of 6 nA. We also observed no difference in current threshold when the Ih kinetics were changed regardless of the gIh/gKLT ratio, although increasing gIh/gKLT did increase the current threshold (cf. Fig. 6B).
Simulation of acoustical stimulation
Although the model produces realistic responses to simulated current stimulation, it is very important that the model also faithfully reflect in vivo responses to "acoustic stimulation." In this section, we examine the model's responses to spike trains of auditory-nerve fibers recorded experimentally using tone burst stimulation.
When the spike trains recorded in response to a 500-Hz tone burst
served as inputs to the model, the model neuron responded with a
threshold of 60 dB SPL and phase-locked to the input signal, as is
evident in the PSTH at 70 dB SPL (Fig.
9A). Such spike entrainment is
typical for octopus cells at low stimulus frequencies (up to a maximum
frequency of 500-2,000 Hz) (Godfrey et al. 1975;
Rhode and Greenberg 1992
). At higher stimulus
frequencies, octopus cells usually respond to stimuli with a major
onset peak in the PSTH. Depending on the steady-state discharge
activity, the PSTHs exhibit OI (little or no
steady-state response) or OL (steady-state
response >10 spikes/s) profiles. Both types of PSTH patterns have been observed from physiologically characterized and morphologically identified octopus cells (Feng et al. 1994
; Rhode
et al. 1983
; Rouiller and Ryugo 1984
). When the
stimulus frequency was 1,000 Hz, the same model system, with no change
in parameters, responded at stimulus onset only (Fig. 9,
B-D). Little steady-state activity was produced during the
50-ms stimulus duration when the stimulus level was incremented from
threshold at this frequency (35 dB SPL) to 70 dB SPL. This response
pattern is classified as an OI response. As the
stimulus level was increased, the latency of the responses also
decreased. These characteristics are similar to those observed
experimentally and suggest that the model functions realistically under
a variety of conditions.
|
The changes in the response of the model neuron to acoustic stimulation
when a large portion of the KLT
conductance was replaced by the h-type conductance are shown in Fig.
10. The same AN fiber spike trains
collected using a 1,000-Hz tone at 70 dB SPL (cf. Fig. 9D)
were used as inputs to the altered model. When the
KLT conductance was replaced gradually
by the h-type conductance, spikes began to appear during the steady
state, and also a second peak emerged after the initial onset peak.
When 75% of the KLT conductance was
replaced, there was substantial activity during the steady state and
the second response mode was observed. Response patterns like these are
classified as OC (onset chopper), and typically
are produced by large multipolar stellate cells in the PVCN
(Smith and Rhode 1989). Such OC
PSTH response patterns are also consistent with the multiple spike
pattern obtained under current stimulation when significant portions of
the KLT conductance are replaced by
the h-type conductance (Fig. 5, B and C).
|
When the h-type conductance was increased and the KLT conductance was unchanged, the model maintained its onset response pattern; however, the threshold was increased (by ~15 dB at 1,000 Hz), as might be expected, due to the increase in overall resting membrane conductance. Figure 11 shows the response of the model neuron when the resting h-type conductance equals the resting KLT conductance. To achieve a similar response threshold to acoustic stimulation, we increased individual synaptic conductance by 25% to 4.6 nS (G = 12.5). It is clear that the model responses to both 500- and 1,000-Hz tone bursts are very similar to those before the increase of the h-type conductance (cf. Fig. 9). This result, together with those in Figs. 9 and 10, suggest that realistic PSTH response patterns can be simulated as long as a large KLT conductance is incorporated in the model.
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DISCUSSION |
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Contributions of the KLT and the h-type conductances
KLT APPEARS TO BE THE MAIN CONTRIBUTOR
TO THE OCTOPUS CELL'S RESPONSE CHARACTERISTICS.
In this study, we implemented a computer model to simulate the
responses of octopus cells and focused on sensitivity to the rate that
membrane potential changes after ramped current stimulation and on the
temporal response properties produced by acoustic stimulation. Our
simulations suggest that KLT is an
important factor underlying the octopus cell's sensitivity to the rate
of change in membrane potential under current stimulation conditions.
When an otherwise sufficient amount of current is delivered to the
model neuron over a relatively long time, the model fails to initiate
an action potential (Fig. 4). This is, presumably, the consequence of a fast KLT activation, i.e., the
concomitant increase in KLT
conductance increased the overall membrane conductance and thus the
amount of current required to initiate an action potential. When the KLT conductance was decreased, with
(Fig. 6A also Fig. 2) or without a change in the overall
resting membrane conductance (Fig. 5), the sensitivity of the model
neuron to the rate that membrane potential changes decreases. This
finding is similar to the effect produced by blocking
KLT with -dendrotoxin and 4-AP
(Ferragamo and Oertel 1998
; Ferragamo and Oertel,
unpublished data).
KLT AND IH
OPERATE IN DIFFERENT MEMBRANE POTENTIAL RANGES.
Because KLT is activated during
depolarization and Ih is activated
during hyperpolarization, both are active in octopus cells, but they
operate in different ranges. In the depolarizing range, the
KLT conductance dominates the membrane
conductance, which is consistent with the data of Ferragamo and Oertel
1998; Ferragamo and Oertel, unpublished data. In the hyperpolarizing
range, the h-type conductance dominates the membrane conductance, which
is consistent with the data of Golding et al. (1995
,
1999
).
POSSIBLE ROLE OF IH.
Because there is no strong evidence suggesting the existence of
inhibitory inputs on octopus cells (Golding et al. 1995;
Saint Marie et al. 1991
; Wenthold et al. 1986
,
1987
; Wickesberg et al. 1991
), it is reasonable
to conclude that octopus cells operate mainly in the depolarizing range
under normal physiological conditions, thus limiting the role that
Ih plays in shaping octopus cell
response properties. This is also consistent with simulation results
showing that the basic onset responses of octopus cells (both
intracellular under current stimulation or in vivo under acoustic
stimulation) do not require a substantial
Ih contribution (Figs. 3, 4, and 9).
Role of a low membrane resistance and synaptic inputs
There is no doubt that a low membrane resistance (large membrane
conductance) is important in octopus cell responses. This is supported
by both experimental findings (Ferragamo and Oertel 1998; Ferragamo and
Oertel, unpublished data; Golding et al. 1995
, 1999
) and
computational simulations that implement low membrane resistance as
their main feature (Cai et al. 1997a
; Evans
1998
; Levy and Kipke 1997
). Because of this low
membrane resistance, octopus cells require highly synchronized inputs
to produce an action potential (i.e., "coincidence detection").
Individual synaptic inputs evoke small, brief synaptic events that are
generally insufficient to trigger an action potential (Golding
et al. 1995
). However, a low membrane resistance alone produces
realistic responses under only limited conditions (Cai et al.
1997a
; Evans 1998
). In this study, when
KLT conductance was replaced by a
leakage conductance, the model neuron exhibited decreased sensitivity
to the rate of change in membrane potential (Fig. 7) and generated
multiple action potentials instead of a single action potential when
current injection was simulated. These results suggest that
KLT plays a dynamic role in
the responses of octopus cells. The dynamic increase in conductance
generated by ion channel(s) to maintain a low-resistance environment
(relative to the strength of the stimulus) is more important than a
large static leakage conductance especially at higher stimulus levels.
Theoretically, such a dynamic role can be provided by other
conductances (e.g., the Hodgkin-Huxley type K+
channel). For example, the K+ channel, like the
KLT, also is activated on
depolarization and is not inactivating. Its conductance undergoes large
changes during the action potential in a manner similar to
KLT conductance and part of the effect
is maintained during the steady-state responses (cf. Fig. 6 of
Cai et al. 1997a). In our model, the maximum
K+ conductance is small, making its contribution
to the overall membrane conductance very small. In the Levy-Kipke model
(Levy and Kipke 1997
, 1998
),
KLT is not included but the maximum
K+ conductance is large. As a result, the
K+ channel might have played a similar role in
their model as KLT plays in our model.
Recently Levy and Kipke (1998) emphasized the importance
of synaptic effectiveness (the ratio of the synaptic conductance to the
leakage conductance) and dynamic spike threshold as factors shaping
octopus cell responses. According to them, thresholds are low at
stimulus onset but increase as the membrane is depolarized during the
steady-state, resulting in a decrease in synaptic effectiveness. We
agree with this general explanation but offer an alternative mechanism
for its underlying basis. In both the Kipke and Levy (1997)
model and our model, increasing synaptic strength
increases steady-state firing rate, producing OL
responses instead of OI patterns. Further
increases in synaptic strength result in an increase in spontaneous
firing rate and produce responses that are not observed experimentally
in octopus cells. Our simulation results suggest that the basis for the
decreased synaptic effectiveness and increased threshold during the
steady state is the dynamic increase in membrane conductance, which in
turn is due to the kinetics of the KLT
channel (Fig. 4).
Model parameters
ION CHANNELS AND THEIR KINETICS.
As partly demonstrated in the simulation results, the model neuron
produces onset responses over a wide range of model parameters under
both current or acoustic stimulation conditions, although the onset
PSTH pattern is more tolerant to parameter changes than is the slope
threshold measurement. We do not claim that this model fully represents
the biophysical basis of octopus cell function. This is largely the
consequence of the fact that many of the octopus cell's
characteristics, especially the kinetics of ion channels, are not
known. As a result, assumptions made in this study about channel
kinetics were based on characteristics of the same ion channels that
have been studied in other cell types in the auditory system or
elsewhere. Additionally, some channels that are known to be expressed
in octopus cells were not incorporated into our model because too
little is known about their relative role(s) during activation. For
example, the experimental data of Golding et al. (1999)
suggest the existence of a relatively slow, voltage-sensitive Ca2+ channel that is activated in a depolarizing
range that is higher than for KLT.
Because this conductance does not contribute significantly to the
membrane conductance, its influence on the transient response of
octopus cells must be limited. This channel, if implemented, should
serve to suppress the repetitive firing and dramatically broaden the
width of action potentials in our model when
KLT conductance is replaced by h-type
conductance (Fig. 5).
MEMBRANE CONDUCTANCE AND MEMBRANE TIME CONSTANTS. Our model produces realistic responses to both current stimulation and acoustic stimulation even when tested over a wide range of resting membrane conductances. This is not surprising because the events that occur after stimulus onset are largely determined by the dynamics of ion channel(s), particularly KLT. To maintain high energy efficiency and/or sensitivity to low-level stimuli, it is desirable to have a relatively small resting membrane conductance (or a relatively large resistance) although the exact value may be large in comparison to other types of neurons.
In experimental studies, the membrane time constant usually is estimated from the time course of membrane potential changes in response to a large hyperpolarizing current. Because octopus cells have unusual characteristics and because they primarily operate in the depolarizing range in vivo, one may not be able to accurately estimate the resting membrane resistance from the membrane time constant, although a short membrane time constant may still imply a low resting membrane resistance. ![]() |
ACKNOWLEDGMENTS |
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The authors thank Dr. Mike J. Ferragamo for helpful discussions, L. Song and Y. Zhang for assistance during data collection, and two reviewers for criticisms and suggestions that helped to improve the manuscript.
This work was supported by National Institute on Deafness and Other Communication Disorders Grants DC-01007 and DC-00982.
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FOOTNOTES |
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Present address and address for reprint requests: Y. Cai, Dept. of Neurobiology and Anatomy, The University of Texas-Houston Medical School, 6431 Fannin St., Suite 7.046, Houston, TX 77030.E-mail: ycai{at}nba19.med.uth.tmc.edu
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.
1 Such independence of slope threshold on stimulus level is relative and does not hold for stimuli that are very short or near current threshold at least in our simulations. Under those conditions, a faster rate of potential change is need to initiate an action potential.
As shown in Fig. 4D, although the rate of change in membrane potential (dV/dt) changed continuously, the peak membrane potential jumped as the rate of change in membrane potential was increased. The jump occurred at about the same membrane potential for different levels of stimuli. A possible explanation is that a certain membrane potential level must be reached before the spiking channels (mainly the Na+ channel in the axon compartment) open and initiate an action potential. However, whether that membrane potential level can be reached is controlled by other factors, which are reflected in the dV/dt measure. By changing the kinetics of the Na+ channel in the axon compartment, we were able to change the membrane potential at which the jump occurs during simulation. Thus the use of the term "slope threshold" is not intended to reflect the underlying mechanism and should not be interpreted as such.
Received 19 July 1999; accepted in final form 23 September 1999.
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REFERENCES |
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