1Laboratoire de Neurobiologie des Réseaux Sensorimoteurs, Centre National de la Recherche Scientifique, Université Paris 5, ESA 7060, 75270 Paris Cedex 06, France; and 2Laboratory of Neurosciences, University of Mons-Hainaut, B-7000 Mons, Belgium
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ABSTRACT |
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Ris, L.,
M. Hachemaoui,
N. Vibert,
E. Godaux,
P. P. Vidal, and
L. E. Moore.
Resonance of Spike Discharge Modulation in Neurons of the Guinea
Pig Medial Vestibular Nucleus.
J. Neurophysiol. 86: 703-716, 2001.
The modulation of action potential
discharge rates is an important aspect of neuronal information
processing. In these experiments, we have attempted to determine how
effectively spike discharge modulation reflects changes in the membrane
potential in central vestibular neurons. We have measured how their
spike discharge rate was modulated by various current inputs to obtain
neuronal transfer functions. Differences in the modulation of spiking
rates were observed between neurons with a single, prominent after
hyperpolarization (AHP, type A neurons) and cells with more complex
AHPs (type B neurons). The spike discharge modulation amplitudes
increased with the frequency of the current stimulus, which was
quantitatively described by a neuronal model that showed a resonance
peak >10 Hz. Modeling of the resonance peak required two putative
potassium conductances whose properties had to be markedly dependent on the level of the membrane potential. At low frequencies (0.4 Hz), the
gain or magnitude functions of type A and B discharge rates were
similar relative to the current input. However, resting input
resistances obtained from the ratio of the membrane potential and
current were lower in type B compared with type A cells, presumably due
to a higher level of active potassium conductances at rest. The lower
input resistance of type B neurons was compensated by a twofold greater
sensitivity of their firing rate to changes in membrane potential,
which suggests that synaptic inputs on their dendritic processes would
be more efficacious. This increased sensitivity is also reflected in a
greater ability of type B neurons to synchronize with low-amplitude
sinusoidal current inputs, and in addition, their responses to steep
slope ramp stimulation are enhanced over the more linear behavior of
type A neurons. This behavior suggests that the type B MVNn are
moderately tuned active filters that promote high-frequency responses
and that type A neurons are like low-pass filters that are well suited
for the resting tonic activity of the vestibular system. However, the more sensitive and phasic type B neurons contribute to both low- and
high-frequency control as well as signal detection and would amplify
the contribution of both irregular and regular primary afferents at
high frequencies.
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INTRODUCTION |
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Although many
experimental and modeling studies have been done to characterize the
membrane properties of central neurons, there is very little
information on the biophysical properties of intact neurons in a
functioning network. The biophysical properties of neurons in their
normal network environment are difficult to assess when action
potentials are spontaneously firing. This situation especially applies
to the vestibular system where the normal input from the vestibular
hair cells causes a modulation of a spontaneous carrier discharge
present in most vestibular neurons at "rest." This modulation is
responsible for the vestibulospinal and vestibuloocular reflex, VOR
(Babalian et al. 1997; Curthoys 1982
;
Serafin et al. 1999
; Vibert et al. 1997
).
Since sensory vestibular input acts as a modulating stimulus, it is reasonable to simulate it by DC input to medial vestibular nucleus neurons (MVNn) to more precisely characterize the responses of central neurons. Our rationale is to determine how MVNn use the modulation of spontaneously occurring action potentials compared with simply responding as some type of signal detector or threshold device. Clearly the most relevant signals for network properties are action potentials and synaptic events, both of which are dependent on the entire neuronal structure. Since continuously firing neurons are likely to have different properties than those at rest, it is important to measure them during activity. This is a problem because most quantitative studies involve experimental conditions in which action potentials are either pharmacologically abolished or controlled in a voltage clamp. Thus the experiments described in this paper involve the development of quantitative techniques to use spike discharge rate as a measure of membrane properties to describe neuronal behavior in situ.
Measurements from guinea pig slices of MVNn have led to a
classification of neurons based on membrane properties as expressed by
their action potential profiles (Gallagher et al. 1985;
Johnston et al. 1994
; Serafin et al.
1991a
). MVNn constitute a continuum of cells (du Lac and
Lisberger 1995b
; Johnston et al. 1994
) in between two canonical classes that can be distinguished by the following characteristics: type A, having single large afterpotentials, and type B, which show more complex afterpotentials including fast and
slow components. In slices, the firing frequencies are reasonably
constant for both A and B neurons (see Table
1, Cv%) in contrast to their presumed behavior in intact preparations where B
units are thought to be much more irregular (Babalian et al.
1997
). Typically, these neurons are spontaneously active and
appear to function as frequency modulators in response to vestibular
input (Serafin et al. 1991a
). In addition, empirical models of type A and B neurons (Av-Ron and Vidal 1999
;
Quadroni and Knöpfel 1994
) suggest that these two
classes of cells should show a difference in their experimentally
measured frequency modulation (FM) (Ris et al. 1998
)
corresponding to a specific relation between intrinsic membrane
properties and network function. For instance, a particular type B
model, but not A, simulated a resonant behavior above 10 Hz
(Av-Ron and Vidal 1999
). The membrane properties
required for type B neuronal behavior, and the results obtained on the isolated whole brain preparation are consistent with the hypothesis that the irregular, phasic firing behavior observed in vivo
(Shimazu and Precht 1965
) is likely to be associated
with type B neurons and regular tonic activity with type A cells
(Babalian et al. 1997
).
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Previous intracellular measurements on vestibular neurons of chick
slices (du Lac and Lisberger 1995a) showed good
sinusoidal modulation of spiking rates in response to sinusoidal
current injections and essentially linear behavior. In addition, the
spike discharge modulation of vestibular neurons showed increasing
amplitudes with increasing stimulating frequency. Similarly, increasing
peak discharge rates have been observed in visual cortical neurons (Carandini et al. 1996
) for neurons that only fire
during the depolarizing part of current sine waves. Thus these latter
neurons rectify and do not show good modulation of a spontaneous
discharge rate, which is either very low or nonexistent. Nevertheless,
whether or not there is a good modulation of a spontaneous firing rate, virtually all resting neurons show an increase in their peak, instantaneous discharge rates as the current stimulation frequency increases. These results strongly suggest that the underlying membrane
potential response must also be increasing, since higher peak discharge
rates generally occur with membrane depolarization. These findings are
completely different from the passive membrane potential responses that
are obtained from the same cells, both vestibular and cortical, during
a maintained hyperpolarization that abolishes spontaneous activity.
Therefore it seems likely that the increase in peak spike discharge
with an increase in sinusoidal stimulating frequency is due to active
voltage-dependent properties of the membrane channels.
It is indeed important to emphasize the difference between
passive and active linear responses. Passive responses
always show decreasing amplitudes as the frequency is increased;
however, active linear responses may show an increase in amplitude to a peak resonant value and then decrease with frequency. We have found
that most neurons show an increase in the amplitude of spike discharge
modulation as the stimulating frequency is increased, which is likely
to be the consequence of an enhanced underlying sinusoidal membrane
potential response. At the usual spontaneous discharge rates of 30 Hz
and above, it is difficult to determine the potential response since it
is mixed with the components of the afterpotentials following each
spike. At lower spontaneous discharge rates the potential response can
be determined using spectral analysis (Carandini et al.
1996) because the dominant frequency of the signal is at the
stimulating frequency; however, this is not the case at higher
discharge rates. Therefore we have restricted our analysis to
instantaneous frequencies since we are only considering responses that
show FM for both the depolarizing and hyperpolarizing phases of the
stimulating current inputs.
In this paper, we have characterized vestibular neurons by their responses to step, ramp, and small sinusoidal inputs over a range of different steady-state conditions that are similar to those encountered in normal network behavior. This approach elicits both linear and nonlinear responses that can be used to evaluate models of intact neurons. In particular, we can quantitatively describe the linear modulation of spike discharge rates by small signals using the linear form of voltage-dependent neuronal models if we assume that the spike discharge is directly proportional to the membrane potential. Larger current inputs cannot be described by linear analysis and would require a complete nonlinear description using essentially all the voltage-dependent conductances present in the neuron. We will show that the sinusoidal linear responses of type B neurons have a greater increase in their modulation amplitude with frequency than the type A neurons. At higher frequencies the type B neurons behave like signal detectors that fire only during depolarization.
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METHODS |
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The experiments reported here were done with sharp
microelectrodes on thick (500 µ) brain stem slices (Lewis et
al. 1987, 1989
) from adult guinea pigs. The experimental
procedures were identical to those described by Serafin et al.
(1991a)
and were in accordance with the European Communities
Council directive of November 24, 1986, and the procedures issued by
the French Ministère de l'Agriculture. Only neurons from the
medial vestibular nucleus were measured, taking the border of the IVth
ventricle as a reference point (see Serafin et al.
1991a
). All measurements were done with an Axoclamp 2A system
in either the bridge or switching discontinuous current clamp (DCC)
mode (Moore et al. 1999
). The electrode resistance was
80-120 M
. Both series resistance (bridge balance) and capacitative
compensation were used. The bridge balance was verified by
demonstrating no change in the potential recording when switching
between the continuous and discontinuous modes. Each neuron was
characterized as type A or B according to their action potential
profiles (see Fig. 1A) as
previously described (Serafin et al. 1991a
). Figure 1
illustrates the traditional method of stimulating with a constant
current and recording a membrane potential response. The constant
current stimuli (Fig. 1D) consisted of sine waves from 0.2 to 20 Hz, which gave an underlying sinusoidal potential response that
was less than 10 mV peak to peak. This frequency range was used in
order to remain well below the spontaneous or carrier frequency, which
imposed the limit in our measurement of the modulated responses. In
addition, depolarizing or hyperpolarizing d.c. currents were
superimposed on the sine waves to measure responses at different steady
state membrane potentials. Finally, increasing ramp currents were
applied at different slopes up to a final steady state value.
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The typical response of these neurons at the resting potential is
illustrated in Fig. 1 by a type B neuron that was stimulated with a
constant current sine wave at 1 Hz. Figure 1C shows a fitted sine wave to the instantaneous firing rate (IF, spikes/s)
that was calculated as the reciprocal of the interval between two
successive action potentials. The IF was determined for all
stimulus protocols with a Mathematica (Wolfram 1999)
script that estimated the time intervals between action potentials
based on the time of their peak value above a threshold value of
10-0 mV. The time at the end of each interval between
action potentials was used to indicate the time for each IF
value. The amplitude of the fitted sine wave and its phase relative to
the current stimulus provide the experimentally determined frequency
domain functions discussed in the following text.
Since the maximum stimulus frequency that will modulate the spiking
rate is dependent on the level of the spontaneous discharge, which in
turn can be modified by the level of membrane depolarization, it is
necessary to experimentally determine the maximum frequency (IFm) at which modulation is still
observed. It should be emphasized that all the analyses of spike
discharge responses to sinusoidal stimulation that are discussed in
this paper were done only for those cases where instantaneous firing
rate (IF) points were obtained for both the depolarizing and
hyperpolarizing parts of each cycle of stimulation, i.e., the neuron
never stopped firing, even during the hyperpolarizing phases of the
current modulation. Thus IFm is the
maximum frequency that fits these criteria. The average spontaneous
firing rates (IFr) for type A and B
neurons were not different in the slice preparation nor their
coefficients of variation (Cv)
expressed as percentage (Table 1). A good indication of the modulation
capabilities of each neuron is the ratio between its spontaneous
discharge (IFr) and its maximum
modulation frequency (IFm). A ratio of
~3-4 was found for both type A and B neurons (Table 1). Thus this
ratio is a reflection of the sampling rate showing that each
instantaneous firing rate cycle is determined by three to four points
(of spontaneous frequency), which seems reasonable since the sampling
intervals cannot be equal. If the sampling intervals could have been
equal, the theoretical Nyquist sampling limit would require a minimum
of two sample points per cycle at the maximum frequency of the analysis
(Marmarelis and Marmarelis 1978).
The data analysis consisted of an estimation of the spontaneous or
carrier frequency and its modulation from 0.2 Hz to a maximum modulation frequency that varied from cell to cell, having a range from
3 to 15 Hz. The ratio, IF(4 Hz)/
IF(0.4 Hz)
(Table 1), of the amplitudes of the spike discharge modulations at high
(4 Hz) and low (0.4 Hz) frequencies were determined for each neuron. Selected parameters from the analysis are given in Table 1, which includes P values from unpaired t-tests (SYSTAT,
SPSS, Chicago, IL) to evaluate the differences between type A and B neurons.
The range of mean membrane potentials and the maximum frequency for which vestibular neurons show modulation is quite variable. Neurons with spontaneous firing rates above 30 Hz showed reasonable FM up to ~10 Hz. Because frequency versus current (F/I) responses are relatively linear for limited displacements, it is reasonable to assume that spiking rates are proportional to small changes of the membrane potential. This simple assumption provides a method to measure the impedance of a neuron in its natural state, for each frequency of sinusoidal stimulation, by monitoring the changes in instantaneous firing rates. In addition, our analysis has been restricted to the linear range by limiting the current input to give a peak to peak membrane potential response <10 mV. The extent of this linear IF range was verified by measuring its limits during current stimulation ramps having different slopes (see Fig. 8).
The calibration of the fitted IF responses versus the
associated membrane potential changes requires an estimate of the
peak-to-peak change in membrane potential associated with the change in
IF. Since the instantaneous firing rate is assumed to
reflect the membrane potential, this relationship between the changes
in IF (IF) and membrane potential
(
V) was assumed constant. The calibration factor was
estimated at 0.2-0.4 Hz by measuring the amplitude of the peak to peak
excursion of both parameters during one stimulus cycle beginning at the
minimum of the negative afterpotential (Fig. 1B). The
stimulus strength was limited to assure that the form of the action
potential did not change during the cycle. Only low stimulating
frequencies were suitable for estimating underlying membrane potential
changes because of the difficulty in determining the form of the
sinusoidal response as the stimulating frequency approached the spiking
rate. The ratio at low frequencies between the membrane potential
variation (
V) in the presence of action potentials and
the injected current (
I) was defined as the active input
resistance, Ractive (0.4 Hz in Table
1). The example of Fig. 1 indicates that the measured spike modulation amplitude (
IF) was 25 spikes/s (Fig. 1C),
which corresponded to a membrane potential sinusoidal deflection of
~4 mV (Fig. 1B). With a peak-to-peak current of 0.08 nA
(Fig. 1D), these values (25/4) would give a calibration
factor of 6.25 spikes · s
1 · mV
1 (
IF/
V)
that converts a modulation of 25 spikes/s to an input resistance of 4 mV/0.08 nA = 50 M
. As the peak-to-peak current underlying the
sinusoidal stimulation at each frequency is constant, any difference in
the amplitude of the action potential modulation at various frequencies
will reflect a change in the natural impedance of the neuron. If the
spike discharge modulation is assumed to be proportional to the
membrane potential modulation, one can directly infer the impedance of
the cell at each given frequency using the constant calibration factor,
IF/
V(0.4 Hz). In addition to
Ractive, an input resistance at
hyperpolarized levels, Rh, was
obtained by superimposing a long duration (500 ms) current pulse on a
steady-state hyperpolarization that had abolished action potentials
(see Table 1). The associated membrane potential change was measured
at the end of the pulse.
Thus the amplitude of the spike discharge modulation
(IF) induced at any frequency is divided by the
calibration factor,
IF/
V(0.4 Hz) (see Table
1), and then by the constant current,
I, to obtain the
impedance, Z(
V/
I), as a
function of frequency. The measurement of Z involves both
magnitude (gain) and phase functions, which are necessary for a
complete description of the data that can then be used to indicate the
presence or absence of active conductances. The calibration of the
spike discharge data are required to allow a direct comparison with
linearized neuronal models. This type of analysis provides estimates of
both the active and passive parameters of the neuronal model (see
APPENDIX) and validates the applicability of linear
analysis for this data.
Linearity of the spiking rate modulation was tested by superimposing
responses to different levels of sinusoidal current stimulation at the
same frequency (du Lac and Lisberger 1995a;
Marmarelis and Marmarelis 1978
). In general, current
levels that evoked peak membrane potential changes <5-10 mV were in a
linear range. The NonLinearFit package of Mathematica (Wolfram
Research, Champaign, IL) was used for fitting the IF data to
single frequency sine waves.
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RESULTS |
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Modulation properties of type A and B neurons
Neurons of the medial vestibular nucleus show spontaneously firing behavior in a slice preparation despite the obvious reduction of afferent input. These neurons can be distinguished from each other by the shape of their hyperpolarizing afterpotentials. Figure 1A illustrates examples of the two extreme forms of afterpotentials (type A and B), both of which are present and regularly firing in the slice preparation. To simulate the effect of afferent input, sinusoidal current was injected into these cells to observe possible response differences between type A and B neurons. Figure 1B illustrates a type B neuron response to a 1-Hz current input. Figure 1C shows a fit of the sinusoidal instantaneous frequency (IF) demonstrating excellent modulation for both the depolarizing and hyperpolarizing portions of the response.
Figure 2A shows a corresponding type A neuron that modulates its spontaneous (carrier) frequency of ~30 Hz from 20 to 40 Hz for a displacement of the membrane potential of just a few millivolts. This modulation response is limited by the carrier frequency as is indicated by the imperfect modulation shown in Fig. 2C for a 12-Hz stimulus. Figure 2B illustrates that the dynamic range of this modulation can be significantly increased by a maintained depolarization, which nearly doubles the average steady state frequency to ~57 Hz. The practical advantage of this increased frequency is seen by the relatively good modulation response at a 12-Hz current input in Fig. 2D.
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Figure 3, A and B, illustrates a type B neuron that shows good modulation at low frequencies; however, at 7.3 Hz, the modulation is insufficient even though the spontaneous carrier discharge was about threefold greater (Fig. 3C). The modulation is clearly restored if the spontaneous frequency is increased by a depolarization (Fig. 3D). Although the modulation at rest was inadequate, the instantaneous firing rates could be fitted with a sine wave that was synchronized with the stimulus current at 7.3 Hz (Fig. 3C). This illustrates an example where the amplitude of the fitted sine wave (7.3 Hz) is completely determined by the IF at the peak of the depolarization, which thus limits its accuracy. In these instances, the action potentials tend to occur on rising phase of the stimulating sine wave and thus show a phase lead. In another type B cell, synchronization on alternate cycles of a 10-Hz stimulus was observed (Fig. 4C). In this neuron, modulation was also restored by a depolarization that increased the carrier frequency (Fig. 4D). Thus although type B neurons show good modulation at low frequencies, they tend to fire in synchrony with the depolarizing phase of the stimulus when the stimulating frequency increases.
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In contrast, at stimulation frequencies approaching the spontaneous firing rate, type A neurons showed a maintained but unsynchronized, relatively constant discharge. The neuron illustrated in Fig. 5 shows that the spontaneous discharge rate can be below high stimulating frequencies at its resting potential (Fig. 5A) or above it during a depolarization (Fig. 5B). Figure 5, C and D, shows the usual type B neuronal response of marked action potential synchronization to small sinusoidal currents both at resting and depolarized levels. Figure 5B shows that at a resting discharge level of ~25 Hz, the action potential responses were one for one with the 25-Hz stimulus, and at depolarized levels, the responses to each sine wave were doublet action potentials (Fig. 5D). In type A neurons, the lack of synchronization occurs above one-half of the spontaneous frequency; however, type B neurons remain synchronized at all stimulating frequencies. Thus the transition between modulated and unmodulated responses are different for the two neuronal types.
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Spike FM at low frequencies (<10 Hz) is clearly present in both type A
and B neurons; however, type A neurons appear to have a more stable
intrinsic firing pattern, which is controlled by the steady-state value
of the membrane potential. Although type B neurons are reasonably
regular in the slice preparation, they tend to have a lower amplitude
after hyperpolarization potential with a greater sensitivity to
external stimuli, which can lead to more irregular behavior
(Av-Ron and Vidal 1999; Babalian et al.
1997
). This increased sensitivity provides a means to
synchronize responses with small stimuli and detect input signals at
relatively high frequencies.
To compare type A and B neurons, the amplitude of the spike FM
(IF) was plotted as a function of frequency and current.
Figure 6A illustrates that the
amplitude of the spike discharge modulation of this type A neuron has a
nearly constant response for frequencies from 0.2 to 14 Hz at current
amplitude levels
0.5 nA. Above this current level, the type A
response is nonlinear as indicated by an enhancement of the modulated
response with an increase in frequency. By contrast, the type B neuron,
illustrated in Fig. 6B, showed a significant enhancement of
its amplitude responses with frequency at all current levels (
0.3
nA). At these current levels the responses could be superimposed and
were therefore linear.
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To further illustrate the contrast between type A and B neurons, the
IF data were plotted relative to current rather than frequency in Fig. 6, C and D. The plots were done
for different frequencies showing that the type A IFs are
nearly superimposed for low current levels; however, at current levels
>0.3 nA, there is a nonlinear increase in
IF as the
stimulating frequency is increased (Fig. 6C). Alternatively,
the type B neuron of Fig. 6D shows an increase in
IF with stimulating frequencies >1 Hz at all levels of
current amplitude. Both type A and B neurons show modulation and linear
responses at low current levels (<0.3 nA). At higher current levels,
type A neurons may continue to show modulated responses; however, they
are clearly nonlinear. In many B neurons, it was not possible to obtain
good modulation responses at high current levels >0.3 nA, as
illustrated in Fig. 6D by the lack of points past 0.2 nA at
4 and 8 Hz. Under these conditions, the IF response is
nonlinear because of rectification. In these instances, increasing the
spontaneous frequency by depolarizing the neuron extended the linear range.
Thus in neuronal systems, linear versus nonlinear responses cannot be separated simply as a dependence of gain on frequency. However, an increase of gain with frequency is dependent on the activation of voltage-dependent conductances that can be linear or nonlinear depending on the size of the stimulus. In general, linearity can be evaluated by the usual criteria of superposition or scaling of responses relative to stimulus amplitude. Figure 6 shows that type A and B neurons are clearly different in their linear responses and that the nonlinear responses evoked in type A neurons at current levels >0.5 nA resemble the linear response of type B neurons at current levels <0.3 nA.
Ramp stimulation
The contrast in spike discharge responses (IF) to
high-frequency sinusoidal stimulation between type A and B neurons can
be dramatically illustrated by responses to ramp current
(Im) stimuli. Figure
7, A and B,
illustrates that type A neurons in a hyperpolarizing range have a
nearly linear IF response with time to a ramp current stimulus (0.8-0 nA) for both high and low slopes. The IF
response during the depolarizing part of the ramp starting at the
resting membrane potential (0-0.2 nA) has a slightly lower slope
compared with the hyperpolarized part of the ramp (
0.8-0 nA) but was
nearly linear up to the maximal current with no overshooting response. The slightly lower slope of the spiking rate increase most likely represents the activation of a potassium conductance as the neuron is
depolarized. Even though the instantaneous firing rate increased from
20 to 100 Hz, the current levels produced <20 mV membrane potential
displacements from the resting potential and appear to approximate
linearity. The lack of an overshoot for ramps with different slopes
suggests that the spike discharge response is not enhanced or
diminished by rapid changes in the current and is thus consistent with
a sinusoidal response whose amplitude is relatively constant with
frequency. Table 1 indicates that type A neurons show an average
overshoot of <2 spikes/s for a ramp duration of 600 ms.
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The type B neuron of Fig. 8, A and B, shows a greater decrease in the slope (IF/Im) for depolarizing versus hyperpolarizing currents and an overshoot in the instantaneous frequency compared with the final steady-state value that is achieved during the maintained maximum current. This overshoot is significantly enhanced at steep slopes (Fig. 8B), which reflects the augmentation in amplitude of spike discharge modulation observed with an increase (resonance) in sinusoidal stimulation frequencies. Thus during a steep ramp stimulation, the instantaneous firing rate is significantly enhanced over its steady-state value at any given potential. At the moment the dynamic stimulus stops and becomes constant, the firing rate (IF) is higher because of the high-frequency stimulus (steep slope), which then relaxes back to its steady state (DC) value. These results support the hypothesis that type B neurons are more sensitive to dynamic changes than type A neurons. Table 1 shows that the average overshoot for a 600-ms ramp was about threefold greater in type B neurons compared with type A.
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Spike discharge modulation
The low-frequency (0.4 Hz) hyperpolarized input resistances, Rh(0.4 Hz), of type A and B neurons are only slightly different (Table 1); however, at rest during the spontaneous firing of action potentials, the input resistance, Ractive(0.4 Hz), of type B cells was 60% of type A. This suggests that the voltage dependent conductances of type B neurons are more open during spontaneous activity than in type A cells, which will lead to smaller potential excursions during spike discharge modulation by current input to the soma.
Although the spike discharge sensitivity to current input of type A and
B neurons is about the same [see Table 1,
IF/
I(0.4 Hz)], the
sensitivity of type B neurons with respect to changes in the membrane
potential is enhanced nearly twofold [see
IF/
V(0.4 Hz), Table 1]. This is an
important effect for synaptic inputs on small dendrites and should
cause an overall increased sensitivity in type B neurons to afferent
synaptic input. Furthermore, the higher sensitivity of type B neurons
means that in these neurons, changes in firing rate are highly
dependent on the membrane potential and thus tend to synchronize with
an imposed sinusoidal stimulus.
Table 1 illustrates that type A neurons at rest show a 20% increase in
their modulation amplitude (IF) between 0.4 [
IF(0.4 Hz)] and 4 Hz [
IF(4 Hz)]. By
contrast type B neurons show a 40% increase over the same frequency
range. Our considerations have been limited to neurons that show good
modulation at relative low input frequencies (<10 Hz); however, in the
absence of modulation due to low firing rates or larger nonmodulating
current inputs, the maximum spiking rates were also shown to increase
with input frequency. Under these nonmodulating conditions, action
potential responses behave more like signal detectors and do not
provide information relative to a mean input that would be needed for a
"push-pull" type of equilibrium control.
Since the action potential discharge rate is dependent on the membrane
potential, the activation of ionic conductances by a membrane
depolarization would be expected to alter the spike discharge
modulation. Figure 9 (data, )
illustrates that both type A and B neurons are sensitive to a
steady-state depolarizing current. At low frequencies, the constant
current depolarization of the membrane potential decreases the
amplitude of the spike discharge modulation of type A neurons, which
then increases to approach the resting response at frequencies >10 Hz
(Fig. 9A,
). In addition Fig. 9, E and
F (
), shows that the phase functions of the modulated
responses shift to higher frequencies with depolarization. This can be
easily seen in Fig. 9E by comparing the phase at
20°, which changes from ~5 Hz at rest to >10 Hz during a depolarization.
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Figure 9B shows the spike discharge modulation
amplitude of a representative type B neuron that has a greater
amplitude increase with frequency than observed in the typical type A
neuron of Fig. 9A, both at rest (see Table 1) and during a
depolarization. The type B phase functions of Fig. 9F also
show positive values that are shifted to higher frequencies than the
corresponding phases of the type A neuron of Fig. 9E. For
example, in Fig. 9F a phase of 20° at rest occurred at
~10 Hz, which shifted to ~20 Hz during a depolarization.
Hyperpolarized neurons
The hypothesis that spike discharge modulation is a measure of the
membrane potential variation is supported by the preceding findings
showing that the spike discharge modulation is altered in the same
manner as the impedance when neurons are depolarized, namely there is a
decrease in amplitude due to the activation of ionic conductances and a
tendency to show some type of resonance phenomena (Moore et al.
1999). Similarly, a hyperpolarization should increase the input
resistance and provide a near passive control measurement. Table 1
indicates that the input resistance determined with a pulse of current
at hyperpolarized values increased about twofold over the resting input
resistance in type B neurons and somewhat less in type A cells. This
difference is consistent with the hypothesis that the mean level of
active conductances during resting spontaneous activity are more
prominent in type B compared with A neurons.
To test our use of spike discharge modulation as a measure of the
membrane potential, we hyperpolarized neurons to abolish action
potential firing and measure directly the sinusoidal membrane potential
responses without relying on spike discharge modulation. Under these
conditions, a moderate peak in the magnitude of the hyperpolarized
impedance was observed at ~5 Hz or below as illustrated in Fig. 9,
C and D. Thus since a passive neuron would not
show a peak or resonance response, these moderately hyperpolarized neurons had only part of their active conductances turned off and it
was possible to observe nonpassive resonant behavior (Moore et
al. 1999) in the absence of action potentials. This occurred because the hyperpolarization of 10-15 mV was used to just block spontaneous action potentials. A further manifestation of resonant behavior can be seen in the phase functions that are slightly positive
at low frequencies and have a zero crossing near the peak of the
resonance after which they become more negative as the frequency increases.
The gain and phase functions (data, ) shown in Fig. 9, C
and D, from neurons that were hyperpolarized to abolish
action potentials show a magnitude that begins to decrease at lower
frequencies than measured by spike discharge modulation at the resting
potentials. This result is a manifestation of increase in membrane
impedance due to a decrease in active conductances caused by the
hyperpolarization. Finally, these findings indicate that both the
modulation of the spike discharge frequency and the membrane potential
data show similar behavior, namely an increase in the magnitude of the
response as the stimulating frequency is increased. Therefore it is
reasonable to interpret the spike discharge modulation as an
approximation of changes in the membrane potential.
Quantitative interpretation of spike discharge modulation
We have presented spike discharge modulation data (Fig. 9, ) for
a range of stimulating frequencies and membrane potential levels.
Furthermore the spike discharge modulation amplitude was assumed to
have a constant relationship at all measured frequencies with membrane
potential deflections, the value of which was based on an estimation
made at 0.4 Hz. This method of calibration was chosen to test the
hypothesis that spike discharge modulation can be interpreted with
linear analysis if the stimulating current evokes membrane potential
changes that are <10 mV. The sinusoidal data were fitted with a single
sine function at each stimulation frequency to give estimated gain and
phase functions, namely an experimentally determined neuronal impedance
over the frequency range 0.4 to ~10 Hz. It is this latter estimated
impedance function that can be interpreted with a theoretical model
(APPENDIX).
Thus the experimentally estimated impedance was fitted with a
linearized neuronal model (theory, Fig. 9, - - -) to obtain estimates
of biophysical parameters (see APPENDIX). The fitting was
done with the nonlinear fitting procedures using Mathematica as
previously described (Moore et al. 1999). Furthermore
the theoretical analysis suggests that the increase in gain or
amplitude observed in the data are consistent with the linear resonant
behavior of the usual potassium voltage dependent conductances
(APPENDIX). This conclusion is important to determine the
linear versus nonlinear contributions of MVNn to the overall gain
functions of vestibular networks.
A major difficulty in this analysis was the inability to determine the
peak resonant frequency due to the frequency limitation of the
measurement. Nevertheless increasing amplitudes are indicative of
resonant phenomena and consistent with models of vestibular neurons
(Av-Ron and Vidal 1999). The data of Fig. 9 were fitted with a neuronal model having two potassium conductances
(gK1 and gK2) that were uniformly distributed
throughout the surface area of the neuron (Figs. 9, C-F).
As a further test of the use of spike discharge modulation for
impedance analysis, three neurons were investigated in the presence of
TTX to abolish action potentials and measure the membrane potential
directly at depolarized membrane potentials. These data showed behavior
similar to spike discharge modulation including a decrease in impedance
with a depolarization and a shift of a resonant peak to higher frequencies.
The ability of the preceding analysis to quantitatively describe the resting and depolarized spike discharge data, hyperpolarized responses, and results in TTX, supports the hypothesis that modulation of the discharge rate can be interpreted with a linearized neuronal model. As pointed out in METHODS, this comparison with the model requires a calibration between the firing rate and the membrane potential. Our calibration procedure requires that the hyperpolarized sinusoidal membrane potential and spike discharge data should asymptotically agree at high frequencies, as illustrated in Fig. 9. Nevertheless this calibration is difficult to evaluate at all frequencies and should be taken as an assumption of the model. This fixed calibration factor leads to a resting membrane impedance at low frequencies that was about one-half of that determined at more hyperpolarized levels.
The parameters used in the hyperpolarized impedance model fits of Fig. 9, C and D, for both type A and B neurons adequately describe the calibrated resting spike discharge modulation data. The resting and depolarized data of the type A neuron were fitted separately with a single potassium conductance having a different set of parameters (Fig. 9A); however, the type B data were fitted with a model having two potassium conductances that had the same parameters at all three potentials. Thus in both type A and B neurons, two potassium conductances were required to quantitatively fit the data at all membrane potentials. Although the magnitude functions shown in these fits are reasonable descriptions, it is clear that the phase functions for spike discharge modulation (Fig. 9, E and F) are not adequately described. This inadequacy of the phase estimates is most likely due the variable sampling that is inherent when using instantaneous firing rates (see DISCUSSION).
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DISCUSSION |
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These results suggest that both type A and B neurons of the medial
vestibular nucleus are able to modulate action potential firing rates
in a way that is dependent on their level of depolarization. Many type
B neurons were not able to modulate well because of low firing rates as
well as a tendency to show complicated plateau like action potentials.
If type B neurons are to be identified with the irregular phasic
neurons seen in vivo, then their ability to modulate would be limited
by this variability. Thus type A neurons could be identified with tonic
neurons and, as such, would be better suited as modulators of a firing
rate. On the other hand, type B neurons respond more reliably at high
frequencies. Thus they act as excellent signal detectors, in part due
to their complex repertoire of nonlinear voltage dependent channels
(Serafin et al. 1990, 1991b
). Sensitivity of modulation
varies with neurons, and there is no clear relation between the
spontaneous discharge and the highest modulation frequency, although it
must limit it.
The most significant differences between the type A and B neurons
(Table 1) were found for the active membrane input resistances at 0.4 Hz and the sensitivity of the spike discharge modulation relative to
the membrane potential (IF/
V) but not
the current (
IF/
I). An additional
difference was found for the effect of stimulation frequency on spike
discharge modulation,
IF(4 Hz)/
IF(0.4 Hz);
however, this effect was not as significant as the low-frequency findings (Table 1). This lack of significance was partly due to an
inability to compare the two cell types at higher frequencies.
The preceding analysis of instantaneous firing rate modulation lends
support to the hypothesis that some vestibular neurons behave like
moderately tuned filters, which resonate to varying degrees dependent
on individual membrane properties. This tuned or resonant behavior is
directly determined by the linearized voltage-dependent membrane
properties, which are correspondingly responsible for the gain
enhancement of action potential firing rates with the stimulus
frequency. Interestingly, although action potentials themselves are
clearly nonlinear responses, the modulation of their discharge rate
appears to be a linear process. It should be emphasized that the
linearized responses of the voltage-dependent conductances are clearly
not passive. Thus the underlying basis of these active responses are
due to fundamentally nonlinear voltage-dependent processes, which can
be linearized if the afferent inputs are sufficiently small. This type
of response in a network has been referred to as "nonlinear" gain
function that increases with frequency (Minor et al.
1999).
A recent study of the VOR (Minor et al. 1999) showed
that inputs from regularly discharging afferents to the reflex pathway had a constant gain across input frequencies; however, other inputs had
a gain that increased with frequency and were therefore modeled as a
nonlinear process. Thus it appears that the overall gain of the reflex
pathway is the sum of two processes, one linear and decreasing with
frequency like a simple linear passive filter and another that is based
on active voltage-dependent conductances, that increases with frequency
before decreasing, i.e., a resonance response or active dynamic filter.
The experiments in this paper show that the resonant responses of
individual medial vestibular nucleus neurons (MVNn) could be
responsible for a large part of these frequency-dependent gain
variations. In the case of type B neurons, the increase in the gain of
the spike FM from 0.4 to 4 Hz is ~40%. This behavior suggests that
the type B MVNn are moderately tuned active filters that promote
high-frequency responses. The marked increase in VOR gain with
increasing stimulus velocity that occurs at 4 Hz, in contrast to a
constant VOR gain at 0.5 Hz (Minor et al. 1999
), can be
compared with our ramp experiments where increasing current levels were
applied. In these experiments, the type B neurons showed greater
nonlinear increases in spike discharge at high frequencies, namely with
steep ramps, than for slow ramps that would evoke low-frequency
responses. Interestingly most type A neurons did not show this type of nonlinearity.
The spike discharge modulation results (Fig. 9) show that the
activation of voltage-dependent conductances with depolarization decreases the low-frequency impedance and shifts resonant behavior to
higher frequencies. Correspondingly, the spike discharge modulation also shows a shift of the positive phase functions to higher
frequencies. By comparison, the membrane potential responses of
hyperpolarized neurons also show increased amplitudes, but phase
functions that have little or no positive component. The values of the
hyperpolarized membrane resistances (Table 1) are lower than previously
reported values of >100 M for both type A and B neurons
(Serafin et al. 1991a
). Part of this difference may be
due to a remaining active potassium conductance as is suggested by the
slight resonance observed for the hyperpolarized neurons of Fig. 9,
C and D. Our measurements were not done at a
sufficient hyperpolarization to turn off all of the active
conductances, which could have given a larger value for the membrane
resistance, i.e., the passive impedance of the neuron. The type B
active input resistance values at rest were lower than type A
(Ractive, Table 1), which is
consistent with a greater number of active ionic channels in type B
cells. It may as well be linked with the reported difference in
dendritic structure, namely that type B neurons have a larger cell body and greater number of branching dendrites compared with type A neurons
(Serafin et al. 1993
).
The tests of linearity displayed in Fig. 6 show that the amplitude of
spike modulation for increasing currents was linear for currents <0.3
nA. The finding that the increase in modulation amplitude for the type
B neuron remains parallel for three current levels strongly supports
the argument that this effect, namely, an enhanced amplitude with
increasing frequencies, is a linear response as long as the current
stimulating level remains <0.3 nA. Thus the active voltage-dependent
conductances are exerting their effects on the steady-state linear
membrane impedance and thereby, directly influencing spike discharge
behavior. These results are consistent with previous findings on chick
vestibular neurons (du Lac and Lisberger 1995a), which
generally show a linear increase in spike modulation amplitudes as the
stimulating frequency is increased. Although spike discharge behavior
is dependent on nonlinear voltage-dependent conductances, this does not
mean that the modulated spike discharge responses with small signal
inputs require a nonlinear analysis. Since the linearization of
Hodgkin-Huxley type neuronal models generally show highly resonant
behavior, it is not surprising that the data obtained in this paper can be described in this manner, namely a piece-wise linear analysis.
If linear analysis provides an adequate description of the modulation
of instantaneous firing rate, then the underlying membrane potential
would be expected to show a similar result. It is difficult to
rigorously verify this point because the presence of action potentials
prevents the accurate measurement of sinusoidal membrane potential
responses to small current inputs. However, membrane potential
responses in the presence of few action potentials have been estimated
by Fourier analysis in cortical neurons during sinusoidal analysis
(Carandini et al. 1996). These data show a small but
clear increase in amplitude with frequency (see Figs. 7 and 8)
(Carandini et al. 1996
) that actually passes through a
maximum resonant value between 2 and 5 Hz. This resonance requires the
presence of voltage-dependent conductances and cannot be quantitatively described by a passive model; however, contrary to what happens in our
case, it is not quantitatively identical to the nonmodulated peak
instantaneous firing rates measured from the same records (Carandini et al. 1996
). Thus the discrepancy observed
in cortical neurons between the membrane potential response and
instantaneous firing rate is quantitative and appears to be a
consequence of the nonlinearities associated with a lack of uniform modulation.
A nonlinear relationship between spiking rate and injected membrane current has been observed in many neurons for current levels that clearly increase the total membrane conductance, which in turn leads to membrane potential responses that decrease nonlinearly with depolarization. Thus the relationship between spike firing rate and membrane potential cannot be linear over wide ranges of membrane potential, which would suggest that the calibration between spike discharge modulation and membrane potential could be potential dependent. Nevertheless linear approximations are probably valid for the limited changes in the membrane potential that were used in these experiments. Although spike train encoding is likely to be nonlinear for large stimulus inputs, it seems likely that some vestibular neurons operate in a stimulus range (Figs. 6-8) that allows modulated linear responses. Nevertheless it should be pointed out that the slice preparation has significantly less synaptic input than present in intact systems, where background activity may depolarize neurons to membrane potentials that could lead to more nonlinear behavior.
The model fits of Fig. 9 show that the amplitude but not the higher
frequency phase response can be reasonably well described by the linear
response. The low-frequency phase responses do indicate a phase lead
that crosses zero and becomes negative (phase lag) as the frequency
increases. After the zero crossing, there is serious deviation from the
model behavior (Fig. 9, E and F). The most likely
reason for the phase discrepancy is insufficient and variable sampling
intervals inherent in the instantaneous firing rate measurement. The
standard procedure of taking the second action potential as the point
in time for instantaneous firing rates causes a delay bias that
progressively increases with frequency. This effect is significant
because the conversion of a digital rate process to an unequally
sampled analog response (IF) assumes that the time of sampling is at
the end of the interval, which clearly gives an extra phase lag. For
similar reasons, if the first action potential is taken as the time
point, there is a phase advance that also increases in frequency. This
latter behavior is apparently the basis of the phase advance shown by
some simple oscillator models (du Lac and Lisberger
1995a), which we have duplicated by using the latter procedure.
Interestingly, a phase advance remains if the midpoint of the interval
is used. In all these cases, the estimated phase does not accurately
represent the response of a linear system; however, the standard
procedure of taking the second time point appears to better reflect the qualitative behavior of neuronal transfer functions up to moderate frequencies.
It is interesting to compare the dynamical properties of regular versus
irregular discharging canal afferents (Goldberg 2000) with those of type A and B neurons. Rotational stimulation has been
used to obtain transfer functions (Anastasio and Correia 1988
; Anastasio et al. 1985
) showing
that regular afferents have less phase difference referenced to head
velocity than irregular afferents (Fernandez and Goldberg
1971
). It has been suggested that the VOR needs a phase lead
that increases with frequency to compensate for the phase lag caused by
the delay in the reflex (Minor et al. 1999
; Tabak
et al. 1997
). Compensatory phase advances between 1 and 10 Hz
have not been consistently observed (Dickman and Correia
1989a
,b
; Highstein et al. 1996
; Rabbitt
et al. 1995
); however, galvanic stimulation in squirrel monkeys
(Goldberg et al. 1982
) and a recent study of regular
afferents in chinchillas (Hullar and Minor 1999
) have
shown such phase leads. In this latter study, the time of the
instantaneous firing rate was the midpoint between impulses, which
might exaggerate the phase advance (see preceding discussion of simple
oscillator models used in du Lac and Lisberger 1995a
).
Nevertheless, it would appear that the MVNn will increase the phase
lead up to the resonant peak, and this effect is more pronounced in
type B versus A neurons.
Despite the limitations in the phase functions, a relatively simple
linear model quantitatively describes the effect of changes in the
resting membrane potential on the spike discharge modulation, which
generally is greater in type B compared with A neurons. It would appear
that the potential dependence of the voltage-dependent conductances is
such that they are more activated at resting levels in B neurons than
in A neurons. Both types of neurons show an enhancement of resonant
behavior during a maintained depolarization, which provides a method to
enhance the high-frequency responses of the overall network behavior.
This range of dynamic filtering properties could compensate in part for
the apparent input divergence of regular and irregular afferents to
different second-order vestibular neurons (Chen-Huang et al.
1997; Goldberg 1991
, 2000
; Goldberg et
al. 1984
, 1987
) since the principal determinant of the
high-frequency responses would thus be the MVNns that would be capable
of responding to both types of afferents. Type B neurons could enhance
the flat response of regular afferents at high frequencies while type A cells could receive additional input from the more sensitive irregular inputs allowing more accurate control signals at low frequencies than
would be provided from just their regular inputs.
In addition to the increase in the linear response as the frequency is
increased, larger stimuli clearly evoke additional nonlinear behavior
that is different in type B versus A neurons. The responses to current
ramps illustrated in Figs. 7 and 8 show that the instantaneous firing
rate responses are increased over their linear responses by steep ramps
in type B cells. Similar behavior has been observed in some cortical
neurons (Stafstrom et al. 1984), which also show a wide
range of behaviors for different neuronal populations. Although the
overshooting response is clearly nonlinear behavior for type B neurons
in the medial vestibular nucleus, it is analogous to the enhanced
response seen with linear sinusoidal analysis. It is interesting that
the type A neurons appear to have nearly linear behavior for ramp
stimuli that evoke large displacements in the membrane potential.
Nevertheless large sinusoidal currents were shown to evoke nonlinear
responses in type A neurons (see Fig. 6). These results suggest that
both type A and B neurons remain linear for instantaneous firing rate
information over a limited range of input stimuli; however, type B
cells show an enhanced response at high frequencies for both linear and
nonlinear stimuli. If the VOR dynamics have both linear and nonlinear
components (Minor et al. 1999
), these results would
suggest that there could be a greater participation of type B versus A
cells in the latter.
The membrane properties (Darlington et al. 1995;
Dutia and Johnston 1998
; Gallagher et al.
1985
; Johnston et al. 1994
) that may give rise
to the different network functions have yet to be quantitatively
determined. Developmental studies suggest that tonic firing behavior
occurs principally in mature animals and is dependent on the potassium
delayed rectifier (Desmadryl et al. 1986
, 1997
;
Gamkrelidze et al. 1998
; Peusner and Giaume
1998
; Peusner et al. 1997
), which is
consistent with our finding that the potassium conductances may be
different between type A and B neurons. Other experiments on the
motoneurons found in the vestibuloocular system show a variety of
firing properties (Gueritaud 1988
) and passive
electrotonic structures that are not correlated with morphological features (Durand 1989
). Finally, there is ample evidence
from action potential behavior that vestibular neurons have a wide range of voltage-dependent conductances (de Waele et al.
1993
; du Lac and Lisberger 1995b
;
Llinás 1988
; Serafin et al. 1990
) that are capable of generating in realistic neuronal models most of the
observed excitability behavior. The quantitative approach developed in
this paper provides one way to assess the more general system behavior
(Anastasio 1998
; Robinson 1981
), which
could be extended to include more components in the VOR or other
vestibular-related reflex pathways.
In summary, the purpose of comparing model predictions with the experimental impedance function was to test the hypothesis that the linear behavior of a neuronal model with only potassium conductances can describe the frequency domain data obtained using spike discharge modulation. Neuronal models with more active ionic conductances could also be investigated and eventually used to generate action potential responses. Our initial analysis has been restricted to show that this approach can be used in the presence of spontaneous activity over a limited range of mean membrane potentials that typically occur in situ. Finally, it was found that the linear responses of vestibular neurons are capable of showing a gain increase with frequency, which is more pronounced in presumed phasic neurons (type B) compared with tonic cells (type A). Physiologically these linear responses are likely to be enhanced by the nonlinearities observed in both type A and B neurons.
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APPENDIX |
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Neuronal model
Neuronal models with active conductances can be extremely complex due to the number of different ionic conductances needed and the nature of their distribution throughout a dendritic structure. The purpose of the limited modeling done in this paper is to determine if subthreshold membrane potential changes estimated from modulation of the firing frequency can be interpreted with a minimal neuronal model having only potassium conductances. This model can quantitatively describe the spike discharge modulation evoked by small signal sinusoidal current inputs to determine if such linear membrane models would be sufficient to explain the gain enhancement at increasing frequencies observed in vestibular neurons. Our analysis shows that the resonance due to the interaction of the passive membrane properties and a single potassium conductance can increase the amplitude of the spike discharge modulation as the frequency is increased if it is assumed that there is an essentially linear relationship between the membrane potential change and modulation of discharge rate at all stimulating frequencies.
Since linearized neuronal models have been presented previously
(Saint-Mleux and Moore 2000a,b
), only a brief
description will be given here. The basic passive structure is
illustrated in Fig. 1B showing a soma and one equivalent
dendritic cylinder. One or two uniformly distributed potassium ionic
conductances were used, and these were described by a simplified
Hodgkin-Huxley set of equations (Murphey et al. 1995
). A
Rall analytical model of single neurons was used to describe cable
properties (Rall 1960
). Parameter values for active and
passive parameters were estimated with the linear analytical form of
the complete model (Moore et al. 1999
) having one or two
potassium conductances, given by the following
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(A1) |
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ACKNOWLEDGMENTS |
---|
L. Ris is Research Assistant of the Belgian National Fund for Scientific Research.
This research was supported by CNRS (France) and by grants from the
Belgian National Fund for Scientific Research, the Belgian Fund for
Scientific Medical Research, the Queen Elisabeth Fund for Medical
Research, and the Interuniversity Poles of Attraction ProgrammeBelgian State, Prime Minister's Office
Federal Office for
Scientific, Technical and Cultural Affairs.
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FOOTNOTES |
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Address for reprint requests: L. E. Moore, Laboratoire de Neurobiologie des Réseaux Sensorimoteurs, CNRS ESA 7060, 45 rue des Saint Pères, 75270 Paris Cedex 06, France (E-mail: moore{at}ccr.jussieu.fr).
Received 31 January 2001; accepted in final form 5 April 2001.
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REFERENCES |
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