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The Journal of Neuroscience, July 15, 1999, 19(14):6090-6101
Synaptic Control of Spiking in Cerebellar Purkinje Cells: Dynamic
Current Clamp Based on Model Conductances
Dieter
Jaeger1 and
James M.
Bower2
1 Department of Biology, Emory University, Atlanta,
Georgia 30322, and 2 Division of Biology, California
Institute of Technology, Pasadena, California 91125
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ABSTRACT |
Previous simulations using a realistic model of a cerebellar
Purkinje cell suggested that synaptic control of somatic spiking in
this cell type is mediated by voltage-gated intrinsic conductances and
that inhibitory rather than excitatory synaptic inputs are more
influential in controlling spike timing. In this paper, we have tested
these predictions physiologically using dynamic current clamping to
apply model-derived synaptic conductances to Purkinje cells in
vitro. As predicted by the model, this input transformed the
in vitro pattern of spiking into a different spike
pattern typically observed in vivo. A net inhibitory
synaptic current was required to achieve such spiking, indicating the
presence of strong intrinsic depolarizing currents. Spike-triggered
averaging confirmed that the length of individual intervals between
spikes was correlated to the amplitude of the inhibitory conductance but was not influenced by excitatory inputs. Through repeated presentation of identical stimuli, we determined that the output spike
rate was very sensitive to the relative balance of excitation and
inhibition in the input conductances. In contrast, the accuracy of
spike timing was dependent on input amplitude and was independent of
spike rate. Thus, information could be encoded in Purkinje cell spiking
in a precise spike time code and a rate code at the same time. We
conclude that Purkinje cell responses to synaptic input are strongly
dependent on active somatic and dendritic properties and that theories
of cerebellar function likely need to incorporate single-cell dynamics
to a greater degree than is customary.
Key words:
cerebellum; Purkinje cell; synapse; excitation; inhibition; dynamic clamp; modeling; in vitro; whole
cell
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INTRODUCTION |
The near-crystalline anatomical
organization of cerebellar cortex has traditionally been the main
impetus for theoretical considerations of cerebellar function (Marr,
1969
; Albus, 1971). In these theories, single neurons are primarily
treated as integrate-and-fire devices, a treatment that is still
customary in large-scale theories of network function. Over the last 20 years, however, it has been well established that Purkinje cells have
complex intrinsic dynamical properties (Llinás and Sugimori,
1980a, 1992). Most notably, a large voltage-gated calcium conductance
is capable of producing dendritic plateau potentials and calcium spikes
(Llinás and Sugimori, 1980b). The Purkinje cell takes a central
position in theories of cerebellar function, because it integrates the
various sources of input to cerebellar cortex and provides its only
source of output. Therefore, a large contribution of active intrinsic
properties of Purkinje cells in synaptic integration could be a key
element in the elusive algorithm of cerebellar cortical computation. To examine how spike responses may be under the combined control of
intrinsic properties and synaptic inputs, we use an interactive approach of computer modeling and physiological recordings.
In previous studies, we have developed a realistic model of a single
Purkinje cell to establish a basis for considering the functional
significance of its active properties (De Schutter and Bower, 1994a).
The model was constructed using the morphology of a real Purkinje cell
(Rapp et al., 1994) and includes the full set of voltage-gated
conductances identified to date in this neuron. It was tuned to
replicate physiological current injection data obtained from the
brain-slice preparation (De Schutter and Bower, 1994a) and was
subsequently tested by comparing its response to synaptic input with
the activity found in real in vivo Purkinje cells (De
Schutter and Bower, 1994b). It was found that the model quite closely
replicates typical Purkinje cell responses to synaptic input (De
Schutter and Bower, 1994c).
Recently, we have more closely analyzed the way in which synaptic input
influences the somatic spiking of the model (Jaeger et al., 1997). We
found that the model could only generate typical in vivo
spiking patterns, when the average inhibitory synaptic current exceeded
the excitatory current. This requires the presence of a continuous
baseline of inhibitory synaptic input. Furthermore, the model predicts
that the largest contribution to fluctuations in the membrane potential
in the soma as well as the dendritic tree is made by the large
intrinsic voltage-dependent currents rather than by the currents
associated with either excitatory or inhibitory synaptic inputs.
Modeling predictions rest on many assumptions made in the construction
of the model (Bhalla and Bower, 1993). Therefore, modeling results need
to be tested experimentally before they can be accepted. The present
study was designed to allow such testing of our model predictions
regarding the involvement of active cell properties in synaptic
integration. To replicate the conditions of the model as closely as
possible, we chose to apply synaptic conductances generated by the
model to Purkinje cells in vitro using the dynamic current-clamp technique (Sharp et al., 1993). As in the model, the
addition of a stochastic baseline of excitatory and inhibitory input
resulted in a transition from an in vitro bursting spike pattern to ongoing irregular spiking, which closely resembles spontaneous spiking recorded in vivo (Jaeger and Bower,
1994). The condition of continuous random input used here and in our previous modeling study (Jaeger et al., 1997) reflects our best estimate of synaptic activity expected to be present as a continuous baseline in vivo. Because little is known about the specific
input modulations occurring during task-related behavior, we restrict our analysis to a stochastic activation of all inputs. By manipulating the balance and amplitude of excitatory and inhibitory inputs, we
address the question of how output spike rate and spike timing reflect
synaptic input patterns in the presence of large intrinsic active properties.
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MATERIALS AND METHODS |
Slice preparation and whole-cell recording. All
animal procedures fully complied with the National Institutes of Health
guidelines on animal care and use. Whole-cell recordings were obtained
from the somata of Purkinje cells in 300 µm sagittal slices from 2- to 4-week-old rats under visual control using a fixed-stage microscope. The slice medium contained (in mM): NaCl 124, KCl 5, NaHCO3 26, K2HPO4 1.2, CaCl2 2.4, MgSO4 1.3, and glucose 10. Electrodes were filled with (in mM): K gluconate 120, KCl
10, HEPES 10, EGTA 10, CaCl 2, MgCl 2, Na-ATP 2, and Na-GTP 0.2, with
impedances ranging from 6 to 12 M
. Recordings were obtained at
32°C. To study the effects of simulated synaptic input in isolation,
we blocked endogenous excitatory and inhibitory inputs with 5 µM CNQX and 40 µM picrotoxin, respectively.
Implementation of the dynamic clamp. Synaptic conductances
obtained from our Purkinje cell model were applied to Purkinje cells
in vitro using the dynamic current-clamp method (Robinson and Kawai, 1993; Sharp et al., 1993). We implemented this technique using dual whole-cell recordings in which one electrode was used to
record membrane potential (Vm) and the other was
used to inject simulated synaptic current. The recording electrode was
connected to channel 1 on an Axoclamp 2A amplifier, and the feedback
current injection was applied through channel 2 of this instrument. The two-electrode approach was chosen because it is not possible to inject
sizeable fluctuating currents through an electrode while maintaining an
accurate voltage recording with the same electrode. In the feedback
condition of dynamic clamping, this problem can easily lead to ringing
artifacts. The amount of simulated synaptic current injected
(Iinj) was calculated at a 10 kHz refresh
rate from the recorded membrane potential (Vm) and
two stored synaptic conductance waveforms representing the sum of
excitatory (Gex) and inhibitory
(Gin) conductances obtained from computer
simulations. The equation to calculate synaptic current is:
Iinj = Iex + Iin = Gex *
(Eex 
Vm) + Gin * (Ein Vm), where Eex and
Ein are the synaptic reversal potentials of 0 mV
for excitation and 70 mV for inhibition, respectively. The recorded
membrane potential (Vm) was low-pass filtered at 5 kHz using the Axoclamp 2A output filter before the potential was fed to
the dynamic-clamp software to prevent possible aliasing. This software
was custom written in Turbo Pascal with in-line assembly code for fast
feedback control under the DOS operating system. It works in
conjunction with a CIO-DAS 16/F analog-to-digital (AD)
board (Computer Boards), which uses an on-board clock to time
simultaneous AD conversion and digital-to-analog (DA) output. The
acquisition program polls the AD conversion and calculates the feedback
equation for the next time step while all external interrupts are
disabled. The system was tested to be reliable for 20 kHz feedback
rates with artificial input voltages consisting of square voltage
pulses. The DAS 16/F DA converters put out voltages from 0 to 5 V. A
hardware device was constructed to subtract 2.5 V from this signal and
to provide low-pass filtering at a cutoff frequency of 10 kHz. This
filtering was needed to eliminate very-high-frequency noise generated
by the computer. The resulting output voltage from 2.5 to 2.5 V was
used as input to the "current command" BNC connector on the back of the Axoclamp 2A amplifier. Because an HS2A 0.1LU head stage was used, the command voltage allowed dynamic current clamping for maximal current values of ±2.5 nA. The maximal value of +2.5 nA
was never reached, whereas 2.5 nA was injected transiently at the
peak of somatic spikes in some recordings.
Recording stability and potential experimental problems.
Data acquisition was started directly after a dual whole-cell
configuration was obtained and was continued for as long as the
physiological characteristics of the cell remained stable. The
characteristics used were spike size (>45 mV), a stable spike rate
during dynamic-clamp stimuli, and the absence of depolarization-induced
spike inactivation. Although a gradual change in cell properties might
be expected because of the perfusion with the pipette solution, such a
change was not observed for the spike responses with dynamic clamping examined here. On theoretical grounds, a junction potential of ~10 mV
can be expected for recording solutions based on K gluconate (Barry,
1994). This junction potential, however, can be mostly offset by a
Donnan potential of opposite sign (Barry and Lynch, 1991). The large
intracellular anions responsible for this Donnan potential equilibrate
with the electrode solution over a few minutes in small cells (Pusch
and Neher, 1988). This equilibration may not occur to a significant
degree in large cells, such as Purkinje cells, during the period of
time over which we acquired data. We examined a possible voltage offset
in our whole-cell recordings by comparing the observed spike threshold
with that of previous recordings we obtained in the same preparation
with sharp electrodes (Jaeger and Bower, 1994). We found no consistent
offset in spike threshold between the two methods of recording.
Therefore we did not subtract a junction potential from the recorded
Vm before feeding it into the dynamic clamp. We cannot
exclude some error in the absolute membrane potential recorded in
individual cells. With respect to dynamic current clamping, an offset
in recorded Vm is equivalent to shifting the synaptic
reversal potentials of excitation and inhibition by the same offset.
Therefore differences in the absolute level of depolarization and the
spike rate of different neurons obtained with the same input pattern
should be interpreted with care.
The use of 10 mM EGTA in our electrode solution could
potentially reduce the activation of Ca-dependent K conductances in the
cell by buffering the required Ca. Thus intrinsic hyperpolarizing currents could be diminished. In a later set of experiments (D. Jaeger,
unpublished observations), the internal solution was changed to contain
only 0.1 mM EGTA. The results of these later experiments show that the intrinsic balance of inward and outward currents during
dynamic current clamping is in the same range with 0.1 or 10 mM EGTA in the recording pipette. The lack of an effect of
EGTA can be explained by its slow-buffering characteristics and by the
possible activation of Ca-dependent K channels via specific Ca channels
located in close proximity. Unfortunately, the dynamics of calcium
handling in Purkinje cells is yet poorly understood.
The construction of simulated synaptic conductances. The
synaptic conductance patterns that we applied in the present study via
dynamic clamping were computed with our Purkinje cell model and were
identical to the inputs we used in our previous modeling study (Jaeger
et al., 1997). The model was constructed to replicate the best estimate
in the number and location of excitatory parallel fiber and inhibitory
stellate cell inputs to a single Purkinje cell. The modeling methods
used to generate synaptic conductances were described in detail in our
previous publications (De Schutter and Bower, 1994a,b; Jaeger et al.,
1997). In brief, the excitatory input from a granule cell was modeled
as an alpha function with an opening time constant of 0.5 msec, a
closing time constant of 1.2 msec, a reversal potential of 0 mV, and a
fixed maximal conductance of 0.7 nS. Inhibitory inputs as expected from
stellate cell input had an opening time constant of 0.9 msec, a closing time constant of 9 msec, a reversal potential of 70 mV, and a variable amplitude proportional to the surface area of the postsynaptic compartment (resulting in a mean amplitude of 3 nS). The reversal potential of inhibitory input was shifted by 10 mV from the value of
80 mV used previously in the model, which is the only difference between synaptic conductance patterns used here and those in our modeling study (Jaeger et al., 1997). Each synapse was activated randomly at a specified mean rate, which resulted in an exponential distribution in the duration of intervals between inputs. All excitatory synapses were activated with the same mean rate, as were all
inhibitory synapses. The rate of activation of each of the 1474 excitatory synapses was increased compared with the expected in
vivo situation to compensate for the reduced number of synapses present in the model (De Schutter and Bower, 1994b; Jaeger et al.,
1997). To apply synaptic conductances through a single electrode with
dynamic current clamping, we pooled conductances from all synapses in
the model by summing. On average, conductance waveforms consisted of
848 inhibitory and 16,225 excitatory inputs per second (Jaeger et al.,
1997).
The choice of synaptic parameters. In our original modeling
efforts, the number of parallel fiber inputs to a single Purkinje cell
were based on known anatomical data (Harvey and Napper, 1988). The
location of synapses on the dendrite was based on EM data (Palay and
Chan-Palay, 1974). The number of stellate cell inputs and the choice of
conductance parameters for single inputs were partly based on
best-guess estimates, however (De Schutter and Bower, 1994b). Since the
original model was constructed, several groups have reported amplitudes
and time constants for both excitatory (Barbour, 1993) and inhibitory
(Vincent et al., 1992; Barbour, 1993; Häusser and Clark, 1997)
synaptic inputs to Purkinje cells. These data show that the original
values chosen in the model were quite accurate, except for the decay
time constant of inhibitory inputs. In the modeling and experimental
results reported in this paper, this decay time constant was shortened
from 26 to 9 msec to conform with the experimental finding (Vincent et
al., 1992). The number of 1695 inhibitory synapses used in the model
was approximately realistic (Jaeger et al., 1997; Sultan and Bower,
1998).
The combined reversal potential of excitatory and inhibitory
conductances defines a partial voltage clamp. The combined
reversal potential of excitatory and inhibitory inputs
(Etot) applied with dynamic clamping can
be calculated as the weighted sum of the reversal potentials of
excitation and inhibition: Etot = (Gex * Eex + Gin *
Ein)/(Gex + Gin). This combined reversal potential (Etot) was termed Vclamp in
our modeling publication (Jaeger et al., 1997) because the dynamic
clamp creates a voltage clamp such that any deviation in membrane
potential from Vclamp is counteracted by an opposing change
in synaptic current. If Vm followed this trajectory of
Vclamp exactly, no synaptic current would be injected at
any time. As with a voltage-clamp amplifier, the amplitude of injected
current is proportional to the deviation of Vm from Vclamp. The gain of the voltage clamp exerted by synaptic
input corresponds to the total amplitude of synaptic conductance
Gex + Gin. Because this
gain is rather low compared with a regular voltage clamp and easily
allows the escape of Vm from Vclamp, we
refer to dynamic clamping as a partial voltage clamp. This analysis
also applies to a baseline of continuous synaptic input conductances
expected to be present in vivo.
The validity of using focalized input to examine the function of
natural inputs. The technique of dynamic current clamping requires
that simulated synaptic input be applied via one command current at a
single point in the cell. In contrast, Purkinje cells in
vivo receive distributed synaptic input. Distributed input is the
situation we recreated in our previous modeling study (Jaeger et al.,
1997) to examine the interaction of intrinsic cell properties with
synaptic input under conditions expected in vivo. To
interpret the results of dynamic current clamping, it is crucial to
establish the effects of focalizing synaptic input at the soma in
comparison with distributed dendritic inputs. In the Purkinje cell
model, the effect of distributed dendritic input is critically
dependent on the activation of dendritic voltage-gated currents (Jaeger et al., 1997). Therefore we need to establish whether synaptic input
focalized at the soma can still evoke these dendritic currents.
When only the passive properties of Purkinje cells are considered,
these cells are electrotonically very compact. The average length from
the soma to the tip of a dendrite is only 0.13 length constants (Rapp
et al., 1994). Therefore, a prolonged current injected into the soma
will lead to a nearly uniform change in membrane potential throughout
the cell (Rall, 1959). The dendritic attenuation increases for higher
frequencies of changes in membrane potential (Vm) at
the soma, however (Spruston et al., 1993). As a result, dendritic
Vm follows slow fluctuations (<10 Hz) in somatic Vm very well, whereas fast fluctuations (>100 Hz) are
severely attenuated in the distal dendrites (Spruston et al., 1993).
Even for a total dendritic length of 1.0 length constants, this
relationship still holds. This is the maximum length expected for
Purkinje cell dendrites in the presence of voltage-gated conductances
(De Schutter and Bower, 1994a). The fluctuations in our simulated synaptic input are almost entirely contained in the frequency band from
0 to 100 Hz. Thus, a large part of this signal is expected to spread to
most of the dendritic tree and to influence the activation of dendritic
conductances. To establish in detail how much the difference between
distributed and focalized input may affect Purkinje cell responses, we
analyzed the results from both input conditions in the model.
Figure 1 compares the model's response
when synaptic input was present throughout the dendrite
(A-C) with data obtained when synaptic input was
focalized at the soma as is the case with dynamic current clamping
(D-F). The focalized input was obtained by summing all synaptic conductances of the simulation using distributed synapses
and by applying the sum to the soma. To achieve a spike rate with
focalized input that matched the spike rate observed with distributed
input, we adjusted the reversal potential of inhibitory input from 80
to 72 mV. This requirement for a less-hyperpolarized inhibitory
reversal potential indicates that inhibitory input focalized at the
soma is somewhat more effective in suppressing spiking than is
distributed dendritic input. Note that the inhibitory reversal
potential of 72 mV in the focalized model is quite close to the 70
mV we used during dynamic current clamping. Shifting the reversal
potential of inhibition between the distributed and focalized input
conditions allowed us to use the same conductance patterns while
retaining a matching spike rate. The resulting voltage traces show that
both types of input induced the irregular pattern of spiking
characteristic of the in vivo state (see Figs. 1A, 3). Furthermore, the total synaptic current and
the evoked intrinsic voltage-gated currents (Fig.
1C,F) were very similar in both cases.
This means that the focalized synaptic inputs at the soma still
resulted in the activation of dendritic voltage-gated currents. In both
cases the voltage-gated conductances in the dendrite produced a
sustained inward current (ICa+K; Fig. 1C,F). This current resulted in a similar
plateau depolarization of the dendrite for distributed and focalized
input (Fig. 1A,D). The mean outward
synaptic current (Fig. 1C,F) indicates
that the depolarizing currents in the cell pushed Vm in the
soma above the net synaptic reversal potential. Therefore, the net
function of synaptic conductances was to counteract intrinsic inward
conductances. Although the exact timing of individual spikes was
different for the distributed and focalized synaptic input, periods of
increased spike rate clearly matched. In both input conditions, these
periods of spiking were carried by a relative increase of inward
dendritic current (horizontal bars in Fig.
1C,F). These similarities indicate that
dendritic input in Purkinje cells does not lead to large nonlinear
local effects in the dendrite. An absence of differences in cell
response to clustered or distributed dendritic input was observed
previously in the model (De Schutter and Bower, 1994c). As may be
expected from the preferential dendritic attenuation of high-frequency
components in somatic input, focalized input resulted in maintained
slow fluctuations in dendritic responses compared with that in
distributed input. In contrast, the fastest components of the response
to input were partly different between the two conditions.
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Figure 1.
Comparison between distributed
(A-C) and focalized (D-F)
synaptic input applied to the model. A,
D, Top, Somatic membrane potential.
Bottom, Dendritic membrane potential averaged over all
dendritic compartments. Somatic spikes have only a small effect on the
averaged dendritic Vm because of the pronounced dendritic
attenuation of high-frequency signals. It should be noted that the main
frequency component of an action potential is ~1000 Hz, which is much
higher than the main frequencies of synaptic input.
dend, Dendrite. B, Total excitatory
(Gsyn+) and inhibitory
(Gsyn ) synaptic conductance obtained by
adding up conductances from all synapses in the distributed model.
E, Combined reversal potential for the synaptic input
(Vclamp) in the focalized case. If
the somatic Vm matched the trajectory of this potential, no
synaptic current would be injected. Note that spike responses in the
model coincide with depolarized phases in vclamp
(horizontal bars in C,
F). C, F, Total
synaptic current (Isyn) and dendritic
voltage-gated channel current (ICa+K)
seen in the simulations. The spikes of synaptic current seen during
action potentials in the focal case (F) were
caused by the large change in synaptic-driving force during somatic
action potentials. Nevertheless, the synaptic spike current was much
smaller than the somatic Na and K spike currents and had little effect
on the results of the simulations.
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The observed similarities in the response of the model to focalized or
distributed synaptic input suggest that dynamic current clamping is a
reasonable approximation to distributed synaptic input for the modeling
predictions we want to test. We therefore proceed to use this method to
apply model-based synaptic input patterns to Purkinje cells in
vitro.
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RESULTS |
Stochastic synaptic inputs are sufficient to elicit in
vivo spike patterns in slice recordings
As shown in Figure
2A and in previous
publications (Llinás and Sugimori, 1980a,b), in vitro
cerebellar Purkinje cells exhibit spontaneous periods of fast regular
somatic spiking that gradually lead to dendritic calcium spike
bursting. In contrast, in vivo patterns of spiking are
slower, more irregular, and never include spontaneous calcium spikes
(Jaeger and Bower, 1994).
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Figure 2.
A, Spontaneous activity of a
Purkinje cell during whole-cell recording in vitro while
synaptic input was blocked pharmacologically is shown. Fast regular
somatic spiking (left) is followed a few seconds later
by spike bursting that is caused by dendritic calcium spikes
(right). After a period of spike bursting, this cell
became quiescent for a few seconds before the fast sodium spiking
resumed (data not shown). B, When purely excitatory
input was given with the dynamic clamp, intrinsic bursting activity
sped up substantially. Spike timing was not related to the input under
these conditions. C, The application of mixed inhibitory
and excitatory conductances resulted in an ongoing irregular spike
pattern characteristic of the in vivo state.
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Our modeling results predict that the addition of continuous excitatory
and inhibitory synaptic input converts the spontaneous in
vitro spike pattern of Purkinje cells to an in vivo
spike pattern (De Schutter and Bower, 1994b; Jaeger et al., 1997). This
modeling prediction was tested here by applying the same conductances
used in the model via the dynamic clamp in vitro. We found
that the in vitro spike pattern (Fig. 2A)
was immediately transformed into irregular ongoing spiking (Fig.
2C). In contrast, when only excitatory inputs were applied
with the dynamic clamp (Fig. 2B), the calcium spike
burst pattern of in vitro neurons was enhanced in all cells tested (n = 8). Similar results were obtained from the
model (Jaeger et al., 1997).
A comparison of interspike interval (ISI) histograms documents the
similarity between in vivo spiking patterns (Fig.
3A) and those obtained in the
model (Fig. 3B,C) and in the
in vitro dynamic current-clamp experiments (Fig.
3D). In each case, ISI distributions showed a sharp modal
peak followed by a tail of longer intervals. Nevertheless, there is not
a perfect match between ISI histograms from the model and the data
collected in vivo or in vitro. In particular, the
exponential falloff from the modal peak appears to be somewhat less
steep in the recordings than in the simulations. This may indicate that
the activation of voltage-gated currents that underlies periods of fast
spiking in the model (Jaeger and Bower, 1994) does not follow exactly
the identical kinetics as in the cells for which recordings are shown.
Note that the identical synaptic input used in the model produced
an ISI distribution in vitro that more closely resembles
the in vivo recording than the modeling results.
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Figure 3.
ISI histograms of Purkinje cell spiking for an
in vivo recording (A), in the
model with distributed (B) and focalized
(C) input, and during dynamic current clamping
in vitro (D). The ISI
distributions were overall similar in all conditions, showing a strong
modal peak at ~10 msec and a tail of long intervals. The total input
conductances in the model and under the dynamic current-clamp condition
were identical. They were obtained from a computer simulation in which
excitatory granule cell (gc) synapses were
activated randomly with a mean rate of 11 Hz and inhibitory stellate
cells (sc) were activated randomly with a mean rate of
0.5 Hz. The in vivo data were obtained with an
extracellular recording from crus IIA in the anesthetized rat [methods
described in Jaeger and Bower (1994)]. The small number of very short ISIs in the
in vivo distribution is attributable to complex spikes
resulting from climbing fiber inputs and was determined by separate
complex spike discrimination (data not shown). This input pathway was
not included in the modeling or dynamic-clamp studies.
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In vivo-type spiking behavior requires a net outward
synaptic current
Our modeling results further predicted that in vivo
spiking patterns are specifically dependent on synaptic inputs summing to a mean outward (inhibitory) current (Jaeger et al., 1997). As shown
in Figure 4, this prediction is supported
by the dynamic-clamp experiments. In all recordings (n = 20), a mean outward synaptic current was necessary to generate
in vivo-type spike patterns. The net outward synaptic
current trace shown in Figure 4D is very similar to
that seen in simulations (Fig. 1). For nine cells analyzed quantitatively with the same stimulus, the mean outward current during
in vivo-type spiking was 0.45 nA (SD between cells, 0.08 nA). This hyperpolarizing synaptic current indicates that on
average intrinsic depolarizing currents push the cell's membrane
potential above the combined reversal potential of inhibition and
excitation (Fig. 4C). In fact, the recorded Vm
was on average 1.3 mV more depolarized than was the combined synaptic
reversal potential (Fig. 4B,C).
This result indicates that in the real cell, as in the model, intrinsic
inward plateau currents produce the depolarization required to reach
spike threshold and that inhibitory synaptic input acts to limit the
activation of these conductances. Candidates for the required
noninactivating inward conductances were identified as a dendritic
P-type calcium conductance and a somatic persistent Na conductance by
Llinás and Sugimori (1980b, 1992). In the absence of inhibitory
input, the activation of these conductances is unstable because of
positive feedback, which ultimately leads to dendritic calcium
spiking.
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Figure 4.
Response of an in vitro neuron to
the application of model-based synaptic conductances. A,
The applied inhibitory and excitatory synaptic conductance
(Gsyn) is shown. B,
C, The somatic membrane potential
(Vm) follows the fluctuations in the clamping
potential (Vclamp) given by the input
conductances. Spiking is inhibited during periods of increased
inhibition (vertical dashed lines). D,
The injected current (Isyn) had an
average gain of 0.25 nA for each millivolt of deviation between
Vclamp and Vm. This gain was
time-varying (proportional to the sum of excitatory and inhibitory
conductances). The mean amplitude of injected current was 0.34 nA,
hyperpolarizing the cell.
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Interspike interval lengths are related to the strength of
inhibitory conductances
Our modeling study (Jaeger et al., 1997) predicted that inhibitory
synaptic conductances have a direct influence on the expected duration
of intervals between somatic action potentials. Consistent with this
prediction, the vertical dashed lines in Figure
4 indicate that periods of increased inhibition resulted in a cessation
of spiking in the experimental data. This relationship is further quantified in Figure 5 in which we use
the technique of spike-triggered averaging to compare the average
levels of synaptic conductances associated with short, medium, and long
interspike intervals. Figure 5, A and B,
reproduces the results of the same analysis reported previously for
model data (Jaeger et al., 1997). Figure 5, C and
D, shows the experimental data. In both cases inhibitory synaptic conductances were larger, and Vm was more
hyperpolarized very early in the time course for long intervals
compared with that for short intervals. This relationship was present
in all cells analyzed (n = 8). Thus, as in the model,
the length of the interspike intervals was correlated with the level of
inhibitory input. A direct correlation of natural inhibitory input with
prolonged interspike intervals was recently demonstrated in an elegant
dual-recording study from interneurons and Purkinje cells
(Häusser and Clark, 1997).
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Figure 5.
Spike-triggered averages of membrane potential
(A, C) and synaptic conductances
(B, D) in the model (A,
B) and with the dynamic clamp in vitro
(C, D). Spikes before or after ISIs with
durations of 10-13, 16-20, or 30-50 msec were separated into three
groups to construct spike-triggered averages of membrane potential
(Vm), inhibitory synaptic conductance
(Gsyn inhibition), and excitatory synaptic
conductance (Gsyn excitation). The data were
obtained from 2.5 sec of cell activity for the model and the dynamic
clamp.
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Excitatory inputs have relatively little direct effect on
spike initiation
The spike-triggered averages shown in Figure 5 also allowed us to
examine the relationship between somatic spiking and simulated excitatory synaptic conductances. In the model (Fig. 5B)
there was virtually no change in the average level of excitatory
conductance before, during, or after an action potential. This modeling
result led to the somewhat surprising suggestion that spike initiation does not reflect a previous increase in excitatory input (Jaeger et
al., 1997). Furthermore, the mean level of excitation was not related
to the control of ISI duration. The spike-triggered averages obtained
from physiological records in these experiments support the same
conclusion (Fig. 5D). The level of excitatory conductances during an ISI was at no time correlated with ISI duration in any of
eight cells analyzed.
The fact that excitatory inputs in the conductances we use are more
frequent, smaller in amplitude, and shorter in duration than are
inhibitory inputs may account for their ineffectiveness in controlling
spike timing. Because of these statistical properties, the total
excitatory conductance exhibits much less fluctuation than the total
inhibitory conductance does (Fig. 4A). The chosen input properties are not arbitrary, because they were based on well
established anatomical and physiological data (see Materials and
Methods). Nevertheless, our assumption of independent stochastic activation of synapses represents only one possible input condition. Many excitatory inputs firing together at the same time does result in
a precisely timed spike (De Schutter and Bower, 1994c). Whether and
under what conditions such highly correlated inputs may occur cannot be
answered by the present study.
The level of excitatory synaptic conductance strongly affects the
rate of spiking via the activation of intrinsic currents
The absence of a correlation between excitatory inputs and the
duration of individual interspike intervals does not imply that
excitatory input is without function. In fact, the model predicts that
Purkinje cells should show a dramatic increase in spike rate for only
moderate increases in the amount of excitation received (De Schutter
and Bower, 1994b). Such a high gain in the change of output spike rate
would make the Purkinje cell a very sensitive rate-coding device for
the average level of excitatory input received (Jaeger et al., 1997).
In the model, this high gain in the spike output rate is primarily
caused by dendritic P-type Ca channel activation (Jaeger et al., 1997).
To investigate the gain function of the output spike rate in
vitro, we increased the amount of baseline excitation in the
dynamic current clamp (Fig. 6). This was
done by adding a constant excitatory conductance such that the
fluctuations in the synaptic conductances remained identical. An
increase of 10 or 30% in the mean excitatory conductance led to an
increase in spike rate of 43 or 115%, respectively (average of eight
cells). Thus, as predicted by the model, the in vitro recordings showed a high gain function for the rate coding of excitatory input levels. The increases in spike rate of 43 and 115%
were accompanied by a depolarizing shift in the average Vm of 1.3 and 3.8 mV, respectively.
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Figure 6.
Spiking response of a single cell to increases in
the constant component of simulated excitation. A, Dot
rasters and single traces for three runs in which the amplitude of
excitatory synaptic inputs was increased. Dot rasters indicate spike
timing for repeated presentations of the same stimulus. The single
Vm trace below each dot raster illustrates
the membrane potential trajectory for a typical response.
B, Cross-correlations for each level of excitation. The
cross-correlation was computed between subsequent responses to the same
stimulus. The total conductance amplitude corresponded to a gain of 2.0 (see Fig. 7).
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The depolarization and increase in spiking seen with increased
excitatory conductance were not caused by an inward current via the
simulated synaptic conductance. In fact the mean synaptic current
remained outward with nearly identical amplitude for the lowest and
highest amount of excitation (0.45 and 0.41 nA, respectively; n = 8 cells). This result was also predicted by the
model. The lack of an increased inward synaptic current with an
increase in excitatory conductance proves that intrinsic inward current is responsible for the additional depolarization. As the cell is
allowed to depolarize more by a depolarizing shift in the combined synaptic reversal potential, inward voltage-dependent currents are
activated more strongly. The P-type calcium channel in particular shows
a steep activation increase in the relevant voltage range of 50 to
35 mV (Regan, 1991). This increased intrinsic inward current again
pushes the cell beyond the synaptic reversal potential, and a net
outward synaptic current is maintained. In principle, this mechanism
allows neurons to achieve arbitrarily high gain functions in spike rate
for small increases in excitatory input. Decreases in inhibitory input
were similarly effective in increasing spike rates (data not shown).
This is not surprising, because decreases in inhibition have a similar
effect on shifting the combined synaptic reversal potential as do
increases in excitation. The appearance of dendritic calcium spikes in
the absence of inhibitory input (Fig.
2A,B) indicates that outward
synaptic current is important in preventing a runaway activation of
intrinsic inward current. The Purkinje cell model further suggests that
intrinsic inward current is also balanced by intrinsic voltage and
Ca-gated K conductances.
The precision of spike timing is dependent on the absolute
amplitude of synaptic conductances
The strong participation of intrinsic currents in mediating the
effect of synaptic input poses the question of how precisely spike
timing can still be controlled by the synaptic conductance pattern. The
precision of spike timing has recently received much attention as a
possible mechanism for neural coding (Mainen and Sejnowski, 1995;
König et al., 1996). To test for the control of precise spike
timing by synaptic conductances in Purkinje cells, we applied synaptic
conductances of different amplitudes. Specifically, we applied synaptic
input conductances with different absolute amplitudes while maintaining
an identical time course in the trajectory of the combined reversal
potential. This was achieved by multiplying both inhibitory and
excitatory conductance patterns by constant gain factors of 0.5, 1.0, or 2.0.
By applying the same conductance traces repeatedly via the dynamic
clamp, we could assess the relationship between a given simulated
synaptic input and the precision of spike timing (Fig. 7). Spike rasters show that an increase
in the synaptic gain results in an improved alignment of individual
spikes between stimulus repetitions (Fig. 7A). This effect
was quantified by a cross-correlation analysis, in which the timing of
spikes for successive pairs of stimulus repetitions was correlated
(Fig. 7B). For all stimulus gains, we find a very sharp peak
in the cross-correlograms, indicating the presence of precisely timed
spikes. The proportion of spikes precisely timed within ±1 msec was
much higher for the input gain of 2 (78%) than for the input gain of
0.5 (50%; average of four cells). In addition, several cells showed a
total loss of correlation with the synaptic input at a gain of 0.5 by
entering an oscillatory bursting pattern (data not shown). Thus the
gain of 0.5 was near the minimum of synaptic conductance needed to
prevent runaway activation of intrinsic currents. These findings
indicate that at a sufficient amplitude of synaptic conductances, a
substantial proportion of spikes can be timed precisely in relation to
the input even in the presence of large intrinsic currents.
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Figure 7.
Spiking responses of a single cell with increasing
input amplitudes. A, Dot rasters of spiking patterns
with repeated presentations of the same input conductances multiplied
by the indicated gain factors are shown. The spike frequency increased
from 43 to 64 Hz when the input conductance was halved and decreased to
32 Hz when the input conductance was doubled. B,
Cross-correlation histograms were computed by correlating spike times
in each response with spike times of the next response.
C, The fluctuations in the injected current increased
proportionally with increasing input conductances; however, the mean
currents changed only slightly from 0.4 nA for the gain of 0.5 to
0.48 nA for the gain of 2.0. Inward current is plotted
downward.
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A striking effect of applying conductances with different gain factors
was consistently found; increasing the conductance amplitude led to a
decrease in spike rate (Fig. 7A). This effect further
substantiates the presence of inward intrinsic currents that push the
membrane potential above the synaptic reversal potential. The ability
of this current to depolarize the cell is reduced in the presence of
large synaptic conductances, because the amount of synaptic current
that opposes the intrinsic current to push the cell away from the
synaptic reversal potential is increased (Fig. 7C). In our
data, the average Vm for the input gain of 1 was 47.7 mV,
whereas for a gain of 2, it was 49.6 mV (n = 4 cells). The resulting spike rates were 32 and 26 Hz, respectively.
Spiking rates are controlled independently of
spiking precision
The previous sections indicate that Purkinje cells are a sensitive
rate encoder with respect to the balance of inhibition and excitation
but that they can also initiate precisely timed spikes with respect to
synaptic conductance fluctuations. We now ask the further question of
whether these two aspects of coding information about the input are
independent of each other. This question can be addressed by a more
detailed analysis of the data with increasing amounts of excitatory
input conductance (Fig. 6). This figure allows the important
observation that the precise timing of particular spikes, which are
present at a low level of excitation, remains largely intact when
additional excitatory conductance is added (Fig.
6A). Because the synaptic reversal potential
is more depolarized with increasing excitation, more spikes are added.
The proportion of these additional spikes that are timed precisely
within ±1 msec is identical to that seen at a low level of excitation.
The cross-correlograms show that the proportion of spikes that occurred
with a precision of ±1 msec was 66-67% for all amounts of excitation
(average of eight cells) and was thus maintained at low and at high
spike rates (Fig. 6B).
Taken together with the findings shown in Figure 7, these data suggest
that spike rate and spike precision are primarily controlled by two
different properties of the input. Spike rate is mainly a function of
the relative level of excitation and inhibition, which determines the
average combined reversal potential. In contrast, spike precision
depends on the total amplitude of synaptic conductance changes.
Therefore, Purkinje cells in principle can transfer information about
the input via precisely timed spikes independent of spike rate. Whether
information is actually transferred via precisely timed spikes depends
on the decoding mechanism at postsynaptic cells and the presence of
precisely timed spikes across different Purkinje cells. These issues
remain to be addressed in future studies.
Variations in responses to applied inputs between
Purkinje cells
Finally, we used the dynamic current clamp to examine variations
in the response of different in vitro Purkinje cells to the same simulated synaptic input. Figure 8
indicates that although each cell again responded consistently with a
near-identical spike pattern for repeated presentations of the same
stimulus, there were clear response differences between different
cells. These differences included overall lower or higher spike rates
in the response as well as different patterns of spiking. In
particular, the amount of burstiness during periods of spiking was
quite variable such that cells with overall low spike rates could show
extremely rapid spiking at some times (Fig. 8C). Similar
differences in spike patterns were observed in a previous modeling
study (De Schutter and Bower, 1994a), when either the density of
specific ion channels or the relative somatic or dendritic size of the cell was changed. These findings indicate that intrinsic conductances make an important contribution to spike timing. Because intrinsic currents are activated in a deterministic pattern by a repeated identical stimulus, the precision of spike timing in relation to the
stimulus can be maintained. Because the dynamics of multiple interacting intrinsic currents is complex, the spike timing resulting from applied synaptic conductances may be a nontrivial function of
fluctuations in the synaptic conductance. The diversity of observed
spike responses teaches the important lesson that Purkinje cells may
not be a homogeneous population of cells responding to inputs in an
identical manner. Whether the input-output function of individual
cells is the result of an adaptive learning process beyond the mere
adjustment of synaptic strength remains to be studied. Recent
experimental and modeling work in other cell types has clearly
indicated that intrinsic currents can be dynamically regulated
(Turrigiano et al., 1994, 1995; Liu et al., 1998).
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Figure 8.
Comparison of spiking behavior for three different
recorded Purkinje cells. All cells were stimulated with the identical
input conductances. It can be seen that each cell has a very similar
response for repeated presentation of the stimulus, whereas the
response of different cells to the same stimulus can be quite
different.
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DISCUSSION |
Testing the validity of modeling predictions
In any modeling study, the usefulness and accuracy of simulation
results are to a large degree dependent on the choice of modeling
parameters (Bhalla and Bower, 1993). Because these parameters are never
fully constrained by experimental data, the results of computer
simulations aimed at replicating a biological system need to be
carefully tested for their validity. On the other hand, modeling can
clearly enhance our grasp of interacting dynamic variables, and only in
a model can all state variables be accessed at the same time. The
present study was designed to test modeling predictions about the
integration of synaptic inputs in the presence of strong intrinsic
currents, which we published previously (Jaeger et al., 1997). The best
experimental method we could find to test our model predictions was to
apply the synaptic conductances produced by the model to Purkinje cells
in vitro by way of dynamic current clamping. In addition to
testing our model predictions, this technique allowed us to pursue the
question of how precisely spike timing can be controlled via synaptic
input in a cell with strong intrinsic conductances. This issue of
precisely timed spikes as a channel of neural coding has recently
attracted much attention (Softky and Koch, 1993; Mainen and Sejnowski,
1995; König et al., 1996; Yuste and Tank, 1996; Shadlen and
Newsome, 1998). Our finding that the control of spiking may to a large
degree depend on intrinsic cell properties indicates that the spike
coding of input may be quite different for neurons with different
active properties. The experimental methods introduced here provide a
means by which both the input and the output of a cell can be assessed
at the same time and may thus prove useful in studying the control of spiking in various cell types. For Purkinje cells, our findings indicate that both rate coding and precise spike time coding can coexist at the same time. The specific interaction of synaptic conductances and intrinsic currents has important implications for
cerebellar cortical function, as discussed below.
Mechanisms underlying the synaptic control of Purkinje
cell spiking
The influence of intrinsic conductances
The experimental results reported here support our modeling
prediction that Purkinje cells generate an intrinsic inward plateau current that pushes the cell above the combined synaptic reversal potential of excitation and inhibition. This intrinsic inward current
then forces the net synaptic current to be outward. As in the model, we
found that this relationship holds for the whole range of realistic
spike rates (Fig. 6). The intrinsic inward current is unstable and
results in spontaneous bursting in the absence of synaptic input (Fig.
2). Thus an ongoing balance of inhibitory and excitatory input is
required to result in an irregular spike train typically seen in
vivo. Our experiments cannot identify the types of ion channels
responsible for the plateau depolarization in vitro.
Previous studies show that the major candidates for a persistent inward
current are given by a dendritic P-type Ca conductance and a somatic
persistent Na conductance (Llinás and Sugimori, 1992). The model
indicates that a large contribution of P-type Ca current is inevitable
on the basis of the voltage dependence of this channel (Regan, 1991).
In fact, in the model this current needs to be counterbalanced by
Ca-dependent K currents [Jaeger et al. (1997), their Fig. 6] as well
as by synaptic current. In the model, the interplay of dendritic Ca and
K conductance activation leads to a complex time course of synaptically
induced voltage transients. The role of intrinsic dendritic currents
therefore goes much beyond a constant plateau depolarization. The
detailed model predictions in this regard could not be tested in the
present study because we cannot measure the time course of dendritic
conductances. The variability in spike patterns between different cells
recorded in vitro with the same input conductances (Fig. 8)
suggests that the interaction of intrinsic and synaptic currents
follows a different time course in different cells.
Persistent somatic sodium currents also provide a considerable inward
current in the model and possibly in vitro. The model indicates, however, that these sodium currents are deactivated during
spike afterhyperpolarization, and a depolarized dendrite is required to
initiate the next spike (Jaeger et al., 1997).
The role of inhibition
Our experimental results show that a tonic baseline of inhibitory
inputs needs to be present to allow the spike mode observed in
vivo (Jaeger and Bower, 1994). This tonic input is required as
otherwise intrinsic depolarizing currents push Purkinje cells into a
burst mode that is not usually present in vivo. Our data show that the mean combined reversal potential of inhibition and excitation has to fall into a narrow range below spike threshold to
allow natural spike patterns. This range in reversal potential is
obtained when there are on the order of 20 times as many unitary excitatory as there are inhibitory inputs over a given time period.
A second important prediction of the model was also borne out in the
experimental data, namely, that the time-varying level of inhibitory
conductance has a direct control over the length of interspike
intervals (Fig. 5). This finding is supported by the recent
demonstration of a strong effect of the input from single inhibitory
interneurons on Purkinje cell spike intervals (Häusser and Clark,
1997). These authors find that even the activation of interneurons in
the outer molecular layer can have such an effect, and thus spike time
control is not limited to basket cell inputs onto the soma. Basket cell
input was not included in our modeling study, and further studies are
needed to assess its influence in detail.
Spike rate coding and spike time coding
We find that Purkinje cells are very sensitive rate encoders in
that small changes in the balance of excitation and inhibition lead to
large changes in spike rate (Fig. 6). The larger changes in output than
in input rate represent an amplification function. This amplification
is carried by the activation of intrinsic plateau currents. Independent
of spike rate, precise spike timing is found to be mediated via rapid
fluctuations in synaptic conductances when the overall amplitude of
synaptic conductance is high (Fig. 7). This spike precision in our data
is limited to a narrow window of maximally ±3 msec, making it a
distinctly different process from rate coding. Thus it seems possible
that the overall spike rate and the timing of individual spikes may
transmit different signals to the next level of neural processing.
Unfortunately, we are still almost entirely ignorant about the decoding
of Purkinje cell spike trains by the neurons in the deep cerebellar
nuclei to which they project.
Significance for cerebellar network function
Reconsidering inhibition
Our results indicate that constant inhibitory input is required in
the control of Purkinje cell spiking and that inhibitory input makes an
important contribution to spike timing as well as to spike rate
control. In contrast, most recent efforts of modeling cerebellar
cortical network function make no use of inhibitory inputs to Purkinje
cells (Kawato and Gomi, 1992; Buonomano and Mauk, 1994; Schweighofer et
al., 1996). This may be inspired by the view of neurons as summation
devices, in which the presence of inhibitory input is equivalent to a
reduced level of excitatory input. Our data indicate that Purkinje
cells cannot operate in this manner. We conclude that pauses in
Purkinje cell spiking are necessarily coupled to the presence of
inhibitory input. (An exception would be a pause in spiking because of
K conductance activation after dendritic calcium spiking.) Such pauses
in spiking may be of great significance, because Purkinje cells are
themselves inhibitory neurons. Thus, a pause in spiking would
disinhibit neurons in the deep cerebellar nuclei and lead to a positive
output from the cerebellum. Pauses in spiking were found to be a
dominant Purkinje cell response after somatosensory stimulation in
anesthetized rats. This was true even along the center of an excited
"beam" of parallel fibers (Bower and Woolston, 1983).
The indirect effects of parallel fiber inputs
Our experiments support the model prediction that parallel fiber
(pf) inputs have a much more indirect effect on Purkinje cell behavior
than is usually assumed. Since the first anatomical descriptions of the
granule cell-parallel fiber system, most theories of cerebellar
function (e.g., Marr, 1969; Fujita, 1982) have assumed that sets
of activated pf synapses directly force Purkinje cells to cross spike
threshold. Our model analysis, now supported by the experimental
results presented here, suggests that pf inputs do not directly produce
somatic action potentials. Instead, continuous pf input contributes
one-half of a partial voltage-clamp mechanism, which stabilizes
Vm at the combined reversal potential of inhibition and
excitation. The trajectory of the combined reversal potential and the
total conductance amplitude in turn regulate the activation of large
intrinsic voltage-dependent conductances. The activation of intrinsic
inward currents then depolarizes the cell and leads to the initiation
of somatic spikes.
What do the parallel fibers do?
Viewing parallel fiber synapses as modulating the state of
dendritic conductances suggests a major change in how to think about
cerebellar cortex (Bower, 1997a). The data presented here suggest that
parallel fiber input acts in the context of counterbalancing inhibition. In this way parallel fibers can be seen as playing a more
modulatory role, as we originally proposed (Bower and Woolston, 1983).
We do, however, believe that the granule cell synapses associated with
the ascending granule cell axon can produce a direct excitatory drive
on Purkinje cells (Bower and Woolston, 1983; Jaeger and Bower, 1994;
Gundappa-Sulur et al., 1999). Recent cerebellar circuit simulations
suggest that in addition to providing multiple and synchronous
excitatory synaptic inputs, synapses of the ascending axon may activate
too quickly after mossy fiber inputs to be counterbalanced by
inhibition via local interneurons (F. Santamaria and J. M. Bower, unpublished observations). An elegant experimental demonstration
of the predominant activation of Purkinje cells via ascending granule
cell axons was recently seen with voltage-sensitive dye imaging in a
guinea pig whole-brain preparation (Cohen and Yarom, 1998). In these
experiments, electrical stimulation of a patch of granule cells
resulted in the activation of overlying Purkinje cells but not along
the extended beam of activated parallel fibers.
The challenge of understanding cerebellar cortical computation
The specialized architecture of cerebellar cortex suggests that a
particular computational algorithm may take place in this structure
(Bloedel, 1992; Bower, 1997b). The strong interaction of synaptic input
and intrinsic conductances that we found in our model is supported by
the present experimental findings. Because this interaction changes the
amplitude and time course of Purkinje cell responses to synaptic input,
active properties likely play an important role in the implementation
of the cerebellar computational algorithm. One key challenge in further
elucidating cerebellar computation consists of determining the control
of spiking in other cerebellar cell types and in the combined network.
We expect that realistic network modeling in conjunction with
experimental testing will be the method of choice in tracing the
complex dynamics of cerebellar computation.
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FOOTNOTES |
Received Jan. 29, 1999; revised April 22, 1999; accepted April 26, 1999.
This work was supported by a Sloan fellowship to D.J., by a grant from
the Human Frontier Science Program to J.M.B., and by National Institute
of Mental Health Grant MH57256-01 to D.J. We thank Erik De Schutter for
helpful comments and simulation scripts.
Correspondence should be addressed to Dr. Dieter Jaeger, Department of
Biology, 1510 Clifton Road, Emory University, Atlanta, GA 30322.
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TOP
ABSTRACT
INTRODUCTION
