Institute of Neuroinformatics, University of Zürich and Federal Institute of Technology, CH-8057 Zurich, Switzerland
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ABSTRACT |
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Ulrich, Daniel and Christian Stricker. Dendrosomatic Voltage and Charge Transfer in Rat Neocortical Pyramidal Cells In Vitro. J. Neurophysiol. 84: 1445-1452, 2000. Most excitatory synapses on neocortical pyramidal cells are located on dendrites, which are endowed with a variety of active conductances. The main origin for action potentials is thought to be at the initial segment of the axon, although local regenerative activity can be initiated in the dendrites. The transfer characteristics of synaptic voltage and charge along the dendrite to the soma remains largely unknown, although this is an essential determinant of neural input-output transformations. Here we perform dual whole-cell recordings from layer V pyramidal cells in slices from somatosensory cortex of juvenile rats. Steady-state and sinusoidal current injections are applied to characterize the voltage transfer characteristics of the apical dendrite under resting conditions. Furthermore, dendrosomatic charge and voltage transfer are determined by mimicking synapses via dynamic current-clamping. We find that around rest, the dendrite behaves like a linear cable. The cutoff frequency for somatopetal current transfer is around 4 Hz, i.e., synaptic inputs are heavily low-pass filtered. In agreement with linearity, transfer resistances are reciprocal in opposite directions, and the centroids of the synaptic time course are on the order of the membrane time constant. Transfer of excitatory postsynaptic potential (EPSP) charge, but not peak amplitude, is positively correlated with membrane potential. We conclude that the integrative properties of dendrites in infragranular neocortical pyramidal cells appear to be linear near resting membrane potential. However, at polarized potentials charge transferred is voltage-dependent with a loss of charge at hyperpolarized and a gain of charge at depolarized potentials.
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INTRODUCTION |
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Neocortical
pyramidal cells receive the majority of excitatory synaptic input onto
their dendrites (DeFelipe and Fariñas 1992). A
variety of active conductances have been found in dendritic recordings
(Amitai et al. 1993
; Huguenard et al.
1988
; Kim and Connors 1993
) and these are likely
to influence the propagation of synaptic signals to the soma
(Deisz et al. 1991
; Markram and Sakmann
1994
; Schwindt and Crill 1998
;
Stafstrom et al. 1985
; Stuart and Sakmann
1994
, 1995
). Sodium-dependent action potential generation is thought to occur mainly at the axon hillock
(Stuart and Sakmann 1994
). Knowledge of the relationship
between synaptic input and spike output in individual neurons is
essential for theories of cortical circuits (e.g., Douglas et
al. 1995
). The size of current flow at the soma after
stimulation of dendritic synapses has been estimated under steady-state
conditions, involving a large and unknown number of synaptic contacts
(Ahmed et al. 1998
; Schwindt and Crill
1996
). However, the exact contribution of individual synapses
to current arriving at the soma remains largely unknown. While passive
dendrites are expected to act as low-pass filters, active dendritic
properties may either boost or attenuate certain signal components.
This could potentially lead to a complex relationship between neural
input and output. In these experiments, we use an experimental design
that circumvents the stochastic nature of transmitter release. We mimic
a synaptic conductance on the apical dendrite with a dynamic
current-clamp and measure somatic voltage and charge with a second
electrode at the soma. This allows us to quantitatively correlate
simulated synaptic input with the current arriving at the soma.
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METHODS |
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Sprague-Dawley rats of either sex (P12-P18) were killed by decapitation. Individual cerebral hemispheres were glued on a stage tilted forward by 15°. Parasagittal slices of 300-µm thickness were cut on a Vibratome (TPI, St. Louis, MI) and incubated at 34°C. Slices were transferred to a recording chamber and superfused at room temperature with standard artificial cerebrospinal fluid containing (in mM) 125 NaCl, 1.25 NaH2PO4, 25 NaHCO3, 2.5 KCl, 1 MgCl2, 2 CaCl2, 10 glucose, pH adjusted to 7.4 with 5% CO2-95% O2.
Patch pipettes were pulled from thick-walled borosilicate glass
(Hilgenberg, Malsfeld, Germany) and filled with a solution containing
(in mM) 125 K-gluconate, 5 KCl, 1 MgCl2, 1 CaCl2, 10 HEPES, 11 EGTA; osmolarity 280 mOsmol,
pH 7.2 adjusted with KOH. Pipettes used for somatic or dendritic
recordings had a tip resistance of about 5 and 15 M, respectively.
Pyramidal cells in layer V of somatosensory cortex were visualized with
infrared differential interference contrast video microscopy
(Dodt and Zieglgänsberger 1990
).
Time-varying sinusoids of a linearly increasing frequency (chirps) with
20 pA peak-to-peak amplitude, I0, were
generated digitally between 0.1 and 20 Hz (Hutcheon et al.
1996). The frequency was varied at eight octaves per second.
The implementation is such that the instantaneous frequency,
, of
the chirp starts at time t = 0, increases linearly with
time, and covers the range between the initial frequency
0 and the final frequency
1, i.e.
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Time centroids of current or voltage transients were calculated from
the first and zeroth moments of current and voltage records as
described by Agmon-Snir and Segev (1993). Data are
presented as mean ± SE and "n" designates the
number of recordings.
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RESULTS |
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Dual whole-cell recordings were obtained from large layer V
pyramidal cells in rat somatosensory cortex to characterize voltage and
charge transfer from the dendrite to the soma and vice versa. Figure
1A shows an example of
simultaneous recordings with somatic and dendritic patch electrodes
separated by 200 µm. The average dendritic recording distance from
the soma was 112 ± 14 µm. All cells were of the regular spiking
type (Connors and Gutnick 1990) and had a mean resting
membrane potential at the soma of
62 ± 1.5 mV
(n = 12). In a linear system, charge transfer and
steady-state voltage decay are equal in opposite directions
(Carnevale and Johnston 1982
; Rall and Segev
1985
). Therefore we first investigated the spread of somatic
voltage into the dendrite. At rest, small hyperpolarizing current steps
were injected into the soma and the membrane voltage deflections were
recorded simultaneously by the somatic and dendritic patch electrodes
(Fig. 1B). As previously shown in layer V pyramids, an
apparent sag in membrane voltage was revealed for hyperpolarizing
voltage transients at both recording sites (Fig. 1B,
Stuart and Spruston 1998
) and was even more pronounced in the dendrite. The mean somatofugal steady-state voltage transfer ratio (k12) was 0.75 ± 0.03 (n = 9; note that k12
is the reciprocal of attenuation). In a passive neuron,
k12 is expected to decrease with
electrotonic distance (X). We calculated the length constant (
) of the proximal apical dendrite as
=
[(d/4) · (Rm/Ri)] with an axial resistivity (Ri) of 100
cm (Stuart and Spruston 1998
) and
Rm =
m/Cm. The
membrane time constant (
m) was estimated from
fitting an exponential function to the late part of the current step
response at the soma (Holmes et al. 1992
; data not
shown). The average
m was 30 ± 3.6 ms.
The specific membrane capacitance (Cm) was
taken as 1 µF cm
2
(Curtis and Cole 1938
). Figure 1C shows a
scatter plot of k12 versus the
electrotonic distance (X) of the two recording electrodes. As predicted, dendritic voltage deflections decrease with distance. In
Fig. 1C the function {cosh (L
X)/cosh (L)} was fitted to the data points by a
least-squares algorithm. This formula describes the DC voltage decay in
a uniform equivalent cylinder of electrotonic length L with
a sealed end. The electrotonic length obtained from the fit
(L = 1.7) is in agreement with previous estimates of
L for the apical dendrite of layer V pyramidal cells based
on morphological data (Larkman et al. 1992
).
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The amplitude ratio between voltage and current at two different sites equals their transfer resistance (R). Figure 1D shows a scatter plot of somatofugal transfer resistances (R12) obtained from somatic current injections and corresponding dendrosomatic transfer resistances (R21). The latter were obtained from fitting an RC circuit to the chirp data by a least-squares algorithm and extrapolating the fit to DC. Note that at rest, transfer resistances in somatofugal and dendrosomatic directions are highly correlated as shown by the linear fit in Fig. 1D (Pearson's r = 0.89, P < 0.05). Reciprocity of transfer resistances is to be expected in a linear system.
Frequency-dependent voltage transfer from the dendrite to the soma was
investigated by sinusoidal current injections through the dendritic
electrode (Fig. 2A). The
resulting voltage was recorded simultaneously by the dendritic and
somatic pipettes at resting membrane potential (Fig. 2A).
Figure 2, B and C, shows an example of transfer
impedance and phase shift between dendritic current and somatic voltage
after fast Fourier transformation. The data points were fitted by an
equivalent cable with sealed ends (Butz and Cowan 1974):
V(f) = I(f) · Z(
) · cosh
(
x) · cosh {
(l
d)}/sinh (
l). V(f) and
I(f) are the Fourier transforms of somatic voltage and dendritic current, and f indicates the
frequency. Z(
) and l are the input impedance
and length of the equivalent cable, respectively. The relative
positions of the recording (x) and stimulation
(d) electrodes require that 0 < x < d < l. The propagation constant (
)
depends on
and
:
=
{(2
if
+ 1)/
} and Z(
) is defined as Z = r/
, where r corresponds to the axial resistance of the cable. The model was fitted to the complex numbers by
a least-squares algorithm. The resulting
and
from five different cells were 30 ± 4 ms and 400 ± 112 µm. The
average length and diameter of the cable are 1169 ± 131 and
2 ± 0.5 µm, respectively. The fitted function in Fig. 2,
B and C, falls monotonically for increasing
frequencies. The inflection point is at 4 Hz and coincides approximately with the
3 dB point (5.3 Hz). The maximal initial roll-off is
17 dB per decade, which approaches
10 dB per decade at
higher frequencies. Therefore at rest, transient synaptic input will be
low-pass filtered by the dendritic cable properties.
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Contrary to simple current injections, real synaptic inputs are
generated by transmembrane conductances. The resulting current flow is
a nonlinear function of the membrane potential. Experimentally, membrane conductances can be mimicked by a hybrid computer system, a
dynamic current-clamp. Control experiments were carried out to show
that the current generated by the conductance imposed at the soma
corresponds to the current that was recovered under voltage-clamp
conditions with a second electrode. Double somatic recordings
(n = 4) were performed on thick-tufted layer V
pyramidal cells as illustrated in Fig.
3A. With one electrode in
current-clamp and the bridge balanced, the conductance time course was
imposed. A second electrode in voltage-clamp measured the actual
current delivered. Such an experiment is shown in Fig. 3B,
where the conductance time course corresponded to an -function with
= 30, an amplitude of 2 nS, and a reversal potential of 0 mV.
The top trace (a) is the membrane potential as measured by
the electrode in current-clamp. The command potential of the second
electrode was set at the resting membrane potential of this cell (
63
mV). At the peak of the conductance, a voltage escape of 1.5 mV was
measured. The second trace (b) illustrates the current that
passed through the electrode in current-clamp. Note the step-like
increments in the tail of the excitatory postsynaptic current (EPSC)
that are due to the finite resolution achieved with the
analog-to-digital converter board. The third time course (c)
is the current measured by the voltage-clamp electrode. Bottom trace,
the two current time courses are superimposed (b + c). The figure indicates an excellent match between the two
currents, except for a small lag during the rising phase (0.7 ms). This is due to incomplete compensation of the series resistance and neutralization of the electrode capacitance.
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To estimate the charge arriving at the soma, the cell should be kept in
voltage-clamp. However, somatic voltage-clamp would artificially force
the membrane potential of the apical dendrite to stay near the command
potential and would affect voltage-dependent conductances. As an
approximation for the charge arriving at the soma under unclamped
conditions, the somatic voltage integral can be divided by the somatic
input resistance obtained by linear regression of current-voltage data
similar to Fig. 1B (not shown). To validate this approach,
we compared the charge delivered by the dynamic current-clamp electrode
with the estimated charge of the voltage integral scaled by
RN (Fig.
4A). In a series of six
experiments, double somatic recordings as in Fig. 3A were obtained in current-clamp. In each case the membrane potential was held
at around 70 mV to provide an equal driving force for the conductance
in each of the cells. A dynamic current-clamp was imposed with the
second electrode simulating a conductance time course using
-functions of different values (30, 200, 500, 1,000) and a magnitude
of 2 nS. In Fig. 4A, the scaled voltage integral is plotted
against the effective charge delivered through feedback from the
dynamic current-clamp. The dashed line indicates equality in charge.
The solid line is the linear regression forced through zero with a
slope of 1.01 ± 0.01 and a Pearson's r = 0.996 (P < 0.001). This suggests that for double somatic
recordings the somatic charge can be inferred from the scaled voltage
integral with excellent accuracy. The scatter in the ordinate for
values of
= 30 is largely due to the spontaneous synaptic
activity encountered in these cells, whereas the scatter in the
abscissa is due to the inaccuracy of holding the cell at
70 mV in
current clamp.
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In a further set of control experiments, we checked if membrane
potential affects input resistance (RN) in
layer V pyramidal cells. In Fig. 4B,
RN is plotted as a function of membrane
potential from three cells of similar input resistance. The result
shows a significant linear correlation of
RN with membrane potential, having a slope
of 4.8 ± 0.7 M per mV polarization (Pearson's r = 0.89, P < 0.005). Therefore
because the scaled voltage integral as a predictor of charge arriving
at the soma is multiplied by (1/RN), it is
expected that with depolarization the actual charge is progressively
underestimated (cf. Fig. 6C and the last paragraph of this section).
To quantify synaptic voltage and charge transfer from dendrite to soma,
a dynamic current-clamp was applied to the dendritic pipette. The
kinetics of the conductance waveforms were described by two exponential
functions with time constants characteristic for fast glutamatergic or
GABAergic synapses (rise = 0.2 ms,
decay = 1.5 ms and
rise = 0.4 ms,
decay = 7.5 ms, respectively). Peak conductance was varied between 1 and a
few nS in agreement with estimates of quantal size (Forti et al.
1997
; Stricker et al. 1996
). The corresponding
(uncorrected) reversal potentials were 0 mV for the EPSC and
65 mV
for the inhibitory postsynaptic current (IPSC). Figure
5A shows an example of a
dendritic dynamic current-clamp EPSP that was simultaneously recorded
at the soma. Figure 5B depicts another experiment simulating
an inhibitory postsynaptic potential (IPSP). Because the driving force
for the IPSC is only a few millivolts at rest, the amplitude of the
dendritic IPSP is relatively small. EPSP charge transfer and amplitude
ratios for EPSPs and IPSPs are summarized in Fig. 5C. As
expected in a linear system (Carnevale and Johnston
1982
; Rall and Segev 1985
), dendritic charge
transfer at rest is on average comparable to somatodendritic
steady-state voltage transfer (Fig. 5C). Due to the
high-frequency components of a glutamatergic conductance, EPSP
amplitude at the soma is significantly reduced (7.7 ± 1.5%, n = 7) compared with the EPSP at the input site.
Because of the slower time course of the conductance, the IPSP peak
amplitudes are reduced less (to about a quarter of the initial size,
i.e., 27 ± 7%, n = 4). Note that, although data
from different experiments are pooled in Fig. 5, C and
D, comparisons were made by a Student's paired
t-test, i.e., data from individual experiments were
compared.
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Neuronal integration not only depends on amplitude transfer but also on
propagation times (Agmon-Snir and Segev 1993). We determined the time centroids of dendritic EPSC/Ps and of the resulting
somatic EPSPs by the method of moments. The centroid delay of synaptic
EPSC and EPSP is called the local delay, whereas the time interval
between the centroids of somatic EPSP and dendritic EPSC is termed the
total delay. Figure 5D shows a summary histogram of
calculated local and total delays in relation to the membrane time
constant. As predicted for a passive neuron, the total delay of
dendritic EPSPs was not significantly different from the corresponding membrane time constant. The local delay (2.7 ± 0.5 ms), which determines the integration time at the synapse, was on the order of a
tenth of the membrane time constant, again in agreement with simulations of pyramidal cells with passive membrane properties (Fig.
5D, cf. Agmon-Snir and Segev 1993
).
Various voltage-dependent membrane conductances can be activated
by small voltage deflections from rest. Therefore the influence of
membrane potential changes on dynamic current-clamp EPSP amplitude and
charge transfer was assessed. Dendritic and somatic membrane voltages
were simultaneously shifted by DC current injections. Figure
6A shows an example of
simultaneously recorded somatic and dendritic dynamic current-clamp
EPSPs at three different holding potentials (56,
71, and
78 mV at
the soma; single traces). There is a small scatter in membrane voltage
between soma and dendrite due to the inability to perfectly clamp the
membrane potential in current-clamp mode. As expected, the dendritic
EPSP amplitude is diminished with depolarization due to a reduced
driving force. At the same time, the somatic EPSP became prolonged.
Figure 6, B and C, show scatter plots of pooled
data (n = 5; results of each cell symbol coded). While
the EPSP peak amplitude ratio was independent of the membrane potential
(Fig. 6B), charge transfer was strongly voltage-dependent
(Fig. 6C). Incomplete series resistance and electrode
capacitance compensation and variable dendritic seal resistances from
experiment to experiment may have contributed to the scatter of the
data points in Fig. 6C. However, these cannot explain the
significant linear relationship between membrane potential and charge
transfer (Pearson's r = 0.44, P < 0.04), which results in a relative charge gain of 30 ± 13% for
10 mV of depolarization. Due to the voltage dependence of
RN, the actual charge gain is expected to
be more pronounced, i.e., our estimate is conservative. We recalculated
the estimates in Fig. 6C for RN
at different holding potentials. The new estimates are still fitted
best with a line, but one with an increased slope of 51 ± 15%
per 10 mV polarization (Pearson's r = 0.59;
P < 0.01). With respect to charge transfer under
passive conditions (horizontal dashed line in Fig. 5C), a
disproportional loss of charge is found below rest, and a gain of
charge between rest and spike threshold (vertical dashed line in Fig.
6C).
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DISCUSSION |
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The main findings of this study are 1) that synaptic charge transfer from dendrite to soma is voltage-dependent, whereas the transfer of peak amplitude is not, and 2) that at rest, voltage and charge transfer from dendrite to soma and vice versa depend on linear cable properties.
The sites of dendritic recordings in this study are relatively proximal
(X < 0.7) compared with the total length
(L ~ 1.7) of the apical dendrite. About 85% of all
excitatory synapses are on spines (DeFelipe and Fariñas
1992; Larkman 1991b
). The apical trunk of a
thick layer V pyramidal cell has a spine density of 6.3/µm and a
total of 3100 spines. Therefore our maximal recording distance is
within the range of ~35% of all synapses on the apical trunk
dendrite. However, a generalization to other synapses of similar
distance on basal and oblique dendrites will have to await experimental
verification. How well are synapses on spines represented by a dynamic
current clamp on the stem dendrite? Recent findings suggest that spines
are more likely to separate synapses biochemically rather than
electrically (Svoboda et al. 1996
). It is therefore reasonable to assume that our main conclusions about synaptic charge
transfer are valid for synapses on spines and on shafts. This point of
view is in agreement with modeling studies of synaptic conductance
inputs on dendritic spines and shafts in pyramidal cells (Turner
1984
).
It has recently been shown that somato-dendritic voltage attenuation
can be best accounted for by a nonuniform
Rm and Ih
(Stuart and Spruston 1998). It is likely that
Ih affects even small voltage deflections
of a few millivolts, as shown by an omnipresent sag in our recordings.
Therefore our estimates of Rm are unlikely to reflect strictly passive conditions. Nevertheless, the reciprocity of transfer resistances and of charge and voltage transfer holds under
our resting conditions as expected for a linear system
(Carnevale and Johnston 1982
; Rall and Segev
1985
). We conclude that within the voltage range of our
observations the interplay of all open conductances still results in a
linear albeit not passive membrane. A similar conclusion was drawn by
studying spatial EPSP summation in hippocampal pyramidal cells
(Cash and Yuste 1999
).
The somatopetal current transfer properties of the apical dendrite
could be satisfactorily approximated by a linear cable model. The
independent estimates of L (1.7) and (400 µm) are in
line with the morphological length of the apical trunk (~0.7 mm) in
these cells (Larkman 1991a
). The simple low-pass
behavior of the apical dendrite agrees with similar findings from
dendrites in spinal neurons (Buchanan et al. 1992
). We
did not find resonance phenomena in our transfer impedance measurements
as described in neuroblastoma neurites (Moore et al.
1988
). In neocortical pyramidal cells, somatic point impedance
measurements revealed a resonance below 2.5 Hz at hyperpolarized
potentials (Hutcheon et al. 1996
). Because our
measurements of transfer impedance were confined to resting conditions,
deviations from linearity cannot be excluded at hyperpolarized membrane voltages.
Our data confirm previous experimental and modeling data
(Cauller and Connors 1992; Markram et al.
1997
) which demonstrated severe EPSP peak attenuation for
unitary input even at moderate electrotonic distances from the soma.
However, quantal current at the soma has been shown to be location
independent (Jack et al. 1981
; Stricker et al.
1996
). This could either result from a location-scaled increase
in input conductance (Stricker et al. 1996
) or an
appropriately balanced boosting mechanism (Cook and Johnston
1999
). In our experiments, we did not scale the conductances of
the dynamic current clamp for dendritic location.
Under unclamped conditions, measuring the charge arriving at the soma
is not possible. However, we were able to show using double somatic
recordings that the voltage integral scaled by RN is a surprisingly precise predictor for
charge estimation with accuracy in the range of 1% (well within the
errors of estimating RN). We also observed
that RN was dependent on the membrane
potential. This is in agreement with the observations of Connors
et al. (1982) and Stafstrom et al. (1984)
in
other cortical slice preparations. This finding can most likely be
explained by rectification in the depolarizing direction due to
INaP (Stafstrom et al.
1982
) and in the hyperpolarizing direction to
Ih (Spain et al. 1987
).
We further obtained evidence that voltage-dependent membrane
nonlinearities influence the flow of charge from a synapse to the soma.
No attempt was made to assess the nature of these conductances but
likely candidates for the prolongation of the EPSP above 60 mV are
INa,p (Stuart and
Sakmann 1995
) and/or INMDA
(activated by ambient glutamate, Sah et al. 1989
).
Ih (Nicoll et al. 1993
;
Stuart and Spruston 1998
) and/or
IA (Hoffman et al. 1997
)
have the potential to cause the truncation of the EPSP below
60 mV.
All four currents have been found in dendritic recordings; they
activate/deactivate or inactivate in the appropriate voltage ranges and
could lead to the required charge gain/loss.
What are the potential functional consequences of voltage-dependent
charge transfer? Modeling studies suggest that the resting membrane
voltage can be depolarized by moderate background activity of
excitatory synapses (Bernander et al. 1991). From our
data we predict that the additional inward current responsible for the
enhanced charge transfer will increase the gain of the relationship between synaptic input and spike output under depolarized conditions. In addition, the time window for nonlinear EPSP summation will be
increased for two reasons: the increase in RN
and the charge gain that is predominantly in the tail of the EPSP.
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ACKNOWLEDGMENTS |
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We are very grateful to Prof. S. J. Redman for carefully reading the manuscript and for excellent advice. We thank Prof. R. J. Douglas, Dr. M. Carandini, and dipl. phys. A. Kern for help with the design, implementation, and analysis of the chirps and stimulating discussions. We are indebted to Dr. A. I. Cowan for experimental support with the double somatic recordings.
This work was supported by Swiss National Science Foundation Schwerpunk Programm Biotechnologie Grants 5002-242787 and 50-52085-97.
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FOOTNOTES |
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Present address and address for reprint requests: D. Ulrich, Dept. of Physiology, University of Bern, Bühlplatz 5, CH-3012 Bern, Switzerland (E-mail: Ulrich{at}pyl.unibe.ch).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 21 January 2000; accepted in final form 25 May 2000.
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REFERENCES |
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