Department of Physiology and Biophysics, University of Washington School of Medicine, Seattle, Washington 98195-7290
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ABSTRACT |
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Oakley, J. C., P. C. Schwindt, and W. E. Crill. Dendritic Calcium Spikes in Layer 5 Pyramidal Neurons Amplify and Limit Transmission of Ligand-Gated Dendritic Current to Soma. J. Neurophysiol. 86: 514-527, 2001. Long-lasting, dendritic, Ca2+-dependent action potentials (plateaus) were investigated in layer 5 pyramidal neurons from rat neocortical slices visualized by infrared-differential interference contrast microscopy to understand the role of dendritic Ca2+ spikes in the integration of synaptic input. Focal glutamate iontophoresis on visualized dendrites caused soma firing rate to increase linearly with iontophoretic current until dendritic Ca2+ responses caused a jump in firing rate. Increases in iontophoretic current caused no further increase in somatic firing rate. This limitation of firing rate resulted from the inability of increased glutamate to change evoked plateau amplitude. Similar nonlinear patterns of soma firing were evoked by focal iontophoresis on the distal apical, oblique, and basal dendrites, whereas iontophoresis on the soma and proximal apical dendrite only evoked a linear increase in firing rate as a function of iontophoretic current without plateaus. Plateau amplitude recorded in the soma decreased as the site of iontophoresis was moved farther from the soma, consistent with decremental propagation of the plateau to the soma. Currents arriving at the soma summed if plateaus were evoked on separate dendrites or if subthreshold responses were evoked from sites on the same dendrite. If plateaus were evoked at two sites on the same dendrite, only the proximal plateau was seen at the soma. Just-subthreshold depolarizations at two sites on the same dendrite could sum to evoke a plateau at the proximal site. We conclude that the plateaus prevent current from ligand-gated channels distal to the plateau-generating region from reaching the soma and directly influencing firing rate. The implications of plateau properties for synaptic integration are discussed.
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INTRODUCTION |
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In the CNS, most of a
neuron's synaptic input occurs on its vast dendritic arbor. Dendritic
membrane properties will affect the transfer of synaptic current to the
region near the soma where a propagated axonal spike is initiated.
Early work exploring the electrical consequences of dendritic structure
assumed a passive dendritic tree (reviewed in Rall
1977). In this view, the current from each synapse, weighted by
its distance from the soma, sums linearly at the spike-generating zone.
Direct dendritic recording, on the other hand, has revealed
voltage-gated conductances in the dendrites of pyramidal neurons
(Hoffman et al. 1997; Magee and Johnston
1995a
,b
; Magee et al. 1996
; Markram and
Sakmann 1994
; Stuart and Sakmann 1994
). The
activation of inward dendritic current of any subthreshold magnitude
increases the transfer of current from dendrites to soma
(Schwindt and Crill 1995
). A net inward dendritic
current would lead to regenerative dendritic potentials that would
further amplify distal excitatory synaptic currents (Spencer and
Kandel 1961
).
In neocortical neurons, focal depolarization of the apical dendrite
evokes both short-duration Ca2+ spikes
(Kim and Connors 1993; Larkum et al.
1999
; Schiller et al. 1997
; Schwindt and
Crill 1997a
) and long-duration
Ca2+ spikes (Kim and Connors 1993
;
Schwindt and Crill 1999
), depending on stimulus
duration. Similar all-or-none Ca2+ spikes have
been evoked by injection of depolarizing current into dendrites
(Kim and Connors 1993
; Schiller et al.
1997
) and by the focal iontophoresis of glutamate on the apical
dendrite (Schwindt and Crill 1997
-1999
). Both an
initial short-duration Ca2+ spike and a
subsequent long-duration Ca2+ spike can be evoked
together during a sufficiently long dendritic depolarization
(Schwindt and Crill 1999
). The transient, short-duration (~100 ms) Ca2+ spike repolarizes even though
dendritic depolarization is maintained, whereas the subsequent
long-duration spike (termed a "plateau") lasts as long as the
dendritic depolarization is maintained and collapses when it is
withdrawn. The purpose of the present study was to investigate the role
of dendritic Ca2+ spikes in the transduction of
current into spike trains. For this purpose, it was most convenient to
focus on the long-duration plateau Ca2+ spike.
Because this response is maintained as long as the dendritic depolarization, which the experimenter can control, firing rate can
attain a steady-state value during the plateau, and the effect of the
Ca2+ spike can thus be quantified in terms of its
effect on the cell's frequency-current (f-I) relation.
Furthermore, the steady-state firing rate is directly related to the
current that is transmitted from dendrite to soma (Powers et al.
1992
; Schwindt and Crill 1996
; Schwindt
et al. 1997
). Thus changes in steady firing rate reflect
changes in the current arriving at the soma in response to the
dendritic Ca2+ spike.
In this study, the dendritic depolarization was caused by the iontophoresis of glutamate on visualized sites on apical, basal, and oblique dendrites of layer 5 pyramidal neurons. The use of iontrophoresed glutamate is convenient for several reasons. Foremost, it allows depolarization amplitude and duration [particularly those durations longer than a single excitatory postsynaptic potential (EPSP)] to be controlled conveniently by the experimenter at a precisely known distance from the soma in a way that is not possible with electrically evoked synaptic input. For these longer depolarizations, glutamate iontophoresis is more convenient than intradendritic recording (with the possibility of associated cellular damage or cytoplasmic washout) and the injection of depolarizing current, and it is more physiological than intradendritic current injection insofar as the glutamate-evoked depolarization is caused by a (purely) excitatory conductance increase similar to that would accompany tonic synaptic excitation. In addition, it allows the response to the same depolarizing stimulus to be compared in the absence and in the presence of channel-blocking agents that would alter or block synaptic transmission.
We find that the depolarization of apical, basal, and apical-oblique dendrites evokes Ca2+ spikes that result in a nonlinearity in the steady-state f-I relation that contrasts markedly with the linear f-I relation obtained from soma depolarization. We also describe the interaction of dendritic ligand-gated depolarization at multiple dendritic sites. Although Ca2+ spikes were postulated previously only to amplify dendritic current, we find an additional, unexpected, current-limiting function of the Ca2+-dependent regenerative responses. We discuss some implications of this current limiting property of dendritic Ca2+ spikes on the transduction of synaptic input into spike output.
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METHODS |
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Tissue preparation and solutions
Sprague-Dawley rats of either sex aged 15-32 days postnatal
were anesthetized with ketamine (150 mg/kg) and xylazine (10 mg/kg) and
killed by carotid section. Following craniotomy, a section of dorsal
frontoparietal (sensorimotor cortex) was removed, fixed with
cyanoacrylite glue to the stage of a microslicer, and submerged in ice
cold physiological saline solution (PSS) containing (in mM) 130 NaCl,
3.0 KCl, 2.0 MgCl2, 1.25 NaH2PO4, 26 NaHCO3, 2 CaCl2, and 20 glucose gassed with 95% O2-5%
CO2 (carbogen). Coronal slices were cut 300 µm
thick and stored in a holding chamber filled with PSS gassed with
carbogen at 34°C. Individual slices were transferred to a recording
chamber where they were maintained submerged in 29-32°C PSS gassed
with carbogen flowing at >2 ml/min. In some experiments, TTX (1 µM,
Sigma Chemical, St. Louis, MO) or
D()-2-amino-5-phosphonopentanoic acid (AP-5) (100 µM,
Precision Neurochemicals, Vancouver, BC, Canada) was added to the PSS,
or 200 µM CdCl2 was substituted for an
equimolar amount of CaCl2 and
NaH2PO4 was omitted to
avoid precipitation.
The bottom of the 20-mm-diam, 3-mm-deep recording chamber was formed by a No. 1 glass coverslip. The slice was held in place on the coverslip by thin glass bars straddling the two arms of a U-shaped platinum wire 300 µm thick. The gravity-fed inflow and suction outflow were positioned to promote laminar flow across the slice. The recording electrode and the iontophoretic electrodes opposed each other so that they could be placed independently anywhere in the chamber.
Recording methods
An upright microscope (Zeiss standard 16 or Olympus BX50WI) fit with ×40 LWD water-immersion objectives and DIC optics was used to view cells in the top 100 µm of the slice. The slice was transilluminated using infrared illumination (Omega 770 ± 40 nm band-pass filter) and viewed using a CCD camera (Sony or Hamamatsu) and a high-resolution video monitor (Sony). The microscope was fixed to an X-Y translation stage that allowed the microscope to be positioned independently of the recording and iontophoretic electrodes so that different portions of the cell could be viewed without disturbing these pipettes.
Micropipettes pulled from 75 µL capillary glass and filled
with standard intracellular solution containing (in mM) 135 KMeSO4, 5 KCl, 2 MgCl2, 10 (3-[N-morpholino]propanesulfonic acid) (MOPS), 0.1 ethylene glycol-bis(-aminoethyl
ether)N,N,N',N'-tetraacetic acid (EGTA), 2 Na-ATP, 0.2 Na-GTP and (in %wt/vol) 0.01 Lucifer yellow K+
salt. In control experiments (n = 4), omitting the
K+ Lucifer yellow dye from the patch solution
caused no measurable change in cell properties.
Extracellular pipette resistance was 2-4 M. The seal resistance
formed with the soma membrane was >1 G
before break-in to the whole
cell configuration. Series resistance in the whole cell configuration
was monitored by maintaining bridge balance during a hyperpolarizing
current pulse. Recordings were discarded if series resistance became
>50 M
.
An Axoclamp-2A amplifier (Axon Instruments, Foster City, CA) was used in bridge mode to record somatic membrane potential and inject current through the recording pipette. Stable recordings lasting 1-2 h were frequently obtained. Resting potential was taken as the difference between intracellular and extracellular potentials recorded on a strip chart recorder. Recorded potentials were corrected for a tip potential of 10 mV. Current and voltage recordings were filtered at 10 kHz and stored on videotape using pulse code modulation (Neurodata) and were later digitized (Axon Instruments TL-1 125 interface) and analyzed using the program WCP written and distributed by John Dempster and the program IGOR (Wavemetrics, Lake Oswego, OR).
Glutamate iontophoresis
Fluorescence microscopy was used to view simultaneously the dendritic arbor and the iontophoretic electrode so that glutamate could be applied to visually identified site on a dendrite at a known distance from the soma. After obtaining a stable whole cell recording, short, hyperpolarizing current pulses (<500 pA) were applied to the recording pipette to iontophorese K+-Lucifer yellow dye into the cell. The DIC analyzer was removed, and the light path was switched from transmitted light to epifluorescence illumination with excitation at 425 nm and emission at 535 nm. In many cells, the dendritic arbor was visible at a distance of >700 µm within 10 min after breaking into the cell.
Iontophoretic electrodes were pulled from 1-mm-OD borosillicate glass
capillary tubes. Their tips were broken to 2 µm diam, and they were
filled with (in mM) 150 glutamatic acid, 2.24 CaCl2, 4 KCl, 30 N-(2
hydroxyethyl)piperizine-N'-(2-ethanesulfonic acid) (HEPES),
and (as % wt/vol) 0.05% K+ Lucifer yellow salt
at pH 7.4. The second current amplifier and headstage of the
Axoclamp-2A amplifier was used to provide positive DC holding current
(+5 nA) and negative iontophoretic pulses (1-2 s duration, 5- to
100-nA amplitude). In some experiments, an additional current-clamp
amplifier (WPI Model M-707, New Haven, CT) was used to pass current
through a second, independently placed, iontophoretic electrode on the
dendrites. Movement of the electrode tip over a range of 10-20 µm
near the visualized dendrite caused the iontophoretically evoked
response to vary from zero to maximal. The glutamate concentration 10 µm from the electrode tip caused by an iontophoretic current
sufficient to evoke a plateau potential was estimated to be
10 mM
(see DISCUSSION). The straight-line distance from the
center of the soma to the iontophoretic electrodes was measured on the
high-resolution video monitor which was previously calibrated using a reticule.
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RESULTS |
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Ninety-two visually identified layer 5 pyramidal neurons were
studied in slices from 59 rats. Stable resting potentials ranged from
62 to
80 mV (mean:
72 mV). Input resistance, measured with long
hyperpolarizing and depolarizing current pulses, varied from 24 to 100 M
(mean: 50 M
), and all recorded cells exhibited regular spiking
(Connors and Gutnick 1990
) in response to depolarization of the soma by injected current. No intrinsic bursting or fast spiking
cells (Connors and Gutnick 1990
) were found. To
investigate the effect of dendritic depolarization on repetitive firing
properties, glutamate was iontophoresed focally (Fig.
1) for 1-2 s on 124 visually identified
sites on the soma and on apical, oblique and basal dendrites. Although
the prolonged focal iontophoresis to glutamate may not mimic synaptic
input it evoked prolonged depolarizations that allowed repetitive
firing to approach a steady-state value.
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Firing patterns evoked by focal depolarization of the apical dendrite
Focal iontophoresis of glutamate was used to depolarize sites on
the apical dendrite up to 730 µm from the soma, and the evoked firing
patterns were studied. The glutamate iontophoresis alone at many distal
dendritic sites did not cause sufficient somatic depolarization to
evoke Na+ spikes. Therefore the spike patterns
evoked by dendritic depolarization were studied by combining a constant
depolarizing injected current at the soma with focal glutamate
iontophoresis at the dendritic site. In response to iontophoresis of
increasing amplitude, these cells displayed the same sequence and types
of firing patterns as cells in which iontophoresis alone evoked
repetitive firing (data not shown) (cf. Schwindt and Crill
1999).
At sites >200 µm from the soma (32 sites tested), low-amplitude
iontophoretic currents evoked regular spiking (Fig.
2, A and B).
Increasing the iontophoretic current to a critical value evoked a
complex firing response that consisted of an initial epoch of burst
firing followed by a longer period of regular spiking
(n = 27/32 sites, Fig. 2C). During the
initial burst firing epoch, each burst of two to four spikes was
separated by large hyperpolarizing afterpotentials (Fig. 2,
C and D). These complex firing responses were
similar to those evoked by glutamate iontophoresis and focal synaptic
input at the apical dendrite in a previous study (Schwindt and
Crill 1999). Increases in iontophoretic current above the "threshold" value that first evoked the complex response reduced the number of initial bursts and increased the duration of the late
regular spiking. For example, the highest iontophoretic current tested
in the cell of Fig. 2 (
90 nA, Fig. 2D), evoked only a single burst followed by late regular spiking. Frequency-time (F-T)
plots illustrate the irregular nature of the instantaneous firing rate
during the burst firing (Fig. 2, G and H) and the nearly constant late regular spiking rate.
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Once the complex firing response was evoked, further increases in
iontophoretic current did not increase the rate of late regular
spiking. This is best appreciated from a plot of the frequency (f) of late regular spiking versus iontophoretic current
(I). Figure 3A
shows a typical nonlinear f-I relation obtained by
depolarization of sites on the apical dendrite >200 µm from the
soma. During smaller iontophoretic currents, regular spiking rate was
graded with iontophoretic current (Fig. 3A, line segment 1).
During the iontophoretic current that first evoked the complex firing
response, the average frequency of late regular spiking during the
complex response was faster than would be expected from an
extrapolation of the graded, linear relation (line segment 1) evoked by
smaller iontophoretic currents. Thus the onset of the complex response was associated with a "jump" of firing rate. No further increase in
firing rate was evoked by larger iontophoretic currents. The average
firing rate during the late regular firing is plotted as line segment 2 in Fig. 3A. Only the duration of the late regular spiking
increased with iontophoretic current (cf. Fig. 2, G and H), not the average rate. Evidence presented in the
following text will show that this apparent saturation of firing rate
is not caused by a saturation of the cell's firing mechanism nor by a
saturation of the iontophoretic system nor by a saturation of the
glutamate receptors at the dendritic site. Rather, as shown previously
(Schwindt and Crill 1999), it is caused by the
initiation of a localized, all-or-nothing, long-duration
Ca2+ spike (a plateau).
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Response to depolarization of the soma and proximal apical dendrite
In contrast to the results of dendritic depolarization,
depolarization of the soma either with injected current
(n = 15) or with glutamate iontophoresis
(n = 3) evoked only regular repetitive firing in every
cell tested (Fig. 4, A-D).
Typical plots of instantaneous firing rate versus time (F-T plots) are
shown for two levels of soma current injection (Fig. 4, E
and F) and for glutamate depolarization of the soma (Fig. 4,
G and H). Firing rate was a linear function of
both somatic iontophoretic current (Fig. 3B, and
)
and injected current (Fig. 3B,
and
). Iontophoresis
of glutamate within the first 100 µm of the apical dendrite also
evoked graded regular spiking and a linear frequency-current relation
(n = 3, data not shown). Both current injected into the
soma and glutamate iontophoresis on the soma could evoke a firing rate
30% faster than the regular spiking rate evoked by dendritic
iontophoresis in the same cell (n = 15 cells tested).
Thus the saturation of the rate of late regular spiking during
dendritic depolarization was due neither to saturation of the cells'
spike-generating mechanism nor to a nonlinear iontophoretic system.
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Plateau properties control late regular spiking during the complex response
To study the properties of the current flowing from dendrite
to soma, a glutamate iontophoresis that evoked a complex response was
combined with a hyperpolarization of the soma (by current injection
through the recording pipette) to reduce or eliminate Na+ spiking. This procedure revealed a late,
long-lasting plateau depolarization that could be evoked all- (Fig.
5, 2) -or-none (Fig. 5, 1) by varying
iontophoretic current strength. In the experiment of Fig. 5, the soma
hyperpolarization was not quite large enough to prevent the initiation
of fast Na+ spikes during the plateau, which
terminated shortly after the iontophoretic current was removed. Plateau
amplitude (18 mV in Fig. 5) was measured as the difference between the
peak depolarization during a plateau (indicated by - - - in Fig. 5)
and the peak depolarization during a just-subthreshold response. The
slow spikes evoked late during the just-subthreshold response in Fig.
5, trace 1 and prior to the plateau in Fig. 5, trace 2 are likely
caused by a transient Ca2+ spike of the type
described previously (Schwindt and Crill 1997-1999
) because they were blocked by Cd2+ application
(see following text). Hyperpolarization of either the soma or the first
100 µm of the apical dendrite during the application of iontophoretic
currents up to 100 nA never revealed a plateau, whereas plateaus were
evident during iontophoresis at more distal dendritic sites (>100 µm
from the soma) in the same cells. In addition, iontophoresis at sites
and at levels that evoked the complex firing response in control
solution revealed underlying plateaus after Na+
spikes were blocked by the addition of 1 µM TTX (see following text).
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Once a plateau was initiated, further increases in iontophoretic
current did not increase plateau amplitude. Instead, the latency to
plateau initiation decreased (Fig.
6A). The responses in Fig.
6A, evoked by increasing iontophoretic current, explain several properties of the late regular spiking and the dendritic f-I relation. Plateau initiation (late in the response to
the 50-nA iontophoresis) adds a depolarizing, membrane-generated, ionic current to the current flowing through the glutamate receptors at
the iontophoretic site. This additional depolarizing current would
cause a jump in the firing rate of the cell. Iontophoretic currents
(
60,
70 nA) greater than that which first evoked the plateau
("suprathreshold" currents) did not increase the amplitude of the
plateau. The constant plateau amplitude (constant depolarization of the
soma) in the face of increased iontophoretic current would result in
the constant rate of late regular spiking. The decreased latency to
plateau initiation evoked by suprathreshold iontophoretic currents
(
60,
70 nA) would result in the increased duration of regular
spiking observed during the application of suprathreshold currents.
Thus the properties of the underlying plateau can explain both the
frequency jump and the subsequent saturation of firing rate seen in the
f-I relation of Fig. 3A.
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Another possible explanation for the insensitivity of plateau amplitude (thus firing rate) to suprathreshold iontophoretic currents would be the saturation of the local dendritic glutamate receptors. Figure 6B shows that plateau amplitude (thus the rate of late regular spiking) was not limited by this putative mechanism. The addition of Cd2+ (200 µM) to the bath abolished the plateau. Soma depolarization was then graded with iontophoretic current amplitude even beyond the iontophoretic current that evoked the plateau in control solution. The response amplitude measured near the end of the iontophoresis (at time indicated by * in Fig. 6, A and B) is plotted as a function of iontophoretic current in Fig. 6, C and D (for the responses of Fig. 6, A and B, respectively) to indicate more clearly the saturation of plateau amplitude in control solution and the graded response in Cd2+. Similar results were obtained in each of three cells tested. Thus a saturation of the local dendritic glutamate receptors cannot explain the inability of suprathreshold glutamate iontophoresis to increase plateau amplitude. A more likely explanation is that the additional glutamate current is shunted through a high membrane conductance in the plateau-generating region and/or the local (dendritic) plateau amplitude approaches glutamate reversal potential.
The abolition of the plateau by 200 µm Cd2+ was
observed in each cell tested in this study (n = 6),
which identifies it as dependent on Ca2+ influx
through voltage-gated Ca2+ channels (cf.
Schwindt and Crill 1999). Previously, it was found that
plateaus at some sites could be blocked completely (but reversibly) by
either Cd2+ or TTX (Schwindt and Crill
1999
). Thus the possible dependence of the plateau on inward
current flowing through other types of ion channels was also
investigated. A role for the persistent Na+
current at some sites was indicated by the blockade of plateaus after
the addition of 1 µM TTX in 3 of 15 cells tested. Current flowing
through N-methyl-D-aspartate (NMDA) channels
also can evoke regenerative responses in neocortical neurons
(Flatman et al. 1986
) as a consequence of the
N-shaped current-voltage relationship of NMDA-sensitive
glutamate receptor channels in the presence of physiological
concentrations of Mg2+ (Nowak et al.
1984
). A role for current through NMDA-sensitive channels at
some sites was indicated by the abolition of plateaus by 100 µM AP-5
in two of five cells tested. To further test the necessity of currents
other than Ca2+ for plateau generation, the
combination of 1 µM TTX plus 100 µM AP-5 was added in 12 other
experiments after plateaus were first evoked in control solution by
iontophoresis at sites 150-650 µm from the soma. This drug
combination blocked the plateau in 3 of the 12 cells. Overall, these
results suggest that current through voltage-gated
Ca2+ channels is essential for plateau generation
at most dendritic sites, but currents through TTX- and/or
AP-5-sensitive channels are also required for plateau generation in a
minority of dendritic sites.
Plateaus are propagated decrementally to the soma
Figure 7A shows that
plateau amplitude (measured at the soma as in Fig. 5) decreased with
the iontophoretic distance from the soma along the apical dendrite.
These data are fit with a line (least-squares method) having a slope of
2.5 mV/100 µm. The data of Fig. 7 are consistent with the
decremental propagation of the plateau to the soma. If propagation
toward the soma was entirely active, plateau amplitude at the soma
should be independent of the propagation distance. That is, the plateau
would always be the same amplitude regardless of where it was initiated
on the dendritic tree. This expected constant amplitude would be similar to that which we observed at the most proximal portion of the
apical dendrite (150-200 µm from the soma) at which we were able to
evoke a plateau. Instead, these data are best explained if the plateau
is initiated at or near the iontophoretic site and subsequently
propagates decrementally to the soma. Similar evidence for decremental
conduction, and its dependence on the activation of dendritic
tetraethylammonium-dependent K+ currents, was
obtained previously for the transient Ca2+ spikes
(Schwindt and Crill 1997
).
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As described in the preceding text, the dendritic f-I
relation usually exhibited a jump in firing rate at the iontophoretic current that first evoked complex spiking. This jump in firing rate is
expected if plateau initiation adds a constant, membrane-generated, ionic current to the current flowing through the glutamate receptors at
the iontophoretic site. According to this idea, the size of the jump in
firing rate should decrease with distance from the soma because plateau
amplitude decreases with distance. Figure 7B shows that the
jump in firing rate at the initiation of complex spiking (as indicated
in Fig. 3A) also decreased as the site of dendritic
depolarization was moved further from the soma. These data are fit with
a line (least-squares method) with a slope of 2.0 Hz/100 mm.
Plateaus can be evoked in basal, oblique, and distal apical dendrites
Because most of the surface area and synaptic contacts of layer 5 pyramidal cells are located in the basal and apical-oblique dendrites
and in the tuft region of the apical dendrite (Gilbert and
Wiesel 1981), we also investigated whether plateaus could be
evoked in these portions of the dendritic tree. Sites on the fine
branches of the distal apical tuft could not be tested because K+-Lucifer yellow dye did not diffuse to these
sites in high enough concentration to visualize them accurately within
the time frame of the experiments. However, sites beyond the primary
apical branch point could be visualized. In the experiment of Fig.
8B, an iontophoretic electrode
was placed at a site 730 µm from the soma (~200 µm beyond the
primary apical branch point), and a plateau (preceded by a transient
Ca2+ spike) was evoked (trace 2). Plateaus were
evoked beyond the primary apical branch point at 14/15 sites tested in
14 cells.
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Plateaus were evoked on apical-oblique dendrites at 7/9 sites tested in seven cells. In Fig. 8C, a plateau was evoked when the iontophoretic electrode was placed 20 µm out on an oblique dendrite that arose from the apical dendrite at 60 µm from the soma. To observe the underlying plateau, it was necessary to hyperpolarize the soma with DC current to block Na+ spikes. In this cell iontophoresis on the apical dendrite within 100 µm of the soma did not evoke all-or-none responses. Thus the all-or-none response of Fig. 8C was not caused by glutamate diffusion to the apical dendrite.
Plateaus were evoked on basal dendrites at 7/8 sites tested in seven cells. Figure 8D shows the all- (traces 2 and 3)-or-none (trace 1) initiation of a much smaller plateau on a basal dendrite 100 µm from the soma. Unlike the responses at other dendrites, no plateau evoked on a basal dendrite was preceded by a Ca2+ spike. Plateaus could be evoked closer to the soma (50-100 µm) on basal dendrites than on the apical dendrite. All plateaus initiated in basal dendrites were much smaller than those initiated on the apical dendrite at comparable distances from the soma (Fig. 7, ×). At all sites tested on distal apical, oblique, and basal dendrites, once the plateau was evoked larger iontophoretic currents did not increase plateau amplitude recorded in the soma.
We also tested whether the f-I curves evoked by depolarization of these dendrites had features similar to those evoked by depolarization of the main apical trunk and whether there was a similar correlation between the f-I relation and plateau properties. The f-I relations shown in Fig. 8, E-G, were obtained from iontophoresis at the sites corresponding to Fig. 8, B-D, respectively. In Fig. 8, E and G (corresponding to distal apical and basal dendritic sites, respectively), plateau amplitude was too small to evoke firing by itself. Thus a steady depolarizing soma current was injected to maintain constant low-rate firing, and the incremental increase in firing rate caused by the dendritic response was plotted.
A complex firing response, similar to that evoked by iontophoresis at more proximal sites, was evoked beyond the primary apical branch point at 6/8 sites tested in eight cells. Similar to results obtained from the more proximal apical dendrite, when the complex firing response commenced, there was a jump in firing rate, and larger iontophoretic currents caused no further increase in firing rate (Fig. 8E).
Repetitive firing patterns evoked by iontophoresis at sites on apical-oblique dendrites were indistinguishable from those evoked by iontophoresis on the apical dendrite (Fig. 8F). A complex firing response was evoked at five of nine sites tested on apical-oblique dendrites.
In records from basal dendrites (Fig. 8G), a jump in firing rate was not readily apparent at the transition between the graded and the flat regions of the f-I relation (n = 5/5), undoubtedly because the small amplitude of the plateau evoked at this site caused little additional depolarizing current at the soma. Iontophoresis, alone or in combination with depolarizing soma current, evoked only regular spiking in basal dendrites. Initial bursts of Na+ spikes were never seen.
Overall, the firing patterns and f-I relations obtained at distal sites on the apical, apical-oblique, and basal dendrites were as would be predicted from the properties of the plateaus evoked at the same sites. It was evident that plateau amplitude remained constant in the face of larger iontophoretic currents. Basal dendrite sites <50 µm from the soma appeared to be incapable of generating plateaus or frequency jumps or saturating f-I relations. At least some sites on oblique dendrites that arise from the apical dendrite within 100 µm from the soma can generate plateaus.
Interactions of depolarizations evoked at two dendritic sites
As described in the preceding text, once a plateau was initiated, the application of more glutamate applied to the same dendritic site generated no additional flow of current to the soma (i.e., no increase of plateau amplitude). If a plateau can limit the somatopetal flow of ligand-gated current from the iontophoretic region, we would expect the flow of ligand-gated current from more distal regions also to be limited. To test this hypothesis, glutamate was iontophoresed at two dendritic sites. At each site the iontophoretic current was adjusted to evoke a all-or-none spike and plateau potential The iontophoretic current at one site (e.g., the distal site in Fig. 9A) was delayed with respect to the iontophoresis at the other site so that response amplitudes before, during, and after a period of simultaneous iontophoresis at both sites could be compared. All experiments were carried out in the presence of 1 µM TTX to avoid the use of soma hyperpolarization, which would otherwise be needed to block Na+ spikes and visualize the plateaus. In Fig. 9A, transient Ca2+ spikes and plateaus of different amplitudes were evoked at the proximal site alone (373 µm from the soma; trace P) and at the distal site alone (580 µm from the soma; trace D). During the period of combined simultaneous iontophoresis (trace C), the amplitudes of both the initial transient Ca2+ spike and the plateau were nearly identical to those evoked by the proximal iontophoresis alone. The depolarization from resting potential during the period of simultaneous iontophoresis (measured at time indicated by * in Fig. 9A) was 23 mV compared with 21.5 mV for the proximal response alone and 15 mV for the distal response alone. Also note that an initial Ca2+ spike preceded the distal plateau when it was evoked alone but this spike was absent during the combined simultaneous iontophoresis. After the proximal iontophoretic current was turned off during the combined iontophoresis (trace C), membrane potential decayed toward the amplitude of the plateau evoked by the distal iontophoresis alone. This latter observation establishes that the plateau was maintained at the distal region throughout the combined simultaneous iontophoresis. If it had collapsed (due, e.g., to Ca2+ channel inactivation caused by the proximal plateau), membrane potential would have declined to a subthreshold level instead of to the amplitude of the distal plateau. In each of four cells tested, simultaneous iontophoresis on proximal and distal sites produced similar results: the simultaneous iontophoresis evoked a plateau whose amplitude was similar to that evoked by the proximal iontophoresis alone. These experiments suggest that, in addition to limiting glutamate-evoked currents in the plateau-generating region, plateaus can also isolate the soma from glutamate currents generated in more distal regions.
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The summing properties of dendritic currents that do not flow through a plateau region was tested by glutamate iontophoresis on separate dendrites. Figure 9B shows plateaus evoked individually by iontophoresis on a basal dendrite 128 µm from the soma (trace B) and on the apical dendrite 580 µm from the soma (trace A). An initial Ca2+ spike preceded the plateau evoked on the apical dendrite (trace A), but, as described in the preceding text, transient Ca2+ spikes never preceded plateaus evoked on basal dendrites. Trace C shows the response evoked by combined iontophoresis on the apical and basal dendrites. During the period of simultaneous iontophoresis on both dendrites, membrane potential both at the peak of the initial Ca2+ spike and during the plateau was more depolarized than during the response evoked by iontophoresis on the apical dendrite alone. Depolarization from resting potential (measured at the time indicated by * in Fig. 9B) was 15.9 mV compared with 6.9 mV during iontophoresis on the basal dendrite alone and 11.9 mV during iontophoresis on the apical dendrite alone. After the basal iontophoretic current was turned off, membrane potential decayed to the amplitude of the plateau evoked by iontophoresis on the apical dendrite alone. This summation of plateaus evoked on basal and apical dendrites was observed in each of two cells tested.
The depolarization evoked by simultaneous iontophoresis at both dendrites in Fig. 9B was smaller than the algebraic sum of the depolarizations evoked by the individual iontophoresis on each dendrite. In a separate experiment, we evoked a plateau (in the presence of TTX) by dendritic glutamate iontophoresis, and we compared the plateau amplitude when it was evoked from resting potential with its amplitude when it was evoked during a 15-mV DC depolarization of the soma caused by intrasomatic injected current. When evoked during the soma depolarization, the amplitude of the plateau decreased by 56% (9 vs. 4 mV) compared with its amplitude when evoked at resting potential (data not shown). This reduction of plateau amplitude depends solely on the shunting of the current that flows from the dendritic plateau by the depolarization-activated outward rectification (e.g., K+ currents) in the soma membrane in the presence of TTX. Thus we ascribe the sublinear summation of the individual plateaus during the simultaneous iontophoresis in Fig. 9B to the same mechanism, namely, outward rectification in the soma membrane. It is likely that the currents flowing to the soma from the individual plateaus to sum more perfectly than indicated by the summed plateau depolarizations.
If the plateau limits the ability of more-distal ligand-gated currents to reach the soma, then we would expect dendritic currents to sum at the soma when dendritic membrane potential remains subthreshold for plateau initiation. In Fig. 10A iontophoretic electrodes were placed on the apical dendrite at 192 µm and at 240 µm from the soma, and iontophoretic current was adjusted to evoke only a subthreshold response at each site. During the period of combined simultaneous iontophoresis, a subthreshold response was recorded at the soma (trace C) that was nearly the algebraic sum of the two individual responses. Depolarization from resting potential (measured at the time indicated by * in Fig. 10A) was 8.4 mV compared with 5.5 mV during proximal iontophoresis alone and 3.1 mV during distal iontophoresis alone. This summation of subthreshold responses evoked at a proximal and a distal site on the apical dendrite was recorded in each of two cells tested.
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Plateaus are preferentially evoked at the proximal border of an adequately depolarized region
Additional summing properties were identified. Figure 10B is from the same cell and sites as Fig. 9A. The iontophoretic current at the proximal site was reduced to evoke a subthreshold response (trace P) while a plateau was still evoked at the distal site (trace D). When the two stimuli were combined (trace C), the amplitude of the plateau was similar to that evoked by proximal iontophoresis alone (cf. Fig. 9A, trace P). Depolarization from resting potential (measured at time indicated by * in Fig. 10B) was 20 mV compared with 15 mV during the distal iontophoresis and 6 mV during the proximal iontophoresis alone. After the proximal iontophoretic current was turned off (trace C), membrane potential decayed to the amplitude of the distal plateau, again indicating that it was maintained during the simultaneous iontophoresis.
Notice in Fig. 10B that the plateau evoked by combined proximal and distal iontophoresis (trace C) reached its maximum amplitude at a time when the membrane potential at the distal site was expected to be subthreshold for plateau initiation based on its time course when that site was stimulated alone (trace D). That is, the initiation of the proximal plateau is caused by the spatial summation of two subthreshold responses. Similar observations made in each of four cells tested suggest that the spatial summation of subthreshold responses at a proximal and distal site can evoke a plateau and that plateau will be generated at the proximal site. Once the proximal plateau is evoked, distal currents will not reach the soma to influence the spike rate of the cell.
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DISCUSSION |
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Tonic focal depolarization of the apical dendrite by glutamate evoked a nonlinear input-output relation characterized by a jump in the rate of regular spiking at the iontophoretic current that evoked a complex firing response and by a saturation of firing rate at larger iontophoretic currents. This nonlinear f-I relation contrasted with the graded, linear, f-I relation evoked by glutamate depolarization of the soma and the most proximal apical or basal dendrites of the same cell. These nonlinear features of the dendritic input-output relation resulted from the properties of an all-or-none dendritic plateau potential that is evoked at a critical level of dendritic depolarization. Plateaus could be evoked by adequate glutamate iontophoresis at sites on apical, basal, and apical-oblique dendrites, but not at the soma, nor the proximal 100 µm of the apical dendrite, nor the proximal 50 µm of the basal dendrites.
As mentioned in the INTRODUCTION, we used glutamate
iontophoresis to depolarize sites on the dendritic arbor because of its many experimental advantages, and we focused on the long-duration (plateau) Ca2+ spike because it allowed changes
of firing rate during Ca2+ spikes both to be
quantified and to directly reflect changes in the flow of current from
dendrite to soma. With these procedures, we hoped to gain insight into
the role of any dendritic Ca2+ spike (short or
long duration) on synaptic integration. While a short-duration
Ca2+ spike will increase firing rate transiently
(e.g., during the initial bursts shown in Fig. 2), quantitative
analysis of the change in firing rate is complicated by the fact that
the instantaneous firing rate is a function of both the amplitude and
the rate of rise of the depolarizing current delivered to the soma
(Schwindt et al. 1997). The rate of rise of the
transient Ca2+ spike is variable among cells,
sequential spikes, and trials, whereas the steady-state firing obtained
during a plateau is well defined and highly reproducible. As we will
discuss in the following text, the most important feature of a
Ca2+ spike for synaptic integration is not
necessarily its duration. Nevertheless, the transient dendritic
Ca2+ spike may be evoked by a single EPSP or
other brief depolarization (Kim and Connors 1993
;
Larkum et al. 1999
; Schiller et al. 2000
; Schwindt and Crill 1998
) whereas the plateau requires a
much longer depolarization, 1-2 s of glutamate iontophoresis in the
present study to evoke the steady-state firing. Since we mean to draw inferences from our results about synaptic integration, the question may arise as to whether the long-lasting glutamate-dependent
depolarization evokes a physiological response.
Several issues relating to possible artifactual results or
pathophysiological responses from long-lasting glutamate iontophoresis have been addressed in detail previously (Schwindt and Crill
1997a). The ultimate measure of the glutamate reaching the
dendrite and the intensity of this input is the intensity of the
cell's output. Tonic firing evoked by the plateau itself was <50 Hz.
Recordings from pyramidal neurons in awake, behaving animals have shown
that they may fire much faster than this for the duration (several seconds) of defined tonic motor tasks (e.g., Cheney and Fetz
1980
). Judging by the cell's output, the tonic stimulus that
we employed is well within the physiological range. Furthermore, it is
important to understand that the dendritic membrane does not experience the concentration of glutamate in the iontophoretic electrode. The
concentration of glutamate ([glu]) at the dendritic membrane nearest
to the iontophoretic electrode may be estimated using Eq. 18 of
Nicholson and Phillips (1981)
, who used iontophoretic electrodes with salt concentrations and tip diameters similar to ours
to show experimentally that this equation was valid for the
iontophoresis of both cations and anions in brain (and brain slices)
(cf. Nicholson and Hounsgaard 1983
). Using the
parameters from their Tables 2 and 3 measured for tetraethylammonium
(TEA), which has a molecular weight slightly less than glutamate, a
distance of 10 µm between electrode tip and dendritic membrane and a
current of 50 nA (a typical value required to evoke a
Ca2+ spike or plateau in our experiments), we
calculate a glutamate concentration of ~18 mM at the dendrite. This
value is likely to be an upper bound, first because glutamate, unlike
TEA, is taken up strongly by neural tissue (Garthwaite
1985
), and second because the most important parameter that
determines the concentration for a given distance and current (namely,
volume fraction) may be significantly larger near the disrupted slice
surface where our cells were recorded. Thus we estimate that the
[glu] required to evoke the Ca2+ spike and
plateau is likely to be on the order of
10 mM.
We have considered both the plateau and the transient
Ca2+ spike as two instances of
Ca2+-dependent regenerative potentials because
all plateaus or transient Ca2+ spikes tested in
this and in previous studies (Schwindt and Crill 1997a,b
,
1999
) have been blocked by the addition of
Cd2+ or by the partial or full substitution of
Mn2+, procedures that block voltage-gated
Ca2+ channels. However, some plateaus and some
transient regenerative Ca2+ responses are also
blocked by TTX (Schwindt and Crill 1997a
,b
, 1999
; this
study). The same plateau can be blocked both by
Cd2+ and by TTX (Schwindt and Crill
1999
). In the present study, we have also observed the blockade
of some plateaus by AP-5, indicating a dependence on current flow
through NMDA channels. Altogether, these results indicate that currents
other than Ca2+ are required to produce a
regenerative response (a net inward ionic current) at some sites or in
some cells, but Ca2+ currents are absolutely
necessary most often. The observation of blockade by TTX or by AP-5
does not imply that Ca2+ currents play no role in
these cases, merely that additional ionic currents are required for the
net current to become inward. Since the plateau collapses when the
glutamate iontophoresis is withdrawn, it is clear that the inward
current flowing through the (non-NMDA) glutamate receptor channels
themselves are also required to make the net current inward. Our
pharmacological results were obtained from glutamate iontophoresis on
the apical dendrite. During a recent study of the basal dendrites of
layer 5 neurons, it was also observed that the application of exogenous
glutamate evoked dendritic spikes (Schiller et al.
2000
). These were transient spikes rather than plateaus
presumably because the duration of the glutamate-evoked depolarization
was brief. These spikes were blocked by Cd2+, by
TTX, and by AP-5, but it was concluded that they were caused predominantly by current flow through NMDA channels based on the observation that spikes could be evoked by a sufficiently large glutamate application in the presence of Cd2+
plus TTX and by results obtained with a multiparameter computer model.
In the present and past experiments in which we employed Cd2+ (or TTX) blockade, we have routinely
increased our iontophoretic current significantly above the value
required to evoke a spike or plateau in physiological saline (e.g.,
Fig. 6), and we have never been able to restore the regenerative
response. Thus we find no evidence that the majority of the
regenerative responses on the apical dendrite depend critically on
current flow through NMDA channels, but if the membrane contains NMDA
receptors, we have no doubt that sufficient glutamate application will
cause an NMDA-dependent regenerative response in the absence of other voltage-gated channels (cf. Flatman et al. 1986
).
The initiation of a transient Ca2+ spike or a
plateau provides a membrane-generated, depolarizing current in addition
to that flowing through dendritic ligand-gated channels. This
"extra" depolarizing current flows from dendrite to soma and causes
a jump in firing rate. This jump in firing rate constitutes the amplification of the dendritic glutamate depolarization that evoked the
plateau. A similar amplifying function of a transient
Ca2+ spike has been postulated previously by many
investigators (e.g., Kim and Connors 1993; Larkum
et al. 1999
; Schiller et al. 1997
; Schwindt and Crill 1997a
). Both the plateau amplitude
and the corresponding jump in firing rate decreased with iontophoretic distance from the soma along the apical dendrite in our experiments. A
similar decrease of the transient Ca2+ spike
amplitude with distance from the soma was described previously (Schwindt and Crill 1997
). Moreover, no clear jump in
firing rate was apparent during iontophoresis on basal dendrites,
undoubtedly because the recorded plateau amplitudes (i.e., the soma
depolarizations) were so small. Thus the jump in firing rate at plateau
onset (the amplifying function) varied both with the proximity of the
plateau to the soma and with the type of dendrite (basal or apical). In contrast, both the insensitivity of plateau amplitude to larger glutamate applications and the corresponding saturation of firing rate
were observed at all dendritic sites that were capable of initiating a
plateau. Thus the plateau also serves to prevent soma depolarization by
any additional ligand-gated current generated at the plateau-generating
region. This constitutes its current limiting function. This is an
unexpected function of a regenerative dendritic potential. Dendritic
spikes have previously been thought of only as mechanisms for
amplifying synaptic input, not as mechanisms for limiting the
spike-generating capability of that input. Moreover, the invariance of
this current limiting function with either distance from the soma or
with the type of dendrite indicates that current limiting, rather than
current amplifying, is the most consistent function of a plateau or
Ca2+ spike.
The fact that increased glutamate application caused no increase in plateau amplitude suggested that the plateau may not only limit the somatopetal flow of ligand-gated current from the plateau-generating region, but it may also prevent the somatopetal flow of ligand-gated current from more distal regions on the same dendrite. This idea was confirmed by the use of simultaneous iontophoresis at a proximal and distal site on the same dendrite. Simultaneously evoked subthreshold responses summed at the soma, whereas the distal response made no contribution to soma depolarization if a plateau was evoked proximally at the same time. Thus the results of our two-site iontophoresis experiments indicate that the plateau limits the delivery of ligand-gated current to the soma not only for ligand-gated arriving at the plateau initiation but for the ligand-gated current arriving at any more distal site on the same dendrite. A corollary of this result is that the soma depolarization generated by a plateau represents the maximum depolarizing current that can be delivered to the soma (during the duration of the plateau) by ligand-gated depolarization of the dendritic segment at and distal to the site of plateau initiation.
Although we examined only plateaus explicitly, several of our
observations suggest that the preceding discussion also applies to the
transient Ca2+ spikes. For example, the distal
Ca2+ spike in Figs. 9A and
10B were occluded during the proximal plateaus, whereas
Ca2+ spikes and plateaus summed at the soma when
each was generated in a different dendrite (Fig. 9B). The
Ca2+ spikes and plateaus have similar amplitudes
(as recorded at the soma) and may arise at similar locations in the
dendrite (Schwindt and Crill 1999). A tonic
depolarization of hundreds of milliseconds is required to evoke a
plateau, whereas Ca2+ spikes can be evoked by
much shorter depolarizations (see Fig. 7). Thus the current-limiting,
dendrite-pruning, function of the plateaus may also apply to the
transient Ca2+ spikes that operate on a much
shorter time scale (
100 ms) than plateaus.
Our experiments were limited to focal depolarization of one or two
sites on the dendritic arbor, but they allow us to predict how the cell
would behave in response to distributed, tonic, excitatory input. If
the excitatory input was distributed uniformly over the dendritic tree
and if the absolute voltage threshold for Ca2+
responses was identical throughout the dendrites, one would expect Ca2+ spikes or plateaus to be evoked first in the
smaller branches of the dendrites because of their greater input
resistance. What would happen as the intensity of this uniform
excitatory input was increased further? In our two-site iontophoresis
experiments, we found that subthreshold distal and proximal dendritic
depolarizations could combine (engage in spatial summation) to evoke a
plateau (Fig. 10B). Most interesting was the observation
that the plateau recorded at the soma corresponded to the plateau
generated at the most proximal of the two dendritic sites. An
implication of this finding is that the adequate uniform depolarization
of a dendritic segment (as opposed to a punctate site) will result in
plateau initiation at the proximal end of that segment. Thus if a
uniformly distributed excitatory input was increased in amplitude, regenerative Ca2+ responses would be evoked at
more proximal dendritic sites. The increased depolarization required to
reach threshold at a more proximal dendritic site would be provided
both by the increased ligand-gated currents at that site and by the
depolarizing currents generated by the regenerative
Ca2+ responses on more distal branches. Thus
dendritic plateaus would be initiated ever closer to the soma as the
uniformly distributed excitatory synaptic input increased in amplitude.
Because soma depolarization increases as a continuous function of the
proximity of the plateau (Fig. 7) or Ca2+ spike
(Schwindt and Crill 1997) to the soma, we would expect the somatopetal movement of the site of regenerative
Ca2+ response to be graded with the amplitude of
the uniform excitatory input. Consequently, the depolarizing current
delivered to the soma (and the evoked firing rate) would also increase
in a graded fashion. According to this reasoning, the cell would give a
graded spike output for a graded, uniform, excitatory input in spite of
the all-or-none nature of the regenerative Ca2+
responses. This idea differs from the present concepts of synaptic integration in three ways. First, it is the depolarizing membrane current generated by the regenerative Ca2+
response (in combination with more-proximal synaptic current) that
flows to the soma to drive repetitive firing. Second, it is the graded
somatopetal movement of the regenerative Ca2+
response-generating regions (again, in combination with more-proximal synaptic current) that grades the repetitive firing rate. Third, the
regenerative Ca2+ response electrically
"prunes" the distal dendritic arbor such that synaptic current from
more distal sites have no direct influence on the soma. The distal
synaptic input would have an indirect effect because it is required to
initiate the regenerative Ca2+ response.
According to this idea, if excitatory synaptic input increased sufficiently, a regenerative Ca2+ response would be evoked ultimately at the most proximal location on each dendrite where it could be supported (within ~100-200 µm of the soma on the apical dendrite and within ~50 µm of the soma on the basal dendrites). These most-proximal regenerative Ca2+ responses would supply the maximal current available to drive repetitive firing, and synaptic input to more distal regions would have no effect other than to maintain the regenerative Ca2+ responses. What maximal firing rates would these most-proximal regenerative Ca2+ responses evoke? We can estimate the tonic rates evoked by the most proximal plateaus. At sites 100-250 µm from the soma on the apical dendrite (the most proximal region that supported plateaus), plateau-evoked regular spiking rates ranged from 40 to 46 Hz. These rates are equivalent, based on those cells' f-I relations, to injected soma currents ranging from 1 to 2.7 nA. This suggests that the maximum depolarizing current that can be generated by excitatory input to the entire apical dendritic tree (beyond ~200 µm from the soma) is <3 nA. Injected currents of this magnitude did not saturate the firing mechanism of the cell, so additional current generated in the basal dendrites and soma could sum with the current from the apical plateau to evoke a higher rate of firing. In two cells, sites at 75 and 80 µm from the soma on the basal dendrite (the most proximal region that supported plateaus) evoked plateaus with peak amplitudes of 13 and 19 mV, respectively (Fig. 7A, ×); this was equivalent to an injected current of 260-380 pA based on the input resistance of these cells. Thus the total current produced by a basal dendrite may be <400 pA. Because the responses evoked on apical and basal dendrites sum (Fig. 9B), the maximum current that the entire dendritic tree can generate is a sum of the maximum currents generated on each dendrite. For a cell with 1 apical dendrite and 10 basal dendrites, the maximum current produced by the dendritic tree would be <7 nA. Based on a typical f-I curve generated by soma current injection in these experiments, 7 nA corresponds to an evoked firing rate of ~150 Hz. Thus plateau generation during increasing, uniformly distributed, excitatory synaptic input would neither result in a nonlinear input-output relation (over a substantial range of synaptic input) nor restrict the cells firing rate to low values (although it would set an ultimate limit to the steady-state firing rate).
In recent theoretical studies of neural coding, it was found necessary
to postulate a balance between tonic synaptic excitation and inhibition
to prevent the saturation of a cell's firing mechanism during only
moderate levels of tonic excitatory synaptic input while matching other
characteristics of neural discharge recorded in vivo (Shadlen
and Newsome 1994, 1998
). As indicated by the preceding
estimates, the plateau potential ensures that firing rate is graded
with total synaptic input and is maintained within the neuron's
dynamic firing range without any need for balanced inhibitory input.
Apparently, the requirement for balanced inhibition in such models can
be substantially relaxed.
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ACKNOWLEDGMENTS |
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We thank G. Hinz for technical assistance.
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-16792 and by the Keck Foundation.
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FOOTNOTES |
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Address for reprint requests: W. E. Crill, Dept. of Physiology and Biophysics, Box 357290, University of Washington School of Medicine, Seattle, WA 98195-7290 (E-mail: wecrill{at}u.washington.edu).
Received 21 June 2000; accepted in final form 19 February 2001.
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REFERENCES |
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