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The Journal of Neuroscience, January 1, 1998, 18(1):10-15
Input Summation by Cultured Pyramidal Neurons Is Linear and
Position-Independent
Sydney
Cash and
Rafael
Yuste
Department of Biological Sciences, Columbia University, New York,
New York 10027
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ABSTRACT |
The role of dendritic morphology in integration and processing of
neuronal inputs is still unknown. Models based on passive cable theory
suggest that dendrites serve to isolate synapses from one another.
Because of decreases in driving force or resistance, two inputs onto
the same dendrite would diminish their joint effect, resulting in
sublinear summation. When on different dendrites, however, inputs would
not interact and therefore would sum linearly. These predictions have
not been rigorously tested experimentally. In addition, recent results
indicate that dendrites have voltage-sensitive conductances and are not
passive cables. To investigate input integration, we characterized the
effects of dendritic morphology on the summation of subthreshold
excitatory inputs on cultured hippocampal neurons with pyramidal
morphologies. We used microiontophoresis of glutamate to systematically
position inputs throughout the dendritic tree and tested the summation
of two inputs by measuring their individual and joint effects. We find
that summation was surprisingly linear regardless of input position.
For small inputs, this linearity arose because no significant shunts or
changes in driving force occurred and no voltage-dependent channels
were opened. Larger inputs also added linearly, but this linearity was
caused by balanced action of NMDA and IA potassium
conductances. Therefore, active conductances can maintain,
paradoxically, a linear input arithmetic. Furthermore, dendritic
morphology does not interfere with this linearity, which may be
essential for particular neuronal computations.
Key words:
hippocampus; cortex; NMDA; iontophoresis; dendrite; potassium
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INTRODUCTION |
One of the most striking and
beautiful features of neurons is their diverse dendritic morphologies
(Ramón y Cajal, 1904 ). The purpose of these geometrically
intricate structures and their role in synaptic integration is still
unknown. In addition, the function of the rich variety of
voltage-sensitive channels distributed heterogenously throughout the
dendritic arbor is also unclear (Johnston et al., 1996; Yuste and Tank,
1996). These morphological and biophysical properties would be expected
to significantly influence input integration, providing the neuron with
complex response properties.
Theoretical analyses of integration began with the assumption that
dendrites can be modeled as passive cables (Rall, 1964; Jack et al.,
1975). Passive cable theory predicts that electrically isolated
synaptic inputs sum algebraically, whereas synapses that are
electrically close are attenuated because of reduction in the driving
force of their ions or current shunting caused by a transient decrease
of input resistance in the dendrite (Rall, 1995). Although these ideas
are widespread, experimental studies of these predictions have been
surprisingly scant. Analysis of synaptic potentials from motoneurons
in vivo revealed summed potentials that were less than those
expected for independent inputs. This discrepancy was ascribed to
sublinear interactions between nearby synapses (Burke, 1967; Kuno and
Miyahara, 1969). Nevertheless, in CA1 hippocampal pyramidal neurons
in vitro, separate inputs summated linearly (Langmoen and
Andersen, 1983). Finally, iontophoresis at multiple sites on dendrites
of turtle spinal cord motoneurons in vitro also showed
linear integration (Skydsgaard and Hounsgaard, 1994). In all of these
experiments, however, the dendritic morphology and exact position of
the inputs was not determined, so the specific effects of morphology on
input summation were not explored.
To examine directly how dendritic morphology and active conductances
influence synaptic integration, we have studied the summation of
simulated subthreshold synaptic inputs in pyramidal hippocampal neurons
in culture using focal microiontophoresis of the excitatory neurotransmitter glutamate. Although cultured neurons may differ in
particular biophysical properties from in vivo neurons,
their rich dendritic morphologies and accessibility make them an ideal model system for studying the effects of dendritic morphology on
neuronal integration. As we show, microiontophoresis can be used to
exactly position a reproducible excitatory input that resembles
endogenous synaptic inputs anywhere on the dendritic tree.
Microiontophoresis also allows pharmacological manipulations that would
be impossible with stimulated transmitter release.
Here, we examine two questions: (1) do dendritic branches serve to
isolate inputs, as predicted by cable theory, and (2) how do active
conductances affect input summation? We find that excitatory inputs sum
linearly regardless of their position, suggesting that the sublinear
scenarios discussed by cable theories do not apply to electrotonically
compact cultured neurons and are even less likely to apply to pyramidal
neurons in vivo. Also, we find that the linear summation is
achieved by a remarkable balance of conductances, canceling each
other's effect.
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MATERIALS AND METHODS |
Hippocampi from newborn Sprague Dawley rats were dissociated and
plated at low density on poly-L-lysine-coated coverglass, without glial support cells, following standard protocols (Goslin and
Banker, 1991). Cells from 7- to 14-d-old cultures were used for
experiments. Recordings from pyramidal neurons were made using the
gigaohm-seal, nystatin perforated-patch technique (Horn and Marty,
1988). Conventional patch pipettes were filled with pipette saline
containing (in mM): 10 NaCl, 10 KCl, 10 HEPES, 140 potassium gluconate, and nystatin (Sigma, St. Louis, MO) at a final
concentration of 150 µM. Nystatin stock (46 mM; 1 mg/ml in Me2SO) was prepared before each
experiment, stored at room temperature in a light-proof container, and
used for up to 6 hr after preparation. A conventional gigaohm seal was
formed by pressing the pipette gently against the soma of a neuron and
providing light suction. Whole-cell recordings developed within 1-5
min of making a seal, with access resistances between 15 and 25 M .
The amplifier (Axopatch 1D or Axoclamp 2B, Axon Instruments, Foster
City, CA) was then switched to current-clamp mode. In all experiments,
potentials were recorded at room temperature, and current was injected
if necessary to keep the resting potential at approximately  65 mV,
unless otherwise indicated. Voltages were filtered at 1 kHz, digitized,
stored, and analyzed using Superscope and an analog-to-digital board
(GW Instruments). The recording solution consisted of (in
mM): 150 NaCl, 5 KCl, 2 CaCl2, 1 MgCl2, 10 HEPES, and 100 µM Phaclophen
(RBI), pH 7.4. Blockers were bath-applied: AP-5 (100 µM;
RBI), tetrodotoxin (TTX) (5 µM; Sigma), NiCl2
(1 mM, Sigma), TEA (10 mM, Sigma), and
4-amino-pyridine (4-AP) (5 mM, Sigma). Iontophoresis
pipettes were pulled to a fine tip with ~150 M resistance when
filled with 2.5 M NaCl. Pipettes were filled with 250 mM sodium glutamate in Milli-Q water, pH 8.0. Four stimulus
isolation units and a Master-8 controller (AMPI, Inc.) were used to
provide holding current (~1-10 nA) and ejection current (~100 nA)
of various durations to the pipettes. Potentials of relatively large
amplitude (1-10 mV) and fast rise time (2.2 ± 0.3 mV/msec) were
obtained with ejection currents between 0.5 and 5 msec. Action
potentials or significantly larger and longer potentials could always
be achieved by increasing the ejection current amplitude or duration,
indicating that neither the neuron nor the amplifier was saturated by
combined iontophoretic events. Each experiment consisted of multiple
trials (between 5 and 15) at a given pipette position and amplitude of
glutamate response. Throughout this paper, measurements are expressed
as the mean ± SEM for a number of experiments unless otherwise
indicated.
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RESULTS |
Microiontophoresis-induced depolarizations resemble EPSPs and can
be precisely localized
For all experiments, we used neurons with pyramidal morphologies,
i.e., neurons having a pyramidal soma, a large, single apical dendrite
that originates from the apex of the soma, and a number of smaller
basal dendrites (Fig.
1A). The dendritic
identity of the processes was established by MAP2 immunocytochemistry
(Caceres et al., 1986). Cells with typical pyramidal
morphologies were present even in low-density cultures, suggesting that
the developmental program that builds pyramidal dendritic trees is
cell-autonomous (Banker and Cowan, 1979; K. Zelevinsky, S. Cash, and R. Yuste, unpublished observations). Whole-cell recordings from the somata of the neurons demonstrated an electrophysiology similar to that of CA1
pyramidal neurons of comparable developmental stages, with resting
membrane potentials of approximately 65 mV and action potential
threshold reached at 55 to 45 mV. Action potentials were 60-125 mV
in amplitude and 3-10 msec in duration and occurred in a regular
spiking pattern with frequency accommodation (Fig. 1B). Finally, many neurons showed
afterhyperpolarizations.
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Figure 1.
Iontophoretic potentials resemble spontaneous
EPSPs and are spatially localized. A, Photomicrograph of
a 12 d in vitro cultured hippocampal neuron showing
a pyramidal morphology, with a single large apical dendrite and several
smaller basal dendrites. Scale bar, 40 µm. B, Examples
of action potentials elicited from two different neurons using either a
short (left) or long (right) glutamate
depolarization. Fast, large action potentials that accommodated in
frequency with long depolarizations were present in the cultured neurons. Calibration: 10 mV, 10 msec for left; 10 mV, 1 sec for right. C, Spontaneous EPSPs
(top set) and iontophoretically induced potentials
(bottom set) from five different cells. Note that the two sets of potentials are nearly identical in waveform.
D, Peak amplitude of the average of five iontophoretic
pulses as the pipette was moved vertically in 1 µm increments away
from the point of maximal amplitude. Data from 10 cells was fit with a
single exponential. Inset shows the decreases of the
responses of a representative cell as the pipette was moved 5 µm from
the original location. Note how the response decreases
e-fold in ~5 µm. Calibration for C,
D: 5 mV, 30 msec.
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Cultured neurons formed excitatory synapses with one another, producing
spontaneous EPSPs (sEPSPs) with both NMDA and non-NMDA components. For
our experiments, iontophoresis pipettes were positioned and the
ejection current amplitude and duration were adjusted so that
iontophoretic depolarizations closely resembled these sEPSPs. Rise and
decay times of iontophoretic and sEPSPs were not significantly
different (0.52 ± 0.25 mV/msec rise and 60 ± 11 msec decay
for sEPSPs; 0.47 ± 0.21 mV/msec and 62 ± 8 msec for
iontophoresis EPSPs; n = 5 cells) (Fig.
1C). Peak amplitudes of sEPSPs ranged from 1 to 15 mV
(mean = 3.8 ± 0.6 mV), and iontophoresis potentials used
throughout this study were matched to this range.
To verify that the recording and iontophoresis conditions were
stable, we characterized the responses to a single pipette by ejecting
glutamate twice, with an interval of 5 sec for repeated trials. The
peak amplitude of the second depolarization differed from the first by
only 0.7% ± 1.7% (mean ± SEM; n = 12 cells), showing that consecutive iontophoretic potentials were identical. We
also characterized the spatial localization of our stimulus because a
large spread of ejected glutamate could produce overlapping activation
of receptors, which would confound true input interactions. We
positioned a single pipette to achieve a maximal depolarization and
then raised it vertically above the dendrite in 1 µm increments, measuring the potential for five trials at each position (Fig. 1C). The amplitude of responses decreased e-fold
for every 5 µm movement. Similar results were found when the pipette
was moved horizontally away from the dendrite (not shown). In addition, the ejected glutamate was not saturating, because larger potentials than those used for the experiments could always be obtained by increasing the duration or ejection current. Microiontophoresis is
therefore a reliable method for excitation of a specific site in the
dendritic arbor.
Input summation is linear and independent of position
and distance
We first established how two inputs summed using simultaneous
iontophoresis at two points on the dendritic tree (Fig.
2). While recordings were made from cells
at a membrane potential of 65mV, iontophoresis pipettes were
positioned at specific dendritic locations. The current from each
pipette was adjusted to evoke a subthreshold depolarization even when
both were activated simultaneously. Trials in which the combined
depolarization triggered an action potential were removed from our
analysis, as were trials with large spontaneous activity. The
depolarization caused by each input was measured separately and then
both were tested together (Fig. 2A). The individual
responses were added, and this algebraic summation was compared with
the potential evoked by simultaneous excitation from both pipettes
(Fig. 2B). As a further control to test whether the
two pipettes interacted electrically, we positioned one pipette next to
the dendrite and a second pipette 20 µm above it, a location that
elicited no response. With this configuration, the depolarization
caused by simultaneous activation was the same as that of the first
pipette (99.5% ± 3.0%; n = 4 cells). This indicates
that the two pipettes act as independent sources of excitation and that
there is no significant glutamate spillover.
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Figure 2.
Synaptic summation is independent of input
position. A, Diagram of the experiment. Two
microiontophoresis pipettes were positioned on the dendritic tree of a
pyramidal neuron in culture. Glutamate was ejected first from each
pipette individually and then from both simultaneously. The algebraic
sum of the individual potentials was then compared with the actual
potential recorded with simultaneous stimuli. B,
Averaged results from a representative cell (5 trials). The two
lower lines are the responses from each of the pipettes, the dashed line indicates their algebraic sum, and the
top solid line is the simultaneous response measured.
Note the overlap between the expected and actual summed
depolarizations, indicating linear summation. Calibration: 2 mV, 25 msec. C, Schematic diagram of a neuron showing pipette
locations studied, including apical (Ap), second or
higher order branches (S), and basal dendrites
(B). D, Histogram of the linearity
of the summed responses, measured by the ratio of actual to expected
peak amplitudes, for different input configurations. No significant
deviations from linearity are observed (ANOVA, p < 0.05; number of experiments in parentheses).
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Summation of the peak depolarization of inputs at any two dendritic
positions was 102 ± 1.5% of expected (n = 75 pairs of inputs on 40 different cells), a result that is not
statistically different from a pure algebraic summation. This linear
summation occurred regardless of the specific position of the inputs
(Fig. 2C,D), ranging from 96 to 108% for the mean
responses. The configurations tested included both inputs on the apical
dendrite, on a basal dendrite, on different basal dendrites, on an
apical and a basal dendrite, on a second order branch of the apical
dendrite and the apical dendrite itself, and on two different second or
higher order branches of the apical tree (Fig. 2C). In
addition, occasional nonlinearities observed in some experiments did
not occur in any particular stimulus configuration. Therefore, the
presence of a branching point or the soma between the inputs does not
significantly affect the linear summation.
Is dendritic integration affected by the distance between inputs? As
predicted by cable models (Rall, 1995), a strong distance dependency
would be expected if inputs would interact. Nevertheless, no
significant correlation between intra-pipette distance and summation
was observed over the range of ~15-120 µm (Fig.
3A), indicating that distance
does not significantly affect spatial summation of inputs. We also
investigated whether there was a relationship between the amplitude of
the stimuli and summation. Such an effect might be expected because of
the voltage-dependent dendritic conductances. Nevertheless, the
linearity was independent of the amplitude of the stimulus (Fig.
3B).
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Figure 3.
Linearity of summation is independent of
intrapipette distance and response amplitude. A, Percent
linearity of the summation of two inputs in all spatial configurations
as a function of distance between the pipettes. Distance was measured
as the shortest length along the neuron between the two inputs.
Dashed line indicates linearity. No systematic
correlation is observed. B, Percent linearity of the
summation of two inputs as a function of combined peak amplitude. No
significant deviation from linearity is seen. Each point
represents a single experiment. More than one experiment may be
performed on a given cell in either different positions or amplitudes.
These data include 75 different experiments on 40 different cells and
are the same data as those plotted in Figure 2.
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Linear summation results from balanced activation of NMDA and
potassium conductances
We were surprised by the essentially linear summation, because it
is well established that dendrites have receptors and voltage-dependent channels, the behavior of which is nonlinear and can be activated by
subthreshold EPSPs (Stafstrom et al., 1985; Sutor and Hablitz, 1989;
Deisz et al., 1991; Hirsch and Gilbert, 1991; Magee and Johnston, 1995;
Stuart and Sakmann, 1995). We dissected the mechanisms underlying the
linearity by examining summation of two inputs on the apical dendrite
under various pharmacological and electrophysiological conditions (Fig.
4). Our logic was first to assess the
role of the NMDA receptor in summation, because it is known to produce boosting of synaptic inputs (Jones and Baughman, 1988; Thomson et al.,
1988; Artola and Singer, 1990), and then to study the contribution of
the voltage-dependent sodium, calcium, and potassium conductances to
the process. Because of the voltage-dependency of the activation of the
channels, we explored two regimens of excitation: either small (<10
mV) combined potentials near rest or large (>10 mV) potentials
approaching spike threshold.
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Figure 4.
Mechanisms underlying linear summation. Effects of
APV, TTX, NiCl2, TEA, 4-AP, and hyperpolarization on
the linearity of two inputs on the apical dendrite. A,
For combined events <10 mV, none of the manipulations produced a
significant change from control conditions or from experiments
performed with APV (ANOVA, p < 0.01). This
suggests that NMDA, Na+, Ca2+,
and K+ conductances do not contribute significantly
to the summation. B, For combined events >10 mV,
application of APV produced a significance sublinearity compared with
controls (*). TEA, 4-AP, and hyperpolarization produced a significant
block of the APV effect (**). The presence of all types of blockers
revealed a significant sublinearity, compared with the
TEA+APV experiments ( , for all cases,
ANOVA, p < 0.002). These results suggests that the
normal linearity for large amplitude events is produced by a balanced
action of NMDA and K+ conductances. Blockade of all
conductances reveals a sublinearity that could be attributable to
driving force reduction or conductance shunting. Number of experiments
in parentheses.
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For small depolarizations, linear summation was unaffected by blocking
NMDA, sodium, calcium, or potassium channels (Fig. 4A). We conclude that small depolarizations do not
depolarize the dendrite enough to activate any of these conductances.
Also, no significant driving force reduction or shunt must occur,
because summation is linear. Thus, the linearity under these conditions is purely a reflection of lack of interaction among inputs.
For larger depolarizations (Fig. 4B), summation was
significantly sublinear when NMDA receptors were blocked with APV
(91 ± 1%; n = 19 cells). This suggests that, in
agreement with previous work (Jones and Baughman, 1988; Thomson et al.,
1988; Artola and Singer, 1990), activation of NMDA receptors boosts
excitatory inputs. We then explored the mechanisms of the sublinearity
revealed under APV by blocking sodium, calcium, and potassium
conductances. The selective sodium channel blocker TTX abolished all
action potentials but did not produce a significant difference in the sublinearity under APV. Application of the voltage-dependent calcium channel blocker NiCl2 also did not produce a statistically
significant difference in the sublinearity. In contrast, blocking of
voltage-dependent K+ channels with
tetraethylammonium (TEA) removed the sublinearity revealed under APV,
making summation linear again (102 ± 1%; n = 6 cells). To investigate which type of potassium channel is responsible,
we used 4-AP (5 mM), a blocker specific for the
IA subtype of potassium conductance. This also reversed the
sublinearity revealed under APV (100 ± 1%; n = 6 cells), suggesting that sublinearity was caused by activation of
IA potassium channels. In agreement with this,
hyperpolarization of the neuron to 75 mV, which moves the membrane
potential away from the activation voltage of the IA
conductance, also reversed the sublinearity (99 ± 1%;
n = 7 cells). We conclude that summation of large
depolarizations is linear because of activation of NMDA and potassium
conductances, the effects of which are remarkably balanced.
Why is summation under blocked NMDA receptors and potassium channels
still linear? To study whether we could reveal an underlying sublinearity caused by passive cable properties of dendrites, we
applied a cocktail of blockers to simultaneously block NMDA, sodium,
calcium, and potassium conductances (Fig. 4B). Under
these conditions the input resistance increased nearly twofold
(738 ± 140 M, n = 7 cells for controls, vs
1311 ± 278 M, n = 5 cells for blockers),
making the neuron electrotonically very compact. These experiments were
performed with two pipettes on the apical dendrite at least 50 µm and
as much as 110 µm apart, a range similar to what was used in all
other experiments. In this situation we observed sublinear summation of
inputs onto the apical dendrite (83 ± 3%; n = 9 cells), which was not significantly affected by hyperpolarization and
may have been caused by reduction in the driving force or shunting of
currents. When only NMDA and potassium channel blockers are present,
however, this sublinearity is opposed by a boosting produced by sodium
and calcium conductances (Stafstrom et al., 1985; Sutor and Hablitz,
1989; Deisz et al., 1991; Hirsch and Gilbert, 1991; Magee and Johnston,
1995; Stuart and Sakmann, 1995). This indicates that unless all
conductances are blocked, these cultured neurons do not experience the
appropriate regimen of passive electrical properties in which driving
force or conductance shunts operate.
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DISCUSSION |
Dendritic branching does not affect linear summation
Altogether, our results using cultured pyramidal neurons as a
model system suggest that the dendritic morphology does not seem to
play a major role in neuronal integration of excitatory inputs.
Contrary to the classic picture that has emerged from cable theory and
is disseminated in current textbooks, we find that two excitatory
inputs sum linearly regardless of whether they are on the same
dendritic branch or on two different branches. In other words, in
cultured cells with pyramidal dendritic morphologies, we do not observe
any sublinearities that could be ascribed to a reduction in driving
force or shunting, as predicted by cable models.
How relevant are these results from cultured neurons for dendritic
integration in vivo? An artifactual lack of interaction could occur if the currents produced by our glutamate iontophoresis on
cultured neurons were substantially smaller than normal EPSPs or if the
two input positions were too distant to interact. However, currents
triggered by our iontophoresis pipettes ranged from approximately 20 to
40 pA, which are larger than EPSCs from CA1 neurons in slices (Bolshakov and Siegelbaum, 1995). Also, the input resistance of our
cultured neurons is substantially higher than that of neurons in slices
or in vivo, making cultured neurons much more compact electronically. In fact, dendrites in vivo are likely to be
electrotonically very long because of constant synaptic bombardment
(Bernarder et al., 1991). Our experiments, therefore, maximize the
likelihood of nonlinear interactions attributable to driving force
reduction or shunting. Yet, even when inputs were located near each
other, at distances as close as 15 µm, we did not observe a
substantial sublinearity. Therefore, synaptic inputs in vivo
should be more isolated, producing an even more linear synaptic
integration. This implies that the regimen in which inputs interact
sublinearly because of pure passive cable conditions may not occur
in vivo.
Pronounced effects of dendritic morphology on input integration,
however, may happen under circumstances that we have not yet tested.
For instance, input position may matter for summation of excitatory and
inhibitory inputs (Koch et al., 1983). Indeed, The highly specific
placement of inhibitory contacts in the dendritic tree (Kisvarday et
al., 1987; Buhl et al., 1994) suggests that their integrative
interactions may be position-dependent, although this has not been
explored experimentally. Another positional effect may arise during
interaction of EPSPs with backpropagating action potentials that fail
to invade particular branches (Spruston et al., 1995). On the other
hand, however, it is also possible that like the branching patterns of
trees, dendritic morphologies may have evolved to provide an efficient
way of distributing postsynaptic targets in space, and that this
branching architecture, intriguing as it may seem, does not play a
major role in the electrical properties of the neuron.
Linear summation is achieved by two complementary mechanisms
The second goal of our study is to understand how dendritic active
conductances contributed to spatial summation in these cultured
neurons. We find that there are two mechanisms underlying the linear
summation of simulated EPSPs in cultured neurons. For small inputs,
summation was still linear under pharmacological blockade of sodium,
calcium, and potassium conductances, indicating that these conductances
were not significantly activated by the inputs. Thus a "passive"
linearity results from the simple addition of noninteracting voltages.
Near resting potential, voltage-dependent channels are not activated
substantially, and conductance shunts or driving force reductions are
too small to alter linear summation. Potentials initiated at one site
may not induce significant depolarization to open channels at a site
20-100 µm away. This is consistent with earlier experiments showing
linear integration in which inputs were probably even farther from each
other (Langmoen and Andersen, 1983; Skydsgaard and Hounsgaard,
1994).
With larger depolarizations, however, APV revealed a sublinearity that
was blocked by TEA and 4-AP. This suggests that in these cultured cells
IA potassium channels are activated by large EPSPs and
reduce the effect of other simultaneous EPSPs. This reduction, however,
is cancelled by the boosting produced by additional activation of NMDA
receptors. Although our data were taken from cultured cells, these
findings are compatible with known properties of pyramidal neurons in
slices, in which NMDA receptors produce EPSP boosting (Thomson et al.,
1988) and dendritic IA currents shunt EPSPs (Hoffman et
al., 1997). It is quite remarkable that two opposing conductances
happen to cancel each other and produce an "active" linear
summation. Because voltage-dependent channels are also found throughout
the dendritic tree in vivo, it is possible that their
actions would also balance each other, as in our experiments. This is
reminiscent of the mechanism proposed for dendritic integration by
distal apical dendrites of layer 5 cortical neurons, in which a
balanced action of calcium and potassium conductances linearizes excitatory inputs (Bernarder et al., 1994). Finally, using a cocktail of blockers (TTX, APV, Ni, and TEA), we uncovered a sublinear summation
that is probably caused by the reduction of driving force or resistance
predicted by passive cable theory. Indeed, this pharmacological
"passification," together with glutamate iontophoresis, could be
used to experimentally test many cable theory predictions in real
dendrites with known morphologies.
Computational relevance of linear summation
What might be the function of linear input summation? A linear
input arithmetic could provide neurons with a system for keeping an
exact count of impinging excitatory inputs, enabling independent processing of multiple channels of information. Indeed, in the visual
system, experiments in vivo have found widespread linear summation of inputs (Wandell, 1995), and linear integration may be
necessary for both orientation and directional selectivity (Ferster,
1994). In the hippocampus, linear summation would be very useful for an
associative memory matrix. Unfortunately, neither the positional
effects nor the mechanisms behind linearity in vivo are
understood. Our results in cultured neurons imply that the exact
position of excitatory inputs in the dendritic tree does not matter for
spatial summation, and they suggest two complementary cellular
mechanisms to maintain linear summation. This implies that the active
dendritic conductances paradoxically may be designed to linearize
inputs regardless of their position and thus may counteract the effects
of their passive cable structure. Nevertheless, our efforts using an
experimentally accessible model system are only a first step in
elucidating this issue experimentally, and additional work is clearly
necessary. Perhaps the ability of two-photon microscopy to identify the
location of individual synaptic inputs in a living cell (Yuste and
Denk, 1995) may enable a similar experimental program in brain slices
or even in vivo (Denk et al., 1994; Svovoda et al.,
1997).
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FOOTNOTES |
Received Aug. 19, 1997; revised Oct. 6, 1997; accepted Oct. 9, 1997.
R.Y. is supported by the Sloan, Klingestein, March of Dimes, and EJLB
Foundations. We thank Stuart Firestein, Jeanette Kuhn, Ania Majewska,
Steven Siegelbaum, and Diana Smetters for comments.
Correspondence should be addressed to Sydney Cash, 1002 Fairchild
Building, Department of Biological Sciences, Columbia University, New
York, NY 10027.
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Abstract
Introduction
