1Division of Life Sciences, University of Texas at San Antonio, San Antonio, Texas 78249; and 2Department of Psychology, Yale University, New Haven, Connecticut 06520
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ABSTRACT |
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Jaffe, David B. and Nicholas T. Carnevale. Passive Normalization of Synaptic Integration Influenced by Dendritic Architecture. J. Neurophysiol. 82: 3268-3285, 1999. We examined how biophysical properties and neuronal morphology affect the propagation of individual postsynaptic potentials (PSPs) from synaptic inputs to the soma. This analysis is based on evidence that individual synaptic activations do not reduce local driving force significantly in most central neurons, so each synapse acts approximately as a current source. Therefore the spread of PSPs throughout a dendritic tree can be described in terms of transfer impedance (Zc), which reflects how a current applied at one location affects membrane potential at other locations. We addressed this topic through four lines of study and uncovered new implications of neuronal morphology for synaptic integration. First, Zc was considered in terms of two-port theory and contrasted with dendrosomatic voltage transfer. Second, equivalent cylinder models were used to compare the spatial profiles of Zc and dendrosomatic voltage transfer. These simulations showed that Zc is less affected by dendritic location than voltage transfer is. Third, compartmental models based on morphological reconstructions of five different neuron types were used to calculate Zc, input impedance (ZN), and voltage transfer throughout the dendritic tree. For all neurons, there was no significant variation of Zc with location within higher-order dendrites. Furthermore, Zc was relatively independent of synaptic location throughout the entire cell in three of the five neuron types (CA3 interneurons, CA3 pyramidal neurons, and dentate granule cells). This was quite unlike ZN, which increased with distance from the soma and was responsible for a parallel decrease of voltage transfer. Fourth, simulations of fast excitatory PSPs (EPSPs) were consistent with the analysis of Zc; peak EPSP amplitude varied <20% in the same three neuron types, a phenomenon that we call "passive synaptic normalization" to underscore the fact that it does not require active currents. We conclude that the presence of a long primary dendrite, as in CA1 or neocortical pyramidal cells, favors substantial location-dependent variability of somatic PSP amplitude. In neurons that lack long primary dendrites, however, PSP amplitude at the soma will be much less dependent on synaptic location.
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INTRODUCTION |
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The computations of single neurons involve the integration of
synaptic inputs, thousands of which may be distributed over the cell
surface. The seminal work of Rall (1962,
1970
, 1977
) provided a theoretical basis for understanding how
location affected the amplitude and shape of synaptic signals. One
prediction of cable theory is that the ability of a synapse to alter
somatic membrane potential (Vm) declines as its
distance from the soma increases. Theoretical and experimental studies
of dendritic electrotonus have generally been presented in terms of the
voltage transfer ratio from synapse to soma, i.e.,
Vsoma/Vsyn, where
Vsyn is the postsynaptic potential (PSP)
amplitude at the synaptic location and Vsoma is
its amplitude observed at the soma. In this paper we will represent
this ratio by ksyn
soma (read as
"k from synapse to soma"), after the notation introduced
by Carnevale and Johnston (1982)
.
Models of neurons, whether based on equivalent cylinders or
multicompartmental representations, have generally demonstrated large
variations in ksynsoma with synaptic location
(Jack et al. 1975
; Rall 1962
,
1970
, 1977
). More recent studies have emphasized the
direction-dependence of voltage transfer, which is less efficient for
signals spreading toward the soma than for somatic voltage spreading
into the dendrites (Carnevale et al. 1997
;
Cauller and Connors 1992
; Mainen et al.
1996
; Nitzan et al. 1990
; Tsai et al.
1994
; Zador et al. 1995
):
ksyn
soma < ksoma
syn.
It is essential to know whether ksynsoma is
the most reliable index of the relationship between synaptic location
and synaptic efficacy, because this has a strong bearing on our
understanding of the integrative properties of neurons. If there is a
large variability in voltage transfer from synapse to soma, and action potentials are generally initiated near the soma (Colbert and Johnston 1996
; Mainen et al. 1995
; Stuart
and Sakmann 1994
), then how do distant synapses trigger action
potentials? All else being equal, proximal excitatory inputs would seem
to exert a much greater depolarizing action on the soma than do distal
inputs. Anderson et al. (1987)
suggested that active
conductances in dendrites might "boost" excitatory PSPs (EPSPs)
as they propagate toward the soma. We now know that the dendrites of
many classes of neurons contain active conductances that could enhance
EPSP amplitude (Gillessen and Alzheimer 1997
;
Lipowsky et al. 1996
; Magee et al.
1995
; Magee and Johnston 1995a
,
b
; Schwindt
and Crill 1995
, 1997
; Stuart and Sakmann 1995
), but
assessing their contribution to synaptic efficacy demands that we first
have a clear grasp of the baseline electrotonic properties of these cells.
Recent results from this laboratory have compelled us to reevaluate the
role of voltage transfer in synaptic integration. In a study of the
electrotonic properties of hippocampal CA3 interneurons, Chitwood et al. (1999) modeled the effects of unitary
synaptic conductances placed at various distances from the soma. They
found that the range of relative EPSP amplitudes measured at the soma was strikingly narrower than the range observed at the synaptic sites.
The relative variation of the somatically recorded EPSP was also much
smaller than the variation of ksyn
soma. This unexpected disparity suggested that ksyn
soma
might not always be the best predictor of synaptic integration.
In this report we examine the basis for this intriguing result, which
leads to the conclusion that it is necessary to consider local input
impedance (ZN), transfer impedance
(Zc), and the magnitude and time course of the
synaptic conductance change (gs) itself when
examining synaptic integration. We demonstrate how some neuron morphologies favor relative uniformity of Zc
throughout the cell in the face of substantial variation of both
ksyn
soma and ZN with
synaptic location. In these cells there is a large class of synaptic
inputs for which location has only a small effect on the amplitude of a
PSP observed at the soma, a phenomenon that we call "passive synaptic
normalization" to emphasize the fact that it does not depend on
contributions from active currents. We illustrate these conclusions by
examining a number of cell types that reveal what is required for
dendritic geometry to be a major determinant of synaptic variability.
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METHODS |
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Neuronal reconstructions
Two sets of neuron morphology were used in this study. In the
first set, input resistance (RN) and the slowest
membrane time constant (0, which was used to calculate
specific membrane resistivity, Rm) were measured
experimentally for each reconstructed cell with the use of standard
whole cell recording methods (Chitwood et al. 1997
).
This set consisted of 15 CA3 nonpyramidal neurons from s.
radiatum and s. lacunosum-moleculare, 3 CA3 pyramidal
neurons, and 1 layer V pyramidal neuron from the medial prefrontal
cortex (PFC). All of these cells were obtained from 17- to 30-day-old Sprague-Dawley rats (see Chitwood et al. 1999
). A
computer-assisted cell reconstruction system was used to determine
three-dimensional morphology (Claiborne 1992
).
Dr. Brenda Claiborne (University of Texas at San Antonio) generously
provided the second data set. These included four CA1 pyramidal neurons
and four CA3 pyramidal neurons, labeled using sharp electrodes filled
with horseradish peroxidase, and reconstructed with morphometric
techniques that were nearly identical to those for the first data set.
These cells have been subjected to other analyses in prior studies
(Carnevale et al. 1997; Claiborne 1992
; Mainen et al. 1996
).
Simulations
All simulations were performed with NEURON (Hines
1989; Hines and Carnevale 1997
) on Silicon
Graphics R4400 workstations. For all models, specific membrane
capacitance Cm was assumed to be 1 µF/cm2. For the morphological models (described below)
intracellular resistance (Ri) was set to 200
cm (Carnevale et al. 1997
), although recent experimental
measurements suggest that this value may be 70-100
cm
(Stuart and Spruston 1998
). Excitatory
non-N-methyl-D-aspartate (NMDA)
receptor-mediated synaptic conductances were modeled using the
reaction scheme proposed by Holmes and Levy (1990)
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Electrotonic analysis tools that are part of the standard distribution
of NEURON (Carnevale et al. 1997) were used to determine Zc, local ZN, and
ksyn
soma. In a number of simulations, we
normalized Zc at any dendritic location to
ZN at the soma
(
c). This facilitated within-cell
comparisons at different signal frequencies and between-cell comparisons.
In a previous study (Chitwood et al. 1999) we found that
the location-dependent distributions of depolarization at the soma, as
well as synapse to soma voltage attenuation, for the non-NMDA receptor-mediated synapse model were best fit by 20-Hz signals. Therefore most calculations of impedance and voltage transfer in the
present study were for 20 Hz.
EQUIVALENT CYLINDER MODEL.
An equivalent cylinder model, modified from Spruston et al.
(1993), was used to simulate generalized electrotonus. The
model emulates the electrotonic properties of a CA3 pyramidal neuron by
having both an apical and basal equivalent cylinder. The somatic compartment was a 50-µm-long cylinder with a diameter of 20 µm. The
apical dendrite was 720 µm long (3 µm diam), and the basal dendrite
was 310 µm long (3.8 µm diam). Both dendritic cylinders for this
model were subdivided into 50 compartments each. Apical tufts were
added to this model as 10 additional dendrites (5 compartments each)
100 µm long and 3 µm diam. Rm for these
models was 50,000
cm2 and Ri was
100
cm.
MORPHOLOGICAL MODELS.
Morphometric data were converted to a format compatible with NEURON
using custom software. The electrical effects of spines on pyramidal
neurons were emulated in some simulations by doubling Cm and halving Rm
(Holmes 1989).
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THEORY |
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Two-port theory
Two-port electrotonic analysis, which was introduced by
Carnevale and Johnston (1982), is a good starting point
for understanding the origins of the disparity between the variability
of Vsyn and Vsoma (see
also Koch 1999
). Although it has been used to describe both current and voltage attenuation in dendrites (Carnevale and Johnston 1982
; Carnevale et al. 1997
;
Tsai et al. 1994
), the functional consequences of the
relationship between input impedance ZN and transfer impedance Zc have not been elaborated.
Two-port electrotonic analysis draws on the basic principle that the
electrical coupling between any two points in a linear system can be
described by an equivalent circuit that consists of three impedances.
The top of Fig. 1 shows a cartoon of a
cell with a recording electrode attached to the soma and an activated synapse located somewhere on its dendritic tree. The membrane potentials at the soma and synapse are Vsoma and
Vsyn. The current injected into the cell through
the electrode at the soma is Isoma, and the
synaptic current is Isyn. The bottom
of this figure shows the electrical equivalent for this experimental
arrangement. Here we have used an equivalent T circuit
(Carnevale and Johnston 1982) to represent the coupling
between the somatic recording electrode and the synaptic location.
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Despite the suggestive appearance of this diagram, the transfer
impedance Zc is not a direct counterpart of the
cell membrane between the synapse and the soma, nor do the axial
impedances Za and Zb
correspond to the resistance of the intervening cytoplasm. These
impedances are complex functions of frequency that depend on the
anatomic and biophysical properties of the entire cell and the
locations of the synapse and the soma (e.g., Eqs. 9 and 10 in
Carnevale et al. 1997). For any finite structure, it
should be noted that generally Za
Zb (Carnevale and Johnston 1982
; Carnevale et al. 1997
) except for two special cases: the
trivial instance where the synapse is located at the soma and the
special case of a uniform cylinder in which the "soma" and the
synapse are equidistant from the geometric midpoint of the cylinder.
According to Kirchhoff's voltage law, the membrane potentials at the
soma and synapse are
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(1) |
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(2) |
SOMATIC AND SYNAPTIC INPUT IMPEDANCES.
The input impedance (ZN) at any point in a cell
is proportional to the local change of Vm
produced by injecting a current at that point, so we have the input
impedances of the cell at the soma
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(3) |
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(4) |
TRANSFER IMPEDANCE.
The transfer impedance (Zc) between two points
is the change of Vm produced at one point by
applying a current at the other. Referring to Fig. 1, it is immediately
clear that transfer impedance is symmetric, i.e., it does not depend on
which point is "upstream" and which is "downstream."
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(5) |
VOLTAGE TRANSFER.
From Eqs. 1-4, the voltage transfer ratio from the soma to
the synapse is
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(6) |
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(7) |
INTEGRATION OF SYNAPTIC INPUTS.
The effect of synaptic location on the somatically observed PSP depends
on whether the synapse acts more like a voltage source or more like a
current source. If a synapse acts like a voltage source, the change of
Vm that it produces in its immediate vicinity (Vsyn) is almost independent of synaptic
location. According to Eq. 7, the PSP at the soma is given
by
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(8) |
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(9) |
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(10) |
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(11) |
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RESULTS |
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Empirical dissociation of Zc and
ksynsoma
To probe the relationship between Zc and
dendritic geometry, we employed two simplified neuron models. The soma
of the first model was bracketed by two cables that correspond to the
apical and basal dendrites of a CA3 pyramidal neuron (Spruston
et al. 1993). The second model was a modification of the first,
with a tuft of 10 short daughter branches attached to the distal end of
the apical cable. For convenience we will call these the "plain" and "tufted" models.
The spatial profile of ksynsoma for 20-Hz
signals along the apical cable was identical in both models (Fig.
2A, top). However,
ZN increased steadily with distance from the
soma in the plain model, whereas it changed little along the apical
cable of the tufted model (Fig. 2A, middle). Consistent with
the relationship of ZN and
ksyn
soma to Zc
(Eq. 10 in THEORY), Zc
was relatively uniform across the apical dendrite of the plain model
(Fig. 2A, bottom). This relative uniformity of
Zc implies that a current applied to any
dendritic location will produce nearly the same change in
Vsoma, i.e., the somatic response to synaptic
inputs is approximately normalized (Fig. 2B, top). We call
this phenomenon passive normalization because it happens even though
active currents are not present. In contrast to the plain model, the
tufted model shows a significant decrease of Zc
with distance so that passive normalization did not occur (Fig.
2B, bottom). Thus a dendritic geometry that leads to an
increase of ZN with distance from the soma may
prevent a steep decline of Zc and result in
passive normalization.
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The spatial profiles of Zc were spatially
symmetric: somatodendritic Zc was equal to
dendrosomatic Zc (simulations not shown). However, unlike Zc, voltage transfer was
spatially asymmetric, with ksynsoma falling
off more quickly with distance than ksoma
syn
(simulations not shown). These symmetry properties confirm the
predictions of two-port linear circuit theory (see prior section) (also
see Cauller and Connors 1992
; Koch 1999
).
Does Zc actually predict the location-dependence
of EPSPs produced by conductance-change synapses? To answer this
question, a 1-nS peak conductance synapse (peak conductance latency
~2 ms) was sequentially placed along the apical dendrite of both
models (Fig. 2B). In both cases, the profile of
Zc normalized to an input onto the soma
(c) for 20-Hz signals closely followed
the peak amplitude of the somatic PSP
(
soma, again normalized to an input onto
the soma) produced by the dendritic synapse. As predicted by the
different profiles of Zc, the model without an
apical tuft exhibited passive normalization.
Because of membrane capacitance, the attenuation of electrical signals
in a neuron increases with frequency (Jack et al. 1975; Johnston and Brown 1983
; Rall 1977
;
Spruston et al. 1993
, 1994
). Therefore we examined the profile of
Zc in the apical dendrite of the plain model at
several frequencies (Fig. 3A).
As frequency increased, the absolute magnitude of
Zc became smaller (Fig. 3A1), and at
frequencies above 10-25 Hz its location-dependence grew progressively
steeper (best seen in the plots of
c,
Fig. 3A2). By 100 Hz,
c at the
distal end of the apical dendrite was only ~60% of its peak value, a
much greater reduction than the ~7% seen at 0 Hz.
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The spatial profile of Zc was also sensitive to
differences in Rm. Uniformly decreasing
Rm from 50 to 1 k cm2 reduced the
magnitude of transfer impedance (Fig. 3B1) and accelerated its decay with distance from the soma (Fig. 3B2).
Because Zc governs the somatic response to
synaptic current flow, these simulations imply that, when signals are
of relatively low frequency (<25 Hz) and Rm is
high (25-50 k cm2), the amplitude of the PSP observed
at the soma will vary significantly less with location than would be
expected from ksyn
soma.
Transfer impedance and voltage transfer in neurons
The simulations presented above suggest that the geometry of a
neuron can have quantitatively different effects on the spatial profiles of ksynsoma and
Zc, and in turn on the peak somatic response to
a dendritic synaptic input (Vsoma). To further
define the role of geometry, we compared the profiles of these
electrotonic indices across five morphologically distinct cell classes,
starting with CA1 and CA3 pyramidal neurons.
Figure 4 shows
ksynsoma and Zc
normalized to the soma (
c) for 20-Hz
signals in a CA1 pyramidal cell model as functions of path distance to
the soma. Points along the basal dendrites are shown at negative
distances to distinguish them from apical locations.
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The voltage transfer ratio (Fig. 4B) fell rapidly below 0.2 within 200 µm of the soma and continued to decrease noticeably all
the way to the distal dendritic terminations. Transfer impedance also
decreased with distance from the soma (Fig. 4C). However, little additional decline was seen along terminal branches, which appear as nearly horizontal chains of points (the derivative of c with respect to path distance is ~0).
This means that a synaptic current that enters anywhere along a
terminal branch will produce almost the same PSP at the soma regardless
of its exact location on that branch. Most of the variation of
c in this cell occurred along the
bifurcated primary apical dendrites, which can be discerned as two
diagonal chains of points. Similar results were observed for three
other CA1 pyramidal neuron reconstructions. This suggests that the
primary apical dendrite sets the electrotonic coupling of synapses to
the soma by virtue of anatomic distance along its length, whereas the
side branches serve some other function, e.g., providing the surface
area needed to receive multiple converging inputs that will all have
the same relative effect on the soma.
As with the simplified models, an important question is how these
properties condition the efficacy of conductance change synapses. To
answer this question, we sequentially placed a 500-pS non-NMDA synapse
(see METHODS) on different dendritic locations of the CA1
pyramidal neuron. The peak EPSP amplitude at the soma (Vsoma) produced by these dendritic inputs is
illustrated in Fig. 4D. Like
c, Vsoma decreased
as synapse distance increased, and there was little further change
along terminal branches. The profile of EPSP amplitudes observed at the
soma paralleled the profile of transfer impedance
Zc. This means that the synaptic conductance amplitude and time course were such that these synapses acted more like
current sources than voltage sources. Further evidence for this
conclusion can be drawn from the peak EPSP amplitudes at the synaptic
locations. For example, in one CA1 pyramidal neuron the mean peak EPSP
amplitude at 200 randomly chosen dendritic synaptic locations was
5.2 ± 2.5 (SE) mV for 500-pS unitary inputs. Because
resting potential was
65 mV in these simulations, this depolarization
represents only ~8% loss of driving force. Finally, increasing the
synaptic conductance from 500 pS to 2 nS to enhance the loss of driving
force (mean peak EPSP amplitude at the same dendritic locations was
9.4 ± 4.2 mV) had no qualitative effect on the
location-dependence of depolarization at the soma (simulations not shown).
The basal dendrites were an interesting feature of this cell type.
Although the range of voltage transfer ratios from the basal dendrites
to the soma was comparable with what was seen in the apical dendrites,
there was much less variability of c and
Vsoma. Therefore these simulations predict that,
from the standpoint of impact on Vsoma, synaptic
locations in the basal dendritic field are significantly more
isoefficient than inputs onto the apical dendrites.
For comparison, we analyzed seven CA3 pyramidal neuron models obtained
from morphometric reconstructions. These cells also exhibited steep
profiles of ksynsoma with distance from the
soma (Fig. 5B). Another
similarity was that high-order branches showed almost no change of
c or Vsoma along
their length (Fig. 5, C and D). In contrast to
CA1 pyramidal neurons, however, the location-dependence of
c and Vsoma
throughout the cell was quite small (Fig. 5, C and
D): they never fell below 80% of their maximum values.
Thus, if a unitary synaptic current was placed at any point in the
cell, there would be very little change in the amplitude (but not the
shape) of the PSP detected at the soma. In addition, like the basal
dendrites of CA1 pyramidal neurons, the basal dendrites of CA3
pyramidal neurons also exhibited very little variation in
c and Vsoma.
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Effects of varying frequency and Rm
We next examined the frequency dependence of
c between CA1 and CA3 pyramidal neuron
geometries. As the preceding simulations suggested, the mean
c was higher for the CA3 neuron at all
frequencies we examined (up to 100 Hz; Fig.
6A). However, the variance of
c was significantly lower for CA3 than
for CA1 pyramidal neurons (Fig. 6B). This combination of
larger mean (approaching 1) and a smaller variance of
c distinguishes the electrotonic
architecture of CA3 pyramidal neurons from CA1 pyramidal neurons. Such
reduced variability of synaptic amplitude, which emerges from the
anatomic and basic passive properties of a cell without requiring the
participation of active currents, is a hallmark of passive synaptic
normalization. At frequencies below 10 Hz, the CA1 variance was almost
four times greater. With increasing frequency, the CA3 variance also
grew larger, so that the two cell classes showed practically identical variance at 100 Hz.
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Assuming that Cm is similar in CA1 and CA3
pyramidal neurons, the apparent twofold difference in 0
between these cells implies a twofold difference in
Rm (Spruston and Johnston 1992
).
To see how differences in Rm might contribute to
the location-dependence of transfer impedance in these cells, we
determined the minimum
c from three data
sets (Fig. 7A). The first set
was four CA1 pyramidal neurons reconstructed from sharp-electrode
impaled cells filled with horseradish peroxidase (HRP). In the second
set, models of CA3 pyramidal neurons (n = 4), also
obtained from sharp-electrode/HRP fills, had significantly larger
values of
c at the most distal locations.
Varying Rm between 30 and 60 k
cm2 had no significant effect on
c for either CA1 or CA3 pyramidal neuron
models (Fig. 7C). The third data set was from CA3 pyramidal neurons filled with biocytin via whole cell pipettes. Minimum values of
c for these cells were also significantly
larger than for the CA1 pyramidal neurons, but not significantly
different from CA3 pyramidal neuron reconstructions obtained from
sharp-electrode fills. The results from these comparisons indicate that
dendritic morphology, rather than Rm, is the
major determinant of Zc between CA1 and CA3
pyramidal neurons.
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There is evidence to suggest that RN in vivo is
smaller than the values observed in vitro because of differences in
synaptic activity (Paré et al. 1998;
Raastad et al. 1998
). The effect of synaptically induced
conductance changes on apparent Rm can be
inferred from the magnitude of the change of RN,
depending on the electrotonic architecture of the cell. Apparent
Rm is nearly proportional to
RN for an isopotential cell and proportional to the square of RN for an infinite cylinder. For
real neurons the relationship between Rm and
RN will lie between these two extremes. Thus a
50% decrease of RN implies a reduction of
Rm by ~50-75% (Fig. 7B).
If Rm is smaller in vivo, then electrical
signals should decay more rapidly with distance (Jack et al.
1975; Rall 1969
; Spruston et al.
1993
). Reducing Rm might also reasonably
be expected to reduce the magnitude and alter the spatial profile of
c (see Fig. 3). To look for such an
effect, we calculated the mean and variance of
c in a CA3 pyramidal neuron model for
Rm ranging from 1 to 100 k
cm2.
In Fig. 7B2, mean
c is plotted
against Rm. Location-independence of
c was consistent over wide ranges of
Rm, and therefore RN. Only when Rm (and in turn
RN) was reduced by ~70% from its original value (66 k
cm2) were the mean and variance of
c decreased and increased more than 10%,
respectively. Such an extreme reduction of RN is
much larger than the synaptic effects observed in neonatal rat spinal cord by Raastad et al. (1998)
and is at the upper limit
of the findings reported by Paré et al. (1998)
for
pyramidal neurons in cat neocortex. It therefore seems unlikely that
the reasonable differences between in vitro and in vivo empirical
observations of RN will have significant effects
on the location-independence of Zc in CA3
pyramidal neurons, or on the spatial profile of
c in other morphological cell types.
These simulations assume that the passive membrane properties are
uniform throughout the dendritic tree. The possibility that the
apparent Rm of a neuron is nonuniform was
examined recently by Stuart and Spruston (1998) and
Magee (1998)
. They found that RN
in both CA1 and neocortical pyramidal neurons decreases progressively with distance from the soma due to a progressively higher density of
hyperpolarization-activated channels (Ih) in the
distal dendrites. Therefore we examined the profile of
c for models in which the decrease of
Rm followed a sigmoidal function, whereas
somatic RN and
0 were
approximately the same as when Rm was uniform. This nonuniformity of Rm had no qualitative
effect on the location-dependence of
c in
CA1 pyramidal neurons or the relative location-independence of
c in CA3 pyramidal or nonpyramidal
neurons. Figure 8 illustrates that
profoundly different spatial distributions of Rm
produced only slight variations in the spatial profile of
Zc in a CA3 pyramidal neuron model.
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Other neuronal geometries
We next examined 15 CA3 nonpyramidal neurons. These cells have
significantly fewer branches and higher RN than
CA3 pyramidal neurons (Chitwood et al. 1999). They also
have very different configurations of dendritic arbors compared to CA3
pyramidal neurons, although their electrotonic architectures display
certain parallels, such as small variation of
c and Vsoma across
the dendritic tree (Fig. 9, C
and D) and similar decay of
ksyn
soma with distance (Fig. 9B;
cf. Fig. 5B).
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The morphology of deep layer cortical neurons differs greatly from
hippocampal pyramidal neurons, being dominated by a very long (~1 mm)
primary apical dendrite that ends in a distal tuft of higher order
dendrites. From a reconstruction of a layer V pyramidal neuron in rat
PFC, we analyzed ksynsoma,
c, and Vsoma. As
in CA1 pyramidal neurons, ksyn
soma decayed rapidly with distance (Fig.
10B). The smallest voltage
transfer ratios were seen in the branches of the apical tuft. The
spatial profiles of
c and
Vsoma in these cells were steeper than for CA3
pyramidal and nonpyramidal neurons (Fig. 10, C and
D). Like CA1 pyramidal neurons, the primary apical dendrite
stood out distinctly from all other branches because of the steady
decay of
c and Vsoma with distance along it. Secondary and
higher order dendrites showed very little change in
c or Vsoma with
location (slope ~0), a feature that was common to all neurons that we
examined. The basal and oblique dendrites of these cells, like those of CA1 and CA3 pyramidal neurons, also showed very little variation in
c and Vsoma with
location.
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The last neuron we studied was a dentate gyrus granule cell (Fig.
11). This cell resembled the basal
dendrites of hippocampal and neocortical pyramidal neurons in that
ksynsoma decayed rapidly with distance,
whereas
c and
Vsoma showed considerably less variation
(compare Fig. 11 with the basal dendritic fields of Figs. 4 and 10).
Other parallels between the anatomic and electrotonic architectures of
these cells and the basal dendrites of hippocampal pyramidal neurons
have been noted by Carnevale et al. (1997)
.
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Spatial variation of input impedance
ZN increases with distance from the soma
and is maximal at the distal dendritic terminations (simulations not
shown). This has been observed in lamprey spinal neurons
(Buchanan et al. 1992) and suggested for a number of
mammalian neuron types (Cauller and Connors 1992
;
Nitzan et al. 1990
; Rapp et al. 1994
;
Segev et al. 1995
). For every compartment of the five
types of model neurons, we plotted the 20-Hz input impedance of that
location versus the 20-Hz transfer impedance
(Zc) between it and the soma (Fig.
12). In all of these cells, the
greatest variation of ZN occurred along the
terminal branches, which are easily discerned in these graphs. This is
consistent with the previous simulations that showed
Zc to be nearly constant along secondary and
higher order branches. Most of the variation of
Zc tended to occur along branches that were more
proximal, especially in pyramidal cells. The existence of a primary
apical dendrite is marked by the presence of a long region where
ZN shows the least variation (CA1 and PFC layer
V). This agrees with the hypothesis that a cable with uniform ZN will exhibit the most dramatic spatial
variation of Zc (see INTEGRATION OF
SYNAPTIC INPUTS in THEORY and see How
ZN and Zc can normalize synaptic responses
in DISCUSSION). In contrast, CA3 pyramidal neurons, CA3
nonpyramidal neurons, and granule cells do not have apical dendrites
with relatively flat ZN profiles. Dendrites in
these cells all had significant changes in ZN
with Zc. Therefore it appears that the presence
of a large primary dendrite is a prerequisite for significant
location-dependent variability of Zc.
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DISCUSSION |
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In general, proximal synaptic inputs tend to produce larger
somatic PSPs than synapses that are distal but otherwise identical (Spruston et al. 1994). Proximal excitatory synapses are
therefore more likely to trigger spikes, assuming a spike-generating
zone in the vicinity of the soma (Colbert and Johnston
1996
; Stuart and Sakmann 1994
). The results of
the simulations presented here are consistent with this rule of thumb
in each of the cell classes that we studied. For example, a synapse
onto a proximal dendrite of a hippocampal CA1 or PFC pyramidal neuron
could elicit a PSP at the soma ~2.5-fold greater than an identical
synaptic input located on one of the most distal branches. This
estimate is based on unitary inputs; synapses with slower kinetics or
trains of synaptic input would show somewhat less location-dependent variability.
It might therefore seem surprising that somatic depolarizations evoked by synaptic inputs onto proximal dendrites were only slightly larger than distally generated signals in CA3 pyramidal neurons, CA3 nonpyramidal neurons, and dentate granule cells. This unexpected finding is explained by the spatial profile of transfer impedance Zc. For example, in CA3 pyramidal neurons Zc for 20-Hz signals in the most proximal dendrites was only 1.1 times larger than for distal inputs. This suggests that a synapse onto a proximal dendrite would produce a somatic PSP that is only 10% larger than the PSP that would result from an identical synapse placed in the most distal locations. Simulations using a fast non-NMDA receptor-mediated synaptic conductance were consistent with this prediction. In other words, the anatomic and "passive" biophysical properties of the cell combine to remove most of the dependence of somatic PSP amplitude on synaptic location. The outcome is an approximate normalization of the impact of synaptic inputs on somatic Vm.
This is in contrast to the voltage transfer ratio
ksynsoma, which could be more than fourfold
larger for proximal synapses than for the most distal inputs. These
simulations point out that analysis of voltage transfer alone does not
reveal how unitary postsynaptic currents would affect somatic
potential. When the amplitude and time course of a synaptic conductance
are such that the synapse acts more like a current source than a
voltage source, the transfer impedance Zc is a
better indicator of the relative efficacy of synapses at different
locations. The decision whether to use Zc or
ksyn
soma depends on both the anatomic and
biophysical properties of the cell and the magnitude and time course of
the
gs. A conductance change synapse will act
like a current source when
gs is relatively
small or of brief duration, so that
Vm in the
subsynaptic region is only a small fraction of the driving force for
current flow. Under this condition, the amplitude and time course of
synaptic current will be relatively independent of synaptic location,
and Zc is the better descriptor. However, if
gs is large and lasts long enough, the
driving force for synaptic current will dissipate. This limits the peak
amplitude of the PSP in the vicinity of the synapse, i.e., the synapse
starts to behave more like a voltage source. In this case,
ksyn
soma is more appropriate.
To the best of our knowledge, this is the first systematic investigation of a mechanism for normalization of synaptic inputs that does not invoke active currents. Our study has the further distinction of documenting this phenomenon, which we call "passive synaptic normalization," in several different types of neurons through simulations of morphometrically detailed models. These simulations also demonstrate that there is very little effect of location on a given secondary or higher order dendrite, for any of the neurons we studied. A synapse placed anywhere along the length of a higher order dendrite will have comparable influence on somatic Vm.
The literature contains isolated reports of insensitivity of peak EPSP
amplitude to synaptic location in previous studies of other cell types.
For example, in an arbitrary fourth-order binary tree model
extrapolated from a ball-and-stick representation of
Cs+-filled retinal ganglion cells, Taylor et al.
(1996) observed that somatic EPSP peak amplitudes were
"essentially independent" of synaptic position. Segev et al.
(1995)
, who were primarily concerned with the effects of spines
in an anatomically detailed model of spiny stellate neurons, noted that
EPSP amplitude at the soma was relatively independent of synaptic
location in the dendritic tree. Models of presumed motoneurons in rat
spinal cord slice cultures by Larkum et al. (1998)
found
that EPSP peak amplitudes were nearly uniform throughout the cell
regardless of synaptic location, except for the immediate vicinity of
the synapse where Vm showed a brief
high-amplitude depolarization. Taken as a whole, these prior studies
and our present findings offer good reason to suppose that synaptic
normalization without the participation of active currents may be an
important principle of synaptic integration that is as common as
temporal summation.
This is also the first description of systematic differences in
Zc between different classes of neurons. Other
measures have been used to characterize and compare different classes
of neurons, such as voltage attenuation
(1/ksynsoma) and its logarithm (Carnevale et al. 1997
). However, the importance of
Zc has largely gone unnoticed (but see
Cauller and Connors 1992
; Koch
1999
). This is most likely due to the fact that convenient
tools for determining Zc and
ZN for large-scale models (~3,000
compartments) have only recently been developed (Carnevale et
al. 1997
; Tsai et al. 1994
).
How ZN and Zc can normalize synaptic responses
These observations demonstrate that, in some neurons, there is a broad class of synaptic inputs that can produce somatic PSPs whose amplitude is practically independent of synaptic location. How does this normalizing effect on somatically observed PSPs arise, and how do differences in neuronal geometry account for it?
The degree of synaptic normalization is a reflection of the spatial
profile of the transfer impedance Zc, which in
turn is related by the two-port theory of electrotonus to the spatial profiles of input impedance
ZNsyn and voltage transfer ratio ksynsoma (Eq. 7). Along any
dendritic branch, the voltage transfer ratio
ksyn
soma falls off with distance from the
soma (Fig. 13, top). If
ZNsyn is roughly constant along a dendritic
branch, then in order to account for the decline of
ksyn
soma there must be a similar drop of
Zc with distance (Fig. 13, middle),
and synaptic normalization will not occur. This is what happens in a
long cylindrical dendrite with no side branches (Fig. 2A)
and in the primary apical branches of CA1 and PFC pyramidal cells
(Figs. 4B and 10B). If instead
ZNsyn increases rapidly enough with distance, the spatial profile of Zc
will be much more shallow (Fig. 13, bottom), creating the
conditions that allow passive synaptic normalization to happen.
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What dendritic properties affect the somatodentritic profile of
ZN to permit passive normalization? One
possibility is that the tapering of dendrites from proximal to distal
terminations could lead to an increasing ZN in
some cells (Holmes 1989) and account for passive
normalization. This is in contrast to the relatively constant diameter
of primary apical dendrites of CA1 and neocortical pyramidal neurons
where there is significant location-dependence of synaptic responses
observed at the soma. However, dendritic branching pattern is also an
important determinant (see Fig. 2). The dendrites of the dentate
granule cells, CA3 interneurons, and CA3 pyramidal neurons modeled here
taper very quickly once they emerge from the soma and are of relatively
constant diameter thereafter. For these neurons, the combination of
their electronically short dendrites and specific branching pattern
leads to the location-independence of Zc.
The similarity between granule cell dendrites and the basal dendrites
of pyramidal cells provides a clue as to why the profiles of
ksynsoma and Zc could
be so different among the different types of neurons: these dendrites
do not have extended primary branches. The apical dendritic fields of
the PFC neuron and the CA1 pyramidal neuron are characterized by long,
large-diameter primary branches that extend from the soma. Input
impedance (ZN) showed only slight variation with
distance along these primary apical dendrites (Fig. 12). Hence for a
given synaptic current there was less variation in local PSP amplitude
but greater variability in the EPSP observed at the soma (Fig. 13,
middle). The proximal dendrites of granule cell, CA3
pyramidal and nonpyramidal neurons, and the basal dendrites of CA1 and
PFC pyramidal neurons are much less prominent, and
ZN increased much more rapidly with distance along them, so Zc was more uniform (Fig. 12).
Consequently local EPSP amplitude would increase rapidly with distance
from the soma, whereas the EPSP at the soma would show little change
(Fig. 13, bottom). Finally, in all neurons, secondary and
higher order branches showed significant increases in
ZN (Fig. 12), whereas Zc
in these dendrites was generally uniform with distance. Therefore a
synaptic input placed at any location on such a dendrite would have
roughly equal potency at the soma.
Physiological relevance
At this point it is useful to reflect on several questions that bear on the relevance of passive synaptic normalization to neuronal function. How might this phenomenon be affected by alterations of Rm produced by generalized synaptic bombardment? How does it vary with the frequency content of the synaptic signal? What about possible contributions from inward or outward voltage-gated currents, and how might it be influenced by nonuniform distributions of passive or active channels? Finally, what implications does synaptic normalization have for information processing in dendrites?
Paré et al. (1998) recently demonstrated that
synaptic bombardment has significant effects on somatic
RN in neocortical neurons. They concluded that
in vitro measurements of RN may be up to ~70% higher than in vivo. However, when we decreased
Rm so that RN was reduced
by ~70%, the mean Zc fell by only 18% (Fig.
7C). Therefore synaptic bombardment that globally reduces
ZN is likely to have only a nominal effect on
Zc and the location-dependence of synaptic integration.
Signal frequency does affect Zc, and our
findings (e.g., Fig. 3) lead us to expect that slow PSPs (i.e., NMDA or
GABAB mediated) or the summed baseline of a burst of fast
PSPs will show the greatest degree of uniformity throughout the cell.
Single, fast PSPs should display greater variability with respect to
dendritic location, with Vm showing a prominent
peak in the near neighborhood of the synapse itself. However, outside
of this narrow spatial zone, the voltage transient evoked by a fast PSP
will have been slowed to the point where its time course approaches
that of a slow PSP, and consequently its amplitude too will be
relatively independent of location. This is supported by the
observations of Larkum et al. (1998), who studied
responses to synaptic currents that were much faster than the membrane
time constant.
Voltage-gated inward current has been proposed as a mechanism for
reducing synaptic variability due to location (Andersen et al.
1987; Cook and Johnston 1997
,
1999
). It is becoming
apparent that many, if not all, mammalian CNS neurons have dendritic
voltage-gated Na+ and Ca2+ channels
(Christie et al. 1995
; Jaffe et al. 1992
,
1994
; Magee et al.
1995
; Magee and Johnston 1995a
,
b
).
The simulations presented here show that extensive normalization may
result from passive membrane properties alone. They also suggest that
the most efficient way to supplement passive synaptic normalization
would be for active Na+ and Ca2+ conductances
to be concentrated in the primary dendrites of cortical or CA1
pyramidal neurons, where the largest changes in
Zc occur, instead of throughout the dendritic
tree. For neocortical neurons, it has been suggested that a high
density or "hot spot" of these channels in the primary apical
dendrite may amplify EPSPs (Schwindt and Crill 1995;
Yuste et al. 1994
). Otherwise, these signals would be
significantly attenuated by passive electrotonus. In contrast, higher
order dendritic branches and the dendrites of CA3 pyramidal neurons,
nonpyramidal neurons, and granule cells do not need to have a high
density of inward current channels to ensure that synapses at all
dendritic locations have equal strengths at the soma.
Recent articles have highlighted possible functional roles of
hyperpolarization-activated currents (Ih) in the
dendrites of neocortical and hippocampal CA1 pyramidal neurons
(Magee 1998; Stuart and Spruston 1998
),
and in particular how Ih may cause significant
reduction of apparent Rm and dendritic
RN. Although Ih may be
quite prominent in these and other cells, and is unquestionably important for neuronal function, there are several reasons why it is
unlikely to confound the synaptic normalization that we describe here.
First, its voltage-dependence and slow time course imply that
Ih will have little effect on low- to
moderate-amplitude EPSPs. Indeed, the results presented by
Stuart and Spruston (1998) and Magee
(1998)
indicate that the principal action of
Ih on somatically observed EPSPs is not to alter
peak amplitude but instead to produce a temporal sharpening of the
waveform, which compensates for much of the broadening caused by
electrotonic filtering. So in a sense Ih
improves the fidelity of the somatic response to the dendritic stimulation. This is particularly noteworthy because the underlying conductance (gh) has been estimated to increase
from the soma to distal dendrites by anywhere from fivefold
(Magee 1998
) to three orders of magnitude (see Fig. 5 in
Stuart and Spruston 1998
). Here we should also point out
that, despite the large estimated variation of
gh, Magee's own data display a remarkable
symmetry: the somatic response to a long dendritic current pulse was
nearly identical to the dendritic response when the same pulse was
applied at the soma, both in the absence and presence of bath-applied Cs+ (Fig. 9, A and B, of Magee
1998
). This is exactly as predicted by two-port linear
electrotonic theory, and it suggests that the notion of transfer
impedance Zc may have practical value even when
active currents make obvious contributions to the time course of
Vm (Fig. 9A of Magee
1998
).
Second, passive synaptic normalization is robust in the face of major reductions of distal dendritic Rm (Figs. 7C and 8). Like other rapid fluctuations of Vm, synaptic potentials are attenuated by ohmic loss via axial resistance (Ra) and the escape of signal currents through membrane capacitance (Cm). Because Ra and Cm are the principal determinants of signal attenuation, it is not surprising that nonuniformity of Rm has little effect on passive normalization. Furthermore, even if a distal Ih current was activated by a large, prolonged hyperpolarization, it would have to cause a quite profound increase of membrane conductance before its effect on normalization would be felt.
It should be noted that passive or active nonuniformities of apparent
Rm would change the response of a cell to DC and
slow inputs, but the synaptic normalization we describe involves
transient signals, and so it is governed primarily by cytoplasmic
resistivity and specific membrane capacitance. Our findings indicate
that passive synaptic normalization will be altered only if local
membrane time constant varies by at least an order of magnitude. In
this connection, the studies of Stuart and Spruston
(1998) and Magee (1998)
suggest only a sevenfold
and twofold reduction in Rm, respectively, between the soma and distal dendrites of neocortical and hippocampal pyramidal neurons.
The simulations presented here should not be taken to imply that
dendrites are not important for local computations. To the contrary,
they predict significant differences in local PSP amplitudes in the
dendrites by virtue of regional variations of
ZN, as Segev et al. (1995) also
found in a model of a spiny stellate neuron. Therefore synapses onto
distal dendrites are more likely to activate voltage-gated conductances
than proximal inputs. This may explain why the density of certain
K+ channels increases with distance from the soma,
particularly those for A-type K+ currents (Hoffman
et al. 1997
). Such channels might compensate for differences in
ZN, but the resulting compensation may be
use-dependent; sustained depolarization, as may occur during bursts of
EPSPs, might transiently inactivate these channels, briefly opening a window in which subsequent synaptic inputs are relatively boosted.
Passive normalization might at first glance seem to have limited
importance for synaptic integration. After all, there is a substantial
body of evidence that active currents can enhance synaptic efficacy
and, under the proper conditions, may be responsible for synaptically
triggered dendritic spikes (Golding and Spruston 1998;
Schwindt and Crill 1997
). We propose that passive
normalization may actually play a much more widespread and important
role in synaptic integration. This suggestion is based on the
observation that low-amplitude fluctuations of
Vm, presumably of synaptic origin, are commonly
seen in many types of neurons, and action potentials generally appear
to be triggered by these noiselike fluctuations. Mainen and
Sejnowski (1995)
have shown how such apparent "noise" can
trigger action potentials reliably and with high temporal precision.
Passive normalization, perhaps in combination with
Ih to achieve some temporal sharpening of the
somatic response as we suggested above, is an ideal mechanism for
transforming locally high-amplitude postsynaptic signals, which are
scattered widely over a cell but have limited range, into low-amplitude fluctuations of Vm at the soma. It ensures that
all synapses have a nearly equal "vote" at the soma, regardless of
where they are located in the dendritic tree.
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ACKNOWLEDGMENTS |
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We thank R. A. Chitwood, A. T. Gulledge, and A. Hubbard for the electrophysiology, histology, and 3D reconstructions that constituted a major portion of the neuron morphology used in this study. We also thank Dr. Brenda J. Claiborne for providing additional neuron morphology data and for assistance with 3D reconstruction.
This work was supported by National Science Foundation Grants IBN-9511309 and HRD-9628514 and National Institute of General Medical Sciences Grant GM08194-17S1.
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FOOTNOTES |
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Address for reprint requests: D. B. Jaffe, Division of Life Sciences, University of Texas at San Antonio, 6900 North Loop 1604 West, San Antonio, TX 78249.
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 23 December 1998; accepted in final form 26 August 1999.
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REFERENCES |
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