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The Journal of Neuroscience, March 15, 2000, 20(6):2086-2093
A Model of High-Frequency Ripples in the Hippocampus Based on
Synaptic Coupling Plus Axon-Axon Gap Junctions between Pyramidal
Neurons
Roger D.
Traub and
Andrea
Bibbig
Division of Neuroscience, University of Birmingham School of
Medicine, Edgbaston, Birmingham B15 2TT, United Kingdom
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ABSTRACT |
So-called 200 Hz ripples occur as transient EEG oscillations
superimposed on physiological sharp waves in a number of limbic regions
of the rat, either awake or anesthetized. In CA1, ripples have maximum
amplitude in stratum pyramidale. Many pyramidal cells fail to fire
during a ripple, or fire infrequently, superimposed on the sharp
wave-associated depolarization, whereas interneurons can fire at high
frequencies, possibly as fast as the ripple itself. Recently, we have
predicted that networks of pyramidal cells, interconnected by
axon-axon gap junctions and without interconnecting chemical synapses,
can generate coherent population oscillations at >100 Hz. Here, we
show that such networks, to which interneurons have been added along
with chemical synaptic interactions between respective cell types, can
generate population ripples superimposed on afferent input-induced
intracellular depolarizations. During simulated ripples, interneurons
fire at high rates, whereas pyramidal cells fire at lower rates. The
model oscillation is generated by the electrically coupled pyramidal
cell axons, which then phasically excite interneurons at ripple
frequency. The oscillation occurs transiently because rippling can
express itself only when axons and cells are sufficiently depolarized.
Our model predicts the occurrence of spikelets (fast prepotentials) in
some pyramidal cells during sharp waves.
Key words:
sharp waves; 200 Hz; electrotonic coupling; oscillations; CA1 area; computer simulation
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INTRODUCTION |
Ripples are high-frequency EEG waves
(180-200 Hz in awake rats in CA1) recorded in hippocampus and other
limbic structures (Buzsáki et al., 1992 ; Ylinen et al., 1995;
Chrobak and Buzsáki, 1996), superimposed on physiological sharp
waves (Buzsáki, 1986). Ripples occur in both awake animals and
anesthetized ones, with frequency slower during anesthesia; the gap
junction-blocking anesthetic halothane, however, suppresses ripples,
without blocking sharp waves themselves (Ylinen et al., 1995).
[Halothane, however, has effects on synaptic transmission (Perouansky
et al., 1996) and intrinsic membrane properties (Patel et al., 1999),
as well as on gap junctions.] In extracellular recordings in CA1,
ripple amplitude is highest in stratum pyramidale (Ylinen et al.,
1995), consistent with generation of the waves by perisomatic IPSCs
and/or action potential-associated currents. Both pyramidal cells and interneurons, on average, increase their firing rates during the ripple, the relative increase being greatest for pyramidal cells (Csicsvári et al., 1998); nevertheless, pyramidal cells fire no
or a few spikes during a ripple, whereas at least some interneurons can
fire at ripple frequency. Firing of pyramidal cells, on average, leads
firing of interneurons by 1-2 msec (Csicsvári et al.,
1999b). In intracellular recordings from pyramidal cells, ripple
waves are 1-4 mV in amplitude, and the waves in a particular neuron are phase-shifted relative to the extracellular average signal by
intracellular hyperpolarization (Ylinen et al., 1995).
In this paper, we present a network model that accounts for the basic
experimental observations on ripples in an economical way. The model
uses AMPA and GABAA receptor-mediated synaptic interactions between and within populations of pyramidal cells and
interneurons; there is also a transient (150 msec) afferent synaptic
excitation of both populations, as would be expected to occur with
synaptic excitation of CA1, via Schaffer collaterals during a sharp
wave. The model incorporates an additional feature, somewhat novel but
critical to model function: gap junctions between axons of the
principal neurons. This feature allows the pyramidal axons to act as a
high-frequency network oscillator, a "signal generator" in effect,
that drives the interneurons. Some general properties of gap junctions
are reviewed elsewhere (Bennett and Verselis, 1992; Jefferys,
1995; Perez Velazquez and Carlen, 2000).
The hypothesis of axon-axon gap junctions is based on previous
physiological and modeling results. Draguhn et al. (1998) described brief, spontaneous 200 Hz multicellular oscillations in hippocampal slices, generated by principal neurons, dependent on gap junctions but
not dependent on chemical synapses. Whole-cell recordings of pyramidal
cells in low
[Ca2+]o media
indicated that local population spikes occurred simultaneously with
either intracellular action potentials or spikelets [also called fast
prepotentials (Spencer and Kandel, 1961) or d-spikes (Schwartzkroin and Prince, 1977)]. These spikelets were presumed to
arise as electrotonic coupling potentials between pairs of neurons.
Simulations of pairs of pyramidal cells, coupled by gap junctions in
soma or dendrites, could not replicate the form of the spikelets,
because the soma-dendritic membranes, together with the gap junction,
acted as a low-pass filter of a spike in the presynaptic cell; rise
times of the coupling potential were too slow. Electrical coupling
between axons, however, easily reproduced the form of spikelets
if the gap junction conductance was large enough; a presynaptic spike
could then evoke a spike in the coupled axon, which would propagate
antidromically in the coupled neuron. If this latter spike failed near
the axon initial segment, a spikelet would result.
Knowles and Schwartzkroin (1981) showed that stimulation of CA1 alveus,
hundreds of microns from a recorded CA1 pyramidal cell in
vitro, could evoke an antidromic spike, or a spikelet, after
strong or weak stimulation, respectively. Taylor and Dudek (1982a)
observed spikelets in antidromically activated CA1 pyramidal cells in
low [Ca2+]o media
and attributed them to electrotonic coupling at some point between the
neurons. Recently, Schmitz and colleagues (D. Schmitz, A. Draguhn, S. Schuchmann, A. Fisahn, E. H. Buhl, R. Dermietzel, U. Heinemann,
R. D. Traub, unpublished data) have obtained
electrophysiological evidence that axon-axon gap junctions between
hippocampal pyramidal cells play a role in spikelet generation, at
least in low
[Ca2+]o media.
Gap junctions act to synchronize. Why then would oscillations arise in
populations of neurons interconnected by axo-axonal gap junctions? This
question was addressed by Traub et al. (1999b) using a variety of
modeling approaches (with 3072 detailed compartmental neurons and with
a cellular automaton model). It was found that (approximately)
synchronized population oscillations could arise under the following
conditions. (1) Action potentials could propagate across the gap
junctions (in detailed models, the propagation took a finite time,
typically <0.5 msec). (2) The density of gap junctions was above the
"percolation limit" (Erdös and Rényi, 1960), so that
each axon connects to more than one other, on average. (3) The density
of gap junctions was low enough that the cells did not fire
continuously. By trial and error, it was found that densities of less
than ~2.5-3.0 gap junctions per axon were required, an extremely
sparse connectivity. (4) There was a background of randomly occurring,
spontaneous action potentials. These could occur at low frequency (as
low as 0.05 Hz in some cases). The resulting population oscillations
could easily occur at 150 Hz or faster. The mechanism appears unique;
the oscillation period is not determined by membrane refractoriness or
by synaptic time constants, but rather by (1) topological structure of
the network and (2) the time for a spike in one axon to induce a spike
in a connected axon.
In short, a network of pyramidal axons can act, in principle, as a
signal generator at frequencies above 100 Hz. In the added presence of
AMPA and sufficiently strong GABAA
receptor-mediated interactions, it has been shown that a system of
pyramidal neurons and interneurons can produce sustained  oscillations dependent on gap junctions (Traub et al., 1999c). Here, we
illustrate how ripple oscillations might also be generated.
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MATERIALS AND METHODS |
The network model used in this paper is a hybrid of the models
described by Traub et al. (1999a,b). That is, there is an array of
pyramidal cells and interneurons, interconnected (randomly or locally
randomly) by chemical synapses. This array, originally developed to
study tetanically induced and  oscillations, is almost exactly
as described in Traub et al. (1999a). (The slight differences are
listed below.) To this "chemical synaptic" array, we add a
pyramidal axon-axon gap junction connectivity, also defined further on.
Briefly, the network consists of 3072 pyramidal cells and 384 interneurons. Each neuron is multicompartmental and includes five
axonal compartments (Traub et al., 1994; Traub and Miles, 1995). The
pyramidal cells are arranged in a 96 × 32 array and the
interneurons in a 96 × 4 array. The interneurons are divided into
four classes of 96 cells each: "basket cells," inhibiting perisomatic regions; "axo-axonic cells," inhibiting axon initial segments; and two types of dendrite-contacting interneuron (for more
proximal or more distal dendrites, respectively). The time constant of
ISPCs induced by basket cells and axo-axonic cells was 10 msec but was
50 msec for dendrite-contacting interneurons. Interneurons other than
axo-axonic cells also synaptically contact other interneurons. Synaptic
connectivity of pyramidal cells was global, but of interneurons was
confined to take place only to cells at most 500 µm away (25 cell
diameters along the long axis of the array). Each pyramidal cell
receives input from 30 other pyramidal cells and from 80 interneurons.
Each interneuron receives input from 60 other interneurons. Only AMPA
and GABAA receptor-mediated synaptic interactions
were simulated, not NMDA, metabotropic, or GABAB
mediated. Further structural details can be found by Traub et al.
(1999a).
Intrinsic properties of the individual neurons were exactly as
described by Traub et al. (1999a), with the exception that gK(AHP) density was uniformly 0.8 mS/cm2 over the soma-dendrites of
pyramidal cells, as in the original paper (Traub et al., 1994). The
time course of unitary EPSCs in the present study was as follows:
0.75 × t × e( t/2) nS on pyramidal cells,
and 0.5 × t × et nS on interneurons. Peak
unitary IPSC values were 2 nS on pyramidal cells, 1 nS for basket
cell-mediated inhibition of interneurons, 0.1 nS for other IPSCs on
interneurons. These values are the "default" values used in this
study; when modified in the figures, it will be duly noted.
Gap junctions (nonrectifying, voltage-independent) were located between
the penultimate axonal compartments (centered 263 µm from the soma)
of randomly selected pairs of pyramidal cell axons, subject to the
constraint that the respective somata were within 200 µm of each
other. The default gap junction resistance (used unless
specified otherwise) was 238 M (conductance of 4.2 nS);
this resistance allowed action potentials to cross from one axon to the
other, at least sometimes (Traub et al., 1999b).
The average number of gap junctions lying on an axon was 1.6. To remind
the reader of the structural implications of this density of gap
junctions (Erdös and Rényi, 1960; Traub et al., 1999b),
this density lies above the percolation limit of one gap junction per
cell. This means that a "large cluster" will exist and that all
cells not on the large cluster are either isolated or lie on small
clusters. [Definitions are as follows: a "cluster" of cells is a
set of cells such that if cell A and cell B both are in the set, then a
gap junctional path A (zero, one, or more intermediate cells,
themselves connected by gap junctions) B exists, with the
intermediate cell(s) also lying in the set. With low-connection
densities, the number of intermediate cells in the path may be big. A
cluster is "large" if its size is of the same order as the whole
network; otherwise the cluster is "small."]
Some structural properties of this particular gap junction network were
noted by Traub et al. (1999b). For example, the large cluster has 1990 cells, and the next largest cluster is small, having only 13 cells. The
mean path length (which measures the average length of the shortest gap
junctional path between randomly selected cell pairs) on the large
cluster is ~17.5. A block diagram of the network model is shown in
Figure 1.
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Figure 1.
Block diagram of network model. The model contains
3072 pyramidal cells and 384 interneurons (basket cells, axo-axonic
cells, and dendrite-contacting cells), with intrinsic properties and
connectivity described in Materials and Methods. The figure highlights
the conceptual distinction we make between the axons of the pyramidal
cells and the soma-dendritic membranes. Interactions between
components of the model are shown. Afferent inputs in the model are
purely excitatory. Only AMPA receptors are simulated for recurrent
excitatory connections, and only GABAA receptors for
recurrent inhibitory connections.
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As in previous studies (Traub et al., 1999a,b), noise was simulated by
the generation of random ectopic spikes, originating from small current
pulses applied to the most distal compartment of the five-compartment
axon. The current pulses had Poisson statistics (as approximated with a
pseudorandom number generator), independent between different axons,
and occurred once per 5 sec in interneurons; in pyramidal cells, in the
figures illustrated here, current pulses were applied on average once
per second, but mean intervals of 0.1-10 sec were also tried. In our
model of high-frequency oscillations in axonal networks (Traub et al.,
1999b), ectopic axonal spikes played a critical role.
Sharp waves were produced by applying a 150 msec excitatory conductance
pulse (reversal potential of 60 mV positive to rest) to both pyramidal
cells and interneurons: the "afferent input." The conductance
developed in four compartments of the midapical dendrites of pyramidal
cells and likewise in four dendritic compartments of the interneurons.
The onset of the conductance was spread (randomly and uniformly) over a
1 msec interval for both cell types. The shape of the conductance pulse
was a cosine function, peaking at 60 nS for pyramidal cells and 4 nS
for interneurons. Further variability was introduced into the system by
having different bias currents applied to the somata of the pyramidal
cells ( 0.15 to 0.05 nA, randomly and uniformly distributed).
Two sharp waves per simulation were generated, separated by 250 msec.
These waves had a similar appearance, although pyramidal cell
afterhyperpolarizing conductances were larger in the second wave
than in the first. For the sake of consistency, figures were made using
data from the second sharp wave of any given simulation.
Simulation programs saved the following types of data: somatic voltages
of selected pyramidal cells (some on the large cluster, some not) and
interneurons; voltages in the axon (at the site of the gap junction) of
selected pyramidal cells; average signals, consisting of somatic
voltages of 224 nearby pyramidal cells or of 28 nearby interneurons;
and total GABAA synaptic conductance to a
pyramidal cell, recurrently generated AMPA conductance to a pyramidal
cell, afferent AMPA conductance to a pyramidal cell, and afferent AMPA
conductance to an interneuron. Autocorrelations and cross-correlations
were computed using the middle 75 msec of data from the simulated sharp
wave. Figures that illustrate an "axonal" signal use the voltage in
the respective axon at the site of the gap junction.
Programs for simulation and analysis were written in FORTRAN.
Simulation programs were written in FORTRAN augmented with instructions for a parallel computer. These latter programs were run on an IBM SP2
with 12 nodes (processors); other programs ran on a single node of the
SP2. Some comments on numerical methods are discussed by Traub et al.
(1999a). Each simulation was of 450 msec of activity and took ~2.7
hr. For further details, please contact Roger D. Traub at
r.d.traub{at}bham.ac.uk.
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RESULTS |
The basic properties of simulated ripples in our model (using
default parameters) are shown in Figures
2 and 3.
The afferent input depolarizes the pyramidal cells and, to a lesser
extent, the interneurons (Fig.
2A,B). An ~140 Hz oscillation,
predominantly subthreshold and ~2 mV in amplitude, becomes apparent
in pyramidal cells, and (as is clearly visible in the average signal)
this oscillation is coherent (Fig.
2A,B). During the sharp
wave-associated depolarization, interneurons begin to fire at high
rates. The interneuron in Figure 2A fires at ripple
frequency, although not all interneurons do. [Note that the afferent
input itself is not enough to induce this high-frequency firing in our
model, as shown by a simulation with recurrent excitatory synapses
blocked (data not shown).] On average, the mean pyramidal cell signal
leads the mean interneuronal signal by 1.3 msec (Fig. 2C),
comparable with in vivo experimental data (Csicsvári
et al., 1999b).
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Figure 2.
Firing properties of pyramidal cells and
interneurons during a simulated ripple. Default parameters were used
(see Materials and Methods). A, Average voltage of 224 nearby e-cell somata (thick line) reveals 140 Hz
oscillation superimposed on a cellular depolarization. An interneuron
(thin line) fires at the same frequency. Spikes
truncated. B, Single pyramidal cell (thick
line) fires once during the ripple but displays intracellular
ripple waves, ~2 mV in amplitude. The axon of the cell
(thin line) fires at more than ripple frequency. Many
axonal spikes are followed by ~1-2 mV spikelets, one of which is
indicated by an arrow. [This cell was on the large
cluster (see Materials and Methods). Axons of cells off the large
cluster do not fire at ripple frequency, and there are virtually no
spikelets, although intracellular rippling still occurs (data not
shown).] Spikes truncated. Signals in A and
B are simultaneous. C, Autocorrelation of
local average pyramidal cell signal (thick line) shows
rhythmicity at 140 Hz. Cross-correlation of local average pyramidal
cells with local average interneurons (thin line) shows
that pyramidal cells lead interneurons by 1.3 msec, on average.
(Cross-correlation shifted and rescaled on vertical axis.)
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Figure 3.
During simulated ripple, the pyramidal cell axonal
plexus oscillates at high frequency and phasically drives interneurons.
A, Interneuron (thin line, spikes
truncated) fires at ripple frequency. The AMPA receptor-mediated input
to this interneuron (thick line) has a slow (afferent)
component lasting >100 msec and a phasic component at ripple
frequency. The phasic waves of synaptic excitation lead the action
potentials. B, The AMPA input to the interneuron
(thick line) lags the oscillatory output axonal network
(thin line), plotted as the number of axons depolarized
above 70 mV from rest. On average, the local mean interneuron potential
lags this axonal signal by 1.5 msec. Data from simulation as in Figure
2. Signals in A and B are
simultaneous.
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Rippling arises in our model as follows. In between the sharp waves,
distal axons are hyperpolarized by several millivolts, which
suppresses the ectopic spikes (data not shown). As the sharp wave
begins, the axonal hyperpolarization is relieved, and ectopic spikes
begin and percolate throughout the axonal plexus, generating a
high-frequency network oscillation (Fig. 3B). The detailed
mechanisms of this oscillation are analyzed by Traub et al. (1999b),
but, briefly, the main ideas are these: if gap junctions allow action potentials to cross from one axon to another and if each axon connects
(on average) to more than one other, then an ectopic action potential,
arising in a single axon, can lead to a wave of activity that spreads
through the axonal network. The pattern of this wave does not depend on
the detailed kinetics of the active currents in the axon, provided that
postspike refractoriness is less than 1 or 2 msec. The period of the
oscillation is determined by two main factors: (1) the time it takes
for an action potential to cross from one axon to another (expected to
be <0.5 msec), and (2) the length of "chains" of gap junctions
crossed as the original ectopic spike spreads to the bulk of the axonal
population (expected to be in the range of 10-20 or so). The
oscillation period is approximately the crossing time multiplied by the
expected length of such chains. Our model predicts that small decreases in junctional conductance, by prolonging the time it takes for spikes
to cross gap junctions, should slow the period, whereas factors that
increase connectivity of the network (i.e., a greater number of gap
junctions) should decrease the period. The latter effect is expected
because, in a more connected network, an ectopic spike can excite the
bulk of the population over relatively shortened chains of gap junctions.
The effects of the axonal network oscillation (Fig. 3) are twofold.
First, antidromic propagation into pyramidal cells (lying on the large
cluster) can evoke spikes or spikelets within <1 msec (Fig.
2B, arrow). With the strength of IPSCs
used, however, the probability of full-spike invasion of pyramidal
cells is low, and pyramidal cells fire rarely during the ripple (see
further on). [Note that for pyramidal cells not lying on the large
cluster, spikelets will not be seen; instead, the ripple appears purely as synaptic potentials (data not shown).] Second, the coherent orthodromic output of the axonal plexus induces, after a very short
delay, phasic AMPA receptor-mediated EPSPs in interneurons, which
entrain their firing (Fig. 3A,B).
Note that orthodromic synaptic excitation of interneurons can take
place without the parent pyramidal cell soma necessarily firing.
When a pyramidal cell somatic voltage was correlated with the local
average pyramidal signal, the peak occurred near 0 msec (Fig.
4), not surprisingly. When the same cell
was hyperpolarized ~20 mV during the ripple, it became nearly
anticorrelated with the local average signal (Fig. 4), again in
agreement with others (Ylinen et al., 1995). This is consistent with
the notion that the ripple waves are predominantly IPSPs. This was
checked in the model by plotting the actual synaptic conductances
"seen" by a pyramidal cell during the rippling (data not shown).
Fluctuations in AMPA receptor conductance were ~5 nS in amplitude,
superimposed on the afferent excitatory conductance. In contrast,
fluctuations in GABAA receptor conductance were
25-50 nS. There was, additionally, a slower component to the
GABAA conductance, produced by the
dendrite-contacting interneurons (whose ISPCs are relatively slow; see
Materials and Methods).
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Figure 4.
Hyperpolarizing a pyramidal cell, during a ripple,
shifts its phase relative to the local average signal. Using data from
the central portion of the ripple in the simulation of Figures 2 and 3,
a pyramidal cell somatic signal was cross-correlated with the local
average signal (224 pyramidal cells) (thick line). The
peak is near 0 msec (0.8 msec). The simulation was repeated, with the
index pyramidal cell hyperpolarized ~20 mV during the ripple,
relative to control. The cross-correlation of the index cell with the
local average (thin line) now reveals a minimum near 0 msec (1.5 msec) (arrow).
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Rippling in the model requires that gap junctional conductance be
sufficiently large, consistent with in vivo data showing that halothane suppresses ripples (Ylinen et al., 1995) (Fig. 5). When the gap junctional conductance
was reduced 25% from its default value, a -frequency rhythm was
superimposed on the sharp wave (Fig. 5A), and many of the
pyramidal cell action potentials were orthodromic. Partial spikes were
seen in the axon, indicative of failed conduction of action potentials
across gap junctions. When gap junctional conductance was reduced only
2.5% relative to default (Fig. 5B), ripple waves begin to
occur but are not sustained, being broken up at ~20 msec intervals.
Spikelets are also to be noted in the pyramidal cell soma. Finally, for
comparison, Figure 5C illustrates rippling, using data from
the simulation of Figures 2 and 3. When the gap junctional conductance
was increased an additional 12.5% above default value, rippling would
still occur but at higher frequency (~200 Hz; data not shown).
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Figure 5.
Oscillatory behavior in the model depends on
axo-axonal gap junction conductance. Each panel shows the soma of a
pyramidal cell lying on the large cluster (thick line)
and the axon of the cell (thin line). Spikes are
truncated. Gap junctional conductance is expressed relative to the
constant c = 10.5 nS and increases in sequence
ABC.
A, With a small gap junctional conductance, the axonal
network cannot sustain high-frequency oscillations. Cellular
oscillation occurs at frequency (~50 Hz), and action potentials
are orthodromic. B, At a higher gap junction
conductance, there is evidence of sustained axonal network activity;
the soma fires only once, but the axon fires seven times, and spikelets
occur in the soma. C, With a still higher gap junction
conductance (as used in Figs. 2 and 3), continuous high-frequency
activity can occur in the axonal network. Individual pyramidal cells
express a high-frequency oscillation as well, with a synaptic
component, and, if the cell is on the large cluster, spikelets occur
also.
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Traub et al. (1999b) showed that axon-axon gap junctions could produce
a high-frequency oscillation superimposed on a spontaneous, synchronized "epileptiform" burst in a disinhibited population of
pyramidal cells, interconnected by recurrent excitatory chemical synapses. This is a type of event that occurs in disinhibited CA3 (Wong
and Traub, 1983). Figure 6 demonstrates
that axo-axonal gap junctions can produce a high-frequency oscillation
(~160 Hz) in an afferently excited, disinhibited population of
pyramidal cells, as would occur in CA1, as it responds to excitatory
input from CA3 (Schwartzkroin and Prince, 1977; Wong and Traub, 1983). In this case, pyramidal cells (lying on the large cluster) fire full
spikes and also 10-20 mV partial spikes during the burst (Fig.
6C). This type of activity occurs in a given cell (provided it lies on the large cluster) at the same frequency as the population activity.
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Figure 6.
Blocking GABAA receptors allows a
ripple frequency oscillation to persist, but pyramidal cell firing
increases. Same parameters as in the simulation of Figure 2, but all
GABAA conductances set to zero. Traces in
A-C are simultaneous. Cells on the large cluster (as in
C) exhibit 10-20 mV partial spikes
(arrows), deriving from partially blocked antidromic
activity. Many of the full action potentials are also antidromic; the
axonal network here acts as a high-frequency signal generator, driving
pyramidal cells antidromically, as well as orthodromically. Compare the
high-frequency oscillation superimposed on CA1 epileptiform field
potentials (Schwartzkroin and Prince, 1977) (see also Traub et al.,
1999b).
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Rippling in the model also requires that IPSCs on pyramidal cells not
be excessively large. Figure 7
illustrates a simulation with parameters identical to the simulation of
Figures 2 and 3, except that unitary IPSCs on pyramidal cells are 50%
larger. In this case, a -frequency oscillation occurs instead of
rippling. [It is interesting that transient runs of -frequency
oscillations have been recorded in CA1 in vivo
(Csicsvári et al., 1999a).] IPSCs interrupt the firing of
interneurons (Fig. 7A), the axonal population (data not
shown), and pyramidal cells (Fig.
7B,C). That axonal activity still
can take place is shown by the occurrence of spikelets in at least some
of the pyramidal cells (Fig. 7C, arrows).
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Figure 7.
Increasing GABAA IPSCs on pyramidal
cells converts the ripples to a -frequency oscillation (~50 Hz in
this case). Same parameters as in the simulation of Figure 2, but
unitary IPSCs on pyramidal cells are 50% larger. In this case, the
axonal network is spontaneously active (Fig. 8A),
but the activity is not continuous, being broken up by IPSPs. The
network of depolarized pyramidal cells and interneurons then produces
oscillations, reminiscent of models of tetanically induced (Traub et al., 1999a) and of glutamate-induced (Burchell et al.,
1998), but with the difference that spontaneous axonal activity is
prominent here. Traces in A-C are
simultaneous. A, Interneuron showing doublets and spikes
followed by EPSPs (arrow) (cf. Whittington et al.,
1997). Average pyramidal signal (B) and pyramidal
cell (C) do not exhibit ripple waves. Note the
spikelets in the pyramidal cell (oblique arrows).
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Figure 8 illustrates the transition from
-frequency oscillation to rippling as the conductance of pyramidal
IPSCs is reduced. (Other parameters are as in the simulation of Fig.
2.) Here, one can see how sufficiently large IPSCs break up the
high-frequency firing of the axon, either repeatedly (Fig.
8A, arrows) or intermittently (Fig.
8B, arrow).
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Figure 8.
Transition from to rippling as synaptic
inhibition is reduced. The simulation of Figure 2 (same as Fig.
8C) was repeated with identical parameters, except for
the conductance of IPSCs on pyramidal cells. Each panel shows the
potential of a pyramidal cell soma and its axon (same cell in all of
the panels). A, rhythm. B, Rippling,
although axonal activity is not continuous. C, Rippling,
with continuous axonal activity. Note in A and
B the IPSP-induced hyperpolarizations in the axonal
potential (some marked with arrows).
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DISCUSSION |
To place our model results in perspective, we shall consider
briefly four possible models of rippling and attempt to identify experiments that could distinguish between the different models. Of
course, these models could possibly work in conjunction with one
another in various combinations, but it is premature to enter into the
resulting complexities. We suspect that ephaptic interactions, as
appear to contribute to field burst synchronization (Jefferys and Haas,
1982; Taylor and Dudek, 1982b; Konnerth et al., 1984), are not of
primary importance during ripples, because the extracellular potentials
are a fraction of a millivolt (Ylinen et al., 1995); hence, we consider
below only mechanisms based on chemical synapses and/or gap junctions.
Could rippling result from slow excitation of pyramidal cell and
interneuron populations, together with purely chemical synaptic interactions? The closest experimental paradigms in vitro
would be the oscillations induced in CA1 or CA3 by tetanic stimulation (Whittington et al., 1997), by glutamate application (Burchell et al.,
1998), or by carbachol (Fisahn et al., 1998). Rippling is not apparent
in any of these experimental protocols, although it is conceivable that
IPSPs are large enough to suppress rippling (Figs. 7, 8). However,
tetanically induced oscillations in CA1 in vitro, in the
presence of bath-applied morphine (which suppresses GABA release), also
do not show rippling (Whittington et al., 1998, their Fig. 1).
In addition, tetanic oscillations in morphine exhibit population
spikes, with pyramidal cells firing at frequencies (Whittington et
al., 1998; Faulkner et al., 1999), a cellular behavior not seen during
ripples. This hypothesis also would not explain the suppression of
ripples by halothane. Nevertheless, in vivo, it is
conceivable that there is relatively more excitation of interneurons
than of pyramidal cells during a sharp wave, occurring in some manner
not captured by the slice protocols.
Could rippling result from GABAergic interactions between interneurons,
in effect, ultrafast "interneuron network ?" In experimental studies of interneuron network , in CA1 in vitro,
application of L-glutamate produced frequencies
only as high as 49 Hz (Traub et al., 1996, their Fig. 1). Again, one
might consider that synaptic inhibition in the experimental situation
is more effective than during a sharp wave. Note, however, that even in
bicuculline (up to 5.0 µM, just short of
blocking the oscillations), frequencies only as high as 65 Hz occurred
(Traub et al., 1996, their Fig. 3). In morphine, a drug that reduces
GABA release, epochs with frequencies as high as ~90 Hz could be
observed in pharmacologically isolated interneuron networks
(Whittington et al., 1998, their Fig. 2); therefore, this hypothesis
cannot be dismissed too lightly.
Theoretical arguments weigh against ultrafast interneuron network ;
as the oscillatory period becomes short relative to the time constant
of GABAA IPSC relaxation, then the effects of
heterogeneity in cellular excitability become more and more pronounced,
and the oscillation breaks up (Wang and Buzsáki, 1996; Chow et
al., 1998; White et al., 1998). If this time constant is ~10 msec
(Traub et al., 1996), then it has been argued (Chow et al., 1998) that 200 Hz oscillations in interneuron networks cannot be stable. One must
be open to the possibility, however, that some subset of interneurons
could exist, mutually inhibitory with extremely fast IPSCs, faster than
those normally encountered. Even then, this hypothesis would not
explain the halothane suppression of ripples.
Could ripples result from purely interneuron networks, interconnected
by gap junctions (Galarreta and Hestrin, 1999; Gibson et al.,
1999)? Such gap junctions might, in principle, occur between dendrites
(as recognized ultrastructurally; Kosaka, 1983) or, hypothetically,
between axons. Networks of interneurons interconnected by dendritic gap
junctions have been shown, using simulations, to be capable of
generating autonomous network bursts (Traub, 1995), but only under
conditions in which the dendrites are excitable enough to support
action potential initiation. Interneuron networks interconnected by
axon-axon and dendrite-dendrite gap junctions can also (in
simulations) generate fast population oscillations (R. D. Traub,
unpublished data) by the same mechanisms as could work for pyramidal
cell networks, provided that mutual GABAergic inhibition between the
interneurons is suppressed. The hypothesis of gap junctionally coupled
interneuron networks is consistent with the halothane data. If the
hypothesis is correct, one would expect to find evidence of axonal
activity in interneuronal recordings in vivo: antidromic
spikes, partial spikes, or spikelets.
Could ripples result primarily from network oscillations generated in
pyramidal cell axon networks, with gap junctional interconnections? This is the hypothesis explored in the present paper. The "core" of
the ripple generator is as shown, in block diagram form, in Figure
9A. The pyramidal cell axonal
network acts as a high-frequency signal generator, working when (1) gap
junctional conductance is large enough for spikes to cross gap
junctions (Traub et al., 1999b) (Fig. 5), and (2) the axons are not too
hyperpolarized. Afferent excitation of pyramidal cells can overcome
axonal hyperpolarization and allow the signal generator to operate
(Figs. 2, 3). The output of the axonal signal generator phasically
excites interneurons and induces many of them to fire at high frequency
(Figs. 2, 3). (In CA1, recurrent excitation of pyramidal cells is of
less importance than the excitation of interneurons, especially with
IPSPs present.) The degree of pyramidal cell firing is regulated by the
strength of inhibition on pyramidal cells (Fig. 6); our proposed
mechanism can in principle work, however, without any firing by the
pyramidal cell somata. If, on the other hand, IPSPs are too large, then axonal activity is broken up and a -frequency oscillation results. This latter behavior is similar to what we propose happens during carbachol- and kainate-induced oscillations in CA3 in vitro
(Traub et al., 1999c). This hypothesis is consistent with the
disruption of ripples by halothane.
View larger version (18K):
[in this window]
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|
Figure 9.
Block diagram of subnetworks believed critical for
generating high-frequency (>100 Hz) oscillations in interneuronal
populations and for gap junction-sensitive oscillations.
A, The pyramidal cell axons, interconnected by gap
junctions, act as a high-frequency signal generator, the output of
which phasically excites interneurons via AMPA receptors. (Each
interneuron will, of course, be excited by many axons.) Some of the
interneurons follow the phasic input at high frequency.
B, If the interneurons also inhibit the axon initial
segments powerfully enough, the high-frequency output of the axon
network can be modulated at a frequency determined by GABAA
IPSC time course; a -frequency rhythm could thereby arise (Traub et
al., 1999c).
|
|
If our proposed mechanism is correct, there are two key
experimental implications. First, there should be evidence of
antidromic activity in some (not all) CA1 pyramidal cells during
ripples: antidromic spikes, partial spikes, or spikelets. Second, there should be evidence of ripple frequency EPSPs in hyperpolarized CA1
interneurons during sharp waves. Because of afferent excitation of CA1
via Schaffer collaterals during the sharp waves, recordings would
optimally be made in interneurons receiving minimal Schaffer input but
which are recurrently excited by CA1 pyramidal cell axons (Sik et al.,
1995; Freund and Buzsáki, 1996; G. Buzsáki, personal communication).
| |
FOOTNOTES |
Received Oct. 18, 1999; revised Dec. 22, 1999; accepted Dec. 27, 1999.
This work was supported by the Wellcome Trust. R.D.T. is a Wellcome
Principal Research Fellow. We thank Eberhard Buhl and György
Buzsáki for helpful discussions.
Correspondence should be addressed to Roger D. Traub, Division of
Neuroscience, University of Birmingham School of Medicine, Vincent
Drive, Edgbaston, Birmingham B15 2TT, UK. E-mail:
r.d.traub{at}bham.ac.uk.
| |
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K. Stenkamp, J. M. Palva, M. Uusisaari, S. Schuchmann, D. Schmitz, U. Heinemann, and K. Kaila
Enhanced Temporal Stability of Cholinergic Hippocampal Gamma Oscillations Following Respiratory Alkalosis In Vitro
J Neurophysiol,
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[Abstract]
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R. D. Traub, R. Bibbig, A. Piechotta, R. Draguhn, and D. Schmitz
Synaptic and Nonsynaptic Contributions to Giant IPSPs and Ectopic Spikes Induced by 4-Aminopyridine in the Hippocampus In Vitro
J Neurophysiol,
March 1, 2001;
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[Abstract]
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B. Teubner, B. Odermatt, M. Guldenagel, G. Sohl, J. Degen, F. F. Bukauskas, J. Kronengold, V. K. Verselis, Y. T. Jung, C. A. Kozak, et al.
Functional Expression of the New Gap Junction Gene Connexin47 Transcribed in Mouse Brain and Spinal Cord Neurons
J. Neurosci.,
February 15, 2001;
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[Abstract]
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Y. Fischer, L. Wittner, T. F Freund, and B. H Gahwiler
Simultaneous activation of gamma and theta network oscillations in rat hippocampal slice cultures
J. Physiol.,
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TOP
ABSTRACT
INTRODUCTION
