Departments of Pediatrics and Neurology, B 182, University of
Colorado Health Sciences Center, Denver, Colorado 80262
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INTRODUCTION |
The periodic discharge
of the hippocampal CA3 pyramidal cell network is a well-studied model
of pathological network synchronization (Jefferys 1993
).
A number of experimental manipulations that induce seizures in vivo
also produce episodic depolarizations and bursts of action potentials
of CA3 pyramidal cells in the in vitro slice preparation
(Buzsaki 1986
; Jefferys 1994
;
Traub and Miles 1991
; Traub and Wong
1982
). This synchronized bursting occurs across the entire CA3
population and closely resembles interictal epileptiform activity
recorded in vivo (Buzsaki 1986
; Matsumoto and
Ajmone Marsan 1964
) that underlies interictal spikes on the
human electroencephalogram (DeCurtis and Avanzini 2001
;
Gloor 1991
; Sundaram et al. 1999
).
Because numerous manipulations of the CA3 in vitro slice preparation
produce robust epileptiform activity, and rapid, precise changes in
drug concentrations are possible, this network is a useful preparation
in which to study convulsant and anticonvulsant mechanisms
(Anderson et al. 1987
; Duong and Chang
1998
; Rose et al. 1986
; Scharfman and
Schwartzkroin 1990
; Schwartzkroin and Prince
1978
; Stasheff et al. 1985
; Swartzwelder
and Wilson 1987
; Swartzwelder et al. 1986
).
Intuitively, a convulsant should increase the probability of bursting
so that bursts become longer and/or more frequent, whereas an
anticonvulsant should decrease the probability of bursting so that
bursts are shorter and/or less frequent.
For example, elevating extracellular potassium
([K+]o) (Korn et
al. 1987
; Rutecki et al. 1985
) depolarizes the
pyramidal cell resting membrane potential (RMP), increasing CA3 burst
probability proportionately to the increased
[K+]o (Staley et
al. 1998
). Raising
[K+]o from 5 to 10 mM, a
convulsant manipulation, decreased both the interburst interval and
burst duration (Korn et al. 1987
; Rutecki et al.
1985
; Staley et al. 1998
). Perplexingly,
anesthetic concentrations of the anticonvulsant pentobarbital also
decreased both the interburst interval and burst duration (Korn
et al. 1987
) in this preparation. Thus when burst probability
is high (8.5 mM [K+]o),
both a convulsant and an anticonvulsant manipulation produced qualitatively similar effects in the periodically discharging CA3
network. However, when CA3 burst probability is low, pentobarbital produces the predicted changes: the interburst interval lengthens and
burst duration decreases (Swartzwelder and Wilson 1987
).
These findings raise the following questions: why does a convulsant and
an anticonvulsant manipulation produce qualitatively similar effects on
the interburst interval and burst duration when burst probability is
high? Why is pentobarbital ineffective when burst probability is high?
What is the mechanism governing the impact of burst probability on
anticonvulsant effects?
To address these questions, we extended a model of CA3 bursting in
which the burst duration is limited by activity-dependent depression of
the CA3 recurrent excitatory synapses, and the interburst interval is
determined by the time required to recover from this depression
(Staley et al. 1998
). We define the "burst end
threshold" as the level of synaptic depression at which bursts
terminate. The "burst start threshold" is the level of synaptic
depression at which burst initiation is possible. The cycling of CA3
between bursting and interburst quiescence depends on the time required to transition between these two thresholds. Next, we examine the effect
of a convulsant and an anticonvulsant manipulation on these bursting
thresholds. The burst start and end thresholds were calculated from
experimentally measured mean interburst interval and mean burst
duration. The convulsant and anticonvulsant manipulations have
predicable and opposing effects on the bursting thresholds, and these
effects are influenced by the baseline burst probability.
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METHODS |
Slice preparation
Wistar rats of age 4-7 wk were used for all experiments.
Housing and treatment of all animals were in accordance with animal welfare protocols approved by the Institutional Animal Care and Use
Committee. After pentobarbital anesthesia (60 mg/kg ip), the rats were
decapitated and hemi-brain slices were cut in the coronal plane. The
slices were incubated in artificial cerebrospinal fluid (ACSF)
containing (in mM) 126 NaCl, 2.5 KCl, 2 MgCl2,
2.0 CaCl2, 1.2 NaH2PO4, 1 glucose, and 26 NaHCO3. ACSF was saturated with 95%
O2 -5% CO2. Slices were
incubated at 31-33°C for 1-2 hr before experimentation. Slices
were recorded at 33°C and superfused continuously with ACSF at a rate
of 1-2 ml/min.
Recordings
Extracellular recordings were made using glass pipettes pulled
on a Narishige electrode puller (Tokyo) and filled with 150 mM NaCl.
For recording spontaneous bursts, a bipolar stimulating electrode and
the recording electrode were placed under visual guidance in the
stratum pyramidal of the CA3 region (Fig.
1A1). Electrodes were adjusted
so that large-amplitude population spikes were elicited as an
indication of slice viability and proper electrode positioning. The
placement of the recording electrode remained unchanged for the
duration of the experiment. Recordings using Axoclamp 2B
amplifiers were digitized at 2 kHz on a PCI-DAS 1602/16 Board
(Measurement, Middleboro, MA) using routines written in Visual Basic
6.0 (Microsoft, Seattle, WA).

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Fig. 1.
Properties of CA3 population bursts. A1: extracellular
recordings of population bursts in the pyramidal cell layer of CA3. We
induced spontaneous bursting of the CA3 pyramidal cell network using 2 methods: elevation of extracellular [K+]o to
8.5 mM (Rutecki et al. 1985 ; Korn et al.
1987 ; Staley et al. 1998 ) or after tetanic
stimulation of the CA3 pyramidal cell layer (Bains et al.
1999 ; Staley et al. 1998 , Stasheff et al.
1985 ). A2: CA3 network activity was quantified
in terms of interburst interval and burst duration. B:
stability of burst duration and interburst interval. B1
(interburst interval) and B2 (burst duration) illustrate
a representative single experiment. In 3.3 mM
[K+]o modified artificial cerebrospinal fluid
(ACSF) (Stasheff et al. 1985 ), the mean interburst
interval was 6 ± 0 s ( ) and the burst
duration was 85 ± 0 ms ( , n = 2). C: flow diagram of experimental protocol.
Spontaneous bursting in CA3 was induced using either 8.5 mM
[K+]o (high burst probability) or 3.3 [K+]o (low burst probability). Picrotoxin
(PTX) was used in experiment 1 only (see
METHODS). In experiments 2
and 3, we were interested in examining the effects of
the GABAergic anticonvulsant pentobarbital.
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Burst induction
Bursting in CA3 (Fig. 1A1) was induced by one of two
methods: a single tetanic stimulation to the CA3 pyramidal cell layer (Bains et al. 1999
; Stasheff et al. 1985
)
or increasing extracellular potassium (Korn et al. 1987
;
Rutecki et al. 1985
). Tetanic stimulation produced a
long-term increase in the synaptic strength so that spontaneous bursts
were possible (Bains et al. 1999
) and consisted of a
100-Hz, 1-s train of stimuli that was of sufficient amplitude to elicit
a population spike when delivered at lower frequency. If a single
tetanus did not induce bursting, it was repeated after a 10-min
interval. When tetanus was used to induce bursting, extracellular solutions were modified as previously described (Bains et al. 1999
; Staley et al. 1998
; Stasheff et al.
1989
): 1.3 mM Ca2+, 0.9 mM
Mg2+, and 3.3 mM K+.
Use of picrotoxin
Picrotoxin (PTX; 100 µM) was used only in
experiment 1, in which
[K+]o was varied from 8.5 to 10.mM, to avoid confounding effects of decreased GABA release and
altered Cl
gradients (Staley and Proctor
1999
; Staley et al. 1995
; Thompson and
Gahwiler 1989
). In experiments 2 and 3, no picrotoxin was used because we wanted to study the effects of the
GABAergic anticonvulsant, pentobarbital.
Data analysis: burst duration
Extracellular burst intensity is measured using a variety of
parameters including the coastline bursting index (CBI), area under a
burst, and burst duration. The CBI is the line integral of the
extracellular waveform (Korn et al. 1987
). We expect the CBI to increase with increases in neuronal synchrony, firing frequency, number of neurons participating in the burst, or the size or duration of the depolarizing wave within the burst. The CBI, however, does not
distinguish among these possibilities and is sensitive to action
potential synchronization between CA3 neurons as well as electrode
placement. The "burst area" represents the area under the burst
waveform. For intracellular recordings of membrane potential, burst
area is an unambiguous measure of the intensity and duration of
membrane depolarization. However, the area under the curve of
extracellular recordings is increased by current flowing out of the
somatic membrane and excitatory currents flowing into the dendritic
membrane. Both inhibitory and excitatory currents therefore increase
burst area. Because of this ambiguity, we chose to use burst duration
to measure burst intensity. The burst duration was calculated as the
time during which the absolute value of the burst was above a threshold
value, generally three times the baseline noise (Fig. 1A2)
(Staley et al. 1998
).
Inter-slice variability of burst duration
When performing extracellular recordings of CA3 population
bursts, the burst duration may vary with the distance from the site of
burst initiation (Korn et al. 1987
), the depth of the recording electrode, the conductivity of the slice (Traub and Miles 1991
), or the location from which the slice was obtained in the septal-temporal axis (Staley et al. 1998
). This
causes inter-slice variability of the burst duration measurements.
However, in any one slice and recording electrode position, burst
duration measurements are stable throughout the control and
experimental manipulations (Fig. 1B). We adjusted for the
inter-slice variability of the burst duration by using each slice as
its own control and reporting changes as "percentage change from control."
Rationale for dose of pentobarbital and co-application of
pentobarbital and acetazolamide
To increase gamma-aminobutyric acid A
(GABAA) receptor-mediated inhibition, we applied
60 µM pentobarbital to CA3. Pentobarbital (PB) has been extensively
studied in vitro and produces anesthesia at CSF levels from 50 to 100 µM (MacDonald 1984
). GABAA
receptors are the principal mediators of synaptic inhibition, yet when
intensely activated (as may occur during spontaneous population
bursts), dendritic GABAA receptors
excite rather than inhibit neurons (Alger and Nicoll
1982b
; Andersen et al. 1980
; Barker and
Ransom 1978
). PB prolongs the average open time of the GABA
receptor and but also increases the depolarizing GABA response in cell
culture (Alger and Nicoll 1982a
; Thalman
1988
) and the hippocampal slice preparation (Alger and
Nicoll 1982a
; Perreault and Avoli 1988
; Wong and Watkins 1982
). To exclude the possibility that
PB was causing proconvulsant effects by depolarizing the dendrites
during bursts, acetazolamide was co-applied with PB (reviewed in
Staley 2002
). This acetazolamide effect has been
experimentally verified in vivo (Archer et al. 2001
;
Sato et al. 1981
).
Summary of experimental design
We performed three experiments in the CA3 in vitro preparation
as delineated in the flow diagram of Fig. 1C. Using these
three experiments, we addressed the three questions posed in the
introduction. First, we examined the effects of a convulsant and an
anticonvulsant manipulation under conditions of high burst probability.
Second, we addressed why PB appears ineffective when burst probability is high. Third, we examined the role of the baseline burst probability on PB effects on burst duration and interburst interval.
Data analysis: interburst interval
The time between bursts is generally described in terms of burst
frequency in units of Hertz. When burst frequency is less than once per
second, we expressed the burst frequency in terms of the period as
"interburst interval" rather than as fractions of Hertz. The
interburst interval was calculated as the point from the beginning of a
burst to the beginning of the next burst (Bains et al.
1999
; Staley et al. 1998
).
Statistical analysis
CA3 burst duration and interburst intervals vary between slices
(Bragdon et al. 1986
; Korn et al. 1987
;
Mueller and Dunwiddie 1983
; Scharfman
1994
; Swartzwelder and Wilson 1987
;
Staley et al. 1998
; Whittington and Jefferys
1994
). Because of this variability, we calculated a
"control value" for each slice, defined as the mean value in the
control situation once the recordings were stable. Mean values were
also calculated after stabilization of the interburst interval and
burst duration for each drug application and normalized to the control
mean. The mean ± SE of each of these "normalized experimental
values" was then calculated. Additionally, a percentage change from
control was calculated as [100 * (drug
control)/control]. We report the effect of the drugs as a "percentage change".
We performed all statistical analysis using Microsoft Excel or Prism
GraphPad software. Significant differences between normalized interburst interval and burst duration, and convulsant or
anticonvulsant maneuvers were assessed by 2-tailed t-test.
Statistical significance was accepted at P
0.05.
Using the experimentally derived mean interburst interval and mean
burst duration (see APPENDIX for derivations), we
calculated values for the bursting thresholds. Differences between
control start and end thresholds were assessed using 2-tailed
t-test. Formulas for calculating the bursting thresholds are
available on request in Microsoft Excel format.
 |
RESULTS |
Baseline stability of slice preparation and burst probability
We assessed CA3 network behavior by measuring the burst duration
and interburst interval (Fig. 1B) (Bains et al.
1999
; Staley et al. 1998
). When bursts were
induced by 8.5 mM [K+]o,
the interburst interval ranged from 2.1 to 4.5 s (high burst probability; see also Table 1, 1st
column). When bursts were induced in 3.3 mM
[K+]o, the intervals
ranged from 5.3 to 24.8 s (low burst probability; see also Table
1, 7th column). For each individual slice, the interburst interval
(Fig. 1B1) and burst duration (Fig. 1B2) were stable.
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Table 1.
Changes in interburst interval and burst duration in response to
convulsant and anticonvulsant manipulations under high and low burst
probability
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When burst probability is high, a convulsant manipulation
decreases both burst interval and duration
Figure 2 displays the effect of a
convulsant manipulation on interburst interval (Fig. 2A1)
and burst duration (Fig. 2A2) when burst probability was
high. Figure 2A, 1 and 2, depicts representative slices. Figure 2B, 1 and 2, reflects pooled data.
The convulsant manipulation consisted of raising
[K+]o from 8.5 to 10.5 mM, which further increased burst probability. PTX (100 µM) was
applied throughout this experiment to avoid confounding effects due to
decreased GABA release and altered Cl
gradients
(see METHODS). The interburst interval decreased by 32 ± 9% and burst duration decreased by 19 ± 8% compared with controls. Table 1, first three columns, shows pooled interburst interval and burst length data during control and experimental conditions.

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Fig. 2.
High burst probability: a proconvulsant manipulation decreases the
burst interval and burst duration in CA3. Increasing
[K+]o from 8.5 to 10.5 mM decreased both the
interburst interval (A1) and burst duration
(A2) (A, 1 and 2, are
representative slices; see also Fig. 6 in Staley et al.
1998 ). PTX (100 µM) was used to avoid confounding effects due
to decreased GABA release and altered Cl gradients. The
interburst interval decreased by 32 ± 9% (B1) and
burst duration decreased by 19 ± 8% (B2) compared
with control (n = 7, Table 1, 1st 3 columns).
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When burst probability is high, an anticonvulsant
manipulation also decreases both burst interval and burst duration
Figure 3 illustrates the
effect of an anticonvulsant manipulation on CA3 bursting when burst
probability is high. Figure 3A shows a representative slice,
whereas Fig. 3B depicts pooled data. Table 1, middle three
columns, displays pooled control and experimental interburst intervals
and burst durations. Spontaneous bursting was induced in 8.5 mM
[K+]o. No PTX was used in this experiment because we were interested in examining GABAergic anticonvulsant effects. To increase GABAA receptor-mediated
inhibition, we applied 60 µM PB, which augments the average open time
of the GABAA receptor but also increases
GABAA receptor-mediated dendritic depolarization (Alger and Nicoll 1982
), and 10 µM ACTZ to inhibit the
depolarization due to intense activation of dendritic
GABAA receptors (Archer et al.
2001
; Staley et al. 1995
). This manipulation
decreased the interburst interval by 9 ± 5% and decreased the
burst duration by 16 ± 5% (Fig. 3B and Table 1,
middle 3 columns).

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Fig. 3.
High burst probability: an anticonvulsant manipulation also decreases
the interburst interval and burst duration in CA3. After the onset of
spontaneous CA3 population bursts by application of 8.5 mM
[K+]o ACSF (A, 1 and
2), we increased the GABAA conductance by
bath application of pentobarbital (PB) 60 µM and acetazolamide (ACTZ)
10 µM. Representative raw tracings for the change in interburst
interval (A1) and burst duration (A2) are
shown. PB + ACTZ also decreased the interburst interval by 9 ± 5% (B1) and the burst duration by 16 ± 5%
(B2, n = 10, Table 1, 2nd 3 columns).
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When burst probability is low, an anticonvulsant manipulation
increases the interburst interval and decrease burst duration
Next, we repeated these experiments under conditions of low burst
probability in 3.3 mM
[K+]o modified ACSF
(Stasheff et al. 1989
). Figure
4A shows a representative slice and B illustrates pooled data. Tetanic stimulation of
the CA3 pyramidal cell layer produced spontaneous bursting
(Bains et al. 1999
; Stasheff et al.
1985
). Table 1, last three columns, shows summary control and
experimental interburst intervals and burst durations. Addition of 60 µM PB +10 µM ACTZ increased the interburst interval from control by
136 ± 41% and decreased the burst duration from
control by 44 ± 3% (Fig. 4B, Table 1, last 3 columns). Similar to Swartzwelder and Wilson (1987)
, we
found that when burst probability is low, anticonvulsant effects on interburst interval and burst duration are more intuitive: burst duration decreased while interburst interval increased.

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Fig. 4.
Low burst probability: an anticonvulsant increases the interburst
interval and decreases the burst duration. Representative traces of the
effects of PB + ACTZ (A, 1 and 2) are
shown when bursting is induced in low burst probability (3.3 mM
[K+]o modified ACSF + tetanic stimulation).
When burst probability is low, addition of PB 60 µM and ACTZ 10 µM
produces the anticipated results. The interburst interval increased by
136 ± 41% (B1) and burst duration decreased by
44 ± 3% compared with control (B2,
n = 10, Table 1, last 3 columns).
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Model
In high burst probability, both proconvulsant (elevating
[K+]o) and anticonvulsant
(increasing GABAA mediated postsynaptic inhibition with PB + ACTZ) manipulations decreased the burst duration and interburst interval (Figs. 2 and 3, Table 1, 1st 3 columns and
middle 3 columns). These qualitatively similar results can be
reconciled using a model of CA3 bursting where cycling between the
bursts and interburst quiescence is determined by the onset of and
recovery from activity-dependent synaptic depression.
Traub and Miles (1991)
and Senn et al.
(1996)
have shown that below a critical level of synaptic
strength, synchronous network activity ceases. Thus activity-dependent
depression is a reasonable mechanism for burst termination
(Staley et al. 1998
). As described in the
APPENDIX, the average synaptic strength of the CA3 network oscillates between burst start and burst end thresholds during a
bursting cycle. We defined the "burst start threshold" as the level
of average network synaptic strength needed for burst initiation and
the "burst end threshold" as the level at which synaptic strength is too low to support burst activity (Fig.
5A). During a burst, synapses
depress to the level of the burst end threshold and in between bursts,
synapses recover from synaptic depression to the level of the burst
start threshold.

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Fig. 5.
CA3 burst timing depends on oscillations of synaptic strength between
the burst start and burst end thresholds. a. In the model, synaptic
strength of the CA3 pyramidal cell network (vertically placed bar,
far left) varies between a theoretical maximum
corresponding to no synaptic depression ("no depression") and a
theoretical minimum ("complete depression"). The actual maximum
synaptic strength occurs when recurrent excitatory synapses have
recovered from depression to the point that a burst is possible (the
burst start threshold). Conversely, the minimum synaptic strength is
the level at which activity-induced depression results in burst
termination (the burst end threshold). Synaptic strength decays with a
time constant depress during a burst and increases with
a time constant recover during the interburst interval.
The difference between the bursting thresholds reflects
the amount that individual synapses can depress before the population
burst fails, and thus determines the burst duration. B1:
convulsants elicit burst initiation before synaptic recovery is
complete. Therefore the synapses are relatively depressed at the
beginning of the next burst and they reach the burst end threshold more
quickly than in control conditions, decreasing the burst duration.
B2: anticonvulsants cause burst termination before
synapses are fully depressed by raising the burst end threshold. Thus
the bursting thresholds are also closer together shortening both the
burst duration and interburst interval. B3: summary of
the convulsant and anticonvulsant effects on burst thresholds.
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The burst duration reflects the time required for CA3 recurrent
collateral synapses to reach the burst end threshold and the interburst
interval reflects the time required for CA3 recurrent collateral
synapses to recover from synaptic depression (inset, Fig.
5A). If synaptic strength oscillates between these two
levels, then changing one threshold will affect both the
time to reach the first threshold and the time to rebound back to the
other threshold, and subsequently both the burst duration and
interburst interval are affected.
The rates of synaptic depression and recovery are not linear but
exponential with time constants
depress and
recover (APPENDIX, Fig.
5A) (Staley et al. 1998
, 2001
; Tsodyks
and Markram 1997
). The behavior of our model is not critically
dependent on the values of these time constants, so we have used
previously published estimates for
depress and
recover (Dobrunz and Stevens
1997
; Liu and Tsien 1995
; Staley et al.
1998
, 2001
). We assumed that these time constants remained
constant throughout the experiment. In the APPENDIX, we
derive the equations that relate the mean interburst interval and burst
duration to the bursting thresholds.
Effects of a convulsant and an anticonvulsant in the model
When burst probability was high (Fig. 2), a convulsant
manipulation increased the burst probability. In our model, this would be interpreted as lowering the burst start threshold so that bursting becomes possible before full recovery from synaptic depression (Fig.
5B1). This decreases the recovery time, which determines the
interburst interval. Bursts also had a shorter duration because synaptic depression was more extensive at the start of the burst, so
that less time was required to reach the level of synaptic depression
where bursting fails.
Figure 5B2 depicts the action of a hypothetical
anticonvulsant when burst probability was high. The anticonvulsant
terminated bursts before the CA3 network reached the
baseline level of synaptic depression by raising the burst end
threshold. The burst duration diminished because bursting ended before
all involved synapses depressed to the baseline level of
activity-dependent synaptic depression. Furthermore, the interburst
interval of subsequent bursts was also shorter because recovery from
synaptic depression began at a higher level of synaptic strength.
Thus in conditions of high burst probability, either convulsant or
anticonvulsant manipulations shorten burst duration and interburst
interval. Analysis using our paradigm explains these seemingly
paradoxical results. While the convulsant manipulation lowers the burst
start threshold, the anticonvulsant manipulation raises the burst end
threshold. In both cases, the bursting thresholds move closer together,
resulting in shortened interburst interval and burst duration. In
summary, the convulsant lowers the burst start and/or end thresholds
and anticonvulsant raises either burst start and/or end thresholds
(Fig. 5B3).
Because convulsants and anticonvulsants alter the bursting thresholds,
we can predict associated changes in burst duration and interburst
interval. Figure
6A1
illustrates a hypothetical increase (heavy line) and decrease (fine
line) in the burst start threshold while holding the burst end
threshold constant. We used the experiment performed in low burst
probability (3.3 mM [K+]o
data) for our control. Figure 6A, 2 and
3, shows changes in the interburst interval and burst
duration. Figure 6B depicts a 20% change in the burst end
threshold while holding the burst start threshold constant. Figure
6C illustrates the additive effect of changes in both
thresholds. The consequences of altering either or both thresholds and
the subsequent effects on interburst interval and burst duration (Figs.
2-4) are not easily ascertained a priori.

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Fig. 6.
Bursting thresholds effects on the interburst interval and burst
duration. Changes in the CA3 bursting cycle are dependent on
transformations in burst start and burst end thresholds as well as the
initial level of burst probability. Control values are experimentally
obtained by measuring the mean interburst interval and mean burst
duration in the spontaneously bursting CA3 in 3.3 mM
[K+]o, i.e., low burst probability (Table 1,
last 3 columns). A1: increasing the burst start
threshold by 20% (control: dotted line; increase 20%: thick
black line; decrease 20%: thin black line) increases both the
interburst interval and burst duration compared with control.
Alternatively, decreasing the burst start threshold by 20% decreases
both the interburst interval and burst duration compared with control
(A, 2 and 3). B1: changes
in the burst end threshold cause opposing effects on the
interburst interval and burst duration compared with changes in the
burst start threshold (B, 2 and 3). C:
increases in both burst start and end
thresholds cause the interburst interval to increase but the
burst duration to decrease. Decreases in both
bursting thresholds cause the interburst interval to decrease
while burst duration increases. The greatest effect on burst interval
occurs when the burst start threshold is increased (A2),
whereas the greatest effect on burst duration occurs when the burst end
threshold is decreased (B3).
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Fitting the experimental data: changes in bursting thresholds when
burst probability is high
CONVULSANT MANIPULATION (ELEVATION OF
[K+]O FROM 8.5 TO 10.0 MM IN THE PRESENT OF
PTX, 100 µM).
Changes in the bursting thresholds under conditions of high burst
probability are displayed in Table 2,
first three columns. When we applied a convulsant manipulation to CA3
by elevating the [K+]o
from 8.5 to 10.5 mM, the burst start threshold decreased by 16 ± 6% and the burst end threshold to decrease by 2 ± 7% (Fig. 7A1). In this experiment, the
bursting thresholds moved closer together. The difference between the
burst start and end thresholds decreased by 28 ± 8% (Table
3, 1st 3 columns).
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Table 2.
Changes in the burst start and burst end thresholds in response to
convulsant and anticonvulsant manipulations under high and low burst
probability
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Fig. 7.
The difference between bursting thresholds in response to convulsant
and anticonvulsant manipulations in high and low burst probability.
A1: elevating [K+]o from 8.5 to 10.5 mM, a convulsant manipulation, decreased both burst start and
burst end thresholds, with a greater decrease in the burst start
threshold (A1, Table 2, 1st 3 columns). The
difference between burst start threshold and burst end
threshold following the elevation of [K+]o
was significantly less, resulting in a shorter burst duration
(A2, Table 3, 1st 3 columns). B1: in 8.5 mM [K+]o (high burst probability), addition
of PB + ACTZ did not change the burst start threshold but raised the
burst end threshold (B1, Table 2, middle 3 columns).
However, as with the convulsant manipulation, the
difference between the burst start threshold and burst
end threshold is significantly smaller (B2, Table 3,
middle 3 columns). This resulted in both shorter burst duration and
interburst interval. C1: in low burst probability, PB + ACTZ increased both bursting thresholds with a greater change in the
burst end threshold (C1, Table 2, last 3 columns). The
difference in the thresholds diminishes
(C2, Table 3, last 3 columns). In all three cases,
(A2, B2, and C2) the difference between
the burst start and burst end thresholds diminishes, accounting for the
decreased burst duration in all 3 experiment.
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Table 3.
Changes in the difference between burst start and burst end thresholds
in response to convulsant and anticonvulsant manipulations under high
and low burst probability
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ANTICONVULSANT MANIPULATION (SPONTANEOUS BURSTING IN 8.5 MM
[K+]O, ADDITION OF PB + ACTZ, NO PTX).
Addition of PB + ACTZ to slices bursting under high burst probability
(8.5 mM [K+]o) did not
change the burst start threshold but increased the burst end threshold
by 8 ± 3% (Fig. 7B1, Table 2, middle 3 columns). In
this experiment, the bursting thresholds also moved closer together.
The difference between the burst start and end thresholds decreased
significantly by 14 ± 3% (Fig. 7B2, Table 3, middle 3 columns). Note that even though the change in interburst interval did
not reach significance under these conditions (Fig. 3B1,
Table 1, middle 3 columns), the thresholds, which are based on both the
burst interval and burst duration, can change significantly.
Thus when burst probability is high, both anticonvulsant and
convulsant manipulations diminish the difference between the start and
end thresholds. This results in an accompanying decrease of the
interburst interval and burst duration.
Fitting the experimental data: changes in bursting thresholds when
burst probability is low
Under conditions of low burst probability (spontaneous bursting
after tetanic stimulation of CA3, no PTX added), addition of PB + ACTZ
increased the start threshold by 17 ± 3% and increased the burst
end threshold by 66 ± 7% (Fig. 7C1, Table 2, last 3 columns). While the bursting thresholds both increased, the
difference between the burst start and burst end thresholds
decreased by 24 ± 4% compared with control (Fig. 7C2,
Table 3, last 3 columns). This decreased the burst duration, but unlike
the high burst probability experiments, the interburst interval
lengthened (Fig. 4) (Swartzwelder and Wilson 1987
). This
occurs because the threshold shift caused the synapses to oscillate in
a region of the synaptic recovery curve where the rate of recovery was
much slower, which increased the interburst interval. Figure
8 illustrates this effect.

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Fig. 8.
Effects of changing burst probability when the inter-threshold
difference is fixed. When burst probability is low (curves a and b),
synaptic recovery is nearly complete, and the rate of
synaptic recovery is slow. A small change in thresholds will cause a
marked lengthening of the interburst interval. When burst probability
is high (curve d), bursting can occur before recovery from synaptic
depression is complete and the rate of synaptic recovery is
relatively fast. A small change in the thresholds may not be
appreciable in terms of changes in the interburst interval. The burst
duration is not significantly affected in either high or low burst
probability because the time constant for depression
( depress) is much shorter than the time constant for
recovery ( recover). Thus the rate of depression is not
very different for these threshold values and consequently the burst
duration is also similar.
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DISCUSSION |
We have analyzed the effects of a convulsant and an anticonvulsant
manipulation on the bursting CA3 network by transforming the mean burst
duration and interburst interval data into thresholds for burst
initiation and termination. Three related observations are difficult to
decipher without this translation: the tendency of the burst interval
and burst duration to change in the same direction when burst
probability is high, the qualitatively similar effects of convulsants
and anticonvulsants on interburst interval and burst duration when
burst probability is high, and the pronounced impact of the baseline
burst probability on the effects of anticonvulsants.
Changes in the interburst interval and burst duration when burst
probability is high
Increasing [K+]o
from 8.5 to 10.0 mM, a convulsant manipulation, decreased the
interburst burst interval and the burst duration (Fig. 2). When we
transform these values into the burst start and end thresholds, the
reason for the shortened burst duration becomes clear. Convulsants
increase the burst probability by lowering the burst start threshold.
Bursting becomes possible before synaptic recovery is complete, so that
synapses are already relatively depressed at the beginning of the
burst. Under these conditions, synapses also reach the burst end
threshold more quickly, which decreases the burst duration (Fig.
5B1, Table 2, 1st 3 columns). Thus convulsants causes the
network to oscillate between two thresholds that are now closer
together due to a decrease in the burst start threshold that exceeded
the decrease in the burst end threshold.
Similar effects of a convulsant and an anticonvulsant when burst
probability is high
An anticonvulsant results in burst termination before synapses are
fully depressed by raising the burst end threshold. Because the burst
start and end thresholds are now closer together, the transitions
between thresholds occur more quickly (Fig. 5B2). This
produces an effect similar to a convulsant that predominately decreased
the burst start threshold as described in the preceding paragraph.
Convulsants and anticonvulsants have opposing actions on the bursting
thresholds. However, when burst probability is high, their net effect
on CA3 network activity is qualitatively similar: a decrease in both
the burst duration and the interburst interval (Fig. 7, A
and B; Table 1, 3rd and 6th columns). This occurs because
the bursting thresholds are now closer together.
Impact of burst probability
Using the synaptic depression model of CA3 bursting, we examined
the impact of initial burst probability on interburst interval and
burst duration. When burst probability is high (8.5 mM
[K+]o), bursting can occur before the
recovery from synaptic depression is complete, and the rate of synaptic
recovery is relatively fast. A small change in the thresholds may not
be appreciable in terms of changes in the interburst interval. However,
when the burst probability is low (3.3 mM
[K+]o), synaptic recovery is nearly complete
and the rate of synaptic recovery is slow. A small change in the
bursting thresholds will cause a marked lengthening of the interburst
interval (Fig. 8). In high burst probability, anticonvulsant effects
are dominated by decreased depression and shortened time to recovery.
In low burst probability, anticonvulsant effects are dominated by
additional time required for more complete recovery from depression.
Assumptions underlying this analysis
The transformation of the burst duration and interburst interval
into periods during which CA3 synapses depress to the burst end
threshold or recover to the burst start threshold is based on three
assumptions. First, we have assumed that depression and recovery are
mono-exponential processes. Although this is a reasonable assumption
(Dobrunz 1997; Liu and Tsien
1995
; Staley et al. 1998
, 2001
; Tsodyks
and Markram 1997
) (APPENDIX), it is not proven. For instance, the rate of depression during a spontaneous burst has not
been measured experimentally, although it has been quantified during
high-frequency stimulation (Selig et al. 1999
). Second, we have assumed that inter-synapse variation in rates of depression and
recovery (Stevens and Wesseling 1998
) can be neglected,
at least to a first approximation. Third, we have assumed that a shorter burst produces less synaptic depression; this is true for
evoked release (Debanne et al. 1996
) but is not proven
for spontaneous bursts. Pacemaker currents and de-inactivation of a
voltage-dependent depolarizing membrane conductance are alternative timing mechanisms for CA3 bursts (discussed in Staley et al.
2001
). We favor the synaptic recovery model described in this
paper because measured rates of depression and recovery are consistent
with the burst durations and interburst intervals, whereas conductances with the appropriate activation/inactivation/de-inactivation kinetics have not been described in this preparation.
Clinical implications
PERIODIC LATERALIZED EPILEPTIFORM DISCHARGES.
This work provides some insight into the limited utility of
anticonvulsants in the treatment of periodic lateralized epileptiform discharges (PLEDs), a condition associated with acute forebrain lesions
due to a variety of catastrophic conditions such as stroke, tumor, or
infection (Chartrian 1964
; Pohlmann-Eden et al.
1996
). The frequency and duration of discharges found in PLEDs
are similar to those seen the CA3 in vitro preparation when bursting is
induced by elevated 8.5 mM
[K+]o. Despite treatment
of patients with PLEDs with anticonvulsants, there may be little
alteration in the pattern of PLEDs (Lawn et al. 2000
),
mimicking the diminished efficacy of anticonvulsants in 8.5 mM
[K+]o (Fig. 2)
(Korn et al. 1987
; Swartzwelder et al.
1986
). We propose that this
high-[K+]o model of
synchronous epileptiform activity may be an appropriate in vitro model
in which to study anticonvulsant therapy for PLEDs.
ANTICONVULSANT EFFECTS ON INTERICTAL SPIKE FREQUENCY.
Interictal spikes on human electroencephalograms are observed in the
setting of an increased probability for spontaneous seizures in
temporal lobe epilepsy (Gloor 1991
; Sundaram et
al. 1999
). Interictal spikes have a long interburst interval
compared with the bursts seen in PLEDs. Figure 8 predicts that
barbiturates will produce a more significant effect on the interburst
interval when the burst probability is low. This is corroborated
clinically in patients with generalized seizures (Buchthal et
al. 1968
) and suggested in those with partial onset seizures
(Kellaway et al. 1978
). However, the depression of the
level of consciousness by barbiturates may also increase the frequency
of interictal spikes (Hellier and Dudek 1999
). Our model
might allow us to directly measure the effects of anticonvulsants on
epileptic networks independently of the effects on loss of consciousness.
Future directions
There are multiple cellular sites for targeting new anticonvulsant
compounds (Dichter 1997
). When we interpret
anticonvulsant actions in the context of burst start and end
thresholds, the CA3 in vitro preparation becomes very useful for
evaluating anticonvulsant mechanisms. Because an anticonvulsant can
raise either the burst start and/or burst end threshold, combination of
anticonvulsants that act differently may prove to be more effective
than choosing anticonvulsants that alter the same threshold. For
instance, an anticonvulsant that enhanced the initial
afterhyperpolarization should raise the burst end threshold. In
contrast, an anticonvulsant that depolarized interneurons and increased
spontaneous GABA release might only change the burst start threshold.
Isolating the locus of action of an anticonvulsant in this system may
focus subsequent research on the cellular basis of the anticonvulsant mechanism.
In contrast to more detailed modeling of CA3 network behavior
(Traub and Miles 1991
), we have developed a simple
quantitative description of synaptic depression and recovery in CA3 to
assess convulsant and anticonvulsant effects on two parameters: the
mean burst duration and the mean interburst interval. We analyzed the mean versus variance of the interburst interval in a separate paper
(Staley et al. 2001
). Due to extensive excitatory
collateral connections, CA3 exists in two stable states, full
synchronous activation (burst) or minimal activity (interburst
quiescence). The degree of synaptic depression at recurrent excitatory
synapses connecting CA3 neurons (Staley et al. 1998
)
determines the transitions between these states. (Alternatively, the
degree of recovery from inactivation of a voltage-dependent conductance
could also determine this transition, although we could find no
conductances with the appropriate time courses of inactivation and
recovery.) As shown in Fig. A1, the
synaptic strength of CA3 can vary between a theoretical maximum (1) and
a theoretical minimum (0). The maximum synaptic strength
corresponds to the level at which all recurrent excitatory synapses in
CA3 are completely recovered from depression, while the
minimum synaptic strength corresponds to the level of
absolute activity-induced depression.
If CA3 network synaptic strength declines continuously from the
theoretical maximum beginning at t = 0 (Fig. A1, dotted
line), then the burst start threshold (S) may be
expressed as a point along this mono-exponential decay curve by