1Department of Neurobiology, University of California at Los Angeles, Los Angeles, California 90095; 2Laboratory of Neuropsychology, National Institute of Mental Health, National Institutes of Health; and 3Laboratory of Developmental Neurobiology, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892
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ABSTRACT |
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Latham, P. E., B. J. Richmond, S. Nirenberg, and P. G. Nelson. Intrinsic Dynamics in Neuronal Networks. II. Experiment. J. Neurophysiol. 83: 828-835, 2000. Neurons in many regions of the mammalian CNS remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at low rates and rhythmic bursting. How these firing patterns are maintained in the presence of powerful recurrent excitation, and how networks switch between them, is not well understood. In the previous paper, we addressed these issues theoretically; in this paper we address them experimentally. We found in both studies that a key parameter in controlling firing patterns is the fraction of endogenously active cells. The theoretical analysis indicated that steady firing rates are possible only when the fraction of endogenously active cells is above some threshold, that there is a transition to bursting when it falls below that threshold, and that networks becomes silent when the fraction drops to zero. Experimentally, we found that all steadily firing cultures contain endogenously active cells, and that reducing the fraction of such cells in steadily firing cultures causes a transition to bursting. The latter finding implies indirectly that the elimination of endogenously active cells would cause a permanent drop to zero firing rate. The experiments described here thus corroborate the theoretical analysis.
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INTRODUCTION |
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Many areas of the mammalian CNS exhibit neuronal
activity in the absence of stimuli. Two patterns of activity that are
commonly observed are steady firing at low rates and rhythmic bursting. How do dynamic interactions between excitatory and inhibitory neurons
produce these firing patterns? Specifically, how do networks remain
stable in the face of powerful recurrent excitation, and how do they
switch between steady firing and bursting? In the previous paper
(Latham et al. 2000) we investigated these questions theoretically. We found that firing patterns are controlled largely by
one parameter, the fraction of endogenously active cells; i.e., the
fraction of cells that fire without input. When no endogenously active
cells are present, networks are either silent or fire at a high rate;
as the number of endogenously active cells increases, there is a
transition to bursting; and with a further increase, there is a second
transition to steady firing at a low rate. The main assumptions in our
theoretical analysis were conventional: excitatory input to a neuron
increases its firing rate, inhibitory input decreases it, and neurons
exhibit spike-frequency adaptation.
In this paper we explore experimentally the link between endogenous
activity and intrinsic firing patterns. To achieve the control
necessary to effectively test the theoretical predictions, we used
cultured mouse spinal cord neurons. Such networks are easily
accessible, are amenable to pharmacological intervention, and are
consistent with critical model assumptions, including the existence of
spike-frequency adaptation (Kernell 1965,
1972
; Tseng and Prince
1993
) and the expression of both excitatory and inhibitory
neurons (Nelson et al. 1981
). In addition, cultured networks retain many of the properties of networks in vivo, such as
rich connectivity and complex patterns of spontaneous activity (Basarsky et al. 1994
; Gross et al. 1993
;
Kamioka et al. 1996
).
We performed two sets of experiments. In the first, we investigated the relationship between low firing rates and the existence of endogenously active cells. As predicted, we found that every culture that fired at low rates contained endogenously active cells. Moreover, the mean fraction was relatively high, ~30% on average. In the second, we investigated the relationship between firing patterns and the fraction of endogenously active cells. Again as predicted, we found that a reduction in the fraction of endogenously active cells led to bursting.
These experimental findings are in agreement with the theoretical results presented in the previous paper. This agreement suggests that we have developed a realistic model for the intrinsic dynamics of large neuronal networks, and supports the idea that the fraction of endogenously active cells plays a key role in shaping firing patterns.
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METHODS |
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Cell culture
Neurons from the ventral horn of the spinal cord were
dissociated from 13.5-day-old fetal mice, and cortical glial
and support cells were dissociated from the cortex of newborn mice
(Nelson et al. 1989, 1990
). The ventral horn neurons were plated on a confluent
layer of nonneuronal cortical cells plated 1 wk previously. The growth
media was Eagle's minimum essential media (MEM, formula no. 82-0234DJ
with Earle's salts, 3.7 g/l of sodium bicarbonate, 6.0 g/l of
D-glucose, and without L-glutamine; pH
7.3-7.5; 320-330 mOsmol; GIBCO Laboratories, Grand Island, NY),
supplemented with 5% horse serum (Summit Biotechnology, Fort Collins,
CO), L-glutamine (2 mM) and the following additional
factors: 200 µg/ml transferrin, 200 nM putrescine, 60 nM sodium
selenite, 20 ng/ml triiodothyronin, 10 µg/ml insulin, 40 nM
progesterone, and 40 ng/ml corticosterone (Fitzgerald
1989
; Romijn et al. 1982
; Sheng et al.
1993
). Cultures were grown at 35°C in a humidified 10%
CO2 atmosphere. Mitosis of nonneuronal cells was inhibited
after 2 days by the addition of 13 µg/ml 5-fluoro-2'-deoxyuridine.
Cultures were maintained with half-media changes.
Patch recording
Recordings were made in three different media as follows.
1) Growth media, as describe above. 2)
NaPO4 buffered media (MEM, catalog no. 11430 with Earle's
salts and without L-glutamine, pH 7.3-7.5, 320-330
mOsmol, GIBCO) supplemented with L-glutamine (2 mM) and the
same additional factors used in the growth media (Fitzgerald
1989; Romijn et al. 1982
; Sheng et al.
1993
). The NaPO4-buffered media differed from the
growth media primarily by the replacement of sodium bicarbonate by
NaPO4 and the elimination of horse serum. 3)
Reduced media, which consisted of (in mM) 145 NaCl, 4.5 KCl, 10 HEPES,
10 glucose, 0.8 MgCl2, and 1.8 CaCl2, along
with 2% BSA (20 g/l); pH 7.3; 325 mOsmol adjusted with sucrose (~5
g/l).
The first two media are referred to as "fortified" media to distinguish them from the third, reduced media, which contains only essential salts and no other factors. This distinction is made because the neurons behaved differently in the third media than they did in the first two, and we exploited this difference to test one of the theoretical predictions made in the previous paper.
Whole cell recordings were made using patch electrodes (2-10 M)
filled with a solution containing (in mM) 145 KAc, 5 NaCl, 2 MgCl2, 5 HEPES, 1 EGTA, and 0.1 CaCl2. Membrane
potential was measured under current-clamp mode. Extracellular patch
recordings (Hamill et al. 1981
) were also made using
patch electrodes (2-10 M
) filled with a solution containing (in mM)
145 NaCl, 4.5 Kcl, 1.8 CaCl2, 0.8 MgCl2, 1.0 HEPES, and 10 glucose. Action potentials were recorded in voltage-clamp
mode. All recordings were at room temperature (21-23°C).
Recordings were made with an Axopatch-1B amplifier (Axon Instruments). Signals were filtered at 500 Hz, digitized at 20 kHz, and stored on a Power Macintosh 7600/132 using a 16-bit analog-to-digital converter (ITC-16; Instruteck, Elmont, NY) under control of the program Synapse (Synergy Research, Silver Spring, MD). Spike extraction was done off-line by thresholding the voltage. Because there was variation in the spike amplitude relative to the noise, the threshold was set individually for each cell.
Measuring the mean firing rate of cultured networks
For each culture, the activity of five or more neurons was monitored using extracellular patch recordings. The mean firing rate was then computed. If two or more of the examined neurons were silent, the culture was discarded.
Treatment with blockers
NEUROTRANSMITTER RECEPTOR ANTAGONISTS. Ten percent of the media from a culture was removed and combined with antagonists. The media was then returned to the culture, bringing the antagonist concentrations to the values shown in Table 1.
TETANUS TOXIN.
Cultures were first washed with NaPO4 buffered media to
remove the horse serum. This is necessary because horse serum contains antibodies to tetanus toxin. The toxin was then applied to the cultures
in NaPO4-buffered media at a concentration of 1 µg/ml. Because tetanus toxin acts slowly, the application was done >6 h
before physiological analysis of the cultures to ensure a complete block of transmitter release (Bergey et al. 1987). The
tetanus toxin (2 × 107 mouse lethal doses per mg
protein) was generously provided by Dr. William Habig, CBER, FDA,
Bethesda, MD.
Burst detection and measurement
Following Dekhuijzen and Bagust (1996) we used
the difference between successive interspike intervals as our assay for
bursting. That difference, denoted
tn
(tn+1
tn)
(tn
tn
1) where
tn is the time of the nth spike, has
a unimodal distribution in nonbursting cultures and a trimodal distribution in bursting ones (Dekhuijzen and Bagust
1996
). The two side peaks in the trimodal distribution
correspond to transitions between long interspike intervals (the time
between bursts) and short interspike intervals (the intervals within a
burst). To establish the existence of side peaks, we computed the
kurtosis, denoted K
, of the distribution of
the
tn: K
(
t
µ)4
/
4,
where angle brackets denote an average over the
tn, µ
t
is the
mean of
t, and
2
(
t
µ)2
is its variance.
Trimodal distributions have large kurtosis compared with those with a
single peak, so, on average, bursting cultures have larger kurtosis
than nonbursting ones. Differences in kurtosis between bursting and
nonbursting cultures were evaluated using the Student's
t-test.
To determine the burst period, we convolved the spike trains with a Gaussian of width 0.5 s and computed the mean time between the peaks of the convolved waveform. Empirically, we found that this method worked well for cells in reduced media when the kurtosis was >6.5. When the kurtosis was below that value, which typically happened when the bursts were irregular or the number of spikes per burst was small, spurious peaks were introduced that gave inaccurate estimates of the true interburst interval. Of the 27 cells in reduced media, 18 had kurtosis greater than 6.5.
To determine the mean firing rate during bursts, we convolved the spike trains with a Gaussian of width 0.5 s, thresholded the resulting waveform at one-fifth of its peak, and averaged the portion of the waveform that was above the threshold. This method was relatively insensitive to our choice of thresholds: cutting the threshold in half produced, on average, a 15% drop in firing rate; doubling it produced, on average, a 30% increase in firing rate. The mean rate during a burst is far less sensitive to irregular bursting and spurious peaks than the interburst interval, so all cells were included when calculating the mean rate.
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RESULTS |
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Cultures that fire steadily at low rates contain endogenously active cells
Cultured networks that fire steadily at low rates were examined for endogenously active cells by blocking synaptic transmission in the network and recording neuronal activity. If cells show activity when all synaptic transmission is blocked, they are considered endogenously active. Transmission was blocked two ways: 1) by binding neurotransmitter receptors with antagonists and 2) by preventing neurotransmitter release using tetanus toxin.
CULTURES WERE ACTIVE IN THE PRESENCE OF NEUROTRANS-MITTER RECEPTOR BLOCKERS. Nineteen cultures were examined to assess mean firing rates as described in METHODS. Ten showed steady firing at low rates, with rates ranging from 0.72 ± 0.18 Hz (mean ± SE, n = 5 cells) to 4.10 ± 1.34 Hz (n = 6 cells); the remaining cultures were silent and not used. Representative examples of the firing patterns of neurons in culture are shown in Fig. 1.
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CULTURES WERE ACTIVE IN THE PRESENCE OF TETANUS TOXIN.
While the absence of fast PSPs and the high degree of regularity in the
firing provide strong indication that the neurotransmitter receptor
antagonists block synaptic transmission, we cannot rule out the
possibility that some transmission remains. In particular, it is
possible that there were slow PSPs that we did not detect, such as
those produced by metabotropic glutamate receptors or neuromodulators.
For this reason, an alternative and independent method was used to
block synaptic transmission, tetanus toxin, which blocks
neurotransmitter release (Bergey et al. 1983). Tetanus toxin also circumvents the potential problem that some receptor antagonists have been reported to act as weak agonists for excitatory amino acid and neuromodulator receptors (Collingridge and Lester 1989
; Colquhoun and Patrick 1997
).
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Reducing the fraction of endogenously active cells leads to bursting
Although low firing rates require endogenously active cells, such
cells do not guarantee steady firing. As shown in the companion paper
(Latham et al. 2000), the fraction of endogenously
active cells must be above some threshold to ensure steady firing;
below that threshold, networks bursts.
In the previous section, we showed that networks exhibiting steady, low firing rates contain, on average, 32% endogenously active cells. In this section, we examine the prediction that reducing the fraction of endogenously active cells produces bursting. To test this prediction, it was necessary to have a method for reducing the fraction of endogenously active cells. We found, serendipitously, that culture media with only essential salts and no growth factors served this purpose. We refer to this as "reduced" media, and refer to the media used in the experiments described above as "fortified" media. When cultures were placed in reduced media, the mean fraction of endogenously active cells, averaged over cultures, was 1.1 ± 1.1% (n = 3 experiments; 0/15, 0/27, and 1/30 active cells). The one active cell fired steadily; i.e., it was not an endogenous burster. The fraction of endogenously active cells in reduced media was significantly lower than the 32 ± 4% seen in fortified media (P < 0.01; Student's t-test). The effect of the reduced media was reversible: when cultures were switched from reduced media back to fortified media, the fraction of endogenously active cells increased to its characteristic level of ~30%.
We compared the firing patterns of cultures in reduced media,
which contained few endogenously active cells, with the firing patterns
of cultures in fortified media, which contained many endogenously
active cells. These experiments were done in the absence of blockers.
In cultures with few endogenously active cells, nearly all neurons
(24/27) displayed bursting patterns (periods of activity regularly
interspersed with periods of silence; see Fig.
7A). The three that were not
obviously bursting were firing at too low a rate to make an accurate
categorization. In contrast, in cultures with many endogenously active
cells, no neurons (0/56) exhibited bursting. To quantify the difference between bursting and steadily firing cells, we computed the kurtosis of
the distribution of the difference between successive interspike intervals. This quantity is sensitive to transitions between long and
short interspike intervals (see METHODS). The kurtosis,
denoted K, is 6 for Poisson spike trains and
generally larger than 6 for bursting spike trains. In cultures with few
endogenously active cells, K
= 16.3 ± 3.0 (n = 27 cells). In cultures with many
endogenously active cells, K
= 5.5 ± 0.3 (n = 56 cells). The difference was significant
at P < 10
4 (Student's
t-test); see also Fig. 7B. The transition to
bursting as the endogenously active cells decreased is consistent with our theoretical predictions.
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Was the bursting in reduced media due to network activity (i.e., did the cells burst coordinately), or was each neuron bursting independently of all the others (i.e., were the neurons endogenous bursters)? Two lines of evidence indicate that the bursting was a network phenomenon. First, of the 72 neurons examined in recording media with antagonists present, none exhibited bursting, and therefore none were endogenous bursters. Second, within a given culture, all cells examined showed similar burst periods. Variation in the burst period, as measured by the standard deviation of the burst period divided by the mean, ranged from 2 to 20%. [For the 3 cultures examined, the burst periods were 8.3 ± 0.2 s, n = 4; 2.7 ± 0.3 s, n = 7; and 14.7 ± 3.1 s, n = 7 (mean ± SD). Only cells with kurtosis greater than 6.5, for which we were able to accurately measure the interburst interval (see METHODS), were included.] This variation among neurons within a culture was comparable to the variation observed over time for individual cells: the mean magnitude of the difference between the first and last 150 s of the 300-s recordings, averaged over the neurons in each culture, ranged from 4 to 18%.
Finally, we can estimate the fraction of endogenously active cells at which the transition to bursting occurs. The lowest observed fraction in fortified media was 5% (Fig. 4, Experiment A), whereas the largest observed fraction in reduced media was 3.3% (1/30, see above). This indicates that, at least under the conditions used here, the transition to bursting is likely to occur in the range ~3.3-5%.
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DISCUSSION |
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Both the previous theoretical study (Latham et al.
2000) and this experimental one were aimed at elucidating the
link between the fraction of endogenously active cells and network
firing patterns. To this end, two sets of experiments were performed.
In the first, we tested whether cultured neuronal networks firing at
low rates contained endogenously active cells. Cells were identified as endogenously active if they fired when synaptic transmission was blocked by neurotransmitter receptor antagonists, tetanus toxin, or
both. We found that every culture that fired at low rates
contained endogenously active cells, and that the mean fraction was
relatively high, ~30% on average. We then tested whether a reduction
in the fraction of endogenously active cells would lead to bursting. We
were able to reduce the fraction of endogenously active cells by
changing from a fortified media to a reduced one, the latter containing
only the essential salts and no other factors. We found that cultures
in reduced media, which contained few endogenously active cells, showed
striking bursting behavior. Bursting was never observed in cultures in
fortified media. These results, and the theoretical analysis presented
in the previous paper, show that there is a transition first from
steady firing to bursting and then from bursting to silence as the
fraction of endogenously active cells decreases.
Are the cells really endogenously active?
It is critical to the interpretation of our experiments that activity in the presence of the neurotransmitter blockers we used implies endogenous activity. There are, however, at least three other possible explanations for the observed activity: 1) the act of patching a cell may have caused it to fire, 2) the neurons may have degraded during the course of the experiments, and 3) the block may have been incomplete.
To guard against the first possibility, we minimized perturbation to the cells by using extracellular patch recordings. These recordings leave the cell membrane intact and thus do not modify the intracellular media. Although there is still the possibility of damage to the cell that could cause a leakage current and thus lead to activity, the length and stability of our recordings make this unlikely: all extracellular patch recordings were at least 5 min, and in a few cases we extended the recordings to ~30 min without observing any drift in firing rate.
To verify that the neurons remained healthy throughout the course of the experiments, in several cases we returned antagonist-treated cells to control media and reexamined their firing patterns. In all cases the neurons reverted to the steady firing patterns exhibited before the cultures were placed in antagonists, and they showed the same range of mean firing rates.
Finally, we took two steps to ensure that transmission was completely blocked. First, we performed whole cell recordings to test for fast postsynaptic potentials, and found none. Second, we blocked transmission both postsynaptically, with neurotransmitter receptor antagonists, and presynaptically, with tetanus toxin, and found virtually identical results.
Thus we conclude that cells that were active in the presence of the blockers we used were endogenously active.
Relationship between media and firing patterns
The experiments using fortified and reduced media gave us a tight estimate of the fraction of endogenously active cells required to maintain steady firing. Although the fraction of endogenously active cells in fortified media was 30% on average, fractions as low as 5% were seen. This was close to the largest fraction in reduced media, which was 3.3%. If the only effect of the reduced media was to decrease the fraction of endogenously active cells, then the transition to bursting occurred at a fraction between ~3.3 and ~5%. However, other confounding factors are possible. The reduced media could have effects on network and single cell properties besides altering the fraction of endogenously active cells. The degree of spike-frequency adaptation and the overall network firing rate, for example, could also affect whether or not a network bursts. Thus, although our experiments show a strong correlation between the fraction of endogenously active cells and bursting, other effects of the media could play a role. Consequently, the actual transition could have occurred outside the range ~3.3-5%. Nonetheless, these results form a solid first estimate of the critical transition range.
Although changing from fortified to reduced media was extremely effective in reducing the fraction of endogenously active cells, we were unable to establish the reason for its effectiveness. We did, however, rule out several possibilities. First, the effect was not due to differences in the concentration of the divalent cations Ca2+ and Mg2+, because the concentrations were the same in both media (1.8 and 0.8 mM, respectively). Reduced media did have a slightly lower concentration of K+ than fortified media, 4.5 versus 5.6 mM. This may have lowered the neurons' resting membrane potential in reduced media, which could, in principle, reduce the fraction of endogenously active cells. However, increasing the K+ concentration to 5.6 mM in reduced media had no effect on bursting. Finally, the results were not due to differences in horse serum or conditioning (co-culturing for extended periods with glial cells): cells examined in growth media, which contained horse serum and were conditioned, and cells examined in NaPO4 buffered media, which did not contain horse serum and were not conditioned, produced essentially identical firing patterns and levels of endogenous activity.
An alternative method for reducing the fraction of endogenously active
cells would have been to alter the K+ concentration, which
plays the dominant role in determining a cell's resting membrane
potential. However, this may have unwanted side effects:
spike-frequency adaptation, which is essential for bursting
(Latham et al. 2000), often relies on a
Ca2+-activated K+ current, so modifying the
concentration of the latter could affect the degree of spike-frequency
adaptation and thus whether or not a network bursts. For this reason,
and because we found that a media change could reduce the fraction of
endogenously active cells without modifying the K+
concentration, we did not explore this possibility.
Finally, to eliminate the possibility that the reduced media was in some way damaging the cells, cultures were cycled from fortified to reduced to fortified media. After the second switch from reduced to fortified media, cells returned to their characteristic irregular firing patterns and low rates. In addition, when antagonists were added after the second switch, the fraction of endogenously active cells returned to their characteristic levels of ~30%.
Was the bursting a network phenomenon?
It is possible that the bursting observed in the reduced media was not a network phenomenon. This might occur if the reduced media changed all cells into endogenous bursters whose firing patterns were independent of, or only weakly dependent on, other cells in the network. Two lines of evidence argue against this. First, in reduced media the cells were not endogenous bursters: in the presence of antagonists they were either silent or firing steadily. Second, within each of the cultures containing reduced media, the variation in the period was relatively small, ranging from 2 to 20%. This was comparable to the drift in burst period seen for individual cells, which ranged from 4 to 18% as determined by comparing the first half of the recording to the last half. Taken together, these two lines of evidence provide strong indication that the observed bursting in recording media is a network phenomenon.
Role of endogenously active cells in shaping network firing patterns
In the previous paper, we developed a theoretical model that described the intrinsic dynamics in large networks of excitatory and inhibitory neurons. This model indicated that a key parameter in controlling firing patterns was the fraction of endogenously active cells: when the fraction is above some threshold, steady firing at low rates is possible; when the fraction falls below that threshold, there is a transition to bursting; and when there are no endogenously active cells in a network, the network either falls silent or fires at high rate.
A somewhat surprising outcome of our model is the existence of a transition to bursting as the fraction of endogenously active cells decreases. The origin of this transition, however, can be explained simply: network bursting is caused by periodic crashes to zero firing rate followed by recovery. In our model, the crash to zero is induced by spike-frequency adaptation: repetitive firing introduces a hyperpolarizing current sufficient to temporarily eliminate endogenously active cells; without those cells, the low firing rate equilibrium vanishes and the network becomes silent. When there are fewer endogenously active cells in the network to begin with, it is easier to eliminate them. It is this last observation that explains the transition to bursting as the fraction of endogenously active cell decreases.
Previous experimental studies have examined the transition to bursting
using pharmacological agents that, presumably, did not change the
fraction of endogenously active cells. Bursting in these experiments
was typically induced in one of two ways: 1) with
neurotransmitter antagonists that block inhibition (Gross 1994; Gross et al. 1995
; MacDonald and
Barker 1981
; Streit 1993
) and 2) with
neuromodulators that enhance the level of spike-frequency adaptation
(Berkinblit et al. 1978
; Kudo and Yamada
1987
; Zoungrana et al. 1997
). Although these two
experimental approaches appear unrelated, our theory provides a link
between them: in both, bursting is produced by the elimination of
endogenously active cells. In the first case, disinhibition causes
firing rates to go up, which enhances the hyperpolarizing current
associated with spike-frequency adaptation. This temporarily eliminates
endogenously active cells and produces the requisite crash to zero
firing rate that leads to bursting. In the second case, neuromodulators
that increase the level of spike-frequency adaptation cause more
endogenously active cells to be eliminated during repetitive firing,
again facilitating bursting.
In the experiments reported here, we directly, rather than indirectly, explored the effect of endogenously active cells on firing patterns. We showed, first, that all cultures examined that fired at low rates contained endogenously active cells. Although this does not prove that endogenously active cells are necessary for low firing, it is a critical test of our theory. We then showed that a reduction in the fraction resulted in bursting. This result is not only consistent with theory, it also lends support to the notion that endogenously active cells are necessary for low firing rates, because it implies that a further reduction to zero endogenously active cells would result in a silent network: once a network crashes to zero firing rate, without endogenously active cells it has no way to recover and resume firing.
These experiments emphasize the critical role of endogenously active cells in shaping network behavior. Moreover, the observed agreement between theory and experiment provides evidence that we have developed a realistic model for the intrinsic dynamics of large neuronal networks. This model provides a framework for understanding the dynamic interactions that lead to stable firing patterns (steady firing at low rates and rhythmic bursting) and for understanding the transitions between those firing patterns. It thus lays the groundwork for detailed models of network function that will ultimately be needed for understanding how networks compute.
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ACKNOWLEDGMENTS |
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We thank C. Del Negro and M. Wiener for insightful discussions and comments on this manuscript.
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FOOTNOTES |
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Address for reprint requests: P. E. Latham, Dept. of Neurobiology, UCLA, Box 95-1763, Los Angeles, CA 90095-1763.
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 5 March 1999; accepted in final form 30 September 1999.
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REFERENCES |
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