 |
 Previous Article | Next Article 
The Journal of Neuroscience, 2000, 20:RC50:1-5
RAPID COMMUNICATION
Synchrony Generation in Recurrent Networks with
Frequency-Dependent Synapses
Misha
Tsodyks,
Asher
Uziel, and
Henry
Markram
Department of Neurobiology, Weizmann Institute of Science, Rehovot
76100, Israel
 |
ABSTRACT |
Throughout the neocortex, groups of neurons have been found to fire
synchronously on the time scale of several milliseconds. This near
coincident firing of neurons could coordinate the multifaceted information of different features of a stimulus. The mechanisms of
generating such synchrony are not clear. We simulated the activity of a
population of excitatory and inhibitory neurons randomly interconnected
into a recurrent network via synapses that display temporal dynamics in
their transmission; surprisingly, we found a behavior of the network
where action potential activity spontaneously self-organized to produce
highly synchronous bursts involving virtually the entire network. These
population bursts were also triggered by stimuli to the network in an
all-or-none manner. We found that the particular intensities of the
external stimulus to specific neurons were crucial to evoke population
bursts. This topographic sensitivity therefore depends on the spectrum
of basal discharge rates across the population and not on the
anatomical individuality of the neurons, because this was random. These
results suggest that networks in which neurons are even randomly
interconnected via frequency-dependent synapses could exhibit a novel
form of reflex response that is sensitive to the nature of the stimulus as well as the background spontaneous activity.
Key words:
synaptic plasticity; action potential encoding; neural
network; modeling; cortical column; spike timing
| |
INTRODUCTION |
Although
increased firing rate of a single neuron is the clearest signature of
its participation in a particular processing, growing evidence
indicates that temporal coherence in the activity of groups of neurons
may be an important component of the neuronal code. Indeed, throughout
the neocortex, the spiking activity of groups of cells has been found
to exhibit various patterns of synchrony, during both spontaneous
activity and under sensory stimulation (Murphy et al., 1985 ; Gray et
al., 1989; Vaadia and Aersten 1992; Sillito et al., 1994; Riehle et
al., 1997; Steriade and Contreras, 1998). Synchrony could allow the
information about external stimuli to be coded in the temporal relation
between the spiking of different neurons (Abeles, 1991; Hopfield, 1995) or provide the basis for binding different features belonging to the
same object (Singer and Gray, 1995).
The mechanisms of inducing synchronous firing in groups of cells are
not yet directly accessible to experimental study. A pair of neurons
could either synchronize via direct synaptic connection between them or
as a result of a common input. Anatomical evidence indicates that most
of the synaptic contacts a cortical cell receives are in fact
originating from the cells that are located in the same cortical area
(Ahmed et al., 1994). It is therefore reasonable to assume that much of
the observed synchronization is generated locally as a consequence of
the population dynamics.
Synchrony generation by networks of interconnected neurons is a subject
of many theoretical and numerical studies. For example, it is easy to
construct a network in which firing of individual neurons is perfectly
locked to each other (Mirollo and Strogatz, 1990). On the other
extreme, the network could be in the regimen of asynchronous activity
with uncorrelated firing of individual neurons (Abbott and van
Vreeswijk, 1993). In this state, the precise timing of individual
spikes is not important, and the activity of the neuron can be
adequately described by its firing rate. An intermediate regimen of
synchronized chaotic activity was obtained in the network of Hansel and
Sompolinsky (1996), where only a fraction, albeit a large one, of
spikes in pairs of neurons was synchronized on the time scale of few milliseconds.
Sharp synchronization between the spiking activity of pairs of neurons
was also reported in several experimental studies (Murphy et al., 1985;
Vaadia and Aersten, 1992; Riehle et al., 1997). In these studies,
however, the spikes were tightly locked for short epochs lasting some
milliseconds, and the rest of the spikes were at most loosely
correlated. This suggests that cortical networks can operate in a
regimen in which asynchronous activity is intermittent with sharp
synchronization on the time scale of single spikes.
Previous modeling studies have not considered potential effects of
nonlinear (frequency-dependent) synapses on synchronization of neuronal
activity in recurrent networks. In the neocortex, diversity of
depressing and facilitating synapses has been reported (Thomson and
Deuchars, 1994; Markram et al., 1998). Nonlinear synaptic transmission
was implicated in shaping the signaling between neocortical neurons
(Grossberg, 1969; Thomson and Deuchars, 1994; Abbott et al., 1997;
Tsodyks and Markram, 1997; Markram et al., 1998). In particular,
synaptic depression, which is ubiquitous in connections between
pyramidal neurons, enables transmission of signals reflecting the
synchrony in presynaptic ensembles (Senn et al., 1998). In the current
study, we demonstrate that when nonlinear synaptic transmission is
incorporated into recurrent networks, intermittent activity with
short-time synchrony naturally emerges. This comes about as a result of
occasional upswings in the network population activity, during which
most of the neurons fire an action potential within a period of several
milliseconds. Moreover, during these periods, the neurons tend to fire
in a specific temporal order, which depends on the distribution of the
average firing rates of the neurons.
| |
MODEL |
We simulated a recurrent network of 400 excitatory and 100 inhibitory neurons. The neurons were connected at random with a probability of a contact between a pair of neurons taken to be 10% in
accordance with anatomical data (Abeles, 1991). Neurons were modeled as
leaky integrate-and-fire units widely used in these kinds of
simulations (Tuckwell, 1988). Each unit was described by its voltage
membrane potential, which evolved according to the circuit
equation:
|
(1)
|
where  denotes the membrane time constant of a neuron,
Isyn represents the synaptic current
mediated by internal connections, and
Ib stands for the nonspecific
background current provided by the distant brain areas. In the
following, we incorporated the input resistance of the neuron,
Rin, into the currents, which were
therefore measured in units of voltage (millivolts). The membrane
potential V was calculated relative to a resting level for a
given neuron. Each time the membrane potential of a neuron reached
threshold, a spike was emitted, and the voltage was put to a reset
value after an absolute refractory period. In our simulations = 30 msec, and the membrane threshold and reset values were 15 and 13.5 mV, respectively. Excitatory neurons had a refractory period of 3 msec,
and inhibitory neurons had a refractory period of 2 msec. The
background current, Ib, had a constant
value for each neuron, randomly distributed across the network. We
chose a uniform distribution centered at the threshold level with a range of 0.05 mV; this resulted in the basal firing rates of the excitatory neurons being between 1 and 20 Hz, with an average of 7 Hz.
The synaptic current, Isyn, was
modeled as a sum of postsynaptic currents (PSCs) from all of the other
neurons in the network which have connections targeting the given
neuron (i):
|
(2)
|
We used the phenomenological description of nonlinear synapses
developed by Markram et al. (1998) and Tsodyks et al. (1998), which was
shown to capture well the experimentally observed properties of
neocortical connections. In this model,
Aij is a parameter describing the
absolute strength of the synaptic connection between neurons j
(presynaptic neuron) and i (postsynaptic neuron). The effective
synaptic strength is determined by the factor
yij, which describes the contribution
to a synaptic current of neuron i because of PSCs from a neuron j. It
evolves according to the system of kinetic equations:
|
(3)
|
where x, y, and z are the
fractions of synaptic resources in the recovered, active, and inactive
states, respectively, tsp denotes the
timing of presynaptic spikes, I is the decay
constant of PSCs, and rec is the recovery time
from synaptic depression. These equations describe the use of synaptic
resources by each presynaptic spike (a fraction u of the
available resources x is used by each presynaptic spike). A
running variable, uij, describes the
effective use of the synaptic resources of the synapses, which is
analogous to the probability of release in the quantal model (Markram
et al., 1998). In facilitating synapses, it is increased with each
presynaptic spike and returns to the baseline value with a time
constant of facil:
|
(4)
|
where the parameter U determines the increase in the
value of u with each spike. If
facil  0, facilitation is not exhibited, and u is identical to U for each spike, as is the
case with depressing synapses between excitatory pyramidal neurons
(Tsodyks and Markram, 1997). The values of the synaptic parameters were
assigned as follows. First, average values were specified for the
parameters for each type of the connections; then for each connection
the actual value was chosen from a Gaussian distribution with a
corresponding mean and with a SD that equals half that mean. The
average values of the parameters used in the simulations were
A(ee) = 1.8 mV; A(ei) = 5.4 mV;
A(ie) = 7.2 mV; A(ii) = 7.2 mV;
U(ee) = U(ei) =0.5; U(ie) = U(ii) = 0.04; rec(ee) = rec(ei) = 800 msec;
rec(ie) = rec(ii) = 100 msec;
facil(ie) = facil(ii) = 1000 msec; and I = 3 msec. In control simulations we verified
that the qualitative behavior of the network is robust against
independently changing the average values by 50%.
| |
RESULTS |
Network dynamics
An epoch of network simulations is illustrated in Figure
1. The raster plot of neuronal activity
(Fig. 1A) and the average network activity (Fig.
1B) indicate that the network dynamics exhibit short
intervals of highly synchronous activity in which large groups of
neurons fire successively population bursts (PB). With the choice of
the parameters values given in Model, the duration of the PB was <15
msec. On average, in each burst 95% excitatory and 98% inhibitory
neurons participated, and the spikes were distributed such that 63% of
them were emitted within 5 msec around the peak of the burst, and 15%
were emitted within 1 msec (Fig. 1B). During the PBs,
95% of the neurons fired once, and the rest of the neurons emitted one
or two additional spikes at the end of the burst. The rate of the
bursts was 0.97 ± 0.4 Hz.
View larger version (46K):
[in this window]
[in a new window]
|
Figure 1.
Network dynamics. A, Spike trains
of every fifth neuron in a time window of 4.3 sec. For each neuron, a
dot is put at each time the neuron emitted an action
potential. B, Network activity, computed as the relative
number of neurons that fire an action potential during consecutive bins
of 1 msec. Inset, Network activity during the time
window of 40 msec around the population burst. C,
Fraction of synaptic resources in the recovered state, describing the
effective strength of depressing synapses (see Model), averaged over
all connections between excitatory neurons.
|
|
Mechanisms of population burst
Once a population burst occurs, it is easy to understand why it
terminates. Because the synapses between excitatory neurons are
depressing, the average effective strength of these connections quickly
declines during the PB (Fig. 1C), and the neuron discharge times become independent of each other. After the burst the strength of
the connections slowly recovers, because the subsequent asynchronous activity is characterized by low firing rates. This recovery of strength augments the probability that the firing of an excitatory cell
will drive other cells to fire, and eventually, after the network has
reached a certain threshold state, an excitatory cell can recruit other
cells to generate a fast-developing synchronous activity.
To confirm the crucial role of synaptic depression between excitatory
neurons in governing the population bursts, we eliminated nonlinearity
from all other connections. Indeed, we observed the same qualitative
behavior of the network activity (data not shown). In fact, PBs could
even be observed in a network without inhibitory interneurons, provided
the strength of recurrent excitation is adjusted appropriately (data
not shown). We found, however, that inhibition allowed the PBs to occur
for a wider range of parameters. Because synaptic depression is
responsible for PBs, it is reasonable to assume that the neurons with
the lower firing rates are important in their generation. This is
because the effective strength of a depressing synapse is decreasing
with the firing rate of the presynaptic neuron. To clarify this issue,
we ordered the excitatory neurons according to their average basal
firing rates (Fig. 2A) over the interval of 20 sec. We then selectively eliminated groups of
30 excitatory neurons, ranked according to their firing rates, and
counted the number of remaining bursts in an interval of 20 sec after
the start of the simulations. As shown in Figure 2B, the bursts disappear completely if the group of neurons with the firing
rates from 1.3 to 2.5 Hz is eliminated. We explain this result by the
fact that these neurons not only have low firing rates, and therefore
effectively strong excitatory synapses, but also are close enough to
threshold to trigger the avalanche of the firing activity leading to
the crescendo PB.
View larger version (17K):
[in this window]
[in a new window]
|
Figure 2.
Mechanism of population bursts. A,
Average firing rates of the excitatory neurons in the network, in an
ascending order, computed over the interval of 20 sec.
B, Number of population bursts over the same interval,
which are observed in simulations in which a group of 30 neurons is
taken out of the network, starting from the neuron indicated on the
horizontal axis. C, Network with the
absolute strength (A) of all connections reduced
by one-third of their original values, resulting in the disappearance
of spontaneous population bursts. For each group of neurons, an input
pulse lasting 5 msec is applied with a frequency of 1 Hz. The minimal
amplitude of the input (in millivolts) that is required to reliably
evoke a population burst is plotted for each group of 30 targeted
neurons.
|
|
Population response to external stimulation
Spontaneous PBs resulted only when the connections between
excitatory neurons were strong enough. External stimuli, however, could
evoke population bursts even when connections were weak. To demonstrate
this possibility, we uniformly reduced the absolute strength of all the
synapses in the network until the PBs disappeared. We then studied the
response of the network to sharp (5 msec) input pulses of
various amplitudes with a frequency of 1 Hz, targeting groups of 30 neurons. In Figure 2C the minimal amplitude of the pulse
needed to evoke a PB in the network is plotted against different choices of the targeted neurons. As the firing rate of targeted neurons
increased, the intensity of the pulse required for PB decreased
gradually, reaching the minimum for about the same group of neurons,
which are mostly responsible for spontaneous burst generation (Fig. 2,
compare B, C). For groups of targeted neurons with higher firing rates, the input intensity required to generate the
bursts increased sharply. Eventually, no bursts could be evoked at any
input intensity when the targeted neurons had rates of >5 Hz. The
network is therefore sensitive to the precise topography of the input
stimulus; i.e., the ability of inputs with the identical amplitude to
evoke a network response depends on the basal firing rates of the
targeted neurons. To illustrate this sensitivity, we show the response
of the network to inputs with the amplitude of 0.5 mV. When applied to
a group of neurons with low basal rates, the input evoked a
full-fledged PB, whereas only minor response was observed when neurons
with higher basal rates were targeted (Fig.
3A,B).
View larger version (24K):
[in this window]
[in a new window]
|
Figure 3.
Sensitivity of the network to the precise
topography of the stimulus. Network activity in response to input
pulses of an amplitude of 0.5 mV and a duration of 5 msec is shown,
targeting 30 neurons with rates of 3.5-5.9 Hz
(A) and 1.1-2.9 Hz
(B).
|
|
Temporal relationship between neuronal firing
The simulation results indicate that the network exhibits
qualitatively different activity patterns during and between the PBs.
To illustrate this difference, we computed the cross-correlation function (CCF) between the firing of different pairs of neurons, over
the period of 1000 sec. In Figure
4A we show an example
of CCF for two neurons having the firing rates close to 10 Hz. A sharp
peak at zero time difference for the CCF is a direct result of the PBs
during which both of the neurons fire within a short time interval. If
one excludes the spikes emitted during the PBs, the resulting CCF does
not exhibit any substantial peaks, indicating that between the bursts
the firing of neurons remains essentially asynchronous. The area under
the central peak in the CCF equals 10% of the overall number of spikes
emitted by each of the neurons, which corresponds to the relative
number of spikes emitted during the PBs. In Figure
4B, we show another pair, this time with one of the
neurons having a low firing rate of ~2 Hz. A small negative bias of 4 msec in the CCF can be detected, indicating that the neuron with the
lower firing rate systematically fired before the neuron with the
higher firing rate. This is consistent with the previous observation
that the neurons with low firing rates play a crucial role in
generating the PBs. Finally, Figure 4C illustrates a pair of
neurons with low rates, which exhibit a CCF with two sharp peaks at
both positive and negative time difference. The shape of CCFs indicates
that there exists a statistically reproducible timing relation between
the firing of different neurons during a PB. To illustrate this
relation, we computed, for each neuron in the network, the CCF between
the spike train of the neuron and the peaks of the population bursts
and marked the time at which CCF was at its maximum (Fig.
4D). As seen by comparison between Figures 2B and 4D,
the neurons that are responsible for PB generation systematically fire
in the advanced phase of the PB.
View larger version (23K):
[in this window]
[in a new window]
|
Figure 4.
Temporal relationship between neuronal firing.
A, Cross-correlation function between the activities of
two neurons with similar rates in the middle of the rate distribution
(10 and 12 Hz). Solid line, Cross-correlation function
computed over the period of 1000 sec of activity; dashed
line cross-correlation function computed over the same period
but subtracting the spikes emitted during the population bursts of the
network. B, Same for a pair of neurons with rates of 1.7 and 12 Hz. C, Pair of neurons with low rates of 2.6 and
1 Hz. D, For each neuron in the network, the
cross-correlation function between its spike train and the times of the
maximums of population bursts was computed, and the time difference at
which the cross-correlation function is at its maximum is
plotted.
|
|
Conditions for the occurrence of population bursts
In the current study, we concentrated on the novel form of network
activity, characterized by (spontaneous or evoked) sharp population
bursts. As follows from the analysis, the necessary condition for this
regimen is a broad distribution of the neuronal basal firing rates,
which must include a substantial fraction of low-rate neurons. Indeed,
if the rate distribution is shifted toward higher rates, e.g., because
of increased tonic input, the bursts eventually disappear. Another
condition concerns the strength of recurrent excitatory connections. We
found that increasing the strength of the connections beyond a certain
range [A(ee) > 2.45 mV for our network] led to broadening of
the bursts such that single neurons were firing multiple spikes within
each PB. We believe that this happens because several spikes are now
needed before synaptic depression weakens the recurrent excitation
sufficiently. In this regimen, bursts are also more regularly spaced in
time, which might therefore correspond to slow cortical oscillations observed during natural sleep in cats and humans (Steriade, 1997). We
emphasize, however, that also in this regimen, the neurons that trigger
the PBs have very little activity between the bursts. Finally, because
of computational constraints, most of the simulations were
performed with small networks consisting of 500 neurons. We checked
that PBs also occurred in larger networks with the same pattern of
connectivity. The frequency and temporal regularity of PBs are complex
functions of the network size and synaptic parameters. In particular,
networks of increasing size with fixed synaptic strength tend to
exhibit more rhythmic activity.
| |
DISCUSSION |
The simulations presented here demonstrate that networks of
neurons interconnected with nonlinear synapses have a striking tendency
to generate a special regimen of activity with population bursts
intermittent with long periods of asynchronous activity. As a result of
the PBs, the neurons exhibit synchronous firing characterized by a
large fraction of neurons firing action potentials within a time window
of a few milliseconds. Within this short window, the neurons fire with
a particular temporal relationship, determined by their basal firing
rates during the preceding activity. The network can also produce a PB
in response to an external excitatory input. In this case, the strength
of excitation, required to evoke the response, strongly depends on the
basal firing rates of the targeted neurons. Thus, the network is
characterized by a high sensitivity to the topography of the input stimulus.
We emphasize that synaptic depression between excitatory neurons plays
a crucial role in generating this network behavior. We also emphasize
that synchronization between neurons on the time scale of few
milliseconds can be achieved in randomly connected networks, without
any specific structures such as synfire chains (Abeles, 1991). The
network simulated in this study has a random pattern of intrinsic
synaptic connections. For example, it could represent a cortical
minicolumn consisting of neurons with similar receptive field
properties. We expect that in larger networks, such as a cortical
hypercolumn, where connections between neurons reflect their receptive
field properties, other regimens of activity, with PBs propagating
between different minicolumns in a quasirandom manner, could exist.
These possibilities are subjects of a further study. The conclusion of
the analysis could be tested experimentally by recordings from multiple
neurons in the same cortical area. The results of the simulations
predict that groups of cells can generate tightly synchronous spikes on
the scale of few milliseconds, intermittent with the long periods with
no synchronization on this scale. This effect could be observed during
either spontaneous firing or during the response to sensory
stimulation. There should also exist a systematic temporal relation
between the timing of spikes in pairs of neurons in relation to their
average firing rate. In particular, the spikes of neurons with low
firing rates should precede the spikes of neurons with higher rates.
We would like to speculate that PBs that seem to be a natural tendency
in recurrent networks with nonlinear synapses could have a functional
significance for cortical networks. Because long-term regulation of
synaptic transmission was shown to be sensitive to relative timing of
spikes between presynaptic and postsynaptic neurons (Markram et al.,
1997), spontaneous PBs could influence the shaping of local functional
connectivity in the cortex. The PBs evoked by the external
input could provide the cortex with the ability for a fast and reliable
processing of the sensory stimuli, in accordance with recent
psychophysical and electrophysiological observations (Bair and Koch,
1996; Thorpe et al., 1996; Eggermont, 1999).
| |
FOOTNOTES |
Received July 8, 1999; revised Oct. 19, 1999; accepted Oct. 21, 1999.
The study was supported by grants from the Israeli Academy of Science,
the Office of Naval Research, Binational Science Foundations, and the
Human Frontier Science Program Organization.
Correspondence should be addressed to Misha Tsodyks at the above
address. E-mail: bnmisha{at}wicc.weizmann.ac.il.
This article is published in
The Journal of Neuroscience, Rapid Communications Section,
which publishes brief, peer-reviewed papers online, not in print. Rapid
Communications are posted online approximately one month earlier than
they would appear if printed. They are listed in the Table of Contents
of the next open issue of JNeurosci. Cite this article as:
JNeurosci, 2000, 20:RC50 (1-5). The
publication date is the date of posting online at
www.jneurosci.org.
| |
REFERENCES |
-
Abbott LF,
van Vreeswijk C
(1993)
Asynchronous states in networks of pulse-coupled oscillators.
Phys Rev E
48:1483-1490.
-
Abbott LF,
Varela JA,
Sen K,
Nelson SB
(1997)
Synaptic depression and cortical gain control.
Science
275:220-224.
-
Abeles M
(1991)
In: Corticonics. New York: Cambridge UP.
-
Ahmed B,
Anderson J,
Douglas R,
Martin K,
Nelson J
(1994)
Polyneural innervation of spiny stellate neurons in cat visual cortex.
J Comp Neurol
341:39-49.
-
Bair W,
Koch C
(1996)
Temporal precision of spike trains in extrastriate cortex of the behaving macaque monkey.
Neural Comput
8:1185-202.
-
Eggermont JJ
(1999)
The magnitude and phase of temporal modulation transfer functions in cat auditory cortex.
J Neurosci
19:2780-2788.
-
Gray CM,
Konig P,
Engel AK,
Singer W
(1989)
Oscillatory responses in visual cortex exhibit intercolumnar synchronization which reflects global stimulus properties.
Nature
338:334-337.
-
Grossberg S
(1969)
On the production and release of chemical transmitters and related topics in cellular control.
J Theor Biol
22:325-364.
-
Hansel D,
Sompolinsky H
(1996)
Chaos and synchrony in a model of a hypercolumn in visual cortex.
J Comp Neurosci
3:7-34.
-
Hopfield JJ
(1995)
Pattern recognition computation using action potential timing for stimulus representation.
Nature
376:33-36.
-
Markram H,
Lubke J,
Frotscher M,
Sakmann B
(1997)
Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs.
Science
275:213-215.
-
Markram H,
Wang Y,
Tsodyks M
(1998)
Differential signaling via the same axon from neocortical layer 5 pyramidal neurons.
Proc Natl Acad Sci USA
95:5323-5328.
-
Mirollo RE,
Strogatz SH
(1990)
Synchronization of pulse-coupled biological oscillators.
SIAM J Appl Math
6:1645-1657.
-
Murphy JT,
Kwan HC,
Wong YC
(1985)
Cross-correlation studies in primate motor cortex: synaptic interaction and shared input.
Can J Neurol Sci
12:11-23.
-
Riehle A,
Grun S,
Diesman M,
Aertsen A
(1997)
Spike synchronization and rate modulation differentially involved in motor cortical function.
Science
278:1950-1953.
-
Senn W,
Segev I,
Tsodyks M
(1998)
Reading neuronal synchrony with depressing synapses.
Neural Comput
10:815-819.
-
Sillito AM,
Jones HE,
Gerstein GL,
West DC
(1994)
Feature-linked synchronization of thalamic relay cell firing induced by feedback from the visual cortex.
Nature
369:479-482.
-
Singer W,
Gray CM
(1995)
Visual feature integration and the temporal correlation hypothesis.
Annu Rev Neurosci
18:555-586.
-
Steriade M
(1997)
Synchronized activities of coupled oscillators in the cerebral cortex and thalamus at different levels of vigilance.
Cereb Cortex
7:583-604.
-
Steriade M,
Contreras D
(1998)
Spike-wave complexes and fast components of cortically generated seizures. i. Role of neocortex and thalamus.
J Neurophysiol
80:1439-1455.
-
Thomson AM,
Deuchars J
(1994)
Temporal and spatial properties of local circuits in neocortex.
Trends Neurosci
17:119-126.
-
Thorpe S,
Fize D,
Marlot C
(1996)
Speed of processing in the human visual system.
Nature
381:520-522.
-
Tsodyks M,
Markram H
(1997)
The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability.
Proc Natl Acad Sci USA
94:719-723.
-
Tsodyks M,
Pawelzik K,
Markram H
(1998)
Neural networks with dynamic synapses.
Neural Comput
10:821-835.
-
Tuckwell HC
(1988)
In: Introduction to theoretical neurobiology. New York: Cambridge UP.
-
Vaadia E,
Aersten A
(1992)
Coding and computation in the cortex: single-neuron activity and cooperative phenomena.
In: Information processing in the cortex (Aertsen A,
Braitenberg V,
eds), pp 81-121. Berlin: Springer.
Copyright © 1999 Society for Neuroscience 0270-6474/99/$05.00/0
This article has been cited by other articles:
|
|
|
|
 
G. Mongillo, O. Barak, and M. Tsodyks
Synaptic Theory of Working Memory
Science,
March 14, 2008;
319(5869):
1543 - 1546.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
C. Wu, M. N. Asl, J. Gillis, F. K. Skinner, and L. Zhang
An In Vitro Model of Hippocampal Sharp Waves: Regional Initiation and Intracellular Correlates
J Neurophysiol,
July 1, 2005;
94(1):
741 - 753.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
L. A. Grande and W. J. Spain
Synaptic Depression as a Timing Device
Physiology,
June 1, 2005;
20(3):
201 - 210.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. R. Deweese and A. M. Zador
Shared and Private Variability in the Auditory Cortex
J Neurophysiol,
September 1, 2004;
92(3):
1840 - 1855.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
U. A. Wiedemann and A. Luthi
Timing of Network Synchronization By Refractory Mechanisms
J Neurophysiol,
December 1, 2003;
90(6):
3902 - 3911.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. Kirischuk, J. D Clements, and R. Grantyn
Presynaptic and postsynaptic mechanisms underlie paired pulse depression at single GABAergic boutons in rat collicular cultures
J. Physiol.,
August 15, 2002;
543(1):
99 - 116.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
TOP
ABSTRACT
INTRODUCTION
