A few strong connections: optimizing information retention in neuronal avalanches.
ABSTRACT How living neural networks retain information is still incompletely understood. Two prominent ideas on this topic have developed in parallel, but have remained somewhat unconnected. The first of these, the "synaptic hypothesis," holds that information can be retained in synaptic connection strengths, or weights, between neurons. Recent work inspired by statistical mechanics has suggested that networks will retain the most information when their weights are distributed in a skewed manner, with many weak weights and only a few strong ones. The second of these ideas is that information can be represented by stable activity patterns. Multineuron recordings have shown that sequences of neural activity distributed over many neurons are repeated above chance levels when animals perform well-learned tasks. Although these two ideas are compelling, no one to our knowledge has yet linked the predicted optimum distribution of weights to stable activity patterns actually observed in living neural networks.
Here, we explore this link by comparing stable activity patterns from cortical slice networks recorded with multielectrode arrays to stable patterns produced by a model with a tunable weight distribution. This model was previously shown to capture central features of the dynamics in these slice networks, including neuronal avalanche cascades. We find that when the model weight distribution is appropriately skewed, it correctly matches the distribution of repeating patterns observed in the data. In addition, this same distribution of weights maximizes the capacity of the network model to retain stable activity patterns. Thus, the distribution that best fits the data is also the distribution that maximizes the number of stable patterns.
We conclude that local cortical networks are very likely to use a highly skewed weight distribution to optimize information retention, as predicted by theory. Fixed distributions impose constraints on learning, however. The network must have mechanisms for preserving the overall weight distribution while allowing individual connection strengths to change with learning.
- SourceAvailable from: wustl.edu[show abstract] [hide abstract]
ABSTRACT: Long-term potentiation of synaptic transmission in the hippocampus is the primary experimental model for investigating the synaptic basis of learning and memory in vertebrates. The best understood form of long-term potentiation is induced by the activation of the N-methyl-D-aspartate receptor complex. This subtype of glutamate receptor endows long-term potentiation with Hebbian characteristics, and allows electrical events at the postsynaptic membrane to be transduced into chemical signals which, in turn, are thought to activate both pre- and postsynaptic mechanisms to generate a persistent increase in synaptic strength.Nature 02/1993; 361(6407):31-9. · 38.60 Impact Factor
- Neuron 03/1998; 20(3):445-68. · 15.77 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: The notion that changes in synaptic efficacy underlie learning and memory processes is now widely accepted, although definitive proof of the synaptic plasticity and memory hypothesis is still lacking. This article reviews recent evidence relevant to the hypothesis, with particular emphasis on studies of experience-dependent plasticity in the neocortex and hippocampus. In our view, there is now compelling evidence that changes in synaptic strength occur as a consequence of certain forms of learning. A major challenge will be to determine whether such changes constitute the memory trace itself or play a less specific supporting role in the information processing that accompanies memory formation. Hippocampus 2002;12:609–636. © 2002 Wiley-Liss, Inc.Hippocampus 12/2001; 12(5):609 - 636. · 5.49 Impact Factor
RESEARCH ARTICLE Open Access
A few strong connections: optimizing information
retention in neuronal avalanches
Wei Chen, Jon P Hobbs, Aonan Tang, John M Beggs*
Background: How living neural networks retain information is still incompletely understood. Two prominent ideas
on this topic have developed in parallel, but have remained somewhat unconnected. The first of these, the
“synaptic hypothesis,” holds that information can be retained in synaptic connection strengths, or weights,
between neurons. Recent work inspired by statistical mechanics has suggested that networks will retain the most
information when their weights are distributed in a skewed manner, with many weak weights and only a few
strong ones. The second of these ideas is that information can be represented by stable activity patterns.
Multineuron recordings have shown that sequences of neural activity distributed over many neurons are repeated
above chance levels when animals perform well-learned tasks. Although these two ideas are compelling, no one to
our knowledge has yet linked the predicted optimum distribution of weights to stable activity patterns actually
observed in living neural networks.
Results: Here, we explore this link by comparing stable activity patterns from cortical slice networks recorded with
multielectrode arrays to stable patterns produced by a model with a tunable weight distribution. This model was
previously shown to capture central features of the dynamics in these slice networks, including neuronal avalanche
cascades. We find that when the model weight distribution is appropriately skewed, it correctly matches the
distribution of repeating patterns observed in the data. In addition, this same distribution of weights maximizes the
capacity of the network model to retain stable activity patterns. Thus, the distribution that best fits the data is also
the distribution that maximizes the number of stable patterns.
Conclusions: We conclude that local cortical networks are very likely to use a highly skewed weight distribution to
optimize information retention, as predicted by theory. Fixed distributions impose constraints on learning, however.
The network must have mechanisms for preserving the overall weight distribution while allowing individual
connection strengths to change with learning.
The question of how the brain stores memories has
generated intense interest. It is widely thought that
information is retained in the strengths of synaptic con-
nections between neurons [1-3]. The “synaptic hypoth-
esis” is supported by numerous studies demonstrating
that synaptic strengths do in fact change after learning,
and that manipulations that block these changes also
interfere with learning . A host of models has
explored how such modifiable synapses, when embedded
in a network of neurons, could store information [5-8].
In these models, different items are represented by
distinct patterns of active neurons in the network.
Recent theoretical work has explored how the distribu-
tion of connection weights affects the capacity of a net-
work to store such patterns [9-13]. These studies have
consistently demonstrated that a skewed distribution,
where most weights are relatively weak and only a few
are strong, maximizes the number of patterns that can
be retained. Electrophysiological studies support this
view, and have shown that the distribution of synaptic
strengths onto neurons in many parts of the brain is
indeed skewed [9,14].
The network activity patterns predicted by the synap-
tic hypothesis have also found experimental support.
Several studies have shown that cortical slice networks,
as well as randomly connected networks of cortical
* Correspondence: firstname.lastname@example.org
Indiana University Department of Physics, 727 East 3rdStreet, Bloomington,
Chen et al. BMC Neuroscience 2010, 11:3
© 2010 Chen et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
neurons, can retain multiple, distinct activity patterns
that spontaneously re-occur more often than expected
by chance [15-19]. These significantly repeating activity
patterns are diverse, temporally precise, and stable for
several hours, suggesting that they may be used by the
brain to retain information [17,19]. Studies from intact
animals are consistent with this, and show that precisely
repeating sequences of neural activity occur when birds
sing a well-learned song [20-22], or when rats recapitu-
late a path taken through an often-traveled maze
To advance these two lines of work, a link must be
made between the distribution of connection strengths
and the patterns retained in living neural networks. In
our previous work, we reported that isolated cortical
networks produced an average of 30 ± 14 (mean ±
s.d.) distinct groups of significantly repeating patterns
. We later published a model that generated
repeating patterns that were remarkably similar to
those from experiments . In addition, this model
reproduced the size distribution of cascades, called
“neuronal avalanches” observed in these networks
[27,28]. By tuning the weight distribution in this model
and comparing its output to the data from cortical
slice networks, we sought to answer two questions:
What distribution of connection strengths will best fit
the statistics of the observed repeating patterns? What
distribution of connection strengths will maximize the
number of repeating activity patterns? Our hypothesis
was that a skewed distribution would both fit the data
and be optimal.
We report here that the distribution of connection
strengths that best fits the data is also the distribution
that maximizes the number of repeating patterns. This
distribution has many weak connections and only a few
strong ones. Portions of this work were previously pre-
sented as a talk  and in abstract form .
The results comprise four sections. First, we describe gen-
eral features of activity from the 60-channel multielec-
trode array recordings in acute cortical slices. Second, we
show that a computational model qualitatively reproduces
the avalanche size distribution and the significantly
repeating avalanches generated by these slice networks.
As very similar findings have been reported previously,
these results are presented only briefly for the sake of
clarity and completeness. Third, we show that the distri-
bution of connection weights in the model has a large
effect on the distribution of repeating activity patterns.
Fourth, we show how the distribution of connection
weights in the model also affects the overall number of
distinct repeating activity patterns.
Activity produced by acute cortical slices
We recorded spontaneous extracellular activity from
acute slices of rat somatosensory cortex (n = 7) with
60-channel multielectrode arrays for two hours per pre-
paration. Each slice network had 35 or more active elec-
trodes. Local field potential (LFP) activity from these
slices was similar to that reported previously for organo-
typic cultures [17,28,31] and consisted of quiescent peri-
ods punctuated by network bursts. Local field potentials
that crossed threshold appeared as negative voltage
peaks approximately 20 ms wide, indicative of a popula-
tion spike (figure 1). Such sharp negative LFPs are
thought to be produced by a group of neurons in the
vicinity of the electrode firing nearly synchronous action
potentials . Data were binned at 4 ms, as this was
the average time between successive activation of two
Figure 1 Electrode array and data representation. A, Photo of cortical tissue on the 60-channel microelectrode array. Electrodes appear as
small black circles at the ends of lines. Interelectrode distance is 200 μm and electrode diameter is 30 μm. B, Arrangement of local field
potential (LFP) signals on electrodes. Note that LFPs can vary in amplitude. C, Suprathreshold LFPs represented by small black squares. LFPs that
exceed three standard deviations of the mean are considered suprathreshold. All subthreshold LFPs are represented by borderless white squares.
Chen et al. BMC Neuroscience 2010, 11:3
Page 2 of 14
electrodes within a network burst when the interelec-
trode spacing was 200 μm, as reported previously .
When activity from all electrodes in an array was
plotted in raster form, we commonly observed multiple
LFPs in the same time bin. We also observed cascades
of consecutively active time bins (figure 2). After cas-
cades were recorded over several hours, it was possible
to plot their size distribution (figure 3), which could be
approximated by a power law. Because this distribution
was not expected by chance , but was similar to that
produced by computational models of sand pile ava-
lanches , we previously named these events “neuro-
nal avalanches” .
Another feature of neuronal avalanches reported earlier
is that many of them display spatio-temporal structure.
When all avalanches of a given length are compared,
many of them are more similar to each other than would
be expected by chance . We found that spontaneous
activity from acute cortical slices shared this property.
These repeating avalanches could be ordered into groups
(figure 4) that were stable over two hours. This long-term
stability, as well as the similarity that these avalanches
have to spatio-temporal sequences of activity found in
vivo, suggest that neuronal avalanches could be used to
retain information in cortical circuits.
Activity produced by the model
We used a simple model based on a branching process
[27,35] to capture the central features of the slice data
(see Methods). Briefly, each node in the network repre-
sented activity at one of the 60 electrodes. When a node
became active, it had some probability, p, of activating
another node in the next time step. In this model, each
node had 10 connections to other nodes, and the set of
p values coming from each node determined the weight
distribution. Figure 3 shows that the avalanche size dis-
tribution produced by the model is qualitatively similar
to that typically produced by an acute cortical slice
Figure 3 The avalanche size distribution produced by cortical
tissue and by the model. The probability of observing an
avalanche of size S is plotted against avalanche size. Distribution
from a cortical slice plotted in dark circles shows a linear portion
that can be approximated by a power law with slope -3/2, shown
as the dashed line. Data deviates from the power law near S = 35
because there are only 60 electrodes in the array and many sites
are refractory after large events. Distribution from model plotted in
open circles closely follows the data.
Figure 4 Sorting a similarity matrix. A, When N avalanches of a
given length are compared to each other, their similarity values can
be entered in an N × N matrix as shown here. Each row of the
matrix corresponds to one avalanche, and each column within that
row indicates how similar that avalanche is to another avalanche.
Shaded scale bar ranges from 0 to 1, with greatest similarity coded
black. In this figure diagonal elements which compare each
avalanche to itself produce perfect similarity. Gray and white pixels
appear in the off-diagonal regions, indicating intermediate to low
similarity. In this unsorted matrix, the order of avalanches along the
margins merely reflects their temporal order of appearance in the
recording, and no obvious grouping of dark pixels is found. B, Here
avalanches are sorted by an algorithm in order of descending
similarity. The highest mutual similarity values appear in the upper
left of the matrix, as shown by the darkened pixels. Squares may be
drawn to separate dark regions from lighter regions, so as to
produce groupings of avalanches.
Figure 2 Example of an avalanche. Seven frames are shown, where each frame represents activity on the electrode array during one 4 ms
time step. Suprathreshold activity at electrodes is shown by small black squares. An avalanche is a series of consecutively active frames that is
preceded by and terminated by blank frames. Avalanche length is given by the number of active frames, while avalanche size is given by the
total number of active electrodes. The avalanche shown here has a length of 5 and a size of 9.
Chen et al. BMC Neuroscience 2010, 11:3
Page 3 of 14
[27,28]. Figure 5 shows that the repeating avalanches
produced by the model are qualitatively similar to those
commonly found in the data [17,27]. These results
demonstrate that the model is a reasonable platform
from which to explore the effects of the weight distribu-
tion on significantly repeating avalanches.
Effect of the exponent B on the distribution of groups
Using this model, we next explored how the distribution
of connection weights affected the distribution of groups
of significantly repeating avalanches. Connection weights
in the model were given by a weighting function (see
Methods) shown in figure 6. Note that the steepness of
the curve was determined by the exponent B. We
sought to determine which value of B produced a distri-
bution of groups of repeating avalanches that best
matched the data. To do this, the model was run ten
times for each value of B, each time for a period that
simulated one hour of real time (900,000 bins of 4 ms
each), and all groups of statistically significant ava-
lanches were extracted. We examined only groups
Figure 5 Repeating avalanches and similarity matrices produced by cortical tissue and by the model. A, Ordered similarity matrix
showing groups of similar avalanches from acute slice data. Matrix of all avalanches of length 5 compared to each other for Boolean similarity.
Scale bar indicates similarity (ranging from 0 to 1), with highest similarity coded black. Arrows (1: 2: 3) point to example regions of the matrix
with groups of similar avalanches. Comparable similarity matrices are also found in data from cultures (see . B, Ordered similarity matrix
produced by the model appears like matrix from data, with similar sized groups along the diagonal. C, Groups of similar avalanches produced by
the model, matching the numbered regions (1, 2, 3) from the model’s similarity matrix. Note that avalanches within groups share general, not
exact, resemblance. D, Groups of similar avalanches produced by the data from regions (1, 2, 3) in the data similarity matrix.
Chen et al. BMC Neuroscience 2010, 11:3
Page 4 of 14
containing avalanches of length 2 through 9. Avalanches
of length 1 had no temporal extent, and were excluded
because their occurrences did not clearly depend on the
connection strengths between units. Statistically signifi-
cant groups with avalanches longer than 9 frames were
not observed in the data or in the simulations.
Figure 7A shows that the number of groups of statisti-
cally significant avalanches produced by acute cortical
slices (n = 7) and organotypic cortical cultures (n = 7;
data from ) declines with the length, L, of the ava-
lanches. The fact that both data sets show this general
trend suggests that similar mechanisms underlie these
avalanches in slices and cultures. The sum of squares
error between these two data sets was 0.016, and was
taken as an estimate of the general variability of the data.
The exponent of the weighting function had a pro-
found effect on the distribution of groups of significant
avalanches. Low values of B (e.g., 0.4) produced distribu-
tions of groups of avalanches that also declined with L
(figure 7B). High values of B (e.g., 3.6) produced distri-
butions with the opposite trend (figure 7C), contrary to
what was seen in the data. Figure 8 shows the distribu-
tions produced by all values of B.
The sum of squares error between the data and all
model distributions is plotted in figure 9A. Low values
of B (0.4 - 1.6) produced relatively good fits to the data
that had errors less than the intrinsic error of the data
itself. Values of B greater than 1.6 produced fits with
errors that exceeded 0.016, the variability of the data
itself. From this we conclude that only weighting func-
tions with B in the range of 0.4-1.6 could reasonably fit
Effect of the exponent B on the number of groups
We also counted the total number of groups of statisti-
cally significant avalanches produced by the model for
all values of B. Figure 9B shows the maximum number
of groups of significantly repeating avalanches varied
widely and peaked at B = 1.2 and B = 1.6. Figure 10
shows all the weighting functions that were considered
good fits for the data. Interestingly, two of these func-
tions were also found to produce the largest number of
groups of significantly repeating avalanches. Thus, two
of the weighting functions that were best-fitting were
Relation to other work
Our results are consistent with several experimental stu-
dies that have examined the distribution of connection
strengths in living neural networks. Song and colleagues
 used patch clamp recording in cortical slices to
measure the amplitudes of post synaptic currents pro-
duced in layer V pyramidal neurons by neighboring neu-
rons. They found that the distribution of amplitudes was
approximately lognormal, with only a few strong con-
nections. Brunel and colleagues, working in the cerebel-
lum, reported similar findings . They found that the
distribution of synaptic strengths from granule cells
Figure 6 The weighting function. A, Equation used to generate weights in model. Here, “weight” refers to the probability that unit i, when
active, will transmit to unit j in the next time step. B, Example of weighting function produced when B = 0.4. C, Example of weighting function
produced when B = 1.6.
Chen et al. BMC Neuroscience 2010, 11:3
Page 5 of 14
onto Purkinje neurons also had very few strong
synapses. Although these two studies examined synaptic
connection strengths, their results are similar to those
of Pajevic and Plenz , who reconstructed activity
flow in cortical slice networks from field potential data.
Pajevic and Plenz  found that connection strengths
from a single electrode were distributed approximately
exponentially, again with only a few strong connections.
Our results are also in agreement with modeling stu-
dies. Gardner  analytically derived the distribution of
connection strengths that would maximize storage capa-
city in the perceptron, a type of feed-forward neural net-
work model that can be used for pattern classification
[37,38]. This distribution again had very few strong con-
nections. Brunel and colleagues noted the correspon-
dence between the optimal weight distribution for the
perceptron and their findings in the cerebellum . In
the recurrent Hopfield neural network model , storage
capacity is actually reduced if each unit has too many
strong connections. This is because an excess of strong
connections produces false associations between patterns
that are actually distinct. When such an over connected
network is annealed from a given starting configuration,
it will often converge to a spurious hybrid state that is a
mixture of two or more previously learned states. This
problem of saturation in neural network models has been
noted by several groups [39,40], whose results suggest
that optimal storage is best achieved when strong con-
nections are sparsely distributed. All of these findings are
consistent with the results of the present study.
None of these previous reports, however, examined
how the distribution of weights was related to spatio-
temporal activity patterns. This is an important topic for
exploration because in vivo studies have increasingly
suggested that memories in behaving animals are linked
to spatio-temporal activity patterns, and not to static
configurations of active neurons [21,24-26]. Our work
builds on previous studies by explicitly linking the capa-
city of a network model to store such spatio-temporal
patterns to the weight distribution between units in the
network. We also go beyond previous work by exploring
how connection weights affect the distribution of groups
of significantly repeating spatio-temporal patterns. We
accomplish this by recording significantly repeating spa-
tio-temporal activity patterns of all lengths over several
hours, something that is presently difficult to do in vivo
and has not yet been reported. In this respect, an in
vitro network preparation is useful as it provides a stable
platform from which to examine all patterns of activity
produced by a network over a long time without inter-
ruption from outside perturbations.
Validity and limitations
This work does have several limitations, though. First,
the spatio-temporal activity patterns reported here were
Figure 7 Changes in the exponent B can drastically affect the
distribution of significant avalanches. A, Probability of observing
a group of statistically significant avalanches of length L, plotted
against L. Plot shows data produced by acute slices (n = 7) and
organotypic cultures (n = 7; data reproduced from figure 10 of ).
Note decline in probability of observing a group of significant
avalanches with increasing L. Sum of squares difference between
these two data distributions was 0.016, and is taken as an estimate
of the intrinsic error of the data itself. B, Distribution of groups of
significant avalanches produced by model with weighting function
having exponent B = 0.4, plotted on top of average distribution
from slice and culture data. Sum of squares error between data and
model was 0.005. C, Same as in B, but here model weighting
function had an exponent of B = 3.6. Sum of squares error was
0.075. Note that changes in the exponent B can produce large
changes in the distribution of groups of significant avalanches.
Chen et al. BMC Neuroscience 2010, 11:3
Page 6 of 14
Figure 9 The exponent B affects the fit between the model and the data, and the number of groups of significant avalanches
produced by the model. A, Left column shows weighting functions produced by different values of B. Right histogram shows sum of squares
error between model and data distributions of groups of significant avalanches. Dashed line at 0.016 is the error between the data produced by
acute cortical slices and the data produced by organotypic cultures. This value is taken as an estimate of the intrinsic error of the data itself.
Weighting functions that cause the model to produce distributions of groups of significant avalanches with error less than this intrinsic error are
considered to have a good fit (B ≤ 1.6). B, Again, left column shows weighting functions produced by different values of B. Right histogram
shows total number of groups of significant avalanches produced by models with different values of B.
Figure 8 Number of groups of avalanches. Number of groups of significant avalanches for all values of the exponent B. Note wide variation
in total number of groups and in shapes of curves.
Chen et al. BMC Neuroscience 2010, 11:3
Page 7 of 14
all recorded from isolated cortical networks. The activity
in these networks was therefore not produced by sen-
sory stimulation, and modulatory systems that are nor-
mally present in vivo were absent. In addition, the
pattern of synaptic connections present in vivo is not
necessarily reproduced in vitro. For neuronal cultures,
connections are not formed in response to sensory
experience. For acute slices, some axons and dendrites
are likely to be cut. Second, the signals analyzed here
were all LFPs, which are difficult to attribute to indivi-
dual neurons or synapses. Caution should therefore be
exercised when using the results of the present study to
predict phenomena in vivo.
Despite these limitations, in vitro preparations are still
widely used as models of local cortical networks because
many of the features characteristic of neocortex are pre-
served: neuronal morphology , cytoarchitecture
[42,43], gross intracortical connectivity , and intrin-
sic electrophysiological properties [45-47]. In addition,
the reproducible activity patterns seen in cultures and in
slices are similar to each other [15,17,48], and are
remarkably similar to activity patterns seen in vivo
With regard to LFPs, several recent reports indicate
that bursts of action potentials, like the kind that could
produce LFPs, as well as LFPs themselves, often contain
more information about the state of a network than do
single action potentials [52-55]. An analysis of LFPs in
cortical slices and cultures is therefore expected to pro-
vide insights into information retention at the local net-
work level. It is also interesting to note that the LFP
bursts that we call neuronal avalanches can be induced in
acute slices by the application of NMDA and dopamine
agonists [28,56]. These agents also have been found to
induce UP states in vivo , suggesting that avalanches
may be related to UP states. Although this link was not
explored in this paper, this potential connection further
motivates the investigation of these LFP bursts.
One might also ask why we did not attempt to recon-
struct weight distributions from the data. Although such
a reconstruction is possible and recently has been done
for cortical slice networks , it is important to note
that reconstruction alone would not have allowed us to
ask how changes in the weight distribution affect the
storage capacity of the network. For our purposes, it
was important to have a tunable network model where
Figure 10 Some weighting functions fit the data and maximize the number of repeating activity patterns. A, B: Weighting functions
with exponents B = 0.4 and B = 0.8 both produce error values lower than the error between slice and culture data, but do not produce the
most groups of significant avalanches. C, D: Weighting functions with exponents B = 1.2 and B = 1.6 (outlined by box) have error values lower
than the error between slice and culture data and produce the most groups of significant avalanches.
Chen et al. BMC Neuroscience 2010, 11:3
Page 8 of 14
we could explore storage capacity as a function of a sin-
gle variable. We adopted this approach because it is pre-
sently unfeasible to experimentally tune the weight
distribution on all nodes in living neural networks. As it
turns out, the number of connections we use in our
model, as well as the shape of the weight distribution,
are consistent with the results of reconstruction .
We also did not attempt to explicitly model the small-
world degree distribution found by Pajevic and Plenz
. This would have involved introducing heterogene-
ity into our model, and would have complicated the
interpretation of our results. Instead, we chose to treat
all nodes as equivalent and gave them random connec-
tivity. The degree distribution of a random network
with a mean degree of 10 would be similar in shape to
that found by reconstruction , suggesting that our
results are unlikely to be affected much by this differ-
ence. Nevertheless, this is an interesting topic that could
be explored more fully in future studies.
The model that we propose here is phenomenological
and is not yet clearly linked to biophysical mechanisms.
Some of our previous modeling work [58-60] has sug-
gested ways in which biophysical mechanisms like firing
rate homeostasis and conservation of synaptic strengths
might play a role in tuning the network to the point
where it would produce avalanches. These predictions
are testable, indicating that the model eventually may be
linked to mechanisms at scales smaller than the network.
Multielectrode recordings from behaving animals indi-
cate that reproducible spatio-temporal patterns of neural
activity are used to represent specific items in memory
[21,24-26]. These findings suggest that the significantly
repeating avalanche patterns that we find in both our in
vitro data and in our models may be used as a platform
from which to explore information retention in local cor-
tical networks. If neuronal avalanches can be used for
this purpose, then our findings may place constraints on
how learning could occur in local cortical networks. It is
presently unclear how a network could maintain an opti-
mal distribution of weights in the face of learning, if
learning involves strengthening or weakening of existing
connections. Learning could disrupt optimal distribu-
tions, pushing the network away from the point of maxi-
mum storage capacity. It is possible that a rescaling
process could allow individual connections to change
strength while approximately preserving the overall dis-
tribution near an optimal point. There is some support
for rescaling of synaptic strengths in response to changes
in overall activity levels , as well as support for con-
servation of synaptic strengths in the face of plasticity
. Modeling studies would be needed to determine
whether such mechanisms could preserve an optimal dis-
tribution in the presence of synaptic plasticity .
It is also interesting to note that network studies in
other areas of biology have found weight distributions
that have relatively few strong connections [63,64], hint-
ing that this distribution is perhaps of more general sig-
nificance. Kauffman and colleagues have shown that two
connections per node in random Boolean networks
leads to systems that are poised at the edge of chaos,
where adaptability is maximized without introducing
instability . This intriguing conjecture has yet to be
explored in neural networks.
Finally, we would like to note that Hebb’s theories on
memory did not just emphasize a particular synaptic
learning rule, but a process whereby groups of cells, or
“assemblies” could activate each other in sequences .
The order in which these assemblies are activated is
expected to have important consequences for memory.
Both theoretical  and experimental [67,68] work has
begun to probe this idea (see also ). Because model-
ing studies suggest that the distribution of connection
strengths influences the dynamics of activation , it is
likely that the distribution of strengths will also place
constraints on the order in which assemblies can be
The main finding of this study is that the set of connec-
tion strengths that best fits the distribution of groups of
significant avalanches also produces the largest number
of groups of significant avalanches. This suggests that
the set of connection strengths actually used in cortical
slice networks is the one that maximizes information
storage capacity. This set of connection strengths is
skewed, with only a few strong connections and many
weak ones. Fixed distributions impose constraints on
learning, however. We conclude that the network must
have mechanisms for preserving the overall weight dis-
tribution while allowing individual connection strengths
to change with learning.
Data used in this study
The output of the model was compared to two data sets,
one recorded from acute slices as a part of this study
and one recorded from organotypic cultures as part of a
previously published study . We compared output
from the model to data from two different preparations
(acute slices and organotypic cultures) to test its gener-
ality. Note that we did not re-analyze the older data set,
but merely compared the output from the model to pre-
viously published graphs.
Tissue preparation and recording
All neural tissue was prepared according to guidelines
from the National Institutes of Health and all animal
procedures were approved by the Indiana University
Chen et al. BMC Neuroscience 2010, 11:3
Page 9 of 14
Animal Care and Use Committee. Acute slices were pre-
pared as previously reported . Sprague-Dawley rats
14-35 days old (Harlan) were deeply anesthetized with
Halothane and then decapitated. Brains were removed
and immediately placed for 3 mins in ice-cold artificial
cerebrospinal fluid (ACSF) containing in mM: Sucrose
125, KCl 3, NaH2PO4*H2O 1.25, NaHCO326, MgSO4
*7H2O 2, CaCl2*2H2O 2, D-glucose 10, saturated with
95% O2/5%CO2. After cooling, brains were blocked into
~5 mm3sections containing somatosensory cortex, stria-
tum and thalamus. Blocks were then sliced into coronal
sections with a thickness of 250 μm using a tissue slicer
(Vibratome). After cutting, slices incubated for ~1 hr at
room temperature in ACSF with the same ingredients as
listed above, but with 125 mM NaCl substituted for
125 mM sucrose to restore Na+and allow cells to fire
action potentials again. After incubation, slices were
adhered to microelectrode arrays with a solution of 0.1%
polyethelinamine that had been previously applied and
let to dry for 2 hrs . We attempted to place the tis-
sue so that neocortical layers I-V covered the array.
Slices were maintained thermostatically at 37°C and were
perfused at 1.0 ml/min with excitable ACSF solution con-
taining 5 mM KCl and 0 mM Mg+2during recording,
which typically lasted 5 hrs. These external ionic concen-
trations are known to produce robust local field potential
(LFP) activity in cortical brain slices [72,73].
Recordings were performed on microelectrode arrays
purchased from Multichannel Systems (Reutlingen, Ger-
many). Each array had 60 electrodes, and each electrode
was 30 μm in diameter. For acute slice recordings, we
used electrodes that came to a point 30 μm high, but in
the previous organotypic culture recordings we used
electrodes that were flat . Electrodes were arranged
in a square grid with 200 μm spacing between electro-
des (figure 1A).
Local field potential (LFP) detection
Extracellular activity from acute slices was recorded in
the same manner as the previous organotypic culture
recordings [17,28,31]. Activity was sampled from all 60
electrodes at 1 kHz and amplified before being stored to
disk for offline analysis. Local field potentials (LFPs)
that showed sharp negative peaks (figure 1B) below a
threshold set at 3 standard deviations of the signal were
marked, and the time of the maximum excursion was
recorded as the time of that LFP (figure. 1C). Time
points were binned at 4 ms resolution, as this was pre-
viously shown to match the average time between suc-
cessive LFP events across electrodes .
Characterizing multielectrode activity
In characterizing network activity, we closely followed
the methods first described in [17,28]. The configuration
of active electrodes during one time step is called a
frame. An avalanche is a sequence of consecutively
active frames that is preceded by a blank frame and ter-
minated by a blank frame. The length of an avalanche is
given by the total number of active frames and the size
of an avalanche is given by the total number of electro-
des activated during the avalanche. For example, the
sequence of frames shown in figure 2 is an avalanche of
length 5 and size 9. These definitions allowed us to
compare the distribution of avalanche sizes generated by
the model with those from the data. In particular, we
wanted to be sure that the number of electrodes acti-
vated in the simulated avalanches was distributed
according to a power law, as was seen in the data
Detecting groups of avalanches
We were also interested in whether the model could
reproduce the significantly repeating avalanches that
were generated by cortical tissue. We here describe our
methods for identifying these significant avalanches.
During spontaneous activity, avalanches of many differ-
ent lengths were produced. We compared only ava-
lanches of the same length, measuring their similarity
with each other. To measure similarity, each 8 × 8
frame was “unfolded” into a 1 × 64 vector (the four cor-
ner electrodes were absent from the array, leaving the
possibility of only 60 active electrodes). An avalanche of
length l frames was then formed by concatenating l lin-
ear vectors of 1 × 64 into a single vector of 1 × 64 l.
These vectors were then compared to each other for
similarity using a Boolean measure, first used in this
context by Jimbo and colleagues . Boolean similarity
S between two vectors X = (x1, x2, x3, ... xn) and Y = (y1,
y2, y3, ... yn) ranged from 0 (least similar) to 1 (perfectly
similar) and was given by their intersection divided by
S X Y
( , )
where 〈·,·〉 indicates a dot product. Note that this
number is sometimes called the Jacquard coefficient in
other literature . Once all avalanches of the same
length were compared for similarity, they were
assembled into a matrix (figure 4A). Ordering this
matrix was accomplished by a greedy algorithm (the
“dendrogram” function in Matlab) that placed ava-
lanches with high similarity scores next to each other
along the margins of the matrix. Other methods like
simulated annealing took longer but produced only
slightly better results . Figure 4B shows an example
of a matrix ordered with the dendrogram algorithm.
Note the dark squares of various sizes along the diago-
nal of the matrix, indicating avalanches sharing high
mutual similarity. Boxes could be drawn around these
Chen et al. BMC Neuroscience 2010, 11:3
Page 10 of 14
squares to separate them from the surrounding lighter
areas of the matrix. In this way groups of mutually simi-
lar avalanches could be extracted. A contrast function
found the grouping that maximized differences in total
similarity between regions within boxes and regions out-
side of boxes. The contrast for a particular set of boxes
was given by:
where Din= (the sum of similarity values inside all
boxes)/(the number of similarity values inside all boxes)
and Dout= (the sum of similarity values outside all
boxes)/(the number of similarity values outside all
boxes). Maximum contrast was obtained when there
was a preponderance of dark pixels within the boxes
and lighter pixels outside the boxes. The arrangement of
boxes that maximized the contrast function was chosen
as the best possible grouping. These groups of ava-
lanches were next compared to groups produced by
chance to assess statistical significance.
Determining statistical significance
To identify groups of avalanches that were statistically
significant, we compared the similarity values from
groups of avalanches from actual data to similarity
values from groups of avalanches produced by random
data sets. Because we desired to compare the output of
the model to previously published data , we followed
the most stringent method of shuffling adopted in our
previous work (figure 11). In that scheme, activity on a
given electrode could only be shuffled to another time
bin on the same electrode, thus preserving the firing
rate on each electrode. The time bins into which activity
was shuffled were restricted to those bins that already
had some activity on at least one other electrode, thus
approximately preserving the overall temporal profile of
network activity. When compared to frame shuffling,
electrode shuffling or jittering, this method was found
to be the least likely to produce false positives .
Once shuffled according to this method, 20 sets of ran-
domized data were compared to the actual data. Groups
of avalanches in the actual data that had a higher aver-
age similarity than all groups of avalanches of the same
length found in the shuffled data were considered signif-
icant at the p < 0.05 level. Shuffled data sets served as
controls to ensure that the effects we observed could
not have been attributed to chance.
Model of slice network activity
The previously published model  qualitatively cap-
tured both the power law distribution of avalanche sizes
 and the groups of significantly repeating avalanches
 seen experimentally. This model is formally equiva-
lent to a critical branching process , which has
found application in diverse areas of physics. Here we
describe the model and our modifications to investigate
the effects of the weight distribution. The model repre-
sented each of the 60 recording electrodes by a binary
processing unit that could be either on (1) or off (0),
since an electrode could receive either suprathreshold or
subthreshold input. We approximated the electrode
array with an 8 × 8 sheet of processing units where
each unit was randomly connected to 10 other units,
which gave the network a recurrent, rather than a feed-
forward, architecture. Each connection from unit i to
unit j had a probability pijof transmitting that was ran-
domly chosen from a weighting function (described
below) and then fixed. The sum of probabilities emanat-
ing from a unit i determined the branching parameter
of that unit:
where 0 ≤ pij≤ 1 and 0 ≤ si≤ 10. Pajevic and Plenz
 reconstructed activity flow in cortical slice networks
recorded with 60 electrode arrays. In their work, it was
found that the distribution of connections per electrode
peaked near a mean value of 10. Although we did not
here attempt to reproduce the distribution of connec-
tions that they found, the number of connections per
node in our model was set at 10, in approximate agree-
ment with their findings. Note that siwas equivalent to
the expected number of descendants an active unit i
produced. When s <1, the network was subcritical and
Figure 11 Shuffling scheme. A, Representation of unshuffled
network activity in raster format. Black squares indicate LFP signals
over threshold; each row is activity from an electrode; each column
is one time bin. B, Shuffling of activity. Gray columns indicate time
bins where at least one electrode was active in the unshuffled data.
Dashed arrows indicate example shuffles allowed by this procedure.
Activity from a given electrode can only be shuffled to another gray
time bin in the same row.
Chen et al. BMC Neuroscience 2010, 11:3
Page 11 of 14
activity died out; when s = 1, the network was critical
and activity was approximately sustained; when s > 1,
the network was supercritical and activity increased. In
all of the simulations described here, we set the model
to operate in the critical regime (s = 1), as that provided
the best fit to the avalanche size distribution observed in
the data [27,33]. We adopted this approach because
recent work has shown that it is difficult to estimate s
correctly from firing times in the data without knowing
details about the geometry of the network .
Each unit had a small probability of becoming sponta-
neously active at any time step, given by pspont. We
chose pspont= 0.005 to reproduce the average firing
rates observed in the data, and found that our results
did not depend strongly on the choice of this parameter.
Units could also become active through driven activity.
For example, unit j at time step t + 1 became active if
unit i in the previous time step t was active and the
connection between them transmitted. A connection
transmitted if rand ≤ pij, where rand was a uniformly
distributed random number drawn from the interval [0,
1]. Processing units updated at each time step to simu-
late the propagation of activity through the network.
After becoming active, a unit would become inactive, or
refractory, for the next 5 time steps. This refractory per-
iod was chosen to mimic that found in the data. Even
though the network was stochastic, certain preferred
avalanches of activity could develop as a result of the
fixed underlying transmission probabilities. This led to
significantly repeating avalanches mentioned earlier.
The weighting function
In previous models [27,33], the distribution of connec-
tion strengths was chosen from a uniform random dis-
tribution; here we investigated how the choice of this
distribution affected model performance. As many stu-
dies report weight distributions with a nearly exponen-
tial form [9,11,14,77,78], we adopted a weighting
function where transmission probabilities pijwere deter-
mined by the following:
The denominator was just a normalizing term to make
the sum of the p values equal one. When B = 0, the dis-
tribution was homogeneous; as B was increased greater
than zero, the distribution of p values became increas-
ingly skewed. We changed B to see how it affected ava-
lanches produced by the network model. In this
manner, we were able to identify the values of B that
best fit the data and that produced the largest number
of groups of significantly repeating avalanches.
Each simulation was run for 900,000 time steps so as to
model 1 hr of data binned at 4 ms. We examined ten
different values of B, and for each value we ran 10 simu-
lations. All software was written in Matlab and run on
This research was supported by NSF grant 0343636 and by the Indiana
METACyt Initiative of Indiana University, funded in part through a major
grant from the Lilly Endowment, Inc.
WC, JH, AT and JMB conceived the experiments. WC, JH and AT performed
the experiments. WC and JMB performed the simulations and wrote the
manuscript. WC, JH, and AT read the manuscript and provided critical
comments. All authors approved the final manuscript.
Received: 22 May 2009
Accepted: 6 January 2010 Published: 6 January 2010
1.Bliss TV, Collingridge GL: A synaptic model of memory: long-term
potentiation in the hippocampus. Nature 1993, 361(6407):31-9.
2.Hebb DO: The organization of behavior; a neuropsychological theory.
New York,: Wiley 1949, xix:335.
3. Milner B, Squire LR, Kandel ER: Cognitive neuroscience and the study of
memory. Neuron 1998, 20(3):445-68.
4.Martin SJ, Morris RG: New life in an old idea: the synaptic plasticity and
memory hypothesis revisited. Hippocampus 2002, 12(5):609-36.
5. McClelland JL, McNaughton BL, O’Reilly RC: Why there are complementary
learning systems in the hippocampus and neocortex: insights from the
successes and failures of connectionist models of learning and memory.
Psychol Rev 1995, 102(3):419-57.
6.Kohonen T: Self-organization and associative memory. Springer series in
information sciences Berlin; New York: Springer-Verlag, 3 1989, xv:32.
7.Steinbuch K: The Learning Matrix. Kybernetik 1961, 1(1):36-45.
8.Hopfield JJ: Neural networks and physical systems with emergent
collective computational abilities. Proc Natl Acad Sci USA 1982, 79(8):2554-8.
9.Brunel N, Hakim V, Isope P, Nadal JP, Barbour B: Optimal information
storage and the distribution of synaptic weights: perceptron versus
Purkinje cell. Neuron 2004, 43(5):745-57.
10. Barbour B, Brunel N, Hakim V, Nadal JP: What can we learn from synaptic
weight distributions? Trends Neurosci 2007, 30(12):622-9.
11.Gardner E: The Space of Interactions in Neural Network Models. Journal
of Physics a-Mathematical and General 1988, 21(1):257-270.
12.Gardner E, Derrida B: Optimal Storage Properties of Neural Network
Models. Journal of Physics a-Mathematical and General 1988, 21(1):271-284.
13.Engel A, Broeck Cvd: Statistical mechanics of learning. Cambridge, UK;
New York, NY: Cambridge University Press 2001, xi:329.
14. Song S, Sjostrom PJ, Reigl M, Nelson S, Chklovskii DB: Highly nonrandom
features of synaptic connectivity in local cortical circuits. PLoS Biol 2005,
15. Ikegaya Y, Aaron G, Cossart R, Aronov D, Lampl I, Ferster D, Yuste R: Synfire
chains and cortical songs: temporal modules of cortical activity. Science
16.Segev R, Baruchi I, Hulata E, Ben-Jacob E: Hidden neuronal correlations in
cultured networks. Physical Review Letters 2004, 92(11).
17. Beggs JM, Plenz D: Neuronal avalanches are diverse and precise activity
patterns that are stable for many hours in cortical slice cultures. J
Neurosci 2004, 24(22):5216-29.
18.Rolston JD, Wagenaar DA, Potter SM: Precisely timed spatiotemporal
patterns of neural activity in dissociated cortical cultures. Neuroscience
19.Madhavan R, Chao ZC, Potter SM: Plasticity of recurring spatiotemporal
activity patterns in cortical networks. Phys Biol 2007, 4(3):181-93.
Chen et al. BMC Neuroscience 2010, 11:3
Page 12 of 14
20.Hahnloser RHR, Kozhevnikov AA, Fee MS: An ultra-sparse code underlies
the generation of neural sequences in a songbird (vol 419, pg 65, 2002).
Nature 2003, 421(6920):294-294.
Dave AS, Margoliash D: Song replay during sleep and computational
rules for sensorimotor vocal learning. Science 2000, 290(5492):812-6.
Kimpo RR, Theunissen FE, Doupe AJ: Propagation of correlated activity
through multiple stages of a neural circuit. J Neurosci 2003, 23(13):5750-
Wilson MA, McNaughton BL: Reactivation of hippocampal ensemble
memories during sleep. Science 1994, 265(5172):676-9.
Ji D, Wilson MA: Coordinated memory replay in the visual cortex and
hippocampus during sleep. Nat Neurosci 2007, 10(1):100-7.
Euston DR, Tatsuno M, McNaughton BL: Fast-forward playback of recent
memory sequences in prefrontal cortex during sleep. Science 2007,
Pastalkova E, Itskov V, Amarasingham A, Buzsaki G: Internally generated
cell assembly sequences in the rat hippocampus. Science 2008,
Haldeman C, Beggs JM: Critical branching captures activity in living
neural networks and maximizes the number of metastable States. Phys
Rev Lett 2005, 94(5):058101.
Beggs JM, Plenz D: Neuronal avalanches in neocortical circuits. J Neurosci
Hobbs J, Chen W, Haldeman C, Tang A, Wang S, Beggs JM: Networks with
fewer and stronger connections may store more information in
neuronal avalanches. 20 min talk given at Computational Neuroscience
Conference, Madison, WI 2005.
Beggs JM, Chen W, Haldeman C, Hobbs J, Tang A, Wang S: A few strong
connections: Optimizing information storage in neuronal avalanches.
Abstract Viewer/Itenerary planner Washington, DC: Society for Neuroscience
2005, Program No. 654.5.
Tang A, Jackson D, Hobbs J, Chen W, Smith JL, Patel H, Prieto A, Petrusca
D, Grivich MI, Sher A, Hottowy P, Dabrowski W, Litke AM, Beggs JM:
A maximum entropy model applied to spatial and temporal correlations
from cortical networks in vitro. J Neurosci 2008, 28(2):505-18.
Johnston D, Wu SM-s: Foundations of cellular neurophysiology.
Cambridge, Mass.: MIT Press 1995, xxxi:676.
Beggs JM: The criticality hypothesis: how local cortical networks might
optimize information processing. Philos Transact A Math Phys Eng Sci 2008,
Bak P: How nature works: the science of self-organized criticality.
New York, NY, USA: Copernicus 1996, xiii:212, p p. of plates.
Harris TE: The theory of branching processes. New York: Dover
Publications 1989, xiv:230.
Pajevic S, Plenz D: Efficient network reconstruction from dynamical
cascades identifies small-world topology of neuronal avalanches. PLoS
Comput Biol 2009, 5(1):e1000271.
Rosenblatt F: The perceptron: a probabilistic model for information
storage and organization in the brain. Psychol Rev 1958, 65(6):386-408.
Haykin SS: Neural networks: a comprehensive foundation. Upper Saddle
River, N.J.: Prentice Hall, 2 1999, xxi:842.
Kanerva P: Sparse distributed memory. Cambridge, Mass.: MIT Press 1988,
Varshney LR, Sjostrom PJ, Chklovskii DB: Optimal information storage in
noisy synapses under resource constraints. Neuron 2006, 52(3):409-23.
Klostermann O, Wahle P: Patterns of spontaneous activity and
morphology of interneuron types in organotypic cortex and thalamus-
cortex cultures. Neuroscience 1999, 92(4):1243-59.
Caeser M, Bonhoeffer T, Bolz J: Cellular organization and development of
slice cultures from rat visual cortex. Exp Brain Res 1989, 77(2):234-44.
Gotz M, Bolz J: Formation and preservation of cortical layers in slice
cultures. J Neurobiol 1992, 23(7):783-802.
Bolz J, Novak N, Gotz M, Bonhoeffer T: Formation of target-specific
neuronal projections in organotypic slice cultures from rat visual cortex.
Nature 1990, 346(6282):359-62.
Plenz D, Aertsen A: Neural dynamics in cortex-striatum co-cultures–I.
anatomy and electrophysiology of neuronal cell types. Neuroscience 1996,
Baker RE, Van Pelt J: Cocultured, but not isolated, cortical explants display
normal dendritic development: a long-term quantitative study. Brain Res
Dev Brain Res 1997, 98(1):21-9.
47.Leiman AL, Seil FJ: Influence of subcortical neurons on the functional
development of cerebral neocortex in tissue culture. Brain Res 1986,
Cossart R, Aronov D, Yuste R: Attractor dynamics of network UP states in
the neocortex. Nature 2003, 423(6937):283-8.
Kenet T, Bibitchkov D, Tsodyks M, Grinvald A, Arieli A: Spontaneously
emerging cortical representations of visual attributes. Nature 2003,
Hahnloser RH, Kozhevnikov AA, Fee MS: An ultra-sparse code underlies
the generation of neural sequences in a songbird. Nature 2002,
Timofeev I, Grenier F, Bazhenov M, Sejnowski TJ, Steriade M: Origin of slow
cortical oscillations in deafferented cortical slabs. Cereb Cortex 2000,
Tsodyks M, Kenet T, Grinvald A, Arieli A: Linking spontaneous activity of
single cortical neurons and the underlying functional architecture.
Science 1999, 286(5446):1943-6.
Butts DA, Rokhsar DS: The information content of spontaneous retinal
waves. J Neurosci 2001, 21(3):961-73.
Pesaran B, Pezaris JS, Sahani M, Mitra PP, Andersen RA: Temporal structure
in neuronal activity during working memory in macaque parietal cortex.
Nat Neurosci 2002, 5(8):805-11.
Scherberger H, Jarvis MR, Andersen RA: Cortical local field potential
encodes movement intentions in the posterior parietal cortex. Neuron
Stewart CV, Plenz D: Inverted-U profile of dopamine-NMDA-mediated
spontaneous avalanche recurrence in superficial layers of rat prefrontal
cortex. J Neurosci 2006, 26(31):8148-59.
Tseng KY, O’Donnell P: Post-pubertal emergence of prefrontal cortical up
states induced by D-1-NMDA co-activation. Cerebral Cortex 2005, 15(1):49-
Hsu D, Beggs JM: Neuronal avalanches and criticality: A dynamical model
for homeostasis. Neurocomputing 2006, 69:1134-1136.
Hsu D, Tang A, Hsu M, Beggs JM: Simple spontaneously active Hebbian
learning model: homeostasis of activity and connectivity, and
consequences for learning and epileptogenesis. Phys Rev E Stat Nonlin
Soft Matter Phys 2007, 76(4 Pt 1):041909.
Hsu D, Chen W, Hsu M, Beggs JM: An open hypothesis: Is epilepsy
learned, and can it be unlearned? Epilepsy & Behavior 2008, 13(3):511-522.
Turrigiano GG: Homeostatic plasticity in neuronal networks: the more
things change, the more they stay the same. Trends Neurosci 1999,
Royer S, Pare D: Conservation of total synaptic weight through balanced
synaptic depression and potentiation. Nature 2003, 422(6931):518-22.
Almaas E, Kovacs B, Vicsek T, Oltvai ZN, Barabasi AL: Global organization of
metabolic fluxes in the bacterium Escherichia coli. Nature 2004,
Kauffman SA: Emergent Properties in Random Complex Automata.
Physica D 1984, 10(1-2):145-156.
Kauffman SA: Antichaos and Adaptation. Scientific American 1991,
Huyck CR: Cell assemblies as an intermediate level model of cognition.
Emergent Neural Computational Architectures Based on Neuroscience: Towards
Neuroscience-Inspired Computing 2001, 2036:383-397.
Carrillo-Reid L, Tecuapetla F, Tapia D, Hernandez-Cruz A, Galarraga E,
Drucker-Colin R, Bargas J: Encoding network states by striatal cell
assemblies. J Neurophysiol 2008, 99(3):1435-1450.
Carrillo-Reid L, Tecuapetla F, Ibanez-Sandoval O, Hernandez-Cruz A,
Galarraga E, Bargas J: Activation of the Cholinergic System Endows
Compositional Properties to Striatal Cell Assemblies. J Neurophysiol 2009,
Plenz D, Thiagarajan TC: The organizing principles of neuronal avalanches:
cell assemblies in the cortex? Trends Neurosci 2007, 30(3):101-10.
Beggs JM, Chen W, Klukas J: Network connectivity and neuronal
dynamics, in Handbook of Brain Connectivity. Springer: BerlinMcIntosh
AR, Jirsa VK 2007, 91-116.
Wirth C, Luscher HR: Spatiotemporal evolution of excitation and
inhibition in the rat barrel cortex investigated with multielectrode
arrays. J Neurophysiol 2004, 91(4):1635-47.
Schiff SJ, Jerger K, Duong DH, Chang T, Spano ML, Ditto WL: Controlling
chaos in the brain. Nature 1994, 370(6491):615-20.
Chen et al. BMC Neuroscience 2010, 11:3
Page 13 of 14
73.Wu JY, Guan L, Tsau Y: Propagating activation during oscillations and
evoked responses in neocortical slices. J Neurosci 1999, 19(12):5005-15.
Jimbo Y, Kawana A, Parodi P, Torre V: The dynamics of a neuronal culture
of dissociated cortical neurons of neonatal rats. Biol Cybern 2000, 83(1):1-
Jacquard A: Heritability - One Word, 3 Concepts. Biometrics 1983,
Priesemann V, Munk MH, Wibral M: Subsampling effects in neuronal
avalanche distributions recorded in vivo. BMC Neurosci 2009, 10(1):40.
Balasubramanian V, Kimber D, Berry MJ: Metabolically efficient information
processing. Neural Computation 2001, 13(4):799-815.
De Polavieja GG: Errors drive the evolution of biological signalling to
costly codes. Journal of Theoretical Biology 2002, 214(4):657-664.
Cite this article as: Chen et al.: A few strong connections: optimizing
information retention in neuronal avalanches. BMC Neuroscience 2010
Submit your next manuscript to BioMed Central
and take full advantage of:
• Convenient online submission
• Thorough peer review
• No space constraints or color figure charges
• Immediate publication on acceptance
• Inclusion in PubMed, CAS, Scopus and Google Scholar
• Research which is freely available for redistribution
Submit your manuscript at
Chen et al. BMC Neuroscience 2010, 11:3
Page 14 of 14