various ways, without altering the total number of GC-to-GC
C 10% Stimulation of 50% Injured
(Control) Network connections in the network, to determine the effects of biolog-
A ically relevant GC-to-GC topologies on network hyperexcitabil-
Dentate Network Schematic
Granule Cell Number
ity. All networks contain GABAergic inhibition, and the ‘‘con-
trol’’ network used in this work is equivalent to the
hyperexcitable, ‘‘50% sclerotic’’ network described and exten-
cell layer sively tested in ref. 11.
Control Network Displays Limited Hyperexcitability. In response to
a simulated perforant path input to 5,000 GCs (10%), 50 basket
0 100 200 300 400 500 cells (10%), and 10 mossy cells (1.3%) (referred to as ‘‘10%
stimulation’’), the control network (which, as described above,
To CA3 includes a simulated moderate injury resulting in cell loss and
D 1% Stimulation of 50% Injured
mossy-fiber sprouting) exhibited limited hyperexcitability (Fig.
1C), in agreement with previous findings (11, 21). Activity
B 50% Injured (Control) Network Schematic spread to the entire network by 83.67 1.07 ms, and GC firing
Granule Cell Number
duration was 207.78 10.35 ms. The mean number of spikes
fired per GC was 14.40 0.42 (n 3 simulations with random
seeds for all values reported SD; see Methods).
To determine the threshold at which the control network
began to display hyperexcitability, we decreased the stimulation
extent in steps of 1% until no GCs outside of the stimulated
0 100 200 300 400 500
lamella (one lamella contains 10% of the GCs in the network;
see SI Text) fired an action potential (data not shown). In
Fig. 1. Control network schematic and simulation results. (A) Schematic of response to simulated perforant path input to 1% of GCs, 1% of
the dentate gyrus model showing the four cell types implemented, the layers basket cells, and one mossy cell (‘‘1% stimulation’’), few action
in which they reside, and their cell type-speciﬁc connectivity. (Left to Right) potentials were fired beyond the initial stimulus (Fig. 1D).
Excitatory granule cells (red), inhibitory somatically projecting basket cells
(green), inhibitory dendritically projecting hilar interneurons with axonal
projections to the perforant path (yellow), and excitatory mossy cells (blue).
Hebbian-Like Connectivity Has No Effect on Hyperexcitability. We
Dashed line, recurrent GC connections (the only connections we modiﬁed in first theorized that if cells received a number of common inputs,
this work). (B) Schematic of the injury-induced structural features that are they would be likely to fire similarly and form small networks that
present in the control network model. A percentage of mossy cells and HIPP could efficiently promote hyperexcitability. We therefore estab-
cells are lost, and GCs sprout recurrent axon collaterals that synapse on other lished a network with ‘‘Hebbian-like’’ connectivity in which the
GCs. Note that basket cells are not depicted in the schematic although they are probability of a connection between two neurons increased
present in the network. (C and D) Raster plots of network activity after proportionally to the number of shared presynaptic neurons (Fig.
applying the 10% and 1% stimulations, respectively, to the 50% injured
2A; see SI Text). In response to 10% stimulation, duration and
control network. Black dots, GC action potentials. (Right) Representative GC
traces. (Scale: 20 mV and 100 ms.)
latency of network activity and GC firing were not significantly
different from control (Fig. 2B, compare with Fig. 1C; see also
Fig. 4 A–C).
Results Despite the similarities between the Hebbian-like network and
We used a published, large-scale model of the rat dentate gyrus, the control in the 10% stimulation case, it was possible that the
complete with 50,000 detailed single-cell models of various cell microcircuit changes altered the stimulation threshold required
types each constructed based on anatomical, cellular, and elec- for network activation. However, the 1% stimulus resulted in
trophysiological data derived from the literature [Fig. 1A and activity that was nearly identical to the control (Fig. 2C, compare
supporting information (SI) Text; detailed information on the with Fig. 1D).
single-cell models and synaptic connections can be found in refs. Taken together, these results suggest that our Hebbian-like
11 and 21] to examine the role of the specific microcircuit connectivity pattern neither promotes nor prevents hyperexcit-
connectivity of the dentate GC network in contributing to ability in the dentate gyrus, and it does not alter the dentate
hyperexcitability after injury. We established a control network hyperexcitability threshold.
simulating a moderate injury that resulted in 50% hilar inter-
neuron and mossy-cell loss and 50% of maximal mossy-fiber Small-Network Motif Overrepresentation Also Has No Significant
sprouting (Fig. 1B). In this network, GC-to-GC connections Effect on Hyperexcitability. Next, we assessed the role of various
were made randomly (Fig. S1), constrained only by the extent of three-neuron small network motifs in promoting hyperexcitabil-
their axonal arbors (see SI Text and ref. 11). We then constructed ity in the model dentate by creating networks in which we
networks with varied GC microcircuit topologies (i.e., we re- manually increased the number of a given motif (Fig. 2D) present
connected the sprouted mossy fibers in biologically plausible, in the GC microcircuit without altering the total number of
nonrandom patterns; see SI Text and Fig. S1) to assess the role connections in the network (see SI Text). Fig. 2E shows the
of nonrandom connectivity features in altering network function results from a representative network that has an abundance of
and specifically augmenting hyperexcitability in a seizure- motif number 8 [Fig. 2D; the feedback loop, which is one of the
susceptible circuit. Note that although numerous cell types were most structurally and dynamically unstable motifs (17), and was
represented in the network, only the injury-induced recurrent thus presumed to be likely to promote hyperexcitability]. The
circuitry between granule cells was altered. Also, critically, in all 10% stimulus (Fig. 2E, compare with Fig. 1C) resulted in no
networks the total number of connections remained the same as significant difference in excitability compared with control (see
in the control. In summary, the general strategy was to take a Fig. 4 A–C; P 0.018 for duration; P 0.022 for latency; and
seizure-prone (i.e., hyperexcitable) network containing sprouted P 0.018 for mean spikes per GC; see Methods for significance
GC-to-GC connections (this is the 50% Injured, Control net- level explanation). Of the networks with overrepresented motifs
work in Fig. 1B) and reconnect only the GC-to-GC synapses in (including motifs with IDs 6–11, and 13; see Fig. 2D), this
6180 www.pnas.org cgi doi 10.1073 pnas.0801372105 Morgan and Soltesz
A Hebbian-like Network Schematic
D Three-Neuron Motifs
A Scale-free Network Connectivity D Hub Network Schematic
p(GC Having k Connections)
1 1 2 3 4
5 6 7 8 10-2
9 10 11 12 -4
10 10 10
Number of Connections (k)
B 10% Stimulation of
E 10% Stimulation of Motif Network B 50000 Stimulation of Scale-free Network E 50000 10% Stimulation of Hub Network
Granule Cell Number
Granule Cell Number
Granule Cell Number
Granule Cell Number
0 100 200 300 400 500 0 100 200 300 400 500
0 0 Time (ms) Time (ms)
0 100 200 300 400 500 0 100 200 300 400 500
Time (ms) Time (ms)
C 50000 Stimulation of Scale-free Network F
1% 1% Stimulation of Hub Network
C 1% Stimulation of F 1% Stimulation of Motif Network
Granule Cell Number
Granule Cell Number
Granule Cell Number
Granule Cell Number
0 100 200 300 400 500 0 100 200 300 400 500
Time (ms) Time (ms)
0 100 200 300 400 500 0 100 200 300 400 500
Time (ms) Time (ms) Fig. 3. Scale-free and structural hub network simulations. (A) Graph of the
power-law connectivity of the scale-free network. (B and C) Raster plots of
Fig. 2. Hebbian-like and feedback loop motif simulations. (A) Schematic of activity in the scale-free network in response to 10% and 1% stimulation,
the Hebbian-like connectivity structure. The connection probability of any respectively. (D) Schematic of a hub network. Average granule cells (black
two neurons in the network (e.g., neurons 2 and 3, white) increased propor- circles) have relatively few connections compared with the highly intercon-
tionally to the number of presynaptic neurons that they shared (e.g., neuron nected hubs (gray diamonds). (E) Raster plot of 210-connection hub network
1, black). (B and C) Raster plots of activity in the Hebbian-like network in activity in response to 10% stimulation. (Right) Representative traces of a
response to 10% and 1% stimulation, respectively. (D) Schematic showing all nonhub (Upper) and hub (Lower) GC. (Scale: 20 mV and 100 ms.) (F) One
possible three-neuron motifs or connectivity patterns. Boxed motif, the feed- percent stimulation of the 210-connection hub network.
back loop, which is the representative motif for which results are shown. (E
and F) Raster plots showing activity of the network with an overrepresenta-
tion of the feedback-loop motif in response to 10% and 1% stimulation, in the GC network would affect the functional properties of the
model dentate gyrus, we implemented a network with a scale-
free topology. Scale-free networks are defined such that the
network was the only one that displayed a strong trend toward distribution of connections among each of the nodes in the
hyperexcitability (data not shown). network (GCs in this case) follows a power law (Fig. 3A and SI
The 1% stimulation paradigm confirmed the lack of a signif- Text). Networks with such a distribution are prevalent in both
icant effect of overrepresenting various motifs. For all networks biological and nonbiological systems (see Discussion), and they
with overrepresented motifs, the results mimicked the control are known to allow for efficient information transfer and prevent
and Hebbian-like networks, with no activity propagation and signal jamming (18). The scale-free network contained a small
most GCs firing no spikes (data shown only for motif 8; Fig. 2F, number of neurons with a very large number of connections (Fig.
compare with Fig. 1D). 3A; 5% of neurons participated in 175 connections), whereas
The results above suggest that the functional properties of the most neurons had relatively few connections (87% of neurons
dentate gyrus are robust when faced with a number of major participated in between 25 and 100 connections, with fewer
alterations to the GC microcircuitry. However, for the topolog- connections being more prevalent; the average control GC
ical changes described thus far, each GC maintained a relatively participated in 68 connections, 34 incoming and 34 outgoing).
constant degree of connectivity, ensuring that the number of The probability of a neuron participating in a given number of
small motifs or circuits in which each cell participated was nearly
connections decayed as a power law with an exponent of 2.6 (Fig.
identical. In the biological dentate, this is not the case, however,
because some granule cells participate in many more connec- 3A), in agreement with many other scale-free networks (24).
tions than average (see Discussion). We therefore sought to The 10% stimulation paradigm revealed that the scale-free
discover how nonrandom changes in the distribution of the network was much more excitable than the control (Fig. 3B,
number of connections across GCs could affect network compare with Fig. 1C). Activity propagation throughout the
excitability. network was faster (latency to full-network activation was
65.87 1.01 ms) and sustained for nearly twice the length of
Scale-Free Topology Greatly Enhances Hyperexcitability. To address activity in the control (duration of GC discharge was 413.90
the question of whether the distribution of connection numbers 24.84 ms). Although some isolated branches of activity persisted
Morgan and Soltesz PNAS April 22, 2008 vol. 105 no. 16 6181
C140 is shown in Fig. 3D. The hub cells (gray diamonds) participate in
A 500 *
120 many more connections than the average GCs (black circles).
* The results of the 10% stimulation paradigm show that as the
300 80 number of connections per hub increased, so did the hyperex-
200 60 citability of the network, in a linearly correlated fashion (squares
40 in Fig. 4D; solid line r2 0.9028). In the network with 210
20 connections (Fig. 3E), activity increased significantly compared
0 0 with control (Fig. 4 A–C; P 0.002 for all three measures), with
Ctrl Hebb Motif SF Hubs Ctrl Hebb Motif SF Hubs
a 32% increase in the number of spikes fired per GC. Repre-
B D Relative120 140 160 180(%200Control)
Connection Strength of sentative traces from both a nonhub and a hub GC are shown in
25 * 100 220
20 Fig. 3E, Right.
Mean Spikes per GC
Mean Spikes per GC
20 18 The 1% stimulation provided further evidence that hubs are
15 16 sufficient to enhance hyperexcitability in the model dentate
14 gyrus in the absence of an accompanying scale-free distribution.
12 The networks with 210, 180, 150, and 120 additional connections
Incoming & Outgoing
all demonstrated a reduced threshold for network activation
compared with control (data not shown, except for 210-
Ctrl Hebb Motif SF Hubs 0 30 60 90 120 150 180 210 240
No. of Connections per Hub
connection hub network in Fig. 3F). However, networks with 90
or fewer additional connections per hub did not display self-
Fig. 4. Quantiﬁcation of network activity and hub characteristics. (A–C) sustained, recurrent excitation in response to the 1% stimulus
Latency to full-network activation (A), duration of granule cell ﬁring (B), and (data not shown).
mean number of spikes per granule cell (C) for the ﬁve major structural These data indicate that the presence of hubs in the GC
connectivity variations implemented in our networks (Ctrl, control; Hebb,
network of the dentate gyrus is sufficient to enhance hyperex-
Hebbian-like; Motif, overrepresentation of motif 8; SF, scale-free; Hubs, 210-
connection hub network). *, statistical signiﬁcance. (D) Mean spikes per GC in
citability and lower the threshold required for a self-sustained,
hub networks with enhanced numbers of incoming (diamonds), outgoing propagating response to stimulation. This finding is true in the
(triangles), and incoming outgoing (squares) connections (all bottom axis), absence of an accompanying scale-free distribution of the re-
and enhanced connection strengths (circles, top axis). maining connections in the network, although the presence of
a scale-free distribution augments the effects seen here. Rela-
tively few hubs are needed (5% was sufficient), but they need
beyond the end point of the simulations (Fig. 3B), longer approximately four to seven times as many connections as the
simulations indicated that this activity terminated soon after average GC. We next asked whether incoming or outgoing
(data not shown). The mean number of spikes fired per GC was connections of the hub were more instrumental in contributing
also significantly increased (22.02 0.69; P 0.0001 for latency, to hyperexcitability.
duration, and GC firing; Fig. 4 A–C).
Analysis of the threshold condition also demonstrated marked Directionality of Hub Connections and Hub Connection Strengths. Our
differences from the control network. Most impressively, the results demonstrate that the presence of hubs in the GC micro-
threshold for network activation was lowered such that the 1% circuitry can greatly augment hyperexcitability. However, the
stimulation yielded full recruitment of the network (Fig. 3C). All hubs we incorporated into the network included an increased
measures of network activity were similar to those in the 10% number of both incoming and outgoing connections. To deter-
stimulation case. mine whether directionality of connectivity was important in
These results indicate that despite the robustness of the promoting hyperexcitability, we created networks that included
functional properties of the model dentate to the inclusion of a hubs with either solely increased incoming or outgoing connec-
number of nonrandom features in the GC microcircuit, some tions. The results of these simulations indicate that only a
network topologies result in markedly altered functional re- combination of enhanced incoming and outgoing connectivity
sponses. In this case, a scale-free topology greatly enhanced the was correlated with increased network activity (Fig. 4D: dia-
hyperexcitability of the dentate gyrus. However, it remained monds, incoming, negatively correlated with activity, r2
unclear exactly which features of this topology were responsible 0.9945; triangles, outgoing, r2 0.0124; squares, incoming
outgoing, positively correlated with activity, r2 0.9028; all
for the enhanced activity in the network. Is a power law
bottom axis). We further show that this enhanced connectivity
connectivity distribution required for increased hyperexcitabil-
does not require increased numbers of physical connections on
ity, or is it sufficient to include the most highly interconnected
hubs but can also arise from increased connection strengths
neurons in the network but maintain randomly distributed
because networks containing 5% of GCs with enhanced synaptic
connectivity throughout the remainder of the network? weights (but control numbers of connections) were also corre-
lated with increased activity (Fig. 4D: circles, positive correla-
Presence of Hubs, Even in the Absence of Power Law Distribution, tion, r2 0.8802; top axis). This correlation persisted compared
Increases Hyperexcitability. To address the question posed above, with a control network that had a randomly chosen 5% of all
we studied networks in which 5% of the GCs were vastly more synaptic weights increased to compensate for the increase in
interconnected than the average GC (these highly intercon- excitatory conductance in the experimental networks (data not
nected cells can be thought of as hubs), but the remaining GC shown).
connectivity did not follow a power law. In the scale-free
network, the 5% of GCs with the most connections all partici- Discussion
pated in at least 175 connections. We therefore created seven This work has two primary findings. First, we show in a large-
networks including hubs that had increasing numbers of added scale, realistic neural network model that specific microcircuit
connections (between 30 and 210 connections, in addition to the connectivity can have important and significant effects on
standard number of random connections) before normalizing epileptiform network activity. Second, we show that in the
the total number of connections to the control value (see SI injured dentate gyrus, the presence of a small population of
Text). All other GCs were connected randomly, as in the control. highly interconnected GC hubs strongly contributes to hyperex-
A schematic diagram of a network with a small number of hubs citability. The latter finding may also provide interesting insights
6182 www.pnas.org cgi doi 10.1073 pnas.0801372105 Morgan and Soltesz
concerning the possible role of GCs with hilar basal dendrites in at its minimum, to provide enough hubs to promote hyperex-
the epileptic dentate gyrus, as we discuss below. citability according to the predictions of our model.
Recent studies have shown that connections within a variety Clearly, in order for GCs with basal dendrites to act as hubs,
of neural networks exhibit a large number of nonrandom prop- they must participate in an extremely large number of connec-
erties (2–4, 8, 15, 16, 25). One common theme in these nonran- tions with other GCs in the circuit. Indeed, recent evidence
dom connectivity patterns is an overabundance of certain small- suggests that basal dendrites receive an extraordinary number of
network motifs. For this reason, it is quite surprising that when excitatory synapses. GC basal dendrites comprise up to 15% of
we overrepresented a wide range of motifs, there was no the total dendritic length of a GC, and synapsing on each
significant effect on network activity. It is possible that the motifs dendrite are 140 inhibitory and 2,500 excitatory synapses (38).
are simply so sparse in the network that even massive overrep- In the biological dentate from epileptic animals, EM analyses
resentation changes network topology only slightly and thus has revealed an average of 275 new mossy-fiber contacts per GC at
little effect on network activity. However, by adding 100,000 of maximal levels of sprouting (22), only one-ninth of the number
each motif (each containing at least three connections) to the of excitatory connections onto basal dendrites. Even if only half
network, we ensured that a vast number of connections (of the of the basal dendrite excitatory connections are mossy-fiber
total 1.7 million) were participating in the desired motif, thereby contacts, the estimated number of connections is in line with the
substantially increasing the number of interacting motifs. Even number we used in simulating the model hub cells.
with this alteration in topology, however, the distribution of Until recently, the main problem with the biological data in
connections across neurons remained relatively constant, and support of hubs in the dentate gyrus was that the available data
each GC was therefore limited in the amount of recurrent regarding GCs with basal dendrites focused exclusively on the
excitation it could provide. In the biological dentate of epileptic incoming connections to these cells. There were no data sug-
animals, it is probable that specific combinations of motifs form gesting whether GCs with basal dendrites form either more
larger recurrent networks and are more important for overall numerous or stronger outgoing connections, thus leaving the
network function than the ubiquitous presence of a single prediction of our model largely unconfirmed. However, an
particular motif. These combinations would be most likely to elegant study of poststatus epilepticus GCs recently revealed a
form and interact if the distribution of connections in the previously unseen increase in axonal protrusions (often within
network is uneven and results in the presence of highly con- the GC layer) among newborn cells that likely corresponds to an
nected neurons, each participating in many more small-network increased number of outgoing connections onto other GCs (37).
motifs than the average cell. Additionally, 40% of post-SE newborn GCs retain a basal
Although topologies incorporating uneven distributions of dendrite in addition to nearly 10% of mature post-SE GCs (37),
connectivity such as scale-free networks or hub-containing
thereby resulting in the probable existence of GCs with both
networks seem highly sophisticated and perhaps unlikely to form
increased axonal protrusions and a basal dendrite. Although
in biological systems, there is indeed substantial precedent for
more experimental work is necessary to characterize fully the
these types of networks both in biology and elsewhere. A number
outgoing connectivity of GCs with basal dendrites, our results
of nonbiological networks that incorporate topologies similar to
combined with the described experimental work strongly sup-
our scale-free or hubs-only network implementations include
port the likelihood that neuronal hubs play a hitherto unrecog-
social networks, the internet, and the electric grid (13, 26–29).
nized, major role in promoting hyperexcitability and seizures.
Included in biological networks that follow a power-law distri-
bution are the neural network of C. elegans and various meta- Methods
bolic and gene regulatory networks such as metabolic flow in
We used a published large-scale computational model of the dentate gyrus to
yeast and yeast transcription regulatory networks (29–32). Ad- study the role of the ﬁne-microcircuit connectivity of the dentate gyrus
ditionally, it was recently demonstrated that a culture of cortical recurrent GC network in contributing to hyperexcitability (11). Because nei-
neurons on a multielectrode array developed such that their ther the healthy dentate in vivo nor the model of the healthy dentate contain
firing patterns were consistent with a scale-free topology of GC-to-GC connections (Fig. S1), we studied the dentate gyrus after a simulated
connectivity (33). Finally, connection strengths between layer 5 injury resulting in 50% loss of hilar interneurons and mossy cells and 50% of
pyramidal neurons in rat visual cortex have been shown to follow maximal mossy-ﬁber sprouting (this network is referred to as the ‘‘control
a log normal distribution with a heavy tail, similar to a power-law network’’; Fig. 1 B–D, Fig. S1). This degree of mossy-ﬁber sprouting corre-
distribution (8). Thus, it is very possible that these network sponds to 34 new connections per GC in the computational model. The
topologies could form and significantly alter activity in complex precise microcircuit connectivity that resulted from these newly formed con-
nections was varied in four major, biologically plausible ways to yield new
neuronal networks such as the dentate gyrus.
networks with: (i) Hebbian-like connectivity; (ii) overrepresentation of small-
Given that networks with highly interconnected hubs are network motifs; (iii) scale-free topology; and (iv) highly interconnected GC
relatively common in complex systems, then perhaps the biggest hubs without a scale-free topology.
question that is left unanswered by this work is related to the very
prediction that our model provides. That is, are hubs actually Control Network. The cells were linked according to cell type-speciﬁc connec-
formed when mossy-fiber sprouting occurs in the pathological tion probabilities derived from the average number of projections from the
dentate gyrus? Although computational modeling can never pre- to the postsynaptic neuronal class in the literature (11). Within these cell
answer this question definitively, there is a substantial amount of type-speciﬁc constraints and the axonal arbors of the cell (SI Text), connections
biological evidence supporting the presence of hubs. were made probabilistically on a neuron-to-neuron basis with a uniform
Virtually all GCs in the healthy dentate gyrus are typical, with synapse density along the axon (21), treating multiple synapses between two
only apical dendrites that extend into the molecular layer and cells as a single link and excluding autapses. Mossy-ﬁber sprouting and hilar
terminate usually in its distal two-thirds (34). After injury, cell loss were implemented at 50% of maximum.
however, a subset of GCs can be found that not only have apical
Experimental Networks with Altered Connectivity. To construct each of the
dendrites but a long basal dendrite as well (23). This dendrite
experimental networks, we made speciﬁc modiﬁcations to the GC-to-GC
does not extend into the molecular layer but rather toward the connections in the network. All other connections were established as de-
hilus, and it synapses with mossy fibers, thereby creating exci- scribed for the control network above. Once all connections were established,
tatory circuits similar to those formed by apical dendrites (35). the number of GC-to-GC connections was reduced to the total number present
The percentage of GCs that have these hilar basal dendrites is in the control network by randomly eliminating connections. In this way, the
relatively small, with estimates ranging from 5 to 20% of GCs total excitatory drive in all of the networks was kept constant. For details on
(23, 35–37). Interestingly, this estimate is sufficiently large, even how each particular network was constructed, see SI Text.
Morgan and Soltesz PNAS April 22, 2008 vol. 105 no. 16 6183
Stimulation and Assessment of the Networks. Activity in the networks was minus the time of the ﬁrst GC action potential; (ii) duration of network
evoked through two separate simulated perforant path stimulation para- activity, deﬁned as the average time of the ﬁnal action potential for each GC
digms. The 10% stimulation paradigm consisted of a single perforant path minus the time of the ﬁrst action potential in the network; and (iii) mean
synaptic input to 5,000 GCs (10%), 10 mossy cells (1.3%), and 50 basket cells number of spikes ﬁred per GC. Although the mechanisms of activity termina-
(10%) situated in the middle lamella of the model network at 5 ms after the tion were not explicitly investigated, they are likely to include synaptic inhi-
start of the simulation, as in ref. 11. We also used a threshold stimulation bition from basket and HIPP cells, activation of calcium and voltage-
paradigm (referred to as 1% stimulation) to determine whether topological or dependent potassium conductances, and the intrinsic properties of the
functional alterations had changed the threshold for recruitment of network granule cells themselves that have a ‘‘default’’ silent state (21). Importantly,
these mechanisms do not differ between the control and experimental net-
activity. This paradigm consisted of a simulated perforant path input to 500
works. Statistical signiﬁcance was assessed by using unpaired, two-tailed t
GCs (1%), 1 mossy cell (0.13%), and 5 basket cells (1%). The threshold was
tests. Because of testing of 12 independent networks, statistical signiﬁcance
established by stepping back from the 10% stimulation in 1% steps until
was set at P 0.004. Data analysis and plotting were done by using Matlab
full-network activity no longer resulted in the control network. Simulations
6.5.1 (The MathWorks, Inc.) and SigmaPlot 8.0 (SPSS, Inc.). Motif detection was
lasted for 500 ms ( 12–18 h per simulation in real time), after which network
done by using FANMOD for Linux (39). All simulations were performed in the
activity was saved and analyzed. Values reported SD values were for simu- NEURON 5.6 simulation environment (40) by using custom hoc and C code and
lations that were run three times with different random seeds. All other bash scripts on a Tyan Thunder 2.0 GHz dual Opteron server (32 GB RAM).
simulations were run once.
Analysis and quantiﬁcation of network activity involved three separate ACKNOWLEDGMENTS. This work was funded by National Institutes of Health
measures: (i) latency to full-network activation, deﬁned as the time at which Grant NS35915 (to I.S.) and the University of California, Irvine, Medical Scien-
the most distant GC from the stimulation site ﬁred its ﬁrst action potential tist Training Program (to R.J.M.).
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