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Proc Natl Acad Sci U S A. 2008 Apr 22; 105(16): 6179–6184.
Published online 2008 Mar 28. doi:  10.1073/pnas.0801372105
PMCID: PMC2299224
From the Cover
Neuroscience

Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures

Abstract

Many complex neuronal circuits have been shown to display nonrandom features in their connectivity. However, the functional impact of nonrandom network topologies in neurological diseases is not well understood. The dentate gyrus is an excellent circuit in which to study such functional implications because proepileptic insults cause its structure to undergo a number of specific changes in both humans and animals, including the formation of previously nonexistent granule cell-to-granule cell recurrent excitatory connections. Here, we use a large-scale, biophysically realistic model of the epileptic rat dentate gyrus to reconnect the aberrant recurrent granule cell network in four biologically plausible ways to determine how nonrandom connectivity promotes hyperexcitability after injury. We find that network activity of the dentate gyrus is quite robust in the face of many major alterations in granule cell-to-granule cell connectivity. However, the incorporation of a small number of highly interconnected granule cell hubs greatly increases network activity, resulting in a hyperexcitable, potentially seizure-prone circuit. Our findings demonstrate the functional relevance of nonrandom microcircuits in epileptic brain networks, and they provide a mechanism that could explain the role of granule cells with hilar basal dendrites in contributing to hyperexcitability in the pathological dentate gyrus.

Keywords: basal dendrite, computational model, epilepsy, granule cell, scale-free

Numerous studies have indicated that connectivity in a wide variety of neural systems exhibits highly nonrandom characteristics. For example, in the nervous system of the Caenorhabditis elegans worm, of which the complete structure has been described (1), it was shown that a number of local connectivity patterns (network motifs) are over- or underrepresented compared with what would be present in a random network (24). Furthermore, computational analysis has indicated that the dynamic properties of these network motifs could contribute to their relative abundance, closely tying functional properties to the structural network (5). Nonrandom connectivity features have been discovered in mammalian cortices as well (610). Such networks exhibit high degrees of local clustering with short path lengths [small-world topology (1113)], power law distributions of connectivity [scale-free topology (11, 13, 14)], and nonrandom distributions of connection strengths (8). Additionally, it has been shown that connection probabilities demonstrate fine-scale specificity that depends both on neuronal type and the presence or absence of other connections in the network (15, 16).

Although nonrandom structural features of neuronal networks have been of great interest recently, and the role of some of these features in network dynamics and information processing has been investigated (5, 1719), the contribution of nonrandom microcircuit connectivity to the functional properties of large, complex brain regions, particularly in epilepsy, remains poorly understood. The mammalian dentate gyrus provides an ideal circuit for investigating this question in a large-scale biophysically realistic model and to examine the potential biological mechanisms that could allow for the formation of nonrandom circuitries that promote seizures.

After insults such as head trauma, ischemia, and repetitive seizures, which often lead to temporal lobe epilepsy, the dentate gyrus undergoes dramatic structural rearrangement. Structural changes include loss of hilar interneurons and mossy cells (11, 20, 21) and the formation of recurrent collaterals between granule cells (GCs) via mossy-fiber (GC axon) sprouting (11, 21, 22). Importantly, in the healthy dentate gyrus, GCs do not synapse on each other. Therefore, the recurrent excitatory GC network is a unique feature of the postinsult, epileptic dentate gyrus. Recently, it has been shown that the postinsult structural alterations can promote hyperexcitability in the dentate even in the absence of any nonstructural alterations such as intrinsic cellular and synaptic modifications (11). This increased hyperexcitability occurs despite a massive decrease in the total number of excitatory connections in the dentate network (caused by loss of the extensive connectivity of mossy cells, many of which die after injury). Thus, the newly formed connections between GCs must be instrumental in creating the hyperexcitable dentate network. However, GC-to-GC connectivity is quite sparse; indeed, the probability of two granule cells connecting, even at maximal levels of sprouting, is only ≈0.55%, and the probability of random formation of a three-neuron “recurrent” circuit of the form A → B → C → A is miniscule at 4.16 × 10−6%. Therefore, the specific patterns of GC-to-GC connections that define the microcircuit structure are likely to play a critical role in affecting network excitability.

Here, we examine the role of several biologically plausible GC microcircuits on dentate excitability after insult. First, we report that the dentate gyrus circuitry is remarkably robust when confronted with a number of GC-to-GC connectivity patterns that would be expected to promote hyperexcitability. We then show that this robustness can be overcome by the inclusion of a small percentage of highly interconnected GCs serving as network “hubs,” even while maintaining a constant number of connections throughout the network. Importantly, our in silico implementation of hubs closely resembles the presence of GCs with hilar basal dendrites in the biological circuit (23). This correspondence, combined with the prediction of our model that effective hubs will have both enhanced incoming and outgoing connectivity, provides a mechanism for the contribution of GCs with hilar basal dendrites in promoting hyperexcitability after brain injury.

Results

We used a published, large-scale model of the rat dentate gyrus, complete with >50,000 detailed single-cell models of various cell types each constructed based on anatomical, cellular, and electrophysiological data derived from the literature [Fig. 1A and supporting information (SI) Text; detailed information on the single-cell models and synaptic connections can be found in refs. 11 and 21] to examine the role of the specific microcircuit connectivity of the dentate GC network in contributing to hyperexcitability after injury. We established a control network simulating a moderate injury that resulted in 50% hilar interneuron and mossy-cell loss and 50% of maximal mossy-fiber sprouting (Fig. 1B). In this network, GC-to-GC connections were made randomly (Fig. S1), constrained only by the extent of their axonal arbors (see SI Text and ref. 11). We then constructed networks with varied GC microcircuit topologies (i.e., we reconnected the sprouted mossy fibers in biologically plausible, nonrandom patterns; see SI Text and Fig. S1) to assess the role of nonrandom connectivity features in altering network function and specifically augmenting hyperexcitability in a seizure-susceptible circuit. Note that although numerous cell types were represented in the network, only the injury-induced recurrent circuitry between granule cells was altered. Also, critically, in all networks the total number of connections remained the same as in the control. In summary, the general strategy was to take a seizure-prone (i.e., hyperexcitable) network containing sprouted GC-to-GC connections (this is the 50% Injured, Control network in Fig. 1B) and reconnect only the GC-to-GC synapses in various ways, without altering the total number of GC-to-GC connections in the network, to determine the effects of biologically relevant GC-to-GC topologies on network hyperexcitability. All networks contain GABAergic inhibition, and the “control” network used in this work is equivalent to the hyperexcitable, “50% sclerotic” network described and extensively tested in ref. 11.

Fig. 1.
Control network schematic and simulation results. (A) Schematic of the dentate gyrus model showing the four cell types implemented, the layers in which they reside, and their cell type-specific connectivity. (Left to Right) Excitatory granule cells (red), ...

Control Network Displays Limited Hyperexcitability.

In response to a simulated perforant path input to 5,000 GCs (10%), 50 basket cells (10%), and 10 mossy cells (1.3%) (referred to as “10% stimulation”), the control network (which, as described above, includes a simulated moderate injury resulting in cell loss and mossy-fiber sprouting) exhibited limited hyperexcitability (Fig. 1C), in agreement with previous findings (11, 21). Activity spread to the entire network by 83.67 ± 1.07 ms, and GC firing 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 lamella (one lamella contains 10% of the GCs in the network; see SI Text) fired an action potential (data not shown). In response to simulated perforant path input to 1% of GCs, 1% of basket cells, and one mossy cell (“1% stimulation”), few action potentials were fired beyond the initial stimulus (Fig. 1D).

Hebbian-Like Connectivity Has No Effect on Hyperexcitability.

We first theorized that if cells received a number of common inputs, they would be likely to fire similarly and form small networks that could efficiently promote hyperexcitability. We therefore established a network with “Hebbian-like” connectivity in which the probability of a connection between two neurons increased proportionally to the number of shared presynaptic neurons (Fig. 2A; see SI Text). In response to 10% stimulation, duration and 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).

Fig. 2.
Hebbian-like and feedback loop motif simulations. (A) Schematic of the Hebbian-like connectivity structure. The connection probability of any two neurons in the network (e.g., neurons 2 and 3, white) increased proportionally to the number of presynaptic ...
Fig. 4.
Quantification of network activity and hub characteristics. (A–C) Latency to full-network activation (A), duration of granule cell firing (B), and mean number of spikes per granule cell (C) for the five major structural connectivity variations ...

Despite the similarities between the Hebbian-like network and the control in the 10% stimulation case, it was possible that the microcircuit changes altered the stimulation threshold required for network activation. However, the 1% stimulus resulted in activity that was nearly identical to the control (Fig. 2C, compare with Fig. 1D).

Taken together, these results suggest that our Hebbian-like connectivity pattern neither promotes nor prevents hyperexcitability in the dentate gyrus, and it does not alter the dentate hyperexcitability threshold.

Small-Network Motif Overrepresentation Also Has No Significant Effect on Hyperexcitability.

Next, we assessed the role of various three-neuron small network motifs in promoting hyperexcitability in the model dentate by creating networks in which we manually increased the number of a given motif (Fig. 2D) present in the GC microcircuit without altering the total number of connections in the network (see SI Text). Fig. 2E shows the results from a representative network that has an abundance of motif number 8 [Fig. 2D; the feedback loop, which is one of the most structurally and dynamically unstable motifs (17), and was thus presumed to be likely to promote hyperexcitability]. The 10% stimulus (Fig. 2E, compare with Fig. 1C) resulted in no significant difference in excitability compared with control (see Fig. 4 A–C; P = 0.018 for duration; P = 0.022 for latency; and P = 0.018 for mean spikes per GC; see Methods for significance level explanation). Of the networks with overrepresented motifs (including motifs with IDs 6–11, and 13; see Fig. 2D), this network was the only one that displayed a strong trend toward hyperexcitability (data not shown).

The 1% stimulation paradigm confirmed the lack of a significant effect of overrepresenting various motifs. For all networks with overrepresented motifs, the results mimicked the control and Hebbian-like networks, with no activity propagation and most GCs firing no spikes (data shown only for motif 8; Fig. 2F, compare with Fig. 1D).

The results above suggest that the functional properties of the dentate gyrus are robust when faced with a number of major alterations to the GC microcircuitry. However, for the topological changes described thus far, each GC maintained a relatively constant degree of connectivity, ensuring that the number of small motifs or circuits in which each cell participated was nearly identical. In the biological dentate, this is not the case, however, because some granule cells participate in many more connections than average (see Discussion). We therefore sought to discover how nonrandom changes in the distribution of the number of connections across GCs could affect network excitability.

Scale-Free Topology Greatly Enhances Hyperexcitability.

To address the question of whether the distribution of connection numbers 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 distribution of connections among each of the nodes in the network (GCs in this case) follows a power law (Fig. 3A and SI Text). Networks with such a distribution are prevalent in both biological and nonbiological systems (see Discussion), and they are known to allow for efficient information transfer and prevent signal jamming (18). The scale-free network contained a small number of neurons with a very large number of connections (Fig. 3A; 5% of neurons participated in >175 connections), whereas most neurons had relatively few connections (87% of neurons participated in between 25 and 100 connections, with fewer connections being more prevalent; the average control GC participated in 68 connections, 34 incoming and 34 outgoing). The probability of a neuron participating in a given number of connections decayed as a power law with an exponent of 2.6 (Fig. 3A), in agreement with many other scale-free networks (24).

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 activity in the scale-free network in response to 10% and 1% stimulation, respectively. (D) Schematic of a ...

The 10% stimulation paradigm revealed that the scale-free network was much more excitable than the control (Fig. 3B, compare with Fig. 1C). Activity propagation throughout the network was faster (latency to full-network activation was 65.87 ± 1.01 ms) and sustained for nearly twice the length of activity in the control (duration of GC discharge was 413.90 ± 24.84 ms). Although some isolated branches of activity persisted beyond the end point of the simulations (Fig. 3B), longer simulations indicated that this activity terminated soon after (data not shown). The mean number of spikes fired per GC was also significantly increased (22.02 ± 0.69; P < 0.0001 for latency, duration, and GC firing; Fig. 4 A–C).

Analysis of the threshold condition also demonstrated marked differences from the control network. Most impressively, the threshold for network activation was lowered such that the 1% stimulation yielded full recruitment of the network (Fig. 3C). All measures of network activity were similar to those in the 10% stimulation case.

These results indicate that despite the robustness of the functional properties of the model dentate to the inclusion of a number of nonrandom features in the GC microcircuit, some network topologies result in markedly altered functional responses. In this case, a scale-free topology greatly enhanced the hyperexcitability of the dentate gyrus. However, it remained unclear exactly which features of this topology were responsible for the enhanced activity in the network. Is a power law connectivity distribution required for increased hyperexcitability, or is it sufficient to include the most highly interconnected neurons in the network but maintain randomly distributed connectivity throughout the remainder of the network?

Presence of Hubs, Even in the Absence of Power Law Distribution, Increases Hyperexcitability.

To address the question posed above, we studied networks in which 5% of the GCs were vastly more interconnected than the average GC (these highly interconnected cells can be thought of as hubs), but the remaining GC connectivity did not follow a power law. In the scale-free network, the 5% of GCs with the most connections all participated in at least 175 connections. We therefore created seven networks including hubs that had increasing numbers of added connections (between 30 and 210 connections, in addition to the standard number of random connections) before normalizing the total number of connections to the control value (see SI Text). All other GCs were connected randomly, as in the control. A schematic diagram of a network with a small number of hubs is shown in Fig. 3D. The hub cells (gray diamonds) participate in many more connections than the average GCs (black circles).

The results of the 10% stimulation paradigm show that as the number of connections per hub increased, so did the hyperexcitability of the network, in a linearly correlated fashion (squares in Fig. 4D; solid line r2 = 0.9028). In the network with 210 connections (Fig. 3E), activity increased significantly compared with control (Fig. 4 A–C; P < 0.002 for all three measures), with a 32% increase in the number of spikes fired per GC. Representative traces from both a nonhub and a hub GC are shown in Fig. 3E, Right.

The 1% stimulation provided further evidence that hubs are sufficient to enhance hyperexcitability in the model dentate gyrus in the absence of an accompanying scale-free distribution. The networks with 210, 180, 150, and 120 additional connections all demonstrated a reduced threshold for network activation compared with control (data not shown, except for 210-connection hub network in Fig. 3F). However, networks with 90 or fewer additional connections per hub did not display self-sustained, recurrent excitation in response to the 1% stimulus (data not shown).

These data indicate that the presence of hubs in the GC network of the dentate gyrus is sufficient to enhance hyperexcitability and lower the threshold required for a self-sustained, propagating response to stimulation. This finding is true in the absence of an accompanying scale-free distribution of the remaining connections in the network, although the presence of a scale-free distribution augments the effects seen here. Relatively few hubs are needed (5% was sufficient), but they need approximately four to seven times as many connections as the average GC. We next asked whether incoming or outgoing connections of the hub were more instrumental in contributing to hyperexcitability.

Directionality of Hub Connections and Hub Connection Strengths.

Our results demonstrate that the presence of hubs in the GC microcircuitry can greatly augment hyperexcitability. However, the hubs we incorporated into the network included an increased number of both incoming and outgoing connections. To determine whether directionality of connectivity was important in promoting hyperexcitability, we created networks that included hubs with either solely increased incoming or outgoing connections. The results of these simulations indicate that only a combination of enhanced incoming and outgoing connectivity was correlated with increased network activity (Fig. 4D: diamonds, incoming, negatively correlated with activity, r2 = 0.9945; triangles, outgoing, r2 = 0.0124; squares, incoming + outgoing, positively correlated with activity, r2 = 0.9028; all bottom axis). We further show that this enhanced connectivity does not require increased numbers of physical connections on hubs but can also arise from increased connection strengths because networks containing 5% of GCs with enhanced synaptic weights (but control numbers of connections) were also correlated with increased activity (Fig. 4D: circles, positive correlation, r2 = 0.8802; top axis). This correlation persisted compared with a control network that had a randomly chosen 5% of all synaptic weights increased to compensate for the increase in excitatory conductance in the experimental networks (data not shown).

Discussion

This work has two primary findings. First, we show in a large-scale, realistic neural network model that specific microcircuit connectivity can have important and significant effects on epileptiform network activity. Second, we show that in the injured dentate gyrus, the presence of a small population of highly interconnected GC hubs strongly contributes to hyperexcitability. The latter finding may also provide interesting insights concerning the possible role of GCs with hilar basal dendrites in the epileptic dentate gyrus, as we discuss below.

Recent studies have shown that connections within a variety of neural networks exhibit a large number of nonrandom properties (24, 8, 15, 16, 25). One common theme in these nonrandom connectivity patterns is an overabundance of certain small-network motifs. For this reason, it is quite surprising that when we overrepresented a wide range of motifs, there was no significant effect on network activity. It is possible that the motifs are simply so sparse in the network that even massive overrepresentation changes network topology only slightly and thus has little effect on network activity. However, by adding 100,000 of each motif (each containing at least three connections) to the network, we ensured that a vast number of connections (of the total 1.7 million) were participating in the desired motif, thereby substantially increasing the number of interacting motifs. Even with this alteration in topology, however, the distribution of connections across neurons remained relatively constant, and each GC was therefore limited in the amount of recurrent excitation it could provide. In the biological dentate of epileptic animals, it is probable that specific combinations of motifs form larger recurrent networks and are more important for overall network function than the ubiquitous presence of a single particular motif. These combinations would be most likely to form and interact if the distribution of connections in the network is uneven and results in the presence of highly connected neurons, each participating in many more small-network motifs than the average cell.

Although topologies incorporating uneven distributions of connectivity such as scale-free networks or hub-containing networks seem highly sophisticated and perhaps unlikely to form in biological systems, there is indeed substantial precedent for these types of networks both in biology and elsewhere. A number of nonbiological networks that incorporate topologies similar to our scale-free or hubs-only network implementations include social networks, the internet, and the electric grid (13, 2629). Included in biological networks that follow a power-law distribution are the neural network of C. elegans and various metabolic and gene regulatory networks such as metabolic flow in yeast and yeast transcription regulatory networks (2932). Additionally, it was recently demonstrated that a culture of cortical neurons on a multielectrode array developed such that their firing patterns were consistent with a scale-free topology of connectivity (33). Finally, connection strengths between layer 5 pyramidal neurons in rat visual cortex have been shown to follow a log normal distribution with a heavy tail, similar to a power-law distribution (8). Thus, it is very possible that these network topologies could form and significantly alter activity in complex neuronal networks such as the dentate gyrus.

Given that networks with highly interconnected hubs are relatively common in complex systems, then perhaps the biggest question that is left unanswered by this work is related to the very prediction that our model provides. That is, are hubs actually formed when mossy-fiber sprouting occurs in the pathological dentate gyrus? Although computational modeling can never answer this question definitively, there is a substantial amount of biological evidence supporting the presence of hubs.

Virtually all GCs in the healthy dentate gyrus are typical, with only apical dendrites that extend into the molecular layer and terminate usually in its distal two-thirds (34). After injury, however, a subset of GCs can be found that not only have apical dendrites but a long basal dendrite as well (23). This dendrite does not extend into the molecular layer but rather toward the hilus, and it synapses with mossy fibers, thereby creating excitatory circuits similar to those formed by apical dendrites (35). The percentage of GCs that have these hilar basal dendrites is relatively small, with estimates ranging from 5 to 20% of GCs (23, 3537). Interestingly, this estimate is sufficiently large, even at its minimum, to provide enough hubs to promote hyperexcitability according to the predictions of our model.

Clearly, in order for GCs with basal dendrites to act as hubs, they must participate in an extremely large number of connections with other GCs in the circuit. Indeed, recent evidence suggests that basal dendrites receive an extraordinary number of excitatory synapses. GC basal dendrites comprise up to 15% of the total dendritic length of a GC, and synapsing on each dendrite are ≈140 inhibitory and 2,500 excitatory synapses (38). In the biological dentate from epileptic animals, EM analyses revealed an average of 275 new mossy-fiber contacts per GC at maximal levels of sprouting (22), only one-ninth of the number of excitatory connections onto basal dendrites. Even if only half of the basal dendrite excitatory connections are mossy-fiber contacts, the estimated number of connections is in line with the number we used in simulating the model hub cells.

Until recently, the main problem with the biological data in support of hubs in the dentate gyrus was that the available data regarding GCs with basal dendrites focused exclusively on the incoming connections to these cells. There were no data suggesting whether GCs with basal dendrites form either more numerous or stronger outgoing connections, thus leaving the prediction of our model largely unconfirmed. However, an elegant study of poststatus epilepticus GCs recently revealed a previously unseen increase in axonal protrusions (often within the GC layer) among newborn cells that likely corresponds to an increased number of outgoing connections onto other GCs (37). Additionally, >40% of post-SE newborn GCs retain a basal dendrite in addition to nearly 10% of mature post-SE GCs (37), thereby resulting in the probable existence of GCs with both increased axonal protrusions and a basal dendrite. Although more experimental work is necessary to characterize fully the outgoing connectivity of GCs with basal dendrites, our results combined with the described experimental work strongly support the likelihood that neuronal hubs play a hitherto unrecognized, major role in promoting hyperexcitability and seizures.

Methods

We used a published large-scale computational model of the dentate gyrus to study the role of the fine-microcircuit connectivity of the dentate gyrus recurrent GC network in contributing to hyperexcitability (11). Because neither the healthy dentate in vivo nor the model of the healthy dentate contain GC-to-GC connections (Fig. S1), we studied the dentate gyrus after a simulated injury resulting in 50% loss of hilar interneurons and mossy cells and 50% of maximal mossy-fiber sprouting (this network is referred to as the “control network”; Fig. 1 B–D, Fig. S1). This degree of mossy-fiber sprouting corresponds to ≈34 new connections per GC in the computational model. The precise microcircuit connectivity that resulted from these newly formed connections was varied in four major, biologically plausible ways to yield new networks with: (i) Hebbian-like connectivity; (ii) overrepresentation of small-network motifs; (iii) scale-free topology; and (iv) highly interconnected GC hubs without a scale-free topology.

Control Network.

The cells were linked according to cell type-specific connection probabilities derived from the average number of projections from the pre- to the postsynaptic neuronal class in the literature (11). Within these cell type-specific constraints and the axonal arbors of the cell (SI Text), connections were made probabilistically on a neuron-to-neuron basis with a uniform synapse density along the axon (21), treating multiple synapses between two cells as a single link and excluding autapses. Mossy-fiber sprouting and hilar cell loss were implemented at 50% of maximum.

Experimental Networks with Altered Connectivity.

To construct each of the experimental networks, we made specific modifications to the GC-to-GC connections in the network. All other connections were established as described for the control network above. Once all connections were established, the number of GC-to-GC connections was reduced to the total number present in the control network by randomly eliminating connections. In this way, the total excitatory drive in all of the networks was kept constant. For details on how each particular network was constructed, see SI Text.

Stimulation and Assessment of the Networks.

Activity in the networks was evoked through two separate simulated perforant path stimulation paradigms. The 10% stimulation paradigm consisted of a single perforant path synaptic input to 5,000 GCs (10%), 10 mossy cells (1.3%), and 50 basket cells (10%) situated in the middle lamella of the model network at 5 ms after the start of the simulation, as in ref. 11. We also used a threshold stimulation paradigm (referred to as 1% stimulation) to determine whether topological or functional alterations had changed the threshold for recruitment of network activity. This paradigm consisted of a simulated perforant path input to 500 GCs (1%), 1 mossy cell (0.13%), and 5 basket cells (1%). The threshold was established by stepping back from the 10% stimulation in 1% steps until full-network activity no longer resulted in the control network. Simulations lasted for 500 ms (≈12–18 h per simulation in real time), after which network activity was saved and analyzed. Values reported ±SD values were for simulations that were run three times with different random seeds. All other simulations were run once.

Analysis and quantification of network activity involved three separate measures: (i) latency to full-network activation, defined as the time at which the most distant GC from the stimulation site fired its first action potential minus the time of the first GC action potential; (ii) duration of network activity, defined as the average time of the final action potential for each GC minus the time of the first action potential in the network; and (iii) mean number of spikes fired per GC. Although the mechanisms of activity termination were not explicitly investigated, they are likely to include synaptic inhibition from basket and HIPP cells, activation of calcium and voltage-dependent potassium conductances, and the intrinsic properties of the granule cells themselves that have a “default” silent state (21). Importantly, these mechanisms do not differ between the control and experimental networks. Statistical significance was assessed by using unpaired, two-tailed t tests. Because of testing of 12 independent networks, statistical significance was set at P < 0.004. Data analysis and plotting were done by using Matlab 6.5.1 (The MathWorks, Inc.) and SigmaPlot 8.0 (SPSS, Inc.). Motif detection was done by using FANMOD for Linux (39). All simulations were performed in the NEURON 5.6 simulation environment (40) by using custom hoc and C code and bash scripts on a Tyan Thunder 2.0 GHz dual Opteron server (32 GB RAM).

Supplementary Material

Supporting Information:

Acknowledgments.

This work was funded by National Institutes of Health Grant NS35915 (to I.S.) and the University of California, Irvine, Medical Scientist Training Program (to R.J.M.).

Footnotes

The authors declare no conflict of interest.

See Commentary on page 5953.

This article contains supporting information online at www.pnas.org/cgi/content/full/0801372105/DCSupplemental.

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