Nonrandom connectivity of the epileptic dentate
gyrus predicts a major role for neuronal hubs
in seizures
various ways, without altering the total number of GC-to-GC
                                             C                ...
  A                          Hebbian-like Network Schematic
C140                                                         is shown in Fig. 3D. The hub cells (gray diamonds) participat...
concerning the possible role of GCs with hilar basal dendrites in        at its minimum, to provide enough ...
Stimulation and Assessment of the Networks. Activity in the networks was                     minus the time of the first GC...
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Nonrandom connectivity of the epileptic dentate gyrus ...

  1. 1. SEE COMMENTARY Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures Robert J. Morgan* and Ivan Soltesz Department of Anatomy and Neurobiology, University of California, 193 Irvine Hall, Irvine, CA 92697 Communicated by Eve E. Marder, Brandeis University, Waltham, MA, February 11, 2008 (received for review November 19, 2007) Many complex neuronal circuits have been shown to display logical mechanisms that could allow for the formation of non- nonrandom features in their connectivity. However, the functional random circuitries that promote seizures. impact of nonrandom network topologies in neurological diseases After insults such as head trauma, ischemia, and repetitive is not well understood. The dentate gyrus is an excellent circuit in seizures, which often lead to temporal lobe epilepsy, the dentate which to study such functional implications because proepileptic gyrus undergoes dramatic structural rearrangement. Structural insults cause its structure to undergo a number of specific changes changes include loss of hilar interneurons and mossy cells (11, 20, in both humans and animals, including the formation of previously 21) and the formation of recurrent collaterals between granule nonexistent granule cell-to-granule cell recurrent excitatory con- cells (GCs) via mossy-fiber (GC axon) sprouting (11, 21, 22). nections. Here, we use a large-scale, biophysically realistic model of Importantly, in the healthy dentate gyrus, GCs do not synapse the epileptic rat dentate gyrus to reconnect the aberrant recurrent on each other. Therefore, the recurrent excitatory GC network granule cell network in four biologically plausible ways to deter- is a unique feature of the postinsult, epileptic dentate gyrus. mine how nonrandom connectivity promotes hyperexcitability Recently, it has been shown that the postinsult structural alter- after injury. We find that network activity of the dentate gyrus is ations can promote hyperexcitability in the dentate even in the absence of any nonstructural alterations such as intrinsic cellular quite robust in the face of many major alterations in granule and synaptic modifications (11). This increased hyperexcitability cell-to-granule cell connectivity. However, the incorporation of a occurs despite a massive decrease in the total number of small number of highly interconnected granule cell hubs greatly excitatory connections in the dentate network (caused by loss of increases network activity, resulting in a hyperexcitable, poten- the extensive connectivity of mossy cells, many of which die after tially seizure-prone circuit. Our findings demonstrate the func- injury). Thus, the newly formed connections between GCs must tional relevance of nonrandom microcircuits in epileptic brain be instrumental in creating the hyperexcitable dentate network. networks, and they provide a mechanism that could explain the However, GC-to-GC connectivity is quite sparse; indeed, the role of granule cells with hilar basal dendrites in contributing to probability of two granule cells connecting, even at maximal hyperexcitability in the pathological dentate gyrus. levels of sprouting, is only 0.55%, and the probability of random formation of a three-neuron ‘‘recurrent’’ circuit of the basal dendrite computational model epilepsy granule cell scale-free form A 3 B 3 C 3 A is miniscule at 4.16 10 6%. Therefore, the specific patterns of GC-to-GC connections that define the NEUROSCIENCE N umerous studies have indicated that connectivity in a wide variety of neural systems exhibits highly nonrandom char- acteristics. For example, in the nervous system of the Caeno- microcircuit structure are likely to play a critical role in affecting network excitability. Here, we examine the role of several biologically plausible GC rhabditis elegans worm, of which the complete structure has been microcircuits on dentate excitability after insult. First, we report described (1), it was shown that a number of local connectivity that the dentate gyrus circuitry is remarkably robust when patterns (network motifs) are over- or underrepresented com- confronted with a number of GC-to-GC connectivity patterns pared with what would be present in a random network (2–4). that would be expected to promote hyperexcitability. We then Furthermore, computational analysis has indicated that the show that this robustness can be overcome by the inclusion of a dynamic properties of these network motifs could contribute to small percentage of highly interconnected GCs serving as net- their relative abundance, closely tying functional properties to work ‘‘hubs,’’ even while maintaining a constant number of the structural network (5). Nonrandom connectivity features connections throughout the network. Importantly, our in silico have been discovered in mammalian cortices as well (6–10). Such implementation of hubs closely resembles the presence of GCs with hilar basal dendrites in the biological circuit (23). This networks exhibit high degrees of local clustering with short path correspondence, combined with the prediction of our model that lengths [small-world topology (11–13)], power law distributions effective hubs will have both enhanced incoming and outgoing of connectivity [scale-free topology (11, 13, 14)], and nonrandom connectivity, provides a mechanism for the contribution of GCs distributions of connection strengths (8). Additionally, it has with hilar basal dendrites in promoting hyperexcitability after been shown that connection probabilities demonstrate fine-scale brain injury. 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 net- Author contributions: R.J.M. and I.S. designed research; R.J.M. performed research; R.J.M. works have been of great interest recently, and the role of some analyzed data; and R.J.M. and I.S. wrote the paper. of these features in network dynamics and information process- The authors declare no conflict of interest. ing has been investigated (5, 17–19), the contribution of non- Freely available online through the PNAS open access option. random microcircuit connectivity to the functional properties of See Commentary on page 5953. large, complex brain regions, particularly in epilepsy, remains *To whom correspondence should be addressed. E-mail: poorly understood. The mammalian dentate gyrus provides an This article contains supporting information online at ideal circuit for investigating this question in a large-scale 0801372105/DCSupplemental. biophysically realistic model and to examine the potential bio- © 2008 by The National Academy of Sciences of the USA cgi doi 10.1073 pnas.0801372105 PNAS April 22, 2008 vol. 105 no. 16 6179 – 6184
  2. 2. 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- 50000 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- Molecular layer trol’’ network used in this work is equivalent to the hyperexcitable, ‘‘50% sclerotic’’ network described and exten- Granule 25000 cell layer sively tested in ref. 11. Hilus Control Network Displays Limited Hyperexcitability. In response to a simulated perforant path input to 5,000 GCs (10%), 50 basket 0 0 100 200 300 400 500 cells (10%), and 10 mossy cells (1.3%) (referred to as ‘‘10% Time (ms) 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 (Control) Network mossy-fiber sprouting) exhibited limited hyperexcitability (Fig. 50000 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 25000 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 0 100 200 300 400 500 Time (ms) 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 cgi doi 10.1073 pnas.0801372105 Morgan and Soltesz
  3. 3. SEE COMMENTARY 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 1 2 3 4 10-1 5 6 7 8 10-2 -3 10 9 10 11 12 -4 10 2 3 -5 13 10 2 3 10 10 10 Number of Connections (k) B 10% Stimulation of Hebbian-like Network E 10% Stimulation of Motif Network B 50000 Stimulation of Scale-free Network E 50000 10% Stimulation of Hub Network 10% 50000 50000 Granule Cell Number Granule Cell Number Granule Cell Number Granule Cell Number Non-hub 25000 25000 25000 25000 Hub 0 0 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 50000 Granule Cell Number Hebbian-like Network Granule Cell Number 50000 50000 Granule Cell Number Granule Cell Number 25000 25000 25000 25000 0 0 0 100 200 300 400 500 0 100 200 300 400 500 Time (ms) Time (ms) 0 0 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 NEUROSCIENCE 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 respectively. 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
  4. 4. 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). 400 Duration (ms) Latency (ms) * 100 * * 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 100 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. 10 12 The networks with 210, 180, 150, and 120 additional connections 5 10 Incoming & Outgoing Incoming Only Outgoing Only all demonstrated a reduced threshold for network activation 0 8 Connection Strengths 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 cgi doi 10.1073 pnas.0801372105 Morgan and Soltesz
  5. 5. SEE COMMENTARY 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 NEUROSCIENCE 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
  6. 6. 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. 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