Topological Determinants of Epileptogenesis in Large-Scale Structural and Functional Models of the Dentate Gyrus Derived From Experimental Data

Dyhrfjeld-Johnsen, Jonas; Santhakumar, Vijayalakshmi; Morgan, Robert J.; Huerta, Ramón; Tsimring, Lev S.; Soltész, Iván

doi:10.1152/jn.00950.2006

Cited by 210 publications

(175 citation statements)

References 107 publications

(200 reference statements)

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“…Nonrandom connectivity features have been discovered in mammalian cortices as well (6)(7)(8)(9)(10). Such networks exhibit high degrees of local clustering with short path lengths [small-world topology (11)(12)(13)], 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).…”

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confidence: 99%

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

Morgan

Soltész

2008

Proc. Natl. Acad. Sci. U.S.A.

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319

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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.basal dendrite ͉ computational model ͉ epilepsy ͉ granule cell ͉ scale-free N umerous 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 (2-4). 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 (6-10). Such networks exhibit high degrees of local clustering with short path lengths [small-world topology (11-13)], 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,(17)(18)(19), the contribution of nonrandom microcircuit connectivity to the functional properties of large, complex brain regions, particularly in epilepsy, remains poorly understood. The...

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confidence: 99%

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

Morgan

Soltész

2008

Proc. Natl. Acad. Sci. U.S.A.

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319

278

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“…4,22,23 In Ref. 22, the connection between network connectivity and epilepsy in the hippocampus was investigated by considering small-world networks of three different types of neurons: noisy and leaky integrate-and-fire neurons, stochastic Hodgkin-Huxley cells, and Poisson spike-train cells.…”

Section: Discussionmentioning

confidence: 99%

“…4, a 1:20 functional model of the rat dentate gyrus was constructed to investigate the functional consequences of two types of changes in network architecture that take place concurrently during epileptogenesis: loss of hillar mossy cells and sprouting of granular cell axons. The removal of mossy cells resulted in a massive reduction in the total number of connections, but this effect was to some extent compensated by an increase in local connectivity due to spatially restricted sprouting of granular cell axons.…”

Section: Discussionmentioning

confidence: 99%

“…Small-world properties of neuronal networks have been found in a comprehensive morphological characterization of in vitro twodimensional networks, 3 and in a 1:1 network model of the rat dentate gyrus that incorporates known data about cell types, cell-specific connectivity, and axonal branch length. 4 The dynamics of elements coupled through the connectivity of a complex network has been studied in detail for the case of oscillatory elements. The emphasis has been in determining the role of network topology in the ability to achieve synchronization in a system of coupled oscillators.…”

Section: Introductionmentioning

confidence: 99%

“…V we discuss our results in light of other work on neural networks with smallworld topology. 4,22,23 …”

Section: Introductionmentioning

confidence: 99%

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Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons

Riecke

Roxin

Madruga

et al. 2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or "shortcuts", and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value. The state of persistent activity below this transition consists of multiple stable periodic attractors, whose number increases at least as fast as the number of neurons in the network. At large shortcut density and for long enough delays the network dynamics exhibit exceedingly long chaotic transients, whose failure times follow a stretched exponential distribution. We show that this functional form arises for the ensemble-averaged activity if the failure time for each individual network realization is exponentially distributed. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2743611͔Many systems in nature can be described as a network of interconnected nodes. Networks in a growing list of systems, from social and ecological webs to the neural anatomy of simple organisms, have been shown to exhibit complex topological features that distinguish them from both ordered lattices and purely random networks. Beyond the investigation of the structural and geometrical properties of such networks, a new class of question arises when dynamical degrees of freedom are placed at their nodes. As the investigation of such dynamical complex networks proceeds, it has become increasingly clear that the network architecture can significantly influence the dynamics of the system. An understanding of emergent dynamics on complex networks requires investigating the interplay between the intrinsic dynamics of the node elements and the connectivity of the network in which they are embedded. In order to address some of these questions in a specific scenario of relevance to the dynamical states of neural ensembles, we study here the collective behavior of excitable model neurons in a network with small-world topology. The small-world network has local lattice order, but includes a number of randomly placed connections that may provide connectivity shortcuts. This topology bears a schematic resemblance to the connectivity of the cerebral cortex, in which neurons are most strongly coupled to nearby cells within 50− 100 m, but also make projections to cells millimeters away. We find that the dynamics of this small-world network of excitable neurons depend mostly on both the density of shortcuts and the delay associated with neuronal projections. In the regime of low shortcut density, the system exhibits persistent activity in the form of propagating waves, which annihilate upon collision and are spawned anew via the reinjection of activity through shortcut connections. As the density of shortcuts reaches a critical value, the system undergoes a transition to failure. The criti...

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Prediction by Modeling That Epilepsy May Be Caused by Very Small Functional Changes in Ion Channels

Thomas¹,

Reid²,

Berkovic³

et al. 2009

Arch Neurol

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Topological Determinants of Epileptogenesis in Large-Scale Structural and Functional Models of the Dentate Gyrus Derived From Experimental Data

Cited by 210 publications

References 107 publications

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

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

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons

Prediction by Modeling That Epilepsy May Be Caused by Very Small Functional Changes in Ion Channels

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