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

Role of sensory input distribution and intrinsic connectivity in lateral amygdala during auditory fear conditioning: a computational study

We propose a novel reduced-order neuronal network modeling framework that includes an enhanced firing rate model and a corresponding synaptic calcium-based synaptic learning rule. Specifically, we propose enhancements to the Wilson-Cowan firing-rate neuron model that permit full spike-frequency adaptation seen in biological lateral amygdala (LA) neurons, while being sufficiently general to accommodate other spike-frequency patterns. We also report a technique to incorporate calcium-dependent plasticity in the synapses of the network using a regression scheme to link firing rate to postsynaptic calcium. Together, the single-cell model and the synaptic learning scheme constitute a general framework to develop computationally efficient neuronal networks that employ biologically realistic synaptic learning. The reduced-order modeling framework was validated using a previously reported biophysical conductance-based neuronal network model of a rodent LA that modeled features of Pavlovian conditioning and extinction of auditory fear (Li et al., 2009). The framework was then used to develop a larger LA network model to investigate the roles of tone and shock distributions and of intrinsic connectivity in auditory fear learning. The model suggested combinations of tone and shock densities that would provide experimental estimates of tone responsive and conditioned cell proportions. Furthermore, it provided several insights including how intrinsic connectivity might help distribute sensory inputs to produce conditioned responses in cells that do not directly receive both tone and shock inputs, and how a balance between potentiation of excitation and inhibition prevents stimulus generalization during fear learning.

Hub GABA neurons mediate gamma-frequency oscillations at ictal-like event onset in the immature hippocampus

Gamma-frequency oscillations (GFOs, >40 Hz) are a general network signature at seizure onset at all stages of development, with possible deleterious consequences in the immature brain. At early developmental stages, the simultaneous occurrence of GFOs in different brain regions suggests the existence of a long-ranging synchronizing mechanism at seizure onset. Here, we show that hippocamposeptal (HS) neurons, which are GABA long-range projection neurons, are mandatory to drive the firing of hippocampal interneurons in a high-frequency regime at the onset of epileptiform discharges in the intact, immature septohippocampal formation. The synchronized firing of interneurons in turn produces GFOs, which are abolished after the elimination of a small number of HS neurons. Because they provide the necessary fast conduit for pacing large neuronal populations and display intra- and extrahippocampal long-range projections, HS neurons appear to belong to the class of hub cells that play a crucial role in the synchronization of developing networks.

Neurogliaform and Ivy Cells: A Major Family of nNOS Expressing GABAergic Neurons

Neurogliaform and Ivy cells are members of an abundant family of neuronal nitric oxide synthase (nNOS) expressing GABAergic interneurons found in diverse brain regions. These cells have a defining dense local axonal plexus, and display unique synaptic properties including a biphasic postsynaptic response with both a slow GABA(A) component and a GABA(B) component following even a single action potential. The type of transmission displayed by these cells has been termed "volume transmission," distinct from both tonic and classical synaptic transmission. Electrical connections are also notable in that, unlike other GABAergic cell types, neurogliaform family cells will form gap junctions not only with other neurogliaform cells, but also with non-neurogliaform family GABAergic cells. In this review, we focus on neurogliaform and Ivy cells throughout the hippocampal formation, where recent studies highlight their role in feedforward inhibition, uncover their ability to display a phenomenon called persistent firing, and reveal their modulation by opioids. The unique properties of this family of cells, their abundance, rich connectivity, and modulation by clinically relevant drugs make them an attractive target for future studies in vivo during different behavioral and pharmacological conditions.

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.

Conedy: a scientific tool to investigate complex network dynamics

We present Conedy, a performant scientific tool to numerically investigate dynamics on complex networks. Conedy allows to create networks and provides automatic code generation and compilation to ensure performant treatment of arbitrary node dynamics. Conedy can be interfaced via an internal script interpreter or via a Python module.

Epilepsy as a disorder of cortical network organization

The brain is naturally considered as a network of interacting elements which, when functioning properly, produces an enormous range of dynamic, adaptable behavior. However, when elements of this network fail, pathological changes ensue, including epilepsy, one of the most common brain disorders. This review examines some aspects of cortical network organization that distinguish epileptic cortex from normal brain as well as the dynamics of network activity before and during seizures, focusing primarily on focal seizures. The review is organized around four phases of the seizure: the interictal period, onset, propagation, and termination. For each phase, the authors discuss the most common rhythmic characteristics of macroscopic brain voltage activity and outline the observed functional network features. Although the characteristics of functional networks that support the epileptic seizure remain an area of active research, the prevailing trends point to a complex set of network dynamics between, before, and during seizures.

Epileptic seizures from abnormal networks: why some seizures defy predictability

Seizure prediction has proven to be difficult in clinically realistic environments. Is it possible that fluctuations in cortical firing could influence the onset of seizures in an ictal zone? To test this, we have now used neural network simulations in a computational model of cortex having a total of 65,536 neurons with intercellular wiring patterned after histological data. A spatially distributed Poisson driven background input representing the activity of neighboring cortex affected 1% of the neurons. Gamma distributions were fit to the interbursting phase intervals, a non-parametric test for randomness was applied, and a dynamical systems analysis was performed to search for period-1 orbits in the intervals. The non-parametric analysis suggests that intervals are being drawn at random from their underlying joint distribution and the dynamical systems analysis is consistent with a nondeterministic dynamical interpretation of the generation of bursting phases. These results imply that in a region of cortex with abnormal connectivity analogous to a seizure focus, it is possible to initiate seizure activity with fluctuations of input from the surrounding cortical regions. These findings suggest one possibility for ictal generation from abnormal focal epileptic networks. This mechanism additionally could help explain the difficulty in predicting partial seizures in some patients.

Morphologic integration of hilar ectopic granule cells into dentate gyrus circuitry in the pilocarpine model of temporal lobe epilepsy

After pilocarpine-induced status epilepticus, many granule cells born into the postseizure environment migrate aberrantly into the dentate hilus. Hilar ectopic granule cells (HEGCs) are hyperexcitable and may therefore increase circuit excitability. This study determined the distribution of their axons and dendrites. HEGCs and normotopic granule cells were filled with biocytin during whole-cell patch clamp recording in hippocampal slices from pilocarpine-treated rats. The apical dendrite of 86% of the biocytin-labeled HEGCs extended to the outer edge of the dentate molecular layer. The total length and branching of HEGC apical dendrites that penetrated the molecular layer were significantly reduced compared with apical dendrites of normotopic granule cells. HEGCs were much more likely to have a hilar basal dendrite than normotopic granule cells. They were about as likely as normotopic granule cells to project to CA3 pyramidal cells within the slice, but were much more likely to send at least one recurrent mossy fiber into the molecular layer. HEGCs with burst capability had less well-branched apical dendrites than nonbursting HEGCs, their dendrites were more likely to be confined to the hilus, and some exhibited dendritic features similar to those of immature granule cells. HEGCs thus have many paths along which to receive synchronized activity from normotopic granule cells and to transmit their own hyperactivity to both normotopic granule cells and CA3 pyramidal cells. They may therefore contribute to the highly interconnected granule cell hubs that have been proposed as crucial to development of a hyperexcitable, potentially seizure-prone circuit.

Exome sequencing of ion channel genes reveals complex profiles confounding personal risk assessment in epilepsy

Ion channel mutations are an important cause of rare Mendelian disorders affecting brain, heart, and other tissues. We performed parallel exome sequencing of 237 channel genes in a well-characterized human sample, comparing variant profiles of unaffected individuals to those with the most common neuronal excitability disorder, sporadic idiopathic epilepsy. Rare missense variation in known Mendelian disease genes is prevalent in both groups at similar complexity, revealing that even deleterious ion channel mutations confer uncertain risk to an individual depending on the other variants with which they are combined. Our findings indicate that variant discovery via large scale sequencing efforts is only a first step in illuminating the complex allelic architecture underlying personal disease risk. We propose that in silico modeling of channel variation in realistic cell and network models will be crucial to future strategies assessing mutation profile pathogenicity and drug response in individuals with a broad spectrum of excitability disorders.

Neurogliaform cells in the molecular layer of the dentate gyrus as feed-forward γ-aminobutyric acidergic modulators of entorhinal-hippocampal interplay

Feed-forward inhibition from molecular layer interneurons onto granule cells (GCs) in the dentate gyrus is thought to have major effects regulating entorhinal-hippocampal interactions, but the precise identity, properties, and functional connectivity of the GABAergic cells in the molecular layer are not well understood. We used single and paired intracellular patch clamp recordings from post-hoc-identified cells in acute rat hippocampal slices and identified a subpopulation of molecular layer interneurons that expressed immunocytochemical markers present in members of the neurogliaform cell (NGFC) class. Single NGFCs displayed small dendritic trees, and their characteristically dense axonal arborizations covered significant portions of the outer and middle one-thirds of the molecular layer, with frequent axonal projections across the fissure into the CA1 and subicular regions. Typical NGFCs exhibited a late firing pattern with a ramp in membrane potential prior to firing action potentials, and single spikes in NGFCs evoked biphasic, prolonged GABA(A) and GABA(B) postsynaptic responses in GCs. In addition to providing dendritic GABAergic inputs to GCs, NGFCs also formed chemical synapses and gap junctions with various molecular layer interneurons, including other NGFCs. NGFCs received low-frequency spontaneous synaptic events, and stimulation of perforant path fibers revealed direct, facilitating synaptic inputs from the entorhinal cortex. Taken together, these results indicate that NGFCs form an integral part of the local molecular layer microcircuitry generating feed-forward inhibition and provide a direct GABAergic pathway linking the dentate gyrus to the CA1 and subicular regions through the hippocampal fissure.

Topological basis of epileptogenesis in a model of severe cortical trauma

Epileptic activity often arises after a latent period following traumatic brain injury. Several factors contribute to the emergence of post-traumatic epilepsy, including disturbances to ionic homeostasis, pathological action of intrinsic and synaptic homeostatic plasticity, and remodeling of anatomical network synaptic connectivity. We simulated a large-scale, biophysically realistic computational model of cortical tissue to study the mechanisms underlying the genesis of post-traumatic paroxysmal epileptic-like activity in the deafferentation model of a severely traumatized cortical network. Post-traumatic generation of paroxysmal events did not require changes of the structural connectivity. Rather, network bursts were induced following the action of homeostatic synaptic plasticity, which selectively influenced functionally dominant groups of intact neurons with preserved inputs. This effect critically depended on the spatial density of intact neurons. Thus in the deafferentation model of post-traumatic epilepsy, a trauma-induced change in functional (rather than anatomical) connectivity might be sufficient for epileptogenesis.

Emergence of physiological oscillation frequencies in a computer model of neocortex

Coordination of neocortical oscillations has been hypothesized to underlie the "binding" essential to cognitive function. However, the mechanisms that generate neocortical oscillations in physiological frequency bands remain unknown. We hypothesized that interlaminar relations in neocortex would provide multiple intermediate loops that would play particular roles in generating oscillations, adding different dynamics to the network. We simulated networks from sensory neocortex using nine columns of event-driven rule-based neurons wired according to anatomical data and driven with random white-noise synaptic inputs. We tuned the network to achieve realistic cell firing rates and to avoid population spikes. A physiological frequency spectrum appeared as an emergent property, displaying dominant frequencies that were not present in the inputs or in the intrinsic or activated frequencies of any of the cell groups. We monitored spectral changes while using minimal dynamical perturbation as a methodology through gradual introduction of hubs into individual layers. We found that hubs in layer 2/3 excitatory cells had the greatest influence on overall network activity, suggesting that this subpopulation was a primary generator of theta/beta strength in the network. Similarly, layer 2/3 interneurons appeared largely responsible for gamma activation through preferential attenuation of the rest of the spectrum. The network showed evidence of frequency homeostasis: increased activation of supragranular layers increased firing rates in the network without altering the spectral profile, and alteration in synaptic delays did not significantly shift spectral peaks. Direct comparison of the power spectra with experimentally recorded local field potentials from prefrontal cortex of awake rat showed substantial similarities, including comparable patterns of cross-frequency coupling.

Interictal spikes precede ictal discharges in an organotypic hippocampal slice culture model of epileptogenesis

In organotypic hippocampal slice cultures, principal neurons form aberrant excitatory connections with other principal cells in response to slicing induced deafferentation, similar to mechanisms underlying epileptogenesis in posttraumatic epilepsy. To investigate the consequences of this synaptogenesis, the authors recorded field-potential activity from area CA3 during perfusion with the complete growth medium used during incubation. At 7 days in vitro, slice cultures only displayed multiunit activity. At 14 days in vitro, the majority displayed population bursts reminiscent of interictal-like spikes, but sustained synchronous activity was rare. Band-pass filtering of interictal discharges revealed fast ripple-like complexes, similar to in vivo recordings. Spontaneous ictal-like activity became progressively more prevalent with age: at 21 days in vitro, 50% of organotypic hippocampal slice cultures displayed long-lasting, ictal-like discharges that could be suppressed by phenytoin, whereas interictal activity was not suppressed. The fraction of cultures displaying ictal events continually increased with incubation time. Quantification of population spike activity throughout epileptogenesis using automatic detection and clustering algorithms confirmed the appearance of interictal-like activity before ictal-like discharges and also revealed high-frequency pathologic multiunit activity in slice cultures at 14 to 17 days in vitro. These experiments indicate that interictal-like spikes precede the appearance of ictal-like activity in a reduced in vitro preparation. Epileptiform activity in cultures resembled in vivo epilepsy, including sensitivity to anticonvulsants and steadily increasing seizure incidence over time, although seizure frequency and rate of epileptogenesis were higher in vitro. Organotypic hippocampal slice cultures comprise a useful model system for investigating mechanisms of epileptogenesis as well as developing antiepileptic and antiepileptogenic drugs.

Rapamycin suppresses mossy fiber sprouting but not seizure frequency in a mouse model of temporal lobe epilepsy

Temporal lobe epilepsy is prevalent and can be difficult to treat effectively. Granule cell axon (mossy fiber) sprouting is a common neuropathological finding in patients with mesial temporal lobe epilepsy, but its role in epileptogenesis is unclear and controversial. Focally infused or systemic rapamycin inhibits the mammalian target of rapamycin (mTOR) signaling pathway and suppresses mossy fiber sprouting in rats. We tested whether long-term systemic treatment with rapamycin, beginning 1 d after pilocarpine-induced status epilepticus in mice, would suppress mossy fiber sprouting and affect the development of spontaneous seizures. Mice that had experienced status epilepticus and were treated for 2 months with rapamycin displayed significantly less mossy fiber sprouting (42% of vehicle-treated animals), and the effect was dose dependent. However, behavioral and video/EEG monitoring revealed that rapamycin- and vehicle-treated mice displayed spontaneous seizures at similar frequencies. These findings suggest mossy fiber sprouting is neither pro- nor anti-convulsant; however, there are caveats. Rapamycin treatment also reduced epilepsy-related hypertrophy of the dentate gyrus but did not significantly affect granule cell proliferation, hilar neuron loss, or generation of ectopic granule cells. These findings are consistent with the hypotheses that hilar neuron loss and ectopic granule cells might contribute to temporal lobe epileptogenesis.

Graph-theoretical analysis reveals disrupted small-world organization of cortical thickness correlation networks in temporal lobe epilepsy

Temporal lobe epilepsy (TLE) is the most common drug-resistant epilepsy in adults. As morphometric studies have shown widespread structural damage in TLE, this condition is often referred to as a system disorder with disrupted structural networks. Studies based on univariate statistical comparisons can only indirectly test such hypothesis. Graph theory provides a new approach to formally analyze large-scale networks. Using graph-theoretical analysis of magnetic resonance imaging-based cortical thickness correlations, we investigated the structural basis of the organization of such networks in 122 TLE patients and 47 age- and sex-matched healthy controls. Networks in patients and controls were characterized by a short path length between anatomical regions and a high degree of clustering, suggestive of a small-world topology. However, compared with controls, patients showed increased path length and clustering, altered distribution of network hubs, and higher vulnerability to targeted attacks, suggesting a reorganization of cortical thickness correlation networks. Longitudinal analysis demonstrated that network alterations intensify over time. Bootstrap simulations showed high reproducibility of network parameters across random subsamplings, indicating that altered network topology in TLE is a consistent finding. Increased network disruption was associated with unfavorable postoperative seizure outcome, implying adverse effects of epileptogenesis on large-scale network organization.

Network recruitment to coherent oscillations in a hippocampal computer model

Coherent neural oscillations represent transient synchronization of local neuronal populations in both normal and pathological brain activity. These oscillations occur at or above gamma frequencies (>30 Hz) and often are propagated to neighboring tissue under circumstances that are both normal and abnormal, such as gamma binding or seizures. The mechanisms that generate and propagate these oscillations are poorly understood. In the present study we demonstrate, via a detailed computational model, a mechanism whereby physiological noise and coupling initiate oscillations and then recruit neighboring tissue, in a manner well described by a combination of stochastic resonance and coherence resonance. We develop a novel statistical method to quantify recruitment using several measures of network synchrony. This measurement demonstrates that oscillations spread via preexisting network connections such as interneuronal connections, recurrent synapses, and gap junctions, provided that neighboring cells also receive sufficient inputs in the form of random synaptic noise. "Epileptic" high-frequency oscillations (HFOs), produced by pathologies such as increased synaptic activity and recurrent connections, were superior at recruiting neighboring tissue. "Normal" HFOs, associated with fast firing of inhibitory cells and sparse pyramidal cell firing, tended to suppress surrounding cells and showed very limited ability to recruit. These findings point to synaptic noise and physiological coupling as important targets for understanding the generation and propagation of both normal and pathological HFOs, suggesting potential new diagnostic and therapeutic approaches to human disorders such as epilepsy.

From network structure to network reorganization: implications for adult neurogenesis

Networks can be dynamical systems that undergo functional and structural reorganization. One example of such a process is adult hippocampal neurogenesis, in which new cells are continuously born and incorporate into the existing network of the dentate gyrus region of the hippocampus. Many of these introduced cells mature and become indistinguishable from established neurons, joining the existing network. Activity in the network environment is known to promote birth, survival and incorporation of new cells. However, after epileptogenic injury, changes to the connectivity structure around the neurogenic niche are known to correlate with aberrant neurogenesis. The possible role of network-level changes in the development of epilepsy is not well understood. In this paper, we use a computational model to investigate how the structural and functional outcomes of network reorganization, driven by addition of new cells during neurogenesis, depend on the original network structure. We find that there is a stable network topology that allows the network to incorporate new neurons in a manner that enhances activity of the persistently active region, but maintains global network properties. In networks having other connectivity structures, new cells can greatly alter the distribution of firing activity and destroy the initial activity patterns. We thus find that new cells are able to provide focused enhancement of network only for small-world networks with sufficient inhibition. Network-level deviations from this topology, such as those caused by epileptogenic injury, can set the network down a path that develops toward pathological dynamics and aberrant structural integration of new cells.

Coalescence and fragmentation of cortical networks during focal seizures

Epileptic seizures reflect a pathological brain state characterized by specific clinical and electrical manifestations. The proposed mechanisms are heterogeneous but united by the supposition that epileptic activity is hypersynchronous across multiple scales, yet principled and quantitative analyses of seizure dynamics across space and throughout the entire ictal period are rare. To more completely explore spatiotemporal interactions during seizures, we examined electrocorticogram data from a population of male and female human patients with epilepsy and from these data constructed dynamic network representations using statistically robust measures. We found that these networks evolved through a distinct topological progression during the seizure. Surprisingly, the overall synchronization changed only weakly, whereas the topology changed dramatically in organization. A large subnetwork dominated the network architecture at seizure onset and preceding termination but, between, fractured into smaller groups. Common network characteristics appeared consistently for a population of subjects, and, for each subject, similar networks appeared from seizure to seizure. These results suggest that, at the macroscopic spatial scale, epilepsy is not so much a manifestation of hypersynchrony but instead of network reorganization.

Granule cells in the CA3 area

A fundamental property of neuronal networks in Ammon's horn is that each area comprises a single glutamatergic cell population and various types of GABAergic neurons. Here we describe an exception to this rule, in the form of granule cells that reside within the CA3 area and function as glutamatergic nonprincipal cells with distinct properties. CA3 granule cells in normal, healthy rats, similarly to dentate gyrus granule cells, coexpressed calbindin and the homeobox protein Prox1. However, CA3 granule cells were located outside of the dentate gyrus, often hundreds of micrometers from the hilar border, in the lucidum and radiatum layers. CA3 granule cells were present in numbers that were comparable to the rarer GABAergic neuronal subtypes, and their somato-dendritic morphology, intrinsic properties, and perforant path inputs were similar to those of dentate gyrus granule cells. CA3 granule cell axons displayed giant mossy fiber terminals with filopodial extensions, demonstrating that not all mossy fibers originate from the dentate gyrus. Somatic paired recordings revealed that CA3 granule cells innervated CA3 pyramidal and GABAergic cells similarly to conventional mossy fiber synapses. However, CA3 granule cells were distinct in the specific organization of their GABAergic inputs. They received GABAergic synapses from cholecystokinin-expressing mossy fiber-associated cells that did not innervate the dentate granule cell layer, and these synapses demonstrated unusually strong activity-dependent endocannabinoid-mediated inhibition of GABA release. These results indicate that granule cells in the CA3 constitute a glutamatergic, nonprincipal neuronal subtype that is integrated into the CA3 synaptic network.

Long-term effects of temporal lobe epilepsy on local neural networks: a graph theoretical analysis of corticography recordings

PURPOSE

Pharmaco-resistant temporal lobe epilepsy (TLE) is often treated with surgical intervention at some point. As epilepsy surgery is considered a last resort by most physicians, a long history of epileptic seizures prior to surgery is not uncommon. Little is known about the effects of ongoing TLE on neural functioning. A better understanding of these effects might influence the moment of surgical intervention. Functional connectivity (interaction between spatially distributed brain areas) and network structure (integration and segregation of information processing) are thought to be essential for optimal brain functioning. We report on the impact of TLE duration on temporal lobe functional connectivity and network characteristics.

METHODS

Functional connectivity of the temporal lobe at the time of surgery was assessed by means of interictal electrocorticography (ECoG) recordings of 27 TLE patients by using the phase lag index (PLI). Graphs (abstract network representations) were reconstructed from the PLI matrix and characterized by the clustering coefficient C (local clustering), the path length L (overall network interconnectedness), and the "small world index" S (network configuration).

RESULTS

Functional connectivity (average PLI), clustering coefficients, and the small world index were negatively correlated with TLE duration in the broad frequency band (0.5-48 Hz).

DISCUSSION

Temporal lobe functional connectivity is lower in patients with longer TLE history, and longer TLE duration is correlated with more random network configuration. Our findings suggest that the neural networks of TLE patients become more pathological over time, possibly due to temporal lobe changes associated with long-standing lesional epilepsy.

Reduced excitability in the dentate gyrus network of betaIV-spectrin mutant mice in vivo

The submembrane cytoskeletal meshwork of the axon contains the scaffolding protein betaIV-spectrin. It provides mechanical support for the axon and anchors membrane proteins. Quivering (qv(3j)) mice lack functional betaIV-spectrin and have reduced voltage-gated sodium channel (VGSC) immunoreactivity at the axon initial segment and nodes of Ranvier. Because VGSCs are critically involved in action potential generation and conduction, we hypothesized that qv(3j) mice should also show functional deficits at the network level. To test this hypothesis, we investigated granule cell function in the dentate gyrus of anesthetized qv(3j) mice after electrical stimulation of the perforant path in vivo. This revealed an impaired input-output relationship between stimulus intensity and granule cell population spikes and an enhanced paired-pulse inhibition of population spikes, indicating a reduced ability of granule cells to generate action potentials and decreased network excitability. In contrast, the input-output curve for evoked field excitatory postsynaptic potentials (fEPSPs) and paired-pulse facilitation of fEPSPs were unchanged, suggesting normal excitatory synaptic transmission at perforant path-granule cell synapses in qv(3j) mutants. To corroborate our findings, we analyzed the influence of VGSC density reduction on dentate network activity using an established computational model of the dentate gyrus network. This in silico approach confirmed that the loss of VGSCs is sufficient to explain the electrophysiological changes observed in qv(3j) mice. Taken together, our findings demonstrate that betaIV-spectrin is required for normal granule cell firing and for physiological levels of network excitability in the mouse dentate gyrus in vivo.

Synaptic noise and physiological coupling generate high-frequency oscillations in a hippocampal computational model

There is great interest in the role of coherent oscillations in the brain. In some cases, high-frequency oscillations (HFOs) are integral to normal brain function, whereas at other times they are implicated as markers of epileptic tissue. Mechanisms underlying HFO generation, especially in abnormal tissue, are not well understood. Using a physiological computer model of hippocampus, we investigate random synaptic activity (noise) as a potential initiator of HFOs. We explore parameters necessary to produce these oscillations and quantify the response using the tools of stochastic resonance (SR) and coherence resonance (CR). As predicted by SR, when noise was added to the network the model was able to detect a subthreshold periodic signal. Addition of basket cell interneurons produced two novel SR effects: 1) improved signal detection at low noise levels and 2) formation of coherent oscillations at high noise that were entrained to harmonics of the signal frequency. The periodic signal was then removed to study oscillations generated only by noise. The combined effects of network coupling and synaptic noise produced coherent, periodic oscillations within the network, an example of CR. Our results show that, under normal coupling conditions, synaptic noise was able to produce gamma (30-100 Hz) frequency oscillations. Synaptic noise generated HFOs in the ripple range (100-200 Hz) when the network had parameters similar to pathological findings in epilepsy: increased gap junctions or recurrent synaptic connections, loss of inhibitory interneurons such as basket cells, and increased synaptic noise. The model parameters that generated these effects are comparable with published experimental data. We propose that increased synaptic noise and physiological coupling mechanisms are sufficient to generate gamma oscillations and that pathologic changes in noise and coupling similar to those in epilepsy can produce abnormal ripples.

Double Trouble? Potential for Hyperexcitability Following Both Channelopathic up- and Downregulation of I(h) in Epilepsy

Studies of pathological ion channel regulation as an underlying mechanism of epilepsy have revealed alterations in the h-current in several animal models. While earlier reports indicate that downregulation of the h-current is pro-excitatory on the single neuron level, we found an upregulation of I(h) in hyperexcitable CA1 pyramidal neuron dendrites following experimental febrile seizures. In addition, in several CA1 pyramidal neuron computational models of different complexity, h-current upregulation has been shown to lead to pro-excitable effects. This focused review examines the complex impact of altered h-current on neuronal resting membrane potential (RMP) and input resistance (R(in)), as well as reported interactions with other ionic conductances.

Multistability, local pattern formation, and global collective firing in a small-world network of nonleaky integrate-and-fire neurons

We investigate numerically the collective dynamical behavior of pulse-coupled nonleaky integrate-and-fire neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for spontaneous firing for each neuron. We study network dynamics evolving from different sets of initial conditions in dependence on coupling strength and rewiring probability. Besides a homogeneous equilibrium state for low coupling strength, we observe different local patterns including cyclic waves, spiral waves, and turbulentlike patterns, which-depending on network parameters-interfere with the global collective firing of the neurons. We attribute the various network dynamics to distinct regimes in the parameter space. For the same network parameters different network dynamics can be observed depending on the set of initial conditions only. Such a multistable behavior and the interplay between local pattern formation and global collective firing may be attributable to the spatiotemporal dynamics of biological networks.

Interaction of cellular and network mechanisms in spatiotemporal pattern formation in neuronal networks

Spatiotemporal patterning of neuronal activity is considered to be an important feature of cognitive processing in the brain as well as pathological brain states, such as seizures. Here, we investigate complex interactions between intrinsic properties of neurons and network structure in the generation of network spatiotemporal patterning in the context of seizure-like synchrony. We show that membrane excitability properties have differential effects on network activity patterning for different network topologies. We consider excitatory networks consisting of neurons with excitability properties varying between type I and type II that exhibit significantly different spike frequency responses to external current stimulation, especially at firing threshold. We find that networks with type II-like neurons show higher synchronization and bursting capacity across a range of network topologies than corresponding networks with type I-like neurons. These differences in activity patterning are persistent across different network sizes, connectivity strengths, magnitudes of random external input, and the addition of inhibitory interneurons to the network, making them highly likely to be relevant to brain function. Furthermore, we show that heterogeneous networks of mixed cell types show emergent dynamical patterns even for very low mixing ratios. Specifically, the addition of a small percentage of type II-like cells into a network of type I-like cells can markedly change the patterning of network activity. These findings suggest that cellular as well as network mechanisms can go hand in hand, leading to the generation of seizure-like discharges, suggesting that a single ictogenic mechanism alone may not be responsible for seizure generation.

Complex brain networks: graph theoretical analysis of structural and functional systems

Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Evolving functional network properties and synchronizability during human epileptic seizures

We assess electrical brain dynamics before, during, and after 100 human epileptic seizures with different anatomical onset locations by statistical and spectral properties of functionally defined networks. We observe a concave-like temporal evolution of characteristic path length and cluster coefficient indicative of a movement from a more random toward a more regular and then back toward a more random functional topology. Surprisingly, synchronizability was significantly decreased during the seizure state but increased already prior to seizure end. Our findings underline the high relevance of studying complex systems from the viewpoint of complex networks, which may help to gain deeper insights into the complicated dynamics underlying epileptic seizures.

Computer modelling of epilepsy

Epilepsy is a complex set of disorders that can involve many areas of the cortex, as well as underlying deep-brain systems. The myriad manifestations of seizures, which can be as varied as déjà vu and olfactory hallucination, can therefore give researchers insights into regional functions and relations. Epilepsy is also complex genetically and pathophysiologically: it involves microscopic (on the scale of ion channels and synaptic proteins), macroscopic (on the scale of brain trauma and rewiring) and intermediate changes in a complex interplay of causality. It has long been recognized that computer modelling will be required to disentangle causality, to better understand seizure spread and to understand and eventually predict treatment efficacy. Over the past few years, substantial progress has been made in modelling epilepsy at levels ranging from the molecular to the socioeconomic. We review these efforts and connect them to the medical goals of understanding and treating the disorder.

Computational models of epileptic activity: a bridge between observation and pathophysiological interpretation

Epilepsy is a neurological disorder characterized by the recurrence of seizures. It affects 50 million people worldwide. Although a considerable number of new antiepileptic drugs with reduced side effects and toxicity have been introduced since the 1950s, 30% of patients remain pharmacoresistant. Although epilepsy research is making progress, advances in understanding drug resistance have been hampered by the complexity of the underlying neuronal systems responsible for epileptic activity. In such systems where short- or long-term plasticity plays a role, pathophysiological alterations may take place at subcellular (i.e., membrane ion channels and neurotransmitter receptors), cellular (neurons), tissular (networks of neurons) and regional (networks of networks of neurons) scales. In such a context, the demand for integrative approaches is high and neurocomputational models become recognized tools for tackling the complexity of epileptic phenomena. The purpose of this report is to provide an overview on computational modeling as a way of structuring and interpreting multimodal data recorded from the epileptic brain. Some examples are briefly described, which illustrate how computational models closely related with either experimental or clinical data can markedly advance our understanding of essential issues in epilepsy such as the transition from background to seizure activity. A commentary is also made on the potential use of such models in the study of therapeutic strategies such as rational drug design or electrical stimulations.

Epilepsy and nonlinear dynamics

This overview summarizes findings obtained from analyzing electroencephalographic (EEG) recordings from epilepsy patients with methods from the theory of nonlinear dynamical systems. The last two decades have shown that nonlinear time series analysis techniques allow an improved characterization of epileptic brain states and help to gain deeper insights into the spatial and temporal dynamics of the epileptic process. Nonlinear EEG analyses can help to improve the evaluation of patients prior to neurosurgery, and with an unequivocal identification of precursors of seizures, they can be of great value in the development of seizure warning and prevention techniques.

Self-sustaining non-repetitive activity in a large scale neuronal-level model of the hippocampal circuit

The mammalian hippocampus is involved in spatial representation and memory storage and retrieval, and much research is ongoing to elucidate the cellular and system-level mechanisms underlying these cognitive functions. Modeling may be useful to link network-level activity patterns to the relevant features of hippocampal anatomy and electrophysiology. Investigating the effects of circuit connectivity requires simulations of a number of neurons close to real scale. To this end, we construct a model of the hippocampus with 16 distinct neuronal classes (including both local and projection cells) and 200,000 individual neurons. The number of neurons in each class and their interconnectivity are drawn from rat anatomy. Here we analyze the emergent network activity and how it is affected by reducing either the size or the connectivity diversity of the model. When the model is run with a simple variation of the McCulloch-Pitts formalism, self-sustaining non-repetitive activity patterns consistently emerge. Specific firing threshold values are narrowly constrained for each cell class upon multiple runs with different stochastic wiring and initial conditions, yet these values do not directly affect network stability. Analysis of the model at different network sizes demonstrates that a scale reduction of one order of magnitude drastically alters network dynamics, including the variability of the output range, the distribution of firing frequencies, and the duration of self-sustained activity. Moreover, comparing the model to a control condition with an equivalent number of (excitatory/inhibitory balanced) synapses, but removing all class-specific information (i.e. collapsing the network to homogeneous random connectivity) has surprisingly similar effects to downsizing the total number of neurons. The reduced-scale model is also compared directly with integrate-and-fire simulations, which capture considerably more physiological detail at the single-cell level, but still fail to reproduce the full behavioral complexity of the large-scale model. Thus network size, cell class diversity, and connectivity details may all be critical to generate self-sustained non-repetitive activity patterns.

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

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.

Technology insight: neuroengineering and epilepsy-designing devices for seizure control

Despite substantial innovations in antiepileptic drug therapy over the past 15 years, the proportion of patients with uncontrolled epilepsy has not changed, highlighting the need for new treatment strategies. New implantable antiepileptic devices, which are currently under development and in pivotal clinical trials, hold great promise for improving the quality of life of millions of people with epileptic seizures worldwide. A broad range of strategies to stop seizures is currently being investigated, with various modes of control and intervention. The success of novel antiepileptic devices rests upon collaboration between neuroengineers, physicians and industry to adapt new technologies for clinical use. The initial results with these technologies are exciting, but considerable development and controlled clinical trials will be required before these treatments earn a place in our standard of clinical care.

Brain architecture: a design for natural computation

Fifty years ago, John von Neumann compared the architecture of the brain with that of the computers he invented and which are still in use today. In those days, the organization of computers was based on concepts of brain organization. Here, we give an update on current results on the global organization of neural systems. For neural systems, we outline how the spatial and topological architecture of neuronal and cortical networks facilitates robustness against failures, fast processing and balanced network activation. Finally, we discuss mechanisms of self-organization for such architectures. After all, the organization of the brain might again inspire computer architecture.

The application of graph theoretical analysis to complex networks in the brain

Considering the brain as a complex network of interacting dynamical systems offers new insights into higher level brain processes such as memory, planning, and abstract reasoning as well as various types of brain pathophysiology. This viewpoint provides the opportunity to apply new insights in network sciences, such as the discovery of small world and scale free networks, to data on anatomical and functional connectivity in the brain. In this review we start with some background knowledge on the history and recent advances in network theories in general. We emphasize the correlation between the structural properties of networks and the dynamics of these networks. We subsequently demonstrate through evidence from computational studies, in vivo experiments, and functional MRI, EEG and MEG studies in humans, that both the functional and anatomical connectivity of the healthy brain have many features of a small world network, but only to a limited extent of a scale free network. The small world structure of neural networks is hypothesized to reflect an optimal configuration associated with rapid synchronization and information transfer, minimal wiring costs, resilience to certain types of damage, as well as a balance between local processing and global integration. Eventually, we review the current knowledge on the effects of focal and diffuse brain disease on neural network characteristics, and demonstrate increasing evidence that both cognitive and psychiatric disturbances, as well as risk of epileptic seizures, are correlated with (changes in) functional network architectural features.

Graph theoretical analysis of complex networks in the brain

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.

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

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.

SenseLab: new developments in disseminating neuroscience information

This article presents the latest developments in neuroscience information dissemination through the SenseLab suite of databases: NeuronDB, CellPropDB, ORDB, OdorDB, OdorMapDB, ModelDB and BrainPharm. These databases include information related to: (i) neuronal membrane properties and neuronal models, and (ii) genetics, genomics, proteomics and imaging studies of the olfactory system. We describe here: the new features for each database, the evolution of SenseLab's unifying database architecture and instances of SenseLab database interoperation with other neuroscience online resources.

Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a "small-world" network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity.

Opposing Modifications in Intrinsic Currents and Synaptic Inputs in Post-Traumatic Mossy Cells: Evidence for Single-Cell Homeostasis in a Hyperexcitable Network

Recent experimental and modeling results demonstrated that surviving mossy cells in the dentate gyrus play key roles in the generation of network hyperexcitability. Here we examined if mossy cells exhibit long-term plasticity in the posttraumatic, hyperexcitable dentate gyrus. Mossy cells 1 wk after fluid percussion head injury did not show alterations in their current-firing frequency ( I-F) and current-membrane voltage ( I-V) relationships. In spite of the unchanged I-F and I-V curves, mossy cells showed extensive modifications in Na+, K+ and h-currents, indicating the coordinated nature of these opposing modifications. Computational experiments in a realistic large-scale model of the dentate gyrus demonstrated that individually, these perturbations could significantly affect network activity. Synaptic inputs also displayed systematic, opposing modifications. Miniature excitatory postsynaptic current (EPSC) amplitudes were decreased, whereas miniature inhibitory postsynaptic current (IPSC) amplitudes were increased as expected from a homeostatic response to network hyperexcitability. In addition, opposing alterations in miniature and spontaneous synaptic event frequencies and amplitudes were observed for both EPSCs and IPSCs. Despite extensive changes in synaptic inputs, cannabinoid-mediated depolarization-induced suppression of inhibition was not altered in posttraumatic mossy cells. These data demonstrate that many intrinsic and synaptic properties of mossy cells undergo highly specific, long-term alterations after traumatic brain injury. The systematic nature of such extensive and opposing alterations suggests that single-cell properties are significantly influenced by homeostatic mechanisms in hyperexcitable circuits.

Modeling the dentate gyrus

Computational modeling has become an increasingly useful tool for studying complex neuronal circuits such as the dentate gyrus. In order to effectively apply computational techniques and theories to answer pressing biological questions, however, it is necessary to develop detailed, data-driven models. Development of such models is a complicated process, akin to putting together a jigsaw puzzle with the pieces being such things as cell types, cell numbers, and specific connectivity. This chapter provides a walkthrough for the development of a very large-scale, biophysically realistic model of the dentate gyrus. Subsequently, it demonstrates the utility of a modeling approach in asking and answering questions about both healthy and pathological states involving the modeled brain region. Finally, this chapter discusses some predictions that come directly from the model that can be tested in future experimental approaches.