Emergent epileptiform activity in neural networks with weak excitatory synapses

Multimodal electrophysiological analyses reveal that reduced synaptic excitatory neurotransmission underlies seizures in a model of NMDAR antibody-mediated encephalitis

Seizures are a prominent feature in N-Methyl-D-Aspartate receptor antibody (NMDAR antibody) encephalitis, a distinct neuro-immunological disorder in which specific human autoantibodies bind and crosslink the surface of NMDAR proteins thereby causing internalization and a state of NMDAR hypofunction. To further understand ictogenesis in this disorder, and to test a potential treatment compound, we developed an NMDAR antibody mediated rat seizure model that displays spontaneous epileptiform activity in vivo and in vitro. Using a combination of electrophysiological and dynamic causal modelling techniques we show that, contrary to expectation, reduction of synaptic excitatory, but not inhibitory, neurotransmission underlies the ictal events through alterations in the dynamical behaviour of microcircuits in brain tissue. Moreover, in vitro application of a neurosteroid, pregnenolone sulphate, that upregulates NMDARs, reduced established ictal activity. This proof-of-concept study highlights the complexity of circuit disturbances that may lead to seizures and the potential use of receptor-specific treatments in antibody-mediated seizures and epilepsy.

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

Alterations in Piriform and Bulbar Activity/Excitability/Coupling Upon Amyloid-β Administration in vivo Related to Olfactory Dysfunction

BACKGROUND

Deficits in odor detection and discrimination are premature symptoms of Alzheimer's disease (AD) that correlate with pathological signs in the olfactory bulb (OB) and piriform cortex (PCx). Similar olfactory dysfunction has been characterized in AD transgenic mice that overproduce amyloid-β peptide (Aβ), which can be prevented by reducing Aβ levels by immunological and pharmacological means, suggesting that olfactory dysfunction depends on Aβ accumulation and Aβ-driven alterations in the OB and/or PCx, as well as on their activation. However, this possibility needs further exploration.

OBJECTIVE

To characterize the effects of Aβ on OB and PCx excitability/coupling and on olfaction.

METHODS

Aβ oligomerized solution (containing oligomers, monomers, and protofibrils) or its vehicle were intracerebroventricularlly injected two weeks before OB and PCx excitability and synchrony were evaluated through field recordings in vivo and in brain slices. Synaptic transmission from the OB to the PCx was also evaluated in slices. Olfaction was assessed through the habituation/dishabituation test.

RESULTS

Aβ did not affect lateral olfactory tract transmission into the PCx but reduced odor habituation and cross-habituation. This olfactory dysfunction was related to a reduction of PCx and OB network activity power in vivo. Moreover, the coherence between PCx-OB activities was also reduced by Aβ. Finally, Aβ treatment exacerbated the 4-aminopyridine-induced excitation in the PCx in slices.

CONCLUSION

Our results show that Aβ-induced olfactory dysfunction involves a complex set of pathological changes at different levels of the olfactory pathway including alterations in PCx excitability and its coupling with the OB. These pathological changes might contribute to hyposmia in AD.

Influence of Autapses on Synchronization in Neural Networks With Chemical Synapses

A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronization. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behavior. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behavior depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.

Dynamical mesoscale model of absence seizures in genetic models

A mesoscale network model is proposed for the development of spike and wave discharges (SWDs) in the cortico-thalamo-cortical (C-T-C) circuit. It is based on experimental findings in two genetic models of childhood absence epilepsy–rats of WAG/Rij and GAERS strains. The model is organized hierarchically into two levels (brain structures and individual neurons) and composed of compartments for representation of somatosensory cortex, reticular and ventroposteriomedial thalamic nuclei. The cortex and the two thalamic compartments contain excitatory and inhibitory connections between four populations of neurons. Two connected subnetworks both including relevant parts of a C-T-C network responsible for SWD generation are modelled: a smaller subnetwork for the focal area in which the SWD generation can take place, and a larger subnetwork for surrounding areas which can be only passively involved into SWDs, but which is mostly responsible for normal brain activity. This assumption allows modeling of both normal and SWD activity as a dynamical system (no noise is necessary), providing reproducibility of results and allowing future analysis by means of theory of dynamical system theories. The model is able to reproduce most time-frequency changes in EEG activity accompanying the transition from normal to epileptiform activity and back. Three different mechanisms of SWD initiation reported previously in experimental studies were successfully reproduced in the model. The model incorporates also a separate mechanism for the maintenance of SWDs based on coupling analysis from experimental data. Finally, the model reproduces the possibility to stop ongoing SWDs with high frequency electrical stimulation, as described in the literature.

Excitation and Inhibition Balance Underlying Epileptiform Activity

OBJECTIVE

The phenomenon of postictal generalized EEG suppression state (PGES) - a period with suppressed activity following seizure termination and has been found to be associated with sudden unexpected death in epilepsy - remains poorly understood. This article aims to examine the how the balance of excitation and inhibition (E/I balance) affect the dynamics of seizure and PGES.

METHODS

A network of 1000 Izhikevich model neurons was developed and only the strengths of synaptic connections were adjusted to recreate the dynamics observed in recordings of seizure and PGES from human patients.

RESULTS

A rapid rise followed by a slow decay of dominant frequency was observed in iEEG recordings of ictal periods and reproduced in the simulated local field potential by changing the E/I balance of the model network. The rate of this dominant frequency evolution was quantified by a single measure, β, which was found to have a significant rank correlation with the duration of PGES in iEEG data and the rate of E/I balance shift in the model. Significance and Conclusion: (i) highlighting the importance of E/I balance in the dynamics of seizure and PGES; (ii) suggesting the measure, β, as a marker for PGES and the shift in E/I balance as a neural correlate for this marker.

Single amyloid-beta injection exacerbates 4-aminopyridine-induced seizures and changes synaptic coupling in the hippocampus

Accumulation of amyloid-beta (Aβ) in temporal lobe structures, including the hippocampus, is related to a variety of Alzheimer's disease symptoms and seems to be involved in the induction of neural network hyperexcitability and even seizures. Still, a direct evaluation of the pro-epileptogenic effects of Aβ in vivo, and of the underlying mechanisms, is missing. Thus, we tested whether the intracisternal injection of Aβ modulates 4-aminopyridine (4AP)-induced epileptiform activity, hippocampal network function, and its synaptic coupling. When tested 3 weeks after its administration, Aβ (but not its vehicle) reduces the latency for 4AP-induced seizures, increases the number of generalized seizures, exacerbates the time to fully recover from seizures, and favors seizure-induced death. These pro-epileptogenic effects of Aβ correlate with a reduction in the power of the spontaneous hippocampal network activity, involving all frequency bands in vivo and only the theta band (4-10 Hz) in vitro. The pro-epileptogenic effects of Aβ also correlate with a reduction of the Schaffer-collateral CA1 synaptic coupling in vitro, which is exacerbated by the sequential bath application of 4-AP and Aβ. In summary, Aβ produces long-lasting pro-epileptic effects that can be due to alterations in the hippocampal circuit, impacting its coordinated network activity and its synaptic efficiency. It is likely that normalizing synaptic coupling and/or coordinated neural network activity (i.e., theta activity) may contribute not only to improve cognitive function in Alzheimer's disease but also to avoid hyperexcitation in conditions of amyloidosis.

A Proposed Mechanism for Spontaneous Transitions between Interictal and Ictal Activity

Epileptic networks are characterized by two outputs: brief interictal spikes and rarer, more prolonged seizures. Although either output state is readily modeled in silico and induced experimentally, the transition mechanisms are unknown, in part because no models exhibit both output states spontaneously. In silico small-world neural networks were built using single-compartment neurons whose physiological parameters were derived from dual whole-cell recordings of pyramidal cells in organotypic hippocampal slice cultures that were generating spontaneous seizure-like activity. In silico, neurons were connected by abundant local synapses and rare long-distance synapses. Activity-dependent synaptic depression and gradual recovery delimited synchronous activity. Full synaptic recovery engendered interictal population spikes that spread via long-distance synapses. When synaptic recovery was incomplete, postsynaptic neurons required coincident activation of multiple presynaptic terminals to reach firing threshold. Only local connections were sufficiently dense to spread activity under these conditions. This coalesced network activity into traveling waves whose velocity varied with synaptic recovery. Seizures were comprised of sustained traveling waves that were similar to those recorded during experimental and human neocortical seizures. Sustained traveling waves occurred only when wave velocity, network dimensions, and the rate of synaptic recovery enabled wave reentry into previously depressed areas at precisely ictogenic levels of synaptic recovery. Wide-field, cellular-resolution GCamP7b calcium imaging demonstrated similar initial patterns of activation in the hippocampus, although the anatomical distribution of traveling waves of synaptic activation was altered by the pattern of synaptic connectivity in the organotypic hippocampal cultures.SIGNIFICANCE STATEMENT When computerized distributed neural network models are required to generate both features of epileptic networks (i.e., spontaneous interictal population spikes and seizures), the network structure is substantially constrained. These constraints provide important new hypotheses regarding the nature of epileptic networks and mechanisms of seizure onset.

Cross-scale effects of neural interactions during human neocortical seizure activity

Small-scale neuronal networks may impose widespread effects on large network dynamics. To unravel this relationship, we analyzed eight multiscale recordings of spontaneous seizures from four patients with epilepsy. During seizures, multiunit spike activity organizes into a submillimeter-sized wavefront, and this activity correlates significantly with low-frequency rhythms from electrocorticographic recordings across a 10-cm-sized neocortical network. Notably, this correlation effect is specific to the ictal wavefront and is absent interictally or from action potential activity outside the wavefront territory. To examine the multiscale interactions, we created a model using a multiscale, nonlinear system and found evidence for a dual role for feedforward inhibition in seizures: while inhibition at the wavefront fails, allowing seizure propagation, feedforward inhibition of the surrounding centimeter-scale networks is activated via long-range excitatory connections. Bifurcation analysis revealed that distinct dynamical pathways for seizure termination depend on the surrounding inhibition strength. Using our model, we found that the mesoscopic, local wavefront acts as the forcing term of the ictal process, while the macroscopic, centimeter-sized network modulates the oscillatory seizure activity.

Transition Dynamics of a Dentate Gyrus-CA3 Neuronal Network during Temporal Lobe Epilepsy

In temporal lobe epilepsy (TLE), the variation of chemical receptor expression underlies the basis of neural network activity shifts, resulting in neuronal hyperexcitability and epileptiform discharges. However, dynamical mechanisms involved in the transitions of TLE are not fully understood, because of the neuronal diversity and the indeterminacy of network connection. Hence, based on Hodgkin–Huxley (HH) type neurons and Pinsky–Rinzel (PR) type neurons coupling with glutamatergic and GABAergic synaptic connections respectively, we propose a computational framework which contains dentate gyrus (DG) region and CA3 region. By regulating the concentration range of N-methyl-D-aspartate-type glutamate receptor (NMDAR), we demonstrate the pyramidal neuron can generate transitions from interictal to seizure discharges. This suggests that enhanced endogenous activity of NMDAR contributes to excitability in pyramidal neuron. Moreover, we conclude that excitatory discharges in CA3 region vary considerably on account of the excitatory currents produced by the excitatory pyramidal neuron. Interestingly, by changing the backprojection connection, we find that glutamatergic type backprojection can promote the dominant frequency of firings and further motivate excitatory counterpropagation from CA3 region to DG region. However, GABAergic type backprojection can reduce firing rate and block morbid counterpropagation, which may be factored into the terminations of TLE. In addition, neuronal diversity dominated network shows weak correlation with different backprojections. Our modeling and simulation studies provide new insights into the mechanisms of seizures generation and connectionism in local hippocampus, along with the synaptic mechanisms of this disease.

Synchronization dynamics on the picosecond time scale in coupled Josephson junction neurons

Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons, and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or antiphase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-flip bifurcation. Firing synchronization states are calculated >70 000 times faster than conventional digital approaches. With their speed and low energy dissipation (10^{-17}J/spike), this set of proof-of-concept experiments establishes Josephson junction neurons as a viable approach for improvements in neuronal computation as well as applications in neuromorphic computing.

Modeling focal epileptic activity in the Wilson-cowan model with depolarization block

Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson-Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson-Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

Quasicritical brain dynamics on a nonequilibrium Widom line

Is the brain really operating at a critical point? We study the nonequilibrium properties of a neural network which models the dynamics of the neocortex and argue for optimal quasicritical dynamics on the Widom line where the correlation length and information transmission are optimized. We simulate the network and introduce an analytical mean-field approximation, characterize the nonequilibrium phase transitions, and present a nonequilibrium phase diagram, which shows that in addition to an ordered and disordered phase, the system exhibits a "quasiperiodic" phase corresponding to synchronous activity in simulations, which may be related to the pathological synchronization associated with epilepsy.

Preictal dynamics of EEG complexity in intracranially recorded epileptic seizure: a case report

Recent findings suggest that neural complexity reflecting a number of independent processes in the brain may characterize typical changes during epileptic seizures and may enable to describe preictal dynamics. With respect to previously reported findings suggesting specific changes in neural complexity during preictal period, we have used measure of pointwise correlation dimension (PD2) as a sensitive indicator of nonstationary changes in complexity of the electroencephalogram (EEG) signal. Although this measure of complexity in epileptic patients was previously reported by Feucht et al (Applications of correlation dimension and pointwise dimension for non-linear topographical analysis of focal onset seizures. Med Biol Comput. 1999;37:208-217), it was not used to study changes in preictal dynamics. With this aim to study preictal changes of EEG complexity, we have examined signals from 11 multicontact depth (intracerebral) EEG electrodes located in 108 cortical and subcortical brain sites, and from 3 scalp EEG electrodes in a patient with intractable epilepsy, who underwent preoperative evaluation before epilepsy surgery. From those 108 EEG contacts, records related to 44 electrode contacts implanted into lesional structures and white matter were not included into the experimental analysis.The results show that in comparison to interictal period (at about 8-6 minutes before seizure onset), there was a statistically significant decrease in PD2 complexity in the preictal period at about 2 minutes before seizure onset in all 64 intracranial channels localized in various brain sites that were included into the analysis and in 3 scalp EEG channels as well. Presented results suggest that using PD2 in EEG analysis may have significant implications for research of preictal dynamics and prediction of epileptic seizures.

MULTIPLE OSCILLATORY STATES IN MODELS OF COLLECTIVE NEURONAL DYNAMICS

In our previous studies, we showed that the both realistic and analytical computational models of neural dynamics can display multiple sustained states (attractors) for the same values of model parameters. Some of these states can represent normal activity while other, of oscillatory nature, may represent epileptic types of activity. We also showed that a simplified, analytical model can mimic this type of behavior and can be used instead of the realistic model for large scale simulations. The primary objective of the present work is to further explore the phenomenon of multiple stable states, co-existing in the same operational model, or phase space, in systems consisting of large number of interconnected basic units. As a second goal, we aim to specify the optimal method for state control of the system based on inducing state transitions using appropriate external stimulus. We use here interconnected model units that represent the behavior of neuronal populations as an effective dynamic system. The model unit is an analytical model (S. Kalitzin et al., Epilepsy Behav. 22 (2011) S102–S109) and does not correspond directly to realistic neuronal processes (excitatory–inhibitory synaptic interactions, action potential generation). For certain parameter choices however it displays bistable dynamics imitating the behavior of realistic neural mass models. To analyze the collective behavior of the system we applied phase synchronization analysis (PSA), principal component analysis (PCA) and stability analysis using Lyapunov exponent (LE) estimation. We obtained a large variety of stable states with different dynamic characteristics, oscillatory modes and phase relations between the units. These states can be initiated by appropriate initial conditions; transitions between them can be induced stochastically by fluctuating variables (noise) or by specific inputs. We propose a method for optimal reactive control, allowing forced transitions from one state (attractor) into another.

DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS

In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

Large-scale modeling of epileptic seizures: scaling properties of two parallel neuronal network simulation algorithms

Our limited understanding of the relationship between the behavior of individual neurons and large neuronal networks is an important limitation in current epilepsy research and may be one of the main causes of our inadequate ability to treat it. Addressing this problem directly via experiments is impossibly complex; thus, we have been developing and studying medium-large-scale simulations of detailed neuronal networks to guide us. Flexibility in the connection schemas and a complete description of the cortical tissue seem necessary for this purpose. In this paper we examine some of the basic issues encountered in these multiscale simulations. We have determined the detailed behavior of two such simulators on parallel computer systems. The observed memory and computation-time scaling behavior for a distributed memory implementation were very good over the range studied, both in terms of network sizes (2,000 to 400,000 neurons) and processor pool sizes (1 to 256 processors). Our simulations required between a few megabytes and about 150 gigabytes of RAM and lasted between a few minutes and about a week, well within the capability of most multinode clusters. Therefore, simulations of epileptic seizures on networks with millions of cells should be feasible on current supercomputers.

Modeling Neural Activity

This paper provides an overview of different types of models for studying activity of nerve cells and their networks with a special emphasis on neural oscillations. One part describes the neuronal models based on the Hodgkin and Huxley formalism first described in the 1950s. It is discussed how further simplifications of this formalism enable mathematical analysis of the process of neural excitability. The focus of the paper’s second component is on network activity. Understanding network function is one of the important frontiers remaining in neuroscience. At present, experimental techniques can only provide global recordings or samples of the activity of the huge networks that form the nervous system. Models in neuroscience can therefore play a critical role by providing a framework for integration of necessarily incomplete datasets, thereby providing insight into the mechanisms of neural function. Network models can either explicitly contain individual network nodes that model the neurons, or they can be based on representations of compound population activity. The latter approach was pioneered by Wilson and Cowan in the 1970s. Finally I provide an overview and discuss how network models are employed in the study of neuronal network pathology such as epilepsy.

The role of voltage dependence of the NMDA receptor in cellular and network oscillation

Unraveling the mechanisms underlying oscillatory behavior is critical for understanding normal and pathological brain processes. Here we used electrophysiology in mouse neocortical slices and principles of nonlinear dynamics to demonstrate how an increase in the N-methyl-d-aspartic acid receptor (NMDAR) conductance can create a nonlinear whole-cell current-voltage (I-V) relationship which leads to changes in cellular stability. We discovered two behaviorally and morphologically distinct pyramidal cell populations. Under control conditions, both cell types responded to depolarizing current injection with regular spiking patterns. However, upon NMDAR activation, an intrinsic oscillatory (IO) cell type (n = 44) showed a nonlinear whole-cell I-V relationship, intrinsic voltage-dependent oscillations plus amplification of alternating input current, and these properties persisted after disabling action potential generation with tetrodotoxin (TTX). The other non-oscillatory (NO) neuronal population (n = 24) demonstrated none of these behaviors. Simultaneous intra- and extracellular recordings demonstrated the NMDAR's capacity to promote low-frequency seizure-like network oscillations via its effects on intrinsic neuronal properties. The two pyramidal cell types demonstrated different relationships with network oscillation--the IO cells were leaders that were activated early in the population activity cycle while the activation of the NO cell type was distributed across network bursts. The properties of IO neurons disappeared in a low-magnesium environment where the voltage dependence of the receptor is abolished; concurrently, the cellular contribution to network oscillation switched to synchronous firing. Thus, depending upon the efficacy of NMDAR in altering the linearity of the whole-cell I-V relationship, the two cell populations played different roles in sustaining network oscillation.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis.

An integrative view of mechanisms underlying generalized spike-and-wave epileptic seizures and its implication on optimal therapeutic treatments

Many types of epileptic seizures are characterized by generalized spike-and-wave discharges. In the past, notable effort has been devoted to understanding seizure dynamics and various hypotheses have been proposed to explain the underlying mechanisms. In this paper, by taking an integrative view of the underlying mechanisms, we demonstrate that epileptic seizures can be generated by many different combinations of synaptic strengths and intrinsic membrane properties. This integrative view has important medical implications: the specific state of a patient characterized by a set of biophysical characteristics ultimately determines the optimal therapeutic treatment. Through the same view, we further demonstrate the potentiation effect of rational polypharmacy in the treatment of epilepsy and provide a new angle to resolve the debate on polypharmacy. Our results underscore the need for personalized medicine and demonstrate that computer modeling and simulation may play an important role in assisting the clinicians in selecting the optimal treatment on an individual basis.

Emergent oscillations in networks of stochastic spiking neurons

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework.

N-methyl-D-aspartate-induced oscillatory properties in neocortical pyramidal neurons from patients with epilepsy

N-Methyl-D-aspartate (NMDA) receptors have been implicated in epileptogenesis, but how these receptors contribute to epilepsy remains unknown. In particular, their role is likely to be complicated because of their voltage-dependent behavior. Here, the authors investigate how activation of NMDA receptors can affect the intrinsic production of oscillation and the resonance properties of neocortical pyramidal neurons from children with intractable epilepsy. Intracellular whole-cell patch clamp recordings in cortical slices from these patients revealed that pyramidal neurons do not produce spontaneous oscillation under control conditions. However, they did exhibit resonance around 1.5 Hz. On NMDA receptor activation, with bath-applied NMDA (10 μM), the majority of neurons produced voltage-dependent intrinsic oscillation associated with a change in the stability of the neuronal system as reflected by the whole-cell I-V curve. Furthermore, the degree of resonance was amplified while the frequency of resonance was shifted to lower frequencies (∼1 Hz) in NMDA. These results suggest that NMDA receptors may both promote the production of low-frequency oscillation and sharpen the response of the cell to lower frequencies. Both these behaviors may be amplified in tissue from patients with epilepsy, resulting in an increased propensity to generate seizures.

Aberrant neuronal avalanches in cortical tissue removed from juvenile epilepsy patients

Some forms of epilepsy may arise as a result of pathologic interactions among neurons. Many forms of collective activity have been identified, including waves, spirals, oscillations, synchrony, and neuronal avalanches. All these emergent activity patterns have been hypothesized to show pathologic signatures associated with epilepsy. Here, the authors used 60-channel multielectrode arrays to record neuronal avalanches in cortical tissue removed from juvenile epilepsy patients. For comparison, they also recorded activity in rat cortical slices. The authors found that some human tissue removed from epilepsy patients exhibited prolonged periods of hyperactivity not seen in rat slices. In addition, they found a positive correlation between the branching parameter, a measure of network gain, and firing rate in human slices during periods of hyperactivity. This relationship was not present in rat slices. The authors suggest that this positive correlation between the branching parameter and the firing rate is part of a positive feedback loop and may contribute to some forms of epilepsy. These results also indicate that neuronal avalanches are abnormally regulated in slices removed from pediatric epilepsy patients.

Systematic comparison of the behaviors produced by computational models of epileptic neocortex

Two existing models of brain dynamics in epilepsy, one detailed (i.e., realistic) and one abstract (i.e., simplified) are compared in terms of behavioral range and match to in vitro mouse recordings. A new method is introduced for comparing across computational models that may have very different forms. First, high-level metrics were extracted from model and in vitro output time series. A principal components analysis was then performed over these metrics to obtain a reduced set of derived features. These features define a low-dimensional behavior space in which quantitative measures of behavioral range and degree of match to real data can be obtained. The detailed and abstract models and the mouse recordings overlapped considerably in behavior space. Both the range of behaviors and similarity to mouse data were similar between the detailed and abstract models. When no high-level metrics were used and principal components analysis was computed over raw time series, the models overlapped minimally with the mouse recordings. The method introduced here is suitable for comparing across different kinds of model data and across real brain recordings. It appears that, despite differences in form and computational expense, detailed and abstract models do not necessarily differ in their behaviors.

From working memory to epilepsy: dynamics of facilitation and inhibition in a cortical network

Persistent states are believed to be the correlate for short-term or working memory. Using a previously derived model for working memory, we show that disruption of the lateral inhibition can lead to a variety of pathological states. These states are analogs of reflex or pattern-sensitive epilepsy. Simulations, numerical bifurcation analysis, and fast-slow decomposition are used to explore the dynamics of this network.

Influence of synaptic interaction on firing synchronization and spike death in excitatory neuronal networks

We investigate the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We find spike death phenomena: namely, the state of neurons transits from the limit cycle to a fixed point or transient state. The phenomena occur under the perturbation of an excitatory synaptic interaction, which has a high efficacy. We show that the decrease of synaptic current results in spike death through depressing the feedback of the sodium ionic current. In the networks with the spike death property the degree of synchronization is lower and insensitive to the heterogeneity of neurons. The mechanism of the influence is that the transition of the neuron state disrupts the adjustment of the rhythm of the neurons oscillation and prevents a further increase of the firing synchronization.

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.

Tonic-clonic transitions in computer simulation

SUMMARY

Network simulations can help identify underlying mechanisms of epileptic activity that are hard to isolate in biologic preparations. To be useful, simulations must be sufficiently realistic to make possible biologic and clinical prediction. This requirement for large networks of sufficiently detailed neurons raises challenges both with regard to computational load and the difficulty of obtaining insights with large numbers of free parameters and the large amounts of generated data. The authors have addressed these problems by simulating computationally manageable networks of moderate size consisting of 1,000 to 3,000 neurons with multiple intrinsic and synaptic properties. Experiments on these simulations demonstrated the presence of epileptiform behavior in the form of repetitive high-intensity population events (clonic behavior) or latch-up with near maximal activity (tonic behavior). Intrinsic neuronal excitability is not always a predictor of network epileptiform activity but may paradoxically produce antiepileptic effects, depending on the settings of other parameters. Several simulations revealed the importance of random coincident inputs to shift a network from a low-activation to a high-activation epileptiform state. Finally, a simulated anticonvulsant acting on excitability tended to preferentially decrease tonic activity.

Framework for interactive million-neuron simulation

SUMMARY

Large simulations have become increasingly complex in many fields, tending to incorporate scale-dependent modeling and algorithms and wide-ranging physical influences. This scale of simulation sophistication has not yet been matched in neuroscience. The authors describe a framework aimed at enabling natural interaction with complex simulations: their configuration, initial conditions, monitoring, and analysis. The architecture is built on three cornerstone components: active probes, adaptive data capture, and visual interface. The resulting synthesis will enable interactive exploration of live simulations running on supercomputing platforms.

propagation of seizure-like activity in a model of neocortex

SUMMARY

Seizures in pediatric epilepsy are often associated with spreading, repetitive bursting activity in neocortex. The authors examined onset and propagation of seizure-like activity using a computational model of cortical circuitry. The model includes two pyramidal cell types and four types of inhibitory interneurons. Each neuron is represented by a multicompartmental model with biophysically realistic ion channels. The authors determined the role of bursting neurons and found that their capability of driving network oscillations is most prominent in networks with either weak or relatively strong excitatory synaptic coupling. Synaptic coupling strength was varied in a separate set of simulations to examine its role in network bursting. Oscillations both between cortical layers (vertical oscillations) and between cortical areas (horizontal oscillations) emerge at moderate excitatory coupling strengths. For horizontal propagation, existence of a fast-conducting fiber system and its properties are critical. Seizure-like oscillatory activity may originate from single neurons or small networks, and that activity may propagate in two principal fashions: one that can be represented by a unidirectional (pacemaker)-type process and the other as multi- or bidirectional propagating waves. The frequency of the bursting patterns relates to underlying propagating activity that can either sustain or disrupt the ongoing oscillation.

Role of persistent sodium current in bursting activity of mouse neocortical networks in vitro

Most types of electrographic epileptiform activity can be characterized by isolated or repetitive bursts in brain electrical activity. This observation is our motivation to determine mechanisms that underlie bursting behavior of neuronal networks. Here we show that the persistent sodium (Na(P)) current in mouse neocortical slices is associated with cellular bursting and our data suggest that these cells are capable of driving networks into a bursting state. This conclusion is supported by the following observations. 1) Both low concentrations of tetrodotoxin (TTX) and riluzole reduce and eventually stop network bursting while they simultaneously abolish intrinsic bursting properties and sensitivity levels to electrical stimulation in individual intrinsically bursting cells. 2) The sensitivity levels of regular spiking neurons are not significantly affected by riluzole or TTX at the termination of network bursting. 3) Propagation of cellular bursting in a neuronal network depended on excitatory connectivity and disappeared on bath application of CNQX (20 microM) + CPP (10 microM). 4) Voltage-clamp measurements show that riluzole (20 microM) and very low concentrations of TTX (50 nM) attenuate Na(P) currents in the neural membrane within a 1-min interval after bath application of the drug. 5) Recordings of synaptic activity demonstrate that riluzole at this concentration does not affect synaptic properties. 6) Simulations with a neocortical network model including different types of pyramidal cells, inhibitory interneurons, neurons with and without Na(P) currents, and recurrent excitation confirm the essence of our experimental observations that Na(P) conductance can be a critical factor sustaining slow population bursting.