Diffusive coupling and network periodicity: a computational study

Diffusive coupling (nearest-neighbor coupling) is the most common type of coupling present in many systems. Previous experimental and theoretical studies have shown that potassium lateral diffusion coupling (i.e., diffusive coupling) can be responsible for synchronization of neuronal activity. Recent in vivo experiments carried out with anesthetized rat hippocampus suggested that the extracellular potassium could play an important role in the generation of a novel type of epileptiform nonsynaptic activity. Yet, the role of potassium in the generation of seizures remains controversial. We tested the hypothesis that potassium lateral diffusion coupling is responsible for the coupling mechanisms for network periodicity in a nonsynaptic model of epilepsy in vivo using a CA1 pyramidal neuron network model The simulation results show that 1), potassium lateral diffusion coupling is crucial for establishing epileptiform activity similar to that generated experimentally; and 2), there exists a scaling relation between the critical coupling strength and the number of cells in the network. The results not only agree with the theoretical prediction, but strongly suggest that potassium lateral diffusion coupling, a physiological realization of the concept of diffusive coupling, can play an important role in entraining periodicity in a nonsynaptic neural network.     

Potassium diffusive coupling in neural networks

Conventional neural networks are characterized by many neurons coupled together through synapses. The activity, synchronization, plasticity and excitability of the network are then controlled by its synaptic connectivity. Neurons are surrounded by an extracellular space whereby fluctuations in specific ionic concentration can modulate neuronal excitability. Extracellular concentrations of potassium ([K⁺]_o) can generate neuronal hyperexcitability. Yet, after many years of research, it is still unknown whether an elevation of potassium is the cause or the result of the generation, propagation and synchronization of epileptiform activity. An elevation of potassium in neural tissue can be characterized by dispersion (global elevation of potassium) and lateral diffusion (local spatial gradients). Both experimental and computational studies have shown that lateral diffusion is involved in the generation and the propagation of neural activity in diffusively coupled networks. Therefore, diffusion-based coupling by potassium can play an important role in neural networks and it is reviewed in four sections. Section 2 shows that potassium diffusion is responsible for the synchronization of activity across a mechanical cut in the tissue. A computer model of diffusive coupling shows that potassium diffusion can mediate communication between cells and generate abnormal and/or periodic activity in small (§3) and in large networks of cells (§4). Finally, in §5, a study of the role of extracellular potassium in the propagation of axonal signals shows that elevated potassium concentration can block the propagation of neural activity in axonal pathways. Taken together, these results indicate that potassium accumulation and diffusion can interfere with normal activity and generate abnormal activity in neural networks.     

Calcium imaging of epileptiform events with single-cell resolution

Epileptic discharges propagate through apparently normal circuits, although it is still unclear how this recruitment takes place. To understand the role of different classes of neurons in neocortical epilepsy, we have developed a novel imaging assay that detects which neurons participate in epileptiform discharges. Using calcium imaging of neuronal populations during bicuculline-induced spontaneous epileptiform events in slices from juvenile mouse somatosensory cortex, we find that fast calcium transients correlate with epileptiform field potentials and intracellular depolarizing shifts and can be used as an optical signature that a given neuron has participated in an epileptiform event. Our results demonstrate a novel method to characterize epileptiform events with single-cell resolution. In addition, our data are consistent with an important role for layer 5 in generating neocortical seizures and indicate that subgroups of neurons are particularly prone to epileptiform recruitment.     

Spiking behavior and epileptiform oscillations in a discrete model of cortical neural networks

Summary We investigate the phenomenon of epileptiform activity using a discrete model of cortical neural networks. Our model is reduced to the elementary features of neurons and assumes simplified dynamics of action potentials and postsynaptic potentials. The discrete model provides a comparably high simulation speed which allows the rendering of phase diagrams and simulations of large neural networks in reasonable time. Further the reduction to the basic features of neurons provides insight into the essentials of a possible mechanism of epilepsy. Our computer simulations suggest that the detailed dynamics of postsynaptic and action potentials are not indispensable for obtaining epileptiform behavior on the system level. The simulation results of autonomously evolving networks exhibit a regime in which the network dynamics spontaneously switch between fluctuating and oscillating behavior and produce isolated network spikes without external stimulation. Inhibitory neurons have been found to play an important part in the synchronization of neural firing: an increased number of synapses established by inhibitory neurons onto other neurons induces a transition to the spiking regime. A decreased frequency accompanying the hypersynchronous population activity has only occurred with slow inhibitory postsynaptic potentials.     

Calcium imaging of epileptiform events with single‐cell resolution

Epileptic discharges propagate through apparently normal circuits, although it is still unclear how this recruitment takes place. To understand the role of different classes of neurons in neocortical epilepsy, we have developed a novel imaging assay that detects which neurons participate in epileptiform discharges. Using calcium imaging of neuronal populations during bicuculline‐induced spontaneous epileptiform events in slices from juvenile mouse somatosensory cortex, we find that fast calcium transients correlate with epileptiform field potentials and intracellular depolarizing shifts and can be used as an optical signature that a given neuron has participated in an epileptiform event. Our results demonstrate a novel method to characterize epileptiform events with single‐cell resolution. In addition, our data are consistent with an important role for layer 5 in generating neocortical seizures and indicate that subgroups of neurons are particularly prone to epileptiform recruitment. © 2001 John Wiley & Sons, Inc. J Neurobiol 48: 215–227, 2001     

Epileptogenesis induces long-term alterations in intracellular calcium release and sequestration mechanisms in the hippocampal neuronal culture model of epilepsy

Calcium and calcium-dependent processes have been hypothesized to be involved in the induction of epilepsy. It has been shown that epileptic neurons have altered calcium homeostatic mechanisms following epileptogenesis in the hippocampal neuronal culture (HNC) and pilocarpine models of epilepsy. To investigate the mechanisms causing these alterations in [Ca2+]i homeostatic processes following epileptogenesis, we utilized the HNC model of in vitro 'epilepsy' which produces spontaneous recurrent epileptiform discharges (SREDs). Using [Ca2+]i imaging, studies were initiated to evaluate the mechanisms mediating these changes in [Ca2+]i homeostasis. 'Epileptic' neurons required much longer to restore a glutamate induced [Ca2+]i load to baseline levels than control neurons. Inhibition of Ca2+ entry through voltage and receptor gated Ca2+ channels and stretch activated Ca2+ channels had no effect on the prolonged glutamate induced increase in [Ca2+]i in epileptic neurons. Employing thapsigargin, an inhibitor of the sarco/endoplasmic reticulum calcium ATPase (SERCA), it was shown that thapsigargin inhibited sequestration of [Ca2+]i by SERCA was significantly decreased in 'epileptic' neurons. Using Ca2+ induced Ca2+ release (CICR) cell permeable inhibitors for the ryanodine receptor (dantrolene) and the IP3 receptor (2-amino-ethoxydiphenylborate, 2APB) mediated CICR, we demonstrated that CICR was significantly augmented in the 'epileptic' neurons, and determined that the IP3 receptor mediated CICR was the major release mechanism altered in epileptogenesis. These data indicate that both inhibition of SERCA and augmentation of CICR activity contribute to the alterations accounting for the impaired calcium homeostatic processes observed in 'epileptic' neurons. The results suggest that persistent changes in [Ca2+]i levels following epileptogenesis may contribute to the long-term plasticity changes manifested in epilepsy and that understanding the basic mechanisms mediating these changes may provide an insight into the development of novel therapeutic approaches to treat epilepsy and prevent or reverse epileptogenesis.     

腺苷抑制海马神经元自发放电和谷氨酸所致癫痫样放电

应用细胞外记录单位放电技术,在大鼠海马脑片上观察腺苷（ａｄｃｎｏｓｉｎｅ,Ａｄｏ）对ＣＡ１区神经元自发和谷氨酸所致癫痫样放电的影响。实验结果如下：⑴２０个海刀ＣＡ１神经元在给予Ａｄｏ（０．０１－０．１μｍｏｌ／Ｌ）时自发放电频率降低,且呈明显的剂量依赖性;⑵在２２个ＣＡ１单位,应用腺苷受体非选择性拮抗剂８－苯茶碱（８－ｐｈｅｎｙｌ－ｔｈｅｏｐｈｙｌｌｉｎｅ,８－ＰＴ,０．５ｍｍｏｌ／Ｌ）和腺苷Ａ１     

In vivo optical mapping of epileptic foci and surround inhibition in ferret cerebral cortex

The population of neurons participating in an epileptiform event varies from moment to moment. Most techniques currently used to localize epileptiform events in vivo have spatial and/or temporal sampling limitations. Here we show in an animal model that optical imaging based on intrinsic signals is an excellent method for in vivo mapping of clinically relevant epileptiform events, such as interictal spikes, ictal onsets, ictal spread and secondary homotopic foci. In addition, a decrease in the optical signal correlates spatially with a decrease in neuronal activity recorded from cortex surrounding an epileptic focus. Optical mapping of epilepsy might be a useful adjunct in the surgical treatment of neocortical epilepsy, which critically depends on the precise localization of intrinsically epileptogenic neurons.     

Spatial propagation of interictal discharges along the cortex

Interictal discharges (IIDs) accompany epileptic seizures and highlight the mechanisms of pathological activity. The propagation of IIDs along the neural tissue is not well understood. To simulate IID propagation, this study proposes a new mathematical model that uses the conductance-based refractory density approach for glutamatergic and GABAergic neuronal populations. The mathematical model is found to be consistent with experimental double-patch registrations in the 4-aminopyridine in vitro model of epilepsy. In slices, the spontaneous activity of interneurons leads to their synchronization by means of the depolarizing GABAmediated response, thus initiating IIDs. Modeling reveals a clustering of interneuronal synchronization followed by IIDs with activity fronts that propagate along the cortex. The GABA-mediated depolarization either remains to be subthreshold for the principal neurons and thus results in pure GABAergic IIDs (IID1s) or leads to glutamatergic excitation, thus resulting in another type of IIDs (IID2s). In both the model and experiment, IIDs propagate as waves, with constant activity profiles and velocity. The speed of IIDs is of the order of tens of mm/s and is larger for IID2s than for IID1s (40 and 20?mm/s, respectively). The simulations, consistent with experimental observations, show that the wavelike propagation of IIDs initiated by interneurons is determined by local synaptic connectivity under the conditions of depolarizing GABA.     

A New Computational Model for Neuro-Glio-Vascular Coupling: Astrocyte Activation Can Explain Cerebral Blood Flow Nonlinear Response to Interictal Events

Developing a clear understanding of the relationship between cerebral blood flow (CBF) response and neuronal activity is of significant importance because CBF increase is essential to the health of neurons, for instance through oxygen supply. This relationship can be investigated by analyzing multimodal (fMRI, PET, laser Doppler…) recordings. However, the important number of intermediate (non-observable) variables involved in the underlying neurovascular coupling makes the discovery of mechanisms all the more difficult from the sole multimodal data. We present a new computational model developed at the population scale (voxel) with physiologically relevant but simple equations to facilitate the interpretation of regional multimodal recordings. This model links neuronal activity to regional CBF dynamics through neuro-glio-vascular coupling. This coupling involves a population of glial cells called astrocytes via their role in neurotransmitter (glutamate and GABA) recycling and their impact on neighboring vessels. In epilepsy, neuronal networks generate epileptiform discharges, leading to variations in astrocytic and CBF dynamics. In this study, we took advantage of these large variations in neuronal activity magnitude to test the capacity of our model to reproduce experimental data. We compared simulations from our model with isolated epileptiform events, which were obtained in vivo by simultaneous local field potential and laser Doppler recordings in rats after local bicuculline injection. We showed a predominant neuronal contribution for low level discharges and a significant astrocytic contribution for higher level discharges. Besides, neuronal contribution to CBF was linear while astrocytic contribution was nonlinear. Results thus indicate that the relationship between neuronal activity and CBF magnitudes can be nonlinear for isolated events and that this nonlinearity is due to astrocytic activity, highlighting the importance of astrocytes in the interpretation of regional recordings.     

Various synaptic activities and firing patterns in cortico-striatal and striatal neurons in vivo

It is commonly assumed that spontaneous activity of striatal output neurons is characterized by a two-state behavior. This assumption is mainly based on in vivo intracellular recordings under urethane and/or ketamine-xylazine anesthesia showing that striatal neurons oscillate between two preferred membrane potentials, a Down state (hyperpolarized level), resulting from an inwardly rectifying potassium conductance, and an Up state (depolarized level) caused by complex interactions between a barrage of cortical synaptic excitation and voltage-dependent potassium conductances. However, a recent comparative study using different anesthetics showed that striatal neurons can exhibit various shapes of synaptic activity depending on the temporal structure and the degree of synchronization of their cortico-striatal afferents. These new data demonstrate that the "classical" Up and Down states do not provide the unique spontaneous activity that can be encountered in striatal neurons in vivo. Rather we propose that striatal neurons should exhibit various synaptic activities and firing patterns depending on the states of vigilance. This hypothesis would be validated in further experiments in which the intracellular activity of striatal neurons will be recorded during the natural sleep-wake cycle.     

Population oscillations in a discrete model of neural networks of the brain

A discrete model of biological neural networks is used to find out how synchronized firing of neurons emerges in a randomly connected neural population. The objective is to understand the mechanisms underlying brain waves and to find and characterize conditions which support spontaneous switching from disordered to rhythmic population activity as in case of an epileptic seizure. The model is kept as simple as possible to achieve on one hand a fast performance of computer simulations of networks with up to 10,000 neurons and to keep on the other hand an overview of parameter dependences. Dynamics of the model can be classified into different regimes: random fluctuations, rhythmic oscillations and silence. When the ratio of the inhibitory/excitatory connectivity is raised the system crosses from the fluctuating regime through the rhythmic oscillating region to the silence regime. Close to the boundary between the fluctuating and the oscillating regimes the network shows spontaneous bursting of high amplitude rhythmic oscillations, which is characteristic of epileptiform behavior. The simulation results are in agreement with recent theories saying that focal epilepsy after injury of the brain could result from axonal sprouting of GABAergic neurons in the injured region.     

Opposite Effects of Low and High Doses of Aβ42 on Electrical Network and Neuronal Excitability in the Rat Prefrontal Cortex

Changes in neuronal synchronization have been found in patients and animal models of Alzheimer''s disease (AD). Synchronized behaviors within neuronal networks are important to such complex cognitive processes as working memory. The mechanisms behind these changes are not understood but may involve the action of soluble β-amyloid (Aβ) on electrical networks. In order to determine if Aβ can induce changes in neuronal synchronization, the activities of pyramidal neurons were recorded in rat prefrontal cortical (PFC) slices under calcium-free conditions using multi-neuron patch clamp technique. Electrical network activities and synchronization among neurons were significantly inhibited by low dose Aβ42 (1 nM) and initially by high dose Aβ42 (500 nM). However, prolonged application of high dose Aβ42 resulted in network activation and tonic firing. Underlying these observations, we discovered that prolonged application of low and high doses of Aβ42 induced opposite changes in action potential (AP)-threshold and after-hyperpolarization (AHP) of neurons. Accordingly, low dose Aβ42 significantly increased the AP-threshold and deepened the AHP, making neurons less excitable. In contrast, high dose Aβ42 significantly reduced the AP-threshold and shallowed the AHP, making neurons more excitable. These results support a model that low dose Aβ42 released into the interstitium has a physiologic feedback role to dampen electrical network activity by reducing neuronal excitability. Higher concentrations of Aβ42 over time promote supra-synchronization between individual neurons by increasing their excitability. The latter may disrupt frontal-based cognitive processing and in some cases lead to epileptiform discharges.     

Neuron to astrocyte communication via cannabinoid receptors is necessary for sustained epileptiform activity in rat hippocampus

Astrocytes are integral functional components of synapses, regulating transmission and plasticity. They have also been implicated in the pathogenesis of epilepsy, although their precise roles have not been comprehensively characterized. Astrocytes integrate activity from neighboring synapses by responding to neuronally released neurotransmitters such as glutamate and ATP. Strong activation of astrocytes mediated by these neurotransmitters can promote seizure-like activity by initiating a positive feedback loop that induces excessive neuronal discharge. Recent work has demonstrated that astrocytes express cannabinoid 1 (CB1) receptors, which are sensitive to endocannabinoids released by nearby pyramidal cells. In this study, we tested whether this mechanism also contributes to epileptiform activity. In a model of 4-aminopyridine induced epileptic-like activity in hippocampal slice cultures, we show that pharmacological blockade of astrocyte CB1 receptors did not modify the initiation, but significantly reduced the maintenance of epileptiform discharge. When communication in astrocytic networks was disrupted by chelating astrocytic calcium, this CB1 receptor-mediated modulation of epileptiform activity was no longer observed. Thus, endocannabinoid signaling from neurons to astrocytes represents an additional significant factor in the maintenance of epileptiform activity in the hippocampus.     

Changes in membrane potential and postsynaptic potentials evoked by strychnine in neocortical neurons

Intracellular responses of neurons of the suprasylvian fissure to intracortical stimulation before and during topical cortical strychnine application was studied in experiments on immobilized, unanesthetized cats (a local anesthetic was used). Untreated cortical neurons responded to intracortical stimulation with a monosynaptic excitatory postsynaptic potential (EPSP) followed by an inhibitory postsynaptic potential (IPSP). Application of strychnine evoked epileptiform population activity and paroxysmal depolarizations of neuronal membrane potentials (MPs), followed by hyperpolarization. Increased hyperpolarizations, and the prolonged duration of their summation were responsible for an increased MP and reduced or abolished tonic spike activity. Intracellular application (as a result of diffusion from the microelectrode) of ethyleneglycoltetraacetate (EGTA) that blocked the calcium-dependent potassium membrane conductance (gK(Ca)) abolished the hyperpolarization. The development of epileptiform activity was accompanied by reduction of the IPSP, and an increase in the monosynaptic EPSP. The role of gK(Ca) and postsynaptic inhibition in epileptogenesis is discussed.I. I. Mechnikov State University, Odessa. Translated from Neirofiziologiya, Vol. 24, No. 6, pp. 684–691, November–December, 1992.     

Do glia contribute to behaviour? A neuromodulatory review

1. The links between behavioural state, gross electrophysiology and the activity of neurons and astrocytes are reviewed to stimulate interest in the contributions that glia make to behaviour. 2. Behavioural arousal in which neuronal responsivity ("sensitivity") is elevated is also associated with a sustained (0.5-10 sec) potential shift (SPS). 3. There is powerful and accumulating evidence that the SPS is primarily of glial origin. 4. In epilepsy neurons are hyperactive and there is a massive SPS during seizures. In seizure free periods, epileptic animals frequently have elevated arousal responses and increased neuronal sensitivity, indicating that seizures may be due to elevation of the activity of a normally adaptive sensitizing mechanism. 5. The common finding of an astrocytic pathology in epilepsy and the links between arousal, neuronal sensitization, SPSs and seizures implicates a modulatory role for astrocytes in both health and disease. 6. Glia, especially astrocytes, may modulate neuronal responsiveness by regulation of the microenvironment. 7. At the current state of knowledge, regulation of extracellular ionic K+, Ca2+ and neurotransmitter glutamate and GABA seem to be the most important candidates for modulating neuronal sensitivity in arousal and abnormally for seizure genesis. 8. Both in phylogeny and in ontogeny, glia and neurons have intimate associations. 9. The functional astrocytic syncitium is in a prime position to control the ecology of neuronal populations and thereby their activity. 10. The physiology and biochemistry of glia-neuronal interactions offers exciting new prospects for developments in behavioural neuroscience.     

The role of parvalbumin-containing interneurons in the regulation of spontaneous synchronous activity of brain neurons in culture

Subtypes of inhibitory GABAergic neurons containing Ca²⁺-binding proteins play a pivotal role in the regulation of spontaneous synchronous [Ca²⁺]_i transients in a neuronal network. In this study it is shown that: (1) the interneurons that containing Ca²⁺-binding proteins at buffer concentration can be identified by the shape of Ca²⁺-signa1 in response to depolarization or activation of ionotropic glutamate receptors; (2) Ca²⁺-binding proteins are involved in desynchronization of spontaneous Ca²⁺ transients. At low frequencies of spontaneous synchronous [Ca²⁺]_i transients (less than 0.2 Hz) neurons show quasi-synchronous pulsations. At higher frequencies, synchronization of spontaneous synchronous [Ca²⁺]_i transients occurs in all neurons; (3) it is established that several synchronous oscillations with different frequencies coexist in the network and the amplitude of their depolarizing pulse also varies. This phenomenon is apparently the mechanism that selectively directs information in separate neurons using the same network; and (4) in one population of interneurons at high frequencies of spontaneous synchronous [Ca²⁺]_i transients the inversion of Cl^– concentration gradient is observed. In this case, the inhibition of GABA(A) receptors suppresses the activity of neurons in this population and excites other neurons in the network. Thus, the GABAergic neurons that contain Ca-binding proteins show different mechanisms to regulate the synchronous neuronal activities in cultured rat hippocampal cells.     

Sonic hedgehog is a regulator of extracellular glutamate levels and epilepsy

Sonic hedgehog (Shh), both as a mitogen and as a morphogen, plays an important role in cell proliferation and differentiation during early development. Here, we show that Shh inhibits glutamate transporter activities in neurons, rapidly enhances extracellular glutamate levels, and affects the development of epilepsy. Shh is quickly released in response to epileptic, but not physiological, stimuli. Inhibition of neuronal glutamate transporters by Shh depends on heterotrimeric G protein subunit Gα_i and enhances extracellular glutamate levels. Inhibiting Shh signaling greatly reduces epileptiform activities in both cell cultures and hippocampal slices. Moreover, pharmacological or genetic inhibition of Shh signaling markedly suppresses epileptic phenotypes in kindling or pilocarpine models. Our results suggest that Shh contributes to the development of epilepsy and suppression of its signaling prevents the development of the disease. Thus, Shh can act as a modulator of neuronal activity, rapidly regulating glutamate levels and promoting epilepsy.     

Alcohol Abuse Promotes Changes in Non-Synaptic Epileptiform Activity with Concomitant Expression Changes in Cotransporters and Glial Cells

Non-synaptic mechanisms are being considered the common factor of brain damage in status epilepticus and alcohol intoxication. The present work reports the influence of the chronic use of ethanol on epileptic processes sustained by non-synaptic mechanisms. Adult male Wistar rats administered with ethanol (1, 2 e 3 g/kg/d) during 28 days were compared with Control. Non-synaptic epileptiform activities (NEAs) were induced by means of the zero-calcium and high-potassium model using hippocampal slices. The observed involvement of the dentate gyrus (DG) on the neurodegeneration promoted by ethanol motivated the monitoring of the electrophysiological activity in this region. The DG regions were analyzed for the presence of NKCC1, KCC2, GFAP and CD11b immunoreactivity and cell density. The treated groups showed extracellular potential measured at the granular layer with increased DC shift and population spikes (PS), which was remarkable for the group E1. The latencies to the NEAs onset were more prominent also for the treated groups, being correlated with the neuronal loss. In line with these findings were the predispositions of the treated slices for neuronal edema after NEAs induction, suggesting that restrict inter-cell space counteracts the neuronal loss and subsists the hyper-synchronism. The significant increase of the expressions of NKCC1 and CD11b for the treated groups confirms the existence of conditions favorable to the observed edematous necrosis. The data suggest that the ethanol consumption promotes changes on the non-synaptic mechanisms modulating the NEAs. For the lower ethanol dosage the neurophysiological changes were more effective suggesting to be due to the less intense neurodegenertation.     

Role of K(ATP) channels in protection against neuronal excitatory insults

ATP-sensitive K⁺ (K_ATP) channels that are gated by intracellular ATP/ADP concentrations are a unique subtype of potassium channels and play an essential role in coupling intracellular metabolic events to electrical activity. Opening of K_ATP channels during energy deficits in the CNS induces efflux of potassium ions and in turn hyperpolarizes neurons. Thus, activation of K_ATP channels is thought to be able to counteract excitatory insults and protect against neuronal death. In this review, we bring together recent studies about what kinds of molecules are needed to build and regulate arrays of K_ATP channel functions in the CNS neurons. We propose a model to explain how K_ATP channel activation regulates glutamate release from the pre-synaptic terminals and how this regulation protects against ischemic neuronal injury and epilepsy.