Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study

An increase of extracellular potassium ion concentration can result in neuronal hyperexcitability, and thus contribute to non-synaptic epileptiform activity. It has been shown that potassium lateral diffusion alone is sufficient for synchronization in the low-calcium epilepsy in-vitro model. However, it is not yet known whether the lateral diffusion can, by itself, induce seizure activity. We hypothesize that spontaneous sustained neuronal activity can be generated by potassium coupling between neurons. To test this hypothesis, neuronal simulations with 2-cell or 4-cell models were used. Each model neuron was embedded in a bath of K+ and surrounded by interstitial space. Interstitial potassium concentration was regulated by both K+-pump and glial buffer mechanisms. Simulations performed with two coupled neurons with parameter values within physiological range show that, without chemical and electrical synapses, potassium lateral diffusion alone can generate and synchronize zero-Ca2+ non-synaptic epileptiform activity. Simulations performed with a network of four zero-Ca2+ CA1 pyramidal neurons modeled in zero-calcium conditions also show that spontaneous sustained activity can propagate by potassium lateral diffusion alone with a velocity of approximately 0.93 mm/sec. This diffusion model used for the simulations is based on physiological parameters, is robust for various kinetics, and is able to reproduce both the spontaneous triplet bursting of non-synaptic activity and speed of propagation in low-Ca2+ non-synaptic epilepsy experiments. These simulations suggest that potassium lateral diffusion can play an important role in the synchronization and generation on non-synaptic epilepsy.     

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.     

The Neuroglial Potassium Cycle during Neurotransmission: Role of Kir4.1 Channels

Neuronal excitability relies on inward sodium and outward potassium fluxes during action potentials. To prevent neuronal hyperexcitability, potassium ions have to be taken up quickly. However, the dynamics of the activity-dependent potassium fluxes and the molecular pathways underlying extracellular potassium homeostasis remain elusive. To decipher the specific and acute contribution of astroglial K_ir4.1 channels in controlling potassium homeostasis and the moment to moment neurotransmission, we built a tri-compartment model accounting for potassium dynamics between neurons, astrocytes and the extracellular space. We here demonstrate that astroglial K_ir4.1 channels are sufficient to account for the slow membrane depolarization of hippocampal astrocytes and crucially contribute to extracellular potassium clearance during basal and high activity. By quantifying the dynamics of potassium levels in neuron-glia-extracellular space compartments, we show that astrocytes buffer within 6 to 9 seconds more than 80% of the potassium released by neurons in response to basal, repetitive and tetanic stimulations. Astroglial K_ir4.1 channels directly lead to recovery of basal extracellular potassium levels and neuronal excitability, especially during repetitive stimulation, thereby preventing the generation of epileptiform activity. Remarkably, we also show that K_ir4.1 channels strongly regulate neuronal excitability for slow 3 to 10 Hz rhythmic activity resulting from probabilistic firing activity induced by sub-firing stimulation coupled to Brownian noise. Altogether, these data suggest that astroglial K_ir4.1 channels are crucially involved in extracellular potassium homeostasis regulating theta rhythmic activity.     

Effects of elevated extracellular potassium on the stimulation mechanism of diastolic cardiac tissue

During cardiac disturbances such as ischemia and hyperkalemia, the extracellular potassium ion concentration is elevated. This in turn changes the resting transmembrane potential and affects the excitability of cardiac tissue. To test the hypothesis that extracellular potassium elevation also alters the stimulation mechanism, we used optical fluorescence imaging to examine the mechanism of diastolic anodal unipolar stimulation of cardiac tissue under 4 mM (normal) and 8 mM (elevated) extracellular potassium. We present several visualization methods that are useful for distinguishing between anodal-make and anodal-break excitation. In the 4-mM situation, stimulation occurred by the make, or stimulus-onset, mechanism that involved propagation out of the virtual cathodes. For 8-mM extracellular potassium, the break or stimulus termination mechanism occurred with propagation out of the virtual anode. We conclude that elevated potassium, as might occur in myocardial ischemia, alters not only stimulation threshold but also the excitation mechanism for anodal stimulation.     

Determinants of functional coupling between astrocytes and respiratory neurons in the pre-Bötzinger complex

Respiratory neuronal network activity is thought to require efficient functioning of astrocytes. Here, we analyzed neuron-astrocyte communication in the pre-Bötzinger Complex (preBötC) of rhythmic slice preparations from neonatal mice. In astrocytes that exhibited rhythmic potassium fluxes and glutamate transporter currents, we did not find a translation of respiratory neuronal activity into phase-locked astroglial calcium signals. In up to 20% of astrocytes, 2-photon calcium imaging revealed spontaneous calcium fluctuations, although with no correlation to neuronal activity. Calcium signals could be elicited in preBötC astrocytes by metabotropic glutamate receptor activation or after inhibition of glial glutamate uptake. In the latter case, astrocyte calcium elevation preceded a surge of respiratory neuron discharge activity followed by network failure. We conclude that astrocytes do not exhibit respiratory-rhythmic calcium fluctuations when they are able to prevent synaptic glutamate accumulation. Calcium signaling is, however, observed when glutamate transport processes in astrocytes are suppressed or neuronal discharge activity is excessive.     

Bistability dynamics in simulations of neural activity in high-extracellular-potassium conditions

Modulation of extracellular potassium concentration ([K]_o) has a profound impact on the excitability of neurons and neuronal networks. In the CA3 region of the rat hippocampus synchronized epileptiform bursts occur in conditions of increased [K]_o. The dynamic nature of spontaneous neuronal firing in high [K]_o is therefore of interest. One particular interest is the potential presence of bistable behaviors such as the coexistence of stable repetitive firing and fixed rest potential states generated in individual cells by the elevation of [K]_o. The dynamics of repetitive activity generated by increased [K]_o is investigated in a 19-compartment hippocampal pyramidal cell (HPC) model and a related two-compartment reduced HPC model. Results are compared with those for the Hodgkin-Huxley equations in similar conditions. For neural models, [K]_o changes are simulated as a shift in the potassium reversal potential (E _K ). Using phase resetting and bifurcation analysis techniques, all three models are shown to have specific regions of E _K that result in bistability. For activity in bistable parameter regions, stimulus parameters are identified that switch high-potassium model behavior from repetitive firing to a quiescent state. Bistability in the HPC models is limited to a very small parameter region. Consequently, our results suggest that it is likely some HPCs in networks exposed to high [K]_o continue to burst such that a stable, quiescent network state does not exist. In [K]_o ranges where HPCs are not bistable, the population may still exhibit bistable behaviors where synchronous population events are reversibly annihilated by phase resetting pulses, suggesting the existence of a nonsynchronous network attractor.     

Nonelectrolyte penetration and sodium fluxes through the axolemma of resting and stimulated medium sized axons of the squid Doryteuthis plei

The penetration of ¹⁴C-labeled erythritol, mannitol, and sucrose through the axolemma was determined in medium sized paired axons, one at rest and the other stimulated 25 times per sec. The resting permeabilities, in 10^-7 cm/sec, are erythritol, 2.9 ± 0.3 (mean ± SEM); mannitol, 2.3 ± 0.4; and sucrose 0.9 ± 0.1. In the stimulated axons they are: erythritol, 5.2 ± 0.3; mannitol, 4.0 ± 0.5; and sucrose, 1.8 ± 0.3. Thus, the calculated permeabilities during activity (1 msec per impulse), in the same units, are: 100, 75, and 38, respectively. These changes in permeability are reversible. The effects of external potassium and sodium concentrations on erythritol penetration were also studied. At rest, erythritol penetration is independent of potassium and sodium concentrations. In the stimulated axons, erythritol penetration decreases when the extracellular sodium is diminished. Sodium influx (not the efflux) decreases during rest and activity when the extracellular sodium is diminished. The diminution during activity of erythritol and sodium entries in low sodium solutions may be related to a decrease of a drag effect of sodium ions on the nonelectrolyte molecules or to independent effects of the sodium concentration on sodium influx and the nonelectrolyte pathways. The axolemma discriminates among erythritol, mannitol, sucrose, and the different ionic species during rest and activity.     

Responses of Retinal Ganglion Cells to Extracellular Electrical Stimulation,from Single Cell to Population: Model-Based Analysis

Retinal ganglion cells (RGCs), which survive in large numbers following neurodegenerative diseases, could be stimulated with extracellular electric pulses to elicit artificial percepts. How do the RGCs respond to electrical stimulation at the sub-cellular level under different stimulus configurations, and how does this influence the whole-cell response? At the population level, why have experiments yielded conflicting evidence regarding the extent of passing axon activation? We addressed these questions through simulations of morphologically and biophysically detailed computational RGC models on high performance computing clusters. We conducted the analyses on both large-field RGCs and small-field midget RGCs. The latter neurons are unique to primates. We found that at the single cell level the electric potential gradient in conjunction with neuronal element excitability, rather than the electrode center location per se, determined the response threshold and latency. In addition, stimulus positioning strongly influenced the location of RGC response initiation and subsequent activity propagation through the cellular structure. These findings were robust with respect to inhomogeneous tissue resistivity perpendicular to the electrode plane. At the population level, RGC cellular structures gave rise to low threshold hotspots, which limited axonal and multi-cell activation with threshold stimuli. Finally, due to variations in neuronal element excitability over space, following supra-threshold stimulation some locations favored localized activation of multiple cells, while others favored axonal activation of cells over extended space.     

Short-term and long-term alterations in neuronal excitability during injury-induced axonal regeneration in ganglia and cell culture

Helisoma neurons B5, regenerating axonal arbors following crush-axotomyin vivo, displayed a transient (<24 h) reduction in excitability followed by a sustained period of hyperexcitability (>13 d). Neurons isolated into outgrowth-permissive cell culture conditions expressed a similar pattern of hypo- and hyperexcitability; however, excitability of neurons B5 in culture was elevated for only 5 d and then declined to a lower, stable level. The expression of these alterations in excitability was neurite outgrowth-independent and required the presence of ganglia-derived conditioning factors in the culture medium. Excitability of neurons in medium lacking conditioning factors fell by day 3 to minimal levels. Conditioned medium was effective in rescuing excitability of neurons deprived of conditioning factors during their first 3 days of cell culture, but not following longer periods of deprivation. Exposure to the protein synthesis inhibitor, anisomycin, blocked the ability of conditioning factors to rescue B5 neuronal excitability. Together, results from cell culture suggest that mechanisms underlying neuronal excitability following nerve injury are independent of process outgrowth state, but require exposure to conditioning factors derived from injured neural tissue within several days of axonal insult. Although changes in B5 neurite outgrowth and neuronal excitability were expressed simultaneously following axonal injury, their independence suggests the existence of an underlying regenerative state that regulates both cellular modifications.     

Signal propagation in feedforward neuronal networks with unreliable synapses

In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on both types of neural activity propagation in this work. We first study networks composed of purely excitatory neurons. Our results show that both the successful transmission probability and excitatory synaptic strength largely influence the propagation of these two types of neural activities, and better tuning of these synaptic parameters makes the considered network support stable signal propagation. It is also found that noise has significant but different impacts on these two types of propagation. The additive Gaussian white noise has the tendency to reduce the precision of the synfire activity, whereas noise with appropriate intensity can enhance the performance of firing rate propagation. Further simulations indicate that the propagation dynamics of the considered neuronal network is not simply determined by the average amount of received neurotransmitter for each neuron in a time instant, but also largely influenced by the stochastic effect of neurotransmitter release. Second, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. We confirm that some differences can be observed in these two different feedforward neuronal network models. Finally, we study the signal propagation in feedforward neuronal networks consisting of both excitatory and inhibitory neurons, and demonstrate that inhibition also plays an important role in signal propagation in the considered networks.     

Epileptic seizures in a heterogeneous excitatory network with short-term plasticity

Epilepsy involves a diverse group of abnormalities, including molecular and cellular disorders. These abnormalities prove to be associated with the changes in local excitability and synaptic dynamics. Correspondingly, the epileptic processes including onset, propagation and generalized seizure may be related with the alterations of excitability and synapse. In this paper, three regions, epileptogenic zone (EZ), propagation area and normal region, were defined and represented by neuronal population model with heterogeneous excitability, respectively. In order to describe the synaptic behavior that the strength was enhanced and maintained at a high level for a short term under a high frequency spike train, a novel activity-dependent short-term plasticity model was proposed. Bifurcation analysis showed that the presence of hyperexcitability could increase the seizure susceptibility of local area, leading to epileptic discharges first seen in the EZ. Meanwhile, recurrent epileptic activities might result in the transition of synaptic strength from weak state to high level, augmenting synaptic depolarizations in non-epileptic neurons as the experimental findings. Numerical simulation based on a full-connected weighted network could qualitatively demonstrate the epileptic process that the propagation area and normal region were successively recruited by the EZ. Furthermore, cross recurrence plot was used to explore the synchronization between neuronal populations, and the global synchronization index was introduced to measure the global synchronization. Results suggested that the synchronization between the EZ and other region was significantly enhanced with the occurrence of seizure. Interestingly, the desynchronization phenomenon was also observed during seizure initiation and propagation as reported before. Therefore, heterogeneous excitability and short-term plasticity are believed to play an important role in the epileptic process. This study may provide novel insights into the mechanism of epileptogenesis.     

Dynamic effective connectivity of inter-areal brain circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities.     

GWAS findings for human iris patterns: associations with variants in genes that influence normal neuronal pattern development

Human iris patterns are highly variable. The origins of this variation are of interest in the study of iris-related eye diseases and forensics, as well as from an embryological developmental perspective, with regard to their possible relationship to fundamental processes of neurodevelopment. We have performed genome-wide association scans on four iris characteristics (crypt frequency, furrow contractions, presence of peripupillary pigmented ring, and number of nevi) in three Australian samples of European descent. Both the discovery (n = 2121) and replication (n = 499 and 73) samples showed evidence for association between (1) crypt frequency and variants in the axonal guidance gene SEMA3A (p = 6.6 × 10⁻¹¹), (2) furrow contractions and variants within the cytoskeleton gene TRAF3IP1 (p = 2.3 × 10⁻¹²), and (3) the pigmented ring and variants in the well-known pigmentation gene SLC24A4 (p = 7.6 × 10⁻²¹). These replicated findings individually accounted for around 1.5%–3% of the variance for these iris characteristics. Because both SEMA3A and TRAFIP1 are implicated in pathways that control neurogenesis, neural migration, and synaptogenesis, we also examined the evidence of enhancement among such genes, finding enrichment for crypts and furrows. These findings suggest that genes involved in normal neuronal pattern development may also influence tissue structures in the human iris.     

Innate synchronous oscillations in freely-organized small neuronal circuits

Background

Information processing in neuronal networks relies on the network''s ability to generate temporal patterns of action potentials. Although the nature of neuronal network activity has been intensively investigated in the past several decades at the individual neuron level, the underlying principles of the collective network activity, such as the synchronization and coordination between neurons, are largely unknown. Here we focus on isolated neuronal clusters in culture and address the following simple, yet fundamental questions: What is the minimal number of cells needed to exhibit collective dynamics? What are the internal temporal characteristics of such dynamics and how do the temporal features of network activity alternate upon crossover from minimal networks to large networks?

Methodology/Principal Findings

We used network engineering techniques to induce self-organization of cultured networks into neuronal clusters of different sizes. We found that small clusters made of as few as 40 cells already exhibit spontaneous collective events characterized by innate synchronous network oscillations in the range of 25 to 100 Hz. The oscillation frequency of each network appeared to be independent of cluster size. The duration and rate of the network events scale with cluster size but converge to that of large uniform networks. Finally, the investigation of two coupled clusters revealed clear activity propagation with master/slave asymmetry.

Conclusions/Significance

The nature of the activity patterns observed in small networks, namely the consistent emergence of similar activity across networks of different size and morphology, suggests that neuronal clusters self-regulate their activity to sustain network bursts with internal oscillatory features. We therefore suggest that clusters of as few as tens of cells can serve as a minimal but sufficient functional network, capable of sustaining oscillatory activity. Interestingly, the frequencies of these oscillations are similar those observed in vivo.     

The permeability to ions of the neural lamella and the extracellular spaces in the C.N.S. of Anodonta cygnea.

Rapid axonal depolarization follows the elevation of [K+]o in the Ringer bathing the surfaces of the connectives of both intact and desheathed cerebrovisceral connectives of Anodonta cygnea. Potassium movements between the blood or medium bathing the surface of the connectives and the axonal membranes can be accounted for in terms of a first-order diffusion process. No visible structural barriers to prevent free movements of materials through the neural lamella and the extracellular spaces can be detected in electron micrographs of the cerebro-visceral connectives. In desheathed preparations fast action potentials are conducted in sodium-free (dextran) Ringer. Mechanisms of axona .l function and ionic regulation in this and other invertebrate central nervous tissues are discussed in the light of these observations.     

Polarized Axonal Surface Expression of Neuronal KCNQ Potassium Channels Is Regulated by Calmodulin Interaction with KCNQ2 Subunit

KCNQ potassium channels composed of KCNQ2 and KCNQ3 subunits give rise to the M-current, a slow-activating and non-inactivating voltage-dependent potassium current that limits repetitive firing of action potentials. KCNQ channels are enriched at the surface of axons and axonal initial segments, the sites for action potential generation and modulation. Their enrichment at the axonal surface is impaired by mutations in KCNQ2 carboxy-terminal tail that cause benign familial neonatal convulsion and myokymia, suggesting that their correct surface distribution and density at the axon is crucial for control of neuronal excitability. However, the molecular mechanisms responsible for regulating enrichment of KCNQ channels at the neuronal axon remain elusive. Here, we show that enrichment of KCNQ channels at the axonal surface of dissociated rat hippocampal cultured neurons is regulated by ubiquitous calcium sensor calmodulin. Using immunocytochemistry and the cluster of differentiation 4 (CD4) membrane protein as a trafficking reporter, we demonstrate that fusion of KCNQ2 carboxy-terminal tail is sufficient to target CD4 protein to the axonal surface whereas inhibition of calmodulin binding to KCNQ2 abolishes axonal surface expression of CD4 fusion proteins by retaining them in the endoplasmic reticulum. Disruption of calmodulin binding to KCNQ2 also impairs enrichment of heteromeric KCNQ2/KCNQ3 channels at the axonal surface by blocking their trafficking from the endoplasmic reticulum to the axon. Consistently, hippocampal neuronal excitability is dampened by transient expression of wild-type KCNQ2 but not mutant KCNQ2 deficient in calmodulin binding. Furthermore, coexpression of mutant calmodulin, which can interact with KCNQ2/KCNQ3 channels but not calcium, reduces but does not abolish their enrichment at the axonal surface, suggesting that apo calmodulin but not calcium-bound calmodulin is necessary for their preferential targeting to the axonal surface. These findings collectively reveal calmodulin as a critical player that modulates trafficking and enrichment of KCNQ channels at the neuronal axon.     

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.     

Induction of neuronal activation by femtosecond‐pulsed laser irradiation and its potential application for amyloid‐β–induced toxicity assessment

Manipulating neural activity is crucial for studying the neural connectivity and the pathophysiology of neurodegenerative disease. Among various techniques for neural activation, direct optical stimulation method with femtosecond‐pulsed laser is simple and can be specifically applied on a single neuron. Brief irradiation of femtosecond laser pulses on a neuron elevates intracellular calcium, and it propagates to adjacent neurons. However, the mechanisms of laser‐induced neural activation are still unclear. In this report, we have elucidated the mechanism of laser‐induced neural activation which could be mediated by superoxide, specifically blocked by diphenyleneiodonium chloride, and depletion in intracellular calcium storage. Furthermore, we also showed that the propagation of calcium initiated by laser stimulation is dependent on the presence of extracellular calcium as well as electrical and chemical synapses. We verified the applicability of such mechanism for the assessment of neuronal functionality, by measuring calcium elevation, intracellular calcium propagation, ROS increase, and performing cell death assay in vehicle and Aβ‐treated neurons. This work suggests promising applications of the potential for implementing such laser‐induced neural activation for rapid and reliable drug screening.