Abstract

The regulation of transmembrane ion flux is crucial for maintaining physiological neuronal activity and preventing the occurrence of epileptic seizures. The net effect (e.g., depolarization or hyperpolarization) of the transmembrane ion flux is determined by the relative ion concentration gradients established across the cellular membrane. Because of the tight regulation of neuronal excitability and dynamics by changes in the ion concentrations, the brain has evolved multiple mechanisms to precisely regulate and maintain these concentration gradients. It has been demonstrated that the breakdown in the maintenance of ion gradients may lead to development of seizure discharges and may underly various forms of pathological neuronal activity. It is now well established that during a seizure discharge, the extracellular potassium concentration substantially increases, while the concentrations of extracellular sodium and calcium decrease. More recently, experimental recordings and computational models have demonstrated preictal increases in the intracellular chloride concentration in pyramidal neurons. This chapter discusses the effects of the ion concentration dynamics on seizure initiation, progression, and termination with the goal of providing novel insights into the underlying biophysical mechanisms of epileptic seizures.

Introduction

Epileptic disorders are characterized by unprovoked spontaneous recurrent seizures. These seizures can manifest as simple (if consciousness is unaffected) or complex (if consciousness is absent or impaired). The seizures may be either convulsive or nonconvulsive events of various durations (seconds to several minutes). Though seizures may display a variety of overt symptoms, there are similarities in their underlying pathophysiological features. Most seizures display large increases in neuronal firing and exhibit periodic transitions between synchronous bursting and less synchronous or even tonic firing dynamics (Lukawski et al., 2018; Hamidi and Avoli, 2015; Timofeev and Steriade, 2004; Niedermeyer, 2005; McNamara, 1994; McCormick and Contreras, 2001). It has been estimated that nearly 30% of epileptic patients have seizures which are not well controlled through pharmacological interventions (Lukawski et al., 2018; Brodie and French, 2000). These types of seizures are termed pharmaco-resistant or intractable and require more extreme interventions such as resection of epileptic foci. A better understanding of the underlying biophysical mechanisms of seizure generation is therefore necessary for reducing the prevalence of intractable epileptic seizures in humans.

Neuronal resting potentials and excitability are maintained and regulated by ion concentration gradients established across the cellular membrane. Due to the neuronal activities, intra- and extracellular ion concentration changes occur continuously in normal and pathological states; for example, an appropriate change in the extracellular ions can easily shift brain from wake to sleep or from sleep to wake (Ding et al., 2016). Due to their critical involvement in regulation of excitability, the brain has evolved multiple mechanisms for maintaining and reestablishing ion concentration gradients (Herreras and Somjen, 1993; Somjen, 2002; Somjen, 2004; Hille, 2001). Breakdown of the maintenance of these concentration gradients has been associated with the generation of seizure discharges (Avoli and de Curtis, 2011; González et al., 2018; Hamidi and Avoli, 2015; Filatov et al., 2011; Frohlich et al., 2008; Frohlich et al., 2010; Krishnan and Bazhenov, 2011; Krishnan et al., 2015; Wei et al., 2014; Cressman et al., 2009; Ullah et al., 2009; Grisar et al., 1992; Kager et al., 2000). It has been well documented that extracellular potassium concentration ([K⁺]_o) displays a substantial increase at the onset of a seizure (Somjen, 2002; Heinemann and Lux, 1977). This increase in [K⁺]_o is accompanied by decreases in both extracellular sodium ([Na⁺]_o) and calcium ([Ca²⁺]_o) concentrations throughout the duration of a seizure (Somjen, 2002). These changes in ion concentration are presumably driven by the influx of Na⁺ and Ca²⁺ and efflux of K⁺ during intensive neuronal firing associated with epileptiform activity. The ion dynamics may depend on the changes in excitability of specific neuron types, for example, inhibitory interneurons, caused by altered intracellular chloride ([Cl⁻]_i), and/or extracellular calcium ([Ca²⁺]_o) and magnesium ([Mg²⁺]_o) concentrations (Lillis et al., 2012; Somjen, 2002; Avoli and de Curtis, 2011; de Curtis and Avoli, 2016; González et al., 2018; Hamidi and Avoli, 2015). As such, an understanding of the specific influence of each ion on seizure dynamics and the interaction between those influences is crucial. In this chapter we will explore how the major ion species (K⁺, Na⁺, Cl⁻, Ca²⁺, and Mg²⁺) influence seizure dynamics and how seizures affect these ion concentrations, and we will highlight biophysical and dynamical mechanisms underlying seizure discharges.

Potassium Ions and the K⁺ Accumulation Hypothesis

Even minor fluctuations in brain activity result in measurable changes in the K⁺ equilibrium potential and, therefore, K⁺ currents. Initial studies on [K⁺]_o were mostly performed in anesthetized in vivo preparations (Lux and Neher, 1973; Prince et al., 1973; Moody et al., 1974), where [K⁺]_o increased in cortex in response to physiological stimuli. These findings indicated that [K⁺]_o is not fixed but represents a dynamic property of brain tissue (Singer and Lux, 1975; Connors et al., 1979). Substantial [K⁺]_o fluctuations were also found in cat suprasylvian cortex during slow oscillations under ketamine-xylazine anesthesia (Amzica and Steriade, 2000). During electrically or pharmacologically induced paroxysmal activity, [K⁺]_o changed substantially, but it never rose above a “ceiling value” of about 12 mM in the absence of spreading depression in the adult animal (Heinemann and Lux, 1977).

Experimental evidence, dating back to the late 1950s, has demonstrated that elevated levels of interstitial or extracellular K⁺ was capable of inducing seizures or seizure-like discharges both in vivo (Feldberg and Sherwood, 1957; Zuckermann and Glaser, 1968) and later in vitro (Jensen and Yaari, 1997; Leschinger et al., 1993; Pan and Stringer, 1997). Early hypotheses regarding the generation of seizure activity were centered on the idea that elevated [K⁺]_o resulted in network hyperexcitability and synchrony (Frohlich et al., 2008; Fertziger and Ranck, 1970; Cressman et al., 2009; Ullah et al., 2009). The so-called K⁺ accumulation hypothesis (Fertziger and Ranck, 1970; Green, 1964) predicted that (1) increases in [K⁺]_o could reach a threshold level and initiate a positive feedback loop with neuronal excitability in which (2) increased [K⁺]_o caused increased neuronal excitability, which in turn further increased [K⁺]_o, until (3) [K⁺]_o reaches a value for which neurons are too depolarized to fire (Fig. 17–1). Indeed, increasing [K⁺]_o to 8–16 mM in vitro (Traynelis and Dingledine, 1988) has been shown to drive paroxysmal activity in the hippocampus. Additionally, in vivo experiments have demonstrated that perfusion with high K⁺ medium over cortical tissue induces seizures (Zuckermann and Glaser, 1968).

Figure 17–1.

Illustration of potassium accumulation hypothesis (Frohlich et al., 2008).

The initial predictions derived from the K⁺ accumulation hypothesis (Fertziger and Ranck, 1970; Green, 1964) eluded experimental verification. In fact, little evidence was found for the following: (1) the presence of a [K⁺]_o threshold for seizure initiation (but see Sypert and Ward, 1974); (2) the monotonic increase in [K⁺]_o during seizures; and (3) the depolarization block of neurons at seizure cessation (Moody et al., 1974; Heinemann and Lux, 1977; Sypert and Ward, 1974). Rather, dynamic changes in [K⁺]_o appeared to be delayed in comparison to changes in neural activity. This delayed rise in [K⁺]_o was interpreted as evidence that increased [K⁺]_o is the result rather than the cause of cortical seizures. Also, [K⁺]_o increased during tonic firing phases and decreased during clonic bursting phases of the electrographic seizure (Sypert and Ward, 1974; Moody et al., 1974). Recently, the interpretation of these findings and the rejection of [K⁺]_o as an important factor in seizure generation have been reconsidered in the light of methodological concerns and novel insights from computational models (Somjen, 2004; Bazhenov et al., 2008). Paroxysmal activities can develop after tens of minutes following [K⁺]_o increase, and if [K⁺]_o was increased and [Ca²⁺]_o was decreased, paroxysmal discharges developed on the order of minutes (Zuckermann and Glaser, 1968; Seigneur and Timofeev, 2010).

Slice electrophysiology experiments in mouse hippocampus have shown that increases in K⁺ concentration in perfused artificial cerebrospinal fluid (ACSF) can result in seizure-like discharges resembling interictal spiking and ictal events in epileptic patients (Filatov et al., 2011). The accumulation of [K⁺]_o most likely leads to depolarization and hyperexcitability through a change in the K⁺ reversal potential, which leads to a reduction of hyperpolarizing outward K⁺ currents. For this reason, increased [K⁺]_o drives neuronal depolarization likely through its direct effects on K⁺ leak currents (Seigneur and Timofeev, 2010; Pedley et al., 1976). In addition, an increase in [K⁺]_o also produces a depolarizing shift in the reversal potential of the hyperpolarization-activated depolarizing mixed cation current (I_h) that may contribute to seizure onset (Timofeev et al., 2002a). Presumably, the balance of intra- and extracellular K⁺ concentrations also affects neuronal excitability by its direct influence on the repolarization phase of the action potential through activation of voltage and Ca⁺-dependent K⁺ currents. Increases in [K⁺]_o would depolarize the reversal potential of these channels and render them ineffective. In doing so, the neurons would have prolonged periods of Na⁺ and Ca²⁺ channel activation leading to prolonged depolarizations and increased excitability.

Computational models predicted that K⁺ dynamics may also play a crucial role in transitions between several characteristic spiking regimes observed during seizure discharges (Frohlich et al., 2006; Ho and Truccolo, 2016; Florence et al., 2009; Kager et al., 2000). Electrographic seizures commonly display transitions between periods of asynchronous tonic spiking and synchronous bursting (Niedermeyer, 2005; Niedermeyer, 2002). Application of dynamical systems analysis to the study of the role of [K⁺]_o in generation of electrical patterns of activity observed during epileptic seizures revealed (1) existence of four distinct activity patterns as a function of [K⁺]_o, that is, silence, tonic firing, bursting, and depolarization block, and (2) bistability with hysteresis between tonic firing and bursting for elevated [K⁺]_o levels (Frohlich and Bazhenov, 2006; Frohlich et al., 2008; Frohlich et al., 2006). Employing bifurcation analysis and using [K⁺]_o as a bifurcation parameter revealed the coexistence of stable attractors representing different firing regimes as a function of [K⁺]_o (Fig. 17–2A). Specifically, neurons remained in tonic-firing mode while [K⁺]_o increased up to the level where they were forced to switch to bursting mode (upper endpoint of hysteresis; Fig. 17–2A, [K⁺]_o ~ 6.35 mM). Conversely, neurons remained in bursting mode while [K⁺]_o decreased until the lower endpoint of the hysteresis was reached where they were forced to switch back to tonic-firing mode (low endpoint of hysteresis; Fig. 17–2A, [K⁺]_o ~ 5.45 mM). A region of bistability (5.45–6.35mM of [K⁺]_o) characterized the coexistence of tonic spiking and bursting states (note overlap between green and blue circles; Fig. 17–2A, boxed region).

Figure 17–2.

Bifurcation analysis of K⁺ regulation of spiking dynamics. A. Minimum/maximum voltage as a function of [K⁺]_o. Solid lines indicate stable fixed points. Circles indicate stable limit cycles. B. Left, Min/max plot showing hysteresis between tonic spiking (more...)

To explore whether bistability between tonic spiking and bursting dynamics persisted in a network of neurons, the same analysis was extended to a network (Fig. 17–2B–D). Treating [K⁺]_o as the bifurcation parameter again revealed bistability between tonic spiking and bursting states similar to that found in a single-cell model (Fig. 17–2B, left) (Frohlich et al., 2006). When [K⁺]_o was allowed to fluctuate naturally (rather than being treated as a parameter) in the network model, the neurons displayed self-sustained oscillations with periodic transitions between tonic spiking and bursting (Fig. 17–2 C,D). [K⁺]_o gradually increased during tonic spiking and gradually decreased during bursting (Fig. 17–2C). Thus, in the network model, bistability between tonic spiking and bursting regimes allowed the existence of self-sustained oscillations. In other words, although it was originally assumed that only positive feedback between [K⁺]_o and neural activity occurred during seizures, these modeling results show the alternating occurrence of positive (tonic firing) and negative (bursting) feedback. Thus, transitions between tonic firing and bursting observed during many types of seizure can be essentially the result of slow alternations between two meta-stable states, tonic firing and bursting states, mediated by [K⁺]_o dynamics. Figure 17–2B (right) summarized the basic schematic explaining the mechanism for the self-sustained oscillations driven by [K⁺]_o dynamics.

Sodium Ions and the Na⁺/K⁺ Pump

While the role of K⁺ in seizure dynamics is relatively well understood, substantially less is known about the role of Na⁺. This is likely due to the technical limitations in directly recording [Na⁺]_i (Somjen, 2002). Measurements of extracellular Na⁺, however, have revealed moderate decreases in [Na⁺]_o during seizures (Somjen, 2004). This reduction is presumed to be accompanied by increases in [Na⁺]_i, as the increased rate of Na⁺ spikes and activation of persistent Na⁺ current (Timofeev et al., 2004) during a seizure would lead to influx of Na⁺ through voltage-gated Na⁺ channels and synaptic currents.

The link between [Na⁺]_i and seizure dynamics was explored in computational models (Krishnan and Bazhenov, 2011; Krishnan et al., 2015; Cressman et al., 2009; Ullah et al., 2009). Altered Na-channel dynamics (in silico) resulted in increased network excitability resembling electrographic signatures of generalized epilepsy with febrile seizures (Spampanato et al., 2004). During seizure-like events, [Na⁺]_i displayed a gradual increase, with [Na⁺]_i reaching maximum values just prior to seizure termination. It was suggested that progressive accumulation of [Na⁺]_i could lead to spontaneous termination of seizures in two ways: (1) it would reduce the Na⁺ reversal potential thereby reducing overall excitability; (2) it would lead to stronger activation of the Na⁺/K⁺ ATPase, which would drive the hyperpolarizing Na⁺/K⁺ ATPase outward current. Indeed, increases in [Na⁺]_i activate the Na⁺/K⁺ ATPase, which exchanges three Na⁺ ions for two K⁺ ions, leading to outward hyperpolarizing current (Somjen, 2004; Hille, 2001). The resulting hyperpolarization of membrane voltage could trigger the termination of a seizure event (Krishnan and Bazhenov, 2011).

The dynamical mechanisms underlying termination of seizures were further explored in Krishnan et al. (2015). To dissect the relative contributions of the proposed mechanisms by which accumulated intracellular Na⁺ drives spontaneous seizure termination, Krishnan et al. (2015) used a combination of detailed computational modeling, in vitro slice electrophysiology, and bifurcation analysis. They found that the Na⁺-dependent activation of the Na⁺/K⁺ pump alone was sufficient to drive seizure termination. Furthermore, modulating the Na⁺/K⁺ pump current influenced seizure duration both in the model and in vitro (Krishnan et al., 2015).

Dynamical systems theory proved to be a powerful tool to explore the underlying dynamics of neuronal spiking/bursting during epileptic seizures. Because changes of some of the network characteristics, such as extracellular [K⁺]_o or intracellular [Ca²⁺]_i concentrations, are relatively slow, these models can be classified as slow-fast dynamical systems comprised of several distinct timescales (e.g., slow and fast) (Shilnikov, 2012). The dynamics of these slow-fast systems are determined by the attracting sets of the so-called slow-motion (or critical) manifolds. The critical manifold is comprised of equilibria and limit cycles of the fast subsystem and describes the dynamics of the slow-fast system with respect to specific parameter perturbations (Shilnikov, 2012).

To understand the dynamics behind the role of Na⁺/K⁺ ATPase in the termination of seizures, the critical manifolds in the 14-dimensional phase space of a single excitatory neuron with fixed ion concentrations were analyzed (Fig. 17–3; Krishnan et al., 2015). Figure 17–3 (A/B) shows the critical manifolds projected into the “[Ca²⁺]_i – V_d” subspace (V_d is dendritic voltage) for different fixed values of [K⁺]_o and [Na⁺]_i. When [K⁺]_o and [Na⁺]_i were fixed at 7.5 and 20 mM, respectively (Fig. 17–3A), the analysis revealed bistability between tonic spiking and bursting as reported before (see Fig. 17–2 in Frohlich et al., 2006). The bistability was due to the coexistence of two attractors: (1) a tonic spiking state represented by stable periodic orbit (limit cycle S in the yellow region of M_lc); this attractor remains stable in the model where [Ca²⁺]_i was a dynamical variable; and (2) a bursting state (gray line) caused by repetitive switching between the depolarized and hyperpolarized branches of the 1D M_eq, mediated by changes of [Ca²⁺]_i in the full model. Increase of [K⁺]_o to 9mM eliminated tonic spiking state (see Fig. 4D in Krishnan et al., 2015). Thus, in the model with freely changing [K⁺]_o, transitions between tonic spiking and bursting were mediated by [K⁺]_o dynamics. Indeed, as reported previously (Frohlich et al., 2006), tonic spiking led to progressive increase of [K⁺]_o due to increased firing rates, which triggered transition to bursting. During bursting, periods of depolarization block during each bursting event resulted in the gradual reduction of [K⁺]_o until the system could no longer support bursting dynamics and returned to the tonic spiking regime.

Figure 17–3.

Bifurcation analysis showing Na⁺-dependent seizure termination. [Ca²⁺]_i-voltage phase space projection showing 1D quiescent state (green line, M_eq) with hyperpolarized voltage states along the lower arm and depolarized states on the upper. 2D tonic spiking (more...)

When [Na⁺]_i was increased and fixed at 22 mM, corresponding to the observed level of [Na⁺]_i just prior to seizure termination in the full network (Krishnan and Bazhenov, 2011; Krishnan et al., 2015), the tonic spiking state was no longer reachable in the phase space for any initial conditions near the bursting cycle. This was due to the shift of the location of the stable periodic orbit relative to the critical manifold (Fig. 17–3B). Thus, in the full model, as [K⁺]_o decreased during bursting dynamics, eventually making bursting impossible, instead of switching to the tonic spiking state, the system transitioned to the silent state. The tonic spiking state was needed to increase [K⁺]_o; the inability of the system to switch between bursting and tonic spiking caused gradual reduction of [K⁺]_o and seizure termination (Krishnan and Bazhenov, 2011; Krishnan et al., 2015).

Chloride

Under normal conditions in adult neurons, chloride reversal potential is around –70 mV, so Cl⁻-mediated currents, such as GABA_A, are hyperpolarizing (Ben-Ari et al., 2007). In immature neurons, the GABA_A generates excitatory/depolarizing currents because of the elevated levels of [Cl⁻]_i (Cherubini et al., 1990; Kakazu et al., 1999; Ehrlich et al., 1999). With maturation, the function of the GABA_A receptor switches to generate inhibitory/hyperpolarizing currents due to the decrease of [Cl⁻]_i. This is attributable to a developmental changes in [Cl⁻]_i regulation, such as the increase of the K⁺-Cl⁻ cotransporter (Plotkin et al., 1997; Kakazu et al., 1999; Rivera et al., 1999) and the decrease of Na⁺-dependent Cl⁻ transport (Kakazu et al., 1999).

Chloride plays a complex role in seizure dynamics, one that remains poorly understood. During paroxysmal activities, the [Cl⁻]_i reversal potential can go from normal –70 mV to somewhere between –55 mV and 0 mV (Timofeev et al., 2002b; Cohen et al., 2002). Early experiments exploring the role of Cl⁻ in seizure generation demonstrated that reduction of [Cl⁻]_o could trigger seizure discharges in vitro and in vivo (Ransom, 1974; Yamamoto and Kawai, 1968). As Cl⁻ influx through GABA_A channels underlies fast IPSPs, it was suggested that the reduction of [Cl⁻]_o would cause reduced IPSPs and lower inhibitory drive. Additionally, in conditions of very low [Cl⁻]_o, GABA_A-induced currents may invert, leading to depolarization rather than hyperpolarization (Voipio and Kaila, 2000). This inversion of the current is due to the efflux of HCO₃⁻ through GABA_A anion channels (Voipio and Kaila, 2000). The role of depolarizing GABA currents was explored in computational models and was shown to possibly underly epileptic seizure-like discharges during early development (Chizhov et al., 2019; Kurbatova et al., 2016). Other studies also found that [Cl⁻]_i progressively increases throughout a bout of seizure (Krishnan and Bazhenov, 2011). Because the Cl⁻ reversal potential is only slightly more negative than the resting potential of neurons, the gradual accumulation of [Cl⁻]_i can quickly drive the system toward an equilibrium, thereby removing the Cl⁻ driving force, and reduce the hyperpolarizing effects of inhibitory synapses, promoting overexcitability and possibly seizures.

This traditional view of a loss of inhibition due to [Cl⁻]_i accumulation has been recently challenged by several experimental and computational studies (Avoli and de Curtis, 2011; González et al., 2018; Hamidi and Avoli, 2015; Shiri et al., 2016). Following 4-aminopyridine (4AP) treatment, increases in [Cl⁻]_i in excitatory neurons and increases in inhibitory interneuron firing at the onset of seizure-like discharges have been reported both in vivo (Grasse et al., 2013; Toyoda et al., 2015) and in vitro (Uva et al., 2015; Lillis et al., 2012; Levesque et al., 2016). Additionally, intense stimulation of GABAergic interneurons has been demonstrated to increase [K⁺]_o and generate long-lasting depolarizations (Rivera et al., 2005; Viitanen et al., 2010). These transient GABAergic excitatory [K⁺]_o signals elicited prolonged depolarizations in rat temporal lobe that could contribute to seizure generation (Viitanen et al., 2010; Lopantsev and Avoli, 1998). Interestingly, the accumulation of [Cl⁻]_i was not accompanied by a substantial depolarization of the Cl⁻ reversal potential sufficient to reduce the hyperpolarizing influence of GABAergic signaling (Lillis et al., 2012). Increases in [Cl⁻]_i were, however, accompanied by substantial increases in [K⁺]_o. Several studies have now implicated the K⁺-Cl⁻ co-transporter isoform 2 (KCC2) in seizure initiation (de Curtis and Avoli, 2016; González et al., 2018; Hamidi and Avoli, 2015; Shiri et al., 2016).

The KCC2 co-transporter is one of the primary membrane-bound proteins responsible for maintaining the Cl⁻ concentration gradient (Payne et al., 2003). It was proposed that reducing efficacy of the KCC2 co-transporter may lead to an increase in the intracellular Cl⁻ concentration, causing a reduction of the hyperpolarizing inhibition and therefore triggering seizure-like activity (Buchin et al., 2016). However, the effect of KCC2 activity on the neuronal excitability can likely be more complex because KCC2 uses Cl⁻ gradient to remove K⁺; that is, KCC2 activation leads to the efflux of one Cl⁻ and one K⁺ ion (Payne et al., 2003). Because of this interaction, GABAergic signaling causes a gradual accumulation of [Cl⁻]_i and activation of the KCC2 co-transporter would initiate the efflux of both Cl⁻ and K⁺, elevating the [K⁺]_o and triggering the positive feedback loop between increases in [K⁺]_o and neuronal excitability as described earlier in this chapter. This hypothesis was explored in a recent computational study (González et al., 2018). This work found that synchronized GABAergic signaling though direct stimulation of inhibitory interneurons could drive seizure-like discharges in the model where the outward K⁺ A-current was reduced to model application of 4AP (Fig. 17–4A/B). To confirm that accumulation of [K⁺]_o due to KCC2 activation was responsible for seizure initiation, the authors impaired the KCC2 sensitivity to changes in [Cl⁻]_i (Fig. 17–4C/D). Effectively, this manipulation reduced KCC2 activation in response to substantial increases in [Cl⁻]_I; however, the effect of [Cl⁻]_i on GABA_A reversal potential was preserved. This eliminated transition to epileptiform activity upon the same sequence of interneuron stimulation (González et al., 2018). Together, these data suggest a novel mechanism by which Cl⁻ dynamics may influence network-wide activity and seizure generation.

Figure 17–4.

Cl⁻-dependent activation of KCC2 drives seizure onset. A. Heatmap shows excitatory neuron network voltages in time. Color indicates voltage. Stimulation of inhibitory population (timing of stimulation indicated by blue trace) triggers seizure. (more...)

Calcium and Magnesium

Ca²⁺ and Mg²⁺ ions are well-known regulators of synaptic transmission. The release of neurotransmitter at the presynaptic terminal is dependent on the local influx of Ca²⁺ through voltage-gated Ca²⁺ channels. Indeed, even slight reductions in [Ca²⁺]_o cause reduced presynaptic release of neurotransmitters (Crochet et al., 2005; Seigneur and Timofeev, 2010; Somjen, 2002). Additionally, the voltage dependency of postsynaptic NMDA receptors is mediated by [Mg²⁺]_o. The negatively charged neuronal membrane attracts the positively charged Mg²⁺ cation. In doing so, the Mg²⁺ ion physical plugs the NMDA pore, preventing the flux of ions across the channel even after the binding of NMDA agonists (e.g., glutamate and aspartate). Experimentally, seizures and seizure-like discharges can be induced by reducing [Mg²⁺]_o (Somjen, 2002). Similarly, combined reduction of [Mg²⁺]_o and increased [K⁺]_o in silico resulted in spontaneous transitions between physiological and seizure-like activity by promoting irregular switching between quasi-periodic and chaotic dynamics (Zalay et al., 2010; Velazquez et al., 1999). The primary mechanism by which reduced [Mg²⁺]_o drives seizure onset is thought to be through the removal of the aforementioned voltage dependence of NMDA channels (Somjen, 2004). In doing so, reduced [Mg²⁺]_o enhances NDMA currents in the postsynaptic neuron, increasing overall excitability and synchronization of neuron populations. This ictogenic mechanism is completely synaptically driven as application of NMDA receptor antagonists abolishes seizures in low [Mg²⁺]_o conditions (Avoli et al., 1991).

Like Mg²⁺, the reduction of [Ca²⁺]_o is also known to drive seizure generation (Haas and Jefferys, 1984; Taylor and Dudek, 1982). Unlike Mg²⁺, however, reduced [Ca²⁺]_o does not mediate hypersynchronization and seizure onset in a synaptically dependent manner. Evidence suggests that while local synchronization during seizures is higher than during normal brain activities (Boucetta et al., 2008), the long-range synchronization during seizures is reduced (Neckelmann et al., 1998; Derchansky et al., 2006; Meeren et al., 2002; Boucetta et al., 2008). These results suggest that the ligand-dependent synaptic interactions alone do not explain the generation of some form of paroxysmal activities (Johnston and Brown, 1981; Polack and Charpier, 2006). Multiple data support this point of view: (1) paroxysmal activities are associated with decreased [Ca²⁺]_o (Amzica et al., 2002; Heinemann et al., 1977), and as a consequence, the effectiveness of synaptic strength decreases (Seigneur and Timofeev, 2010), but the intrinsic neuronal excitability increases (Hille, 2001); (2) the use of low or even 0 mM [Ca²⁺]_o in hippocampal (Pan and Stringer, 1997; Bikson et al., 1999; Leschinger et al., 1993) and cortical (Seigneur and Timofeev, 2011) slices in vitro results in the development of epileptiform discharges; (3) the synaptic responsiveness during and after electrographic seizures in vivo decreases (Steriade and Amzica, 1999; Cisse et al., 2004; Nita et al., 2008; Seigneur and Timofeev, 2010); (4) the long-range synchronization during seizures, particularly during fast runs, is low or absent; and finally, (5) the neuronal firing reduces toward the end of the seizure, while intracellular and field potential activities are more ample as compared to the beginning of the seizure (Bazhenov et al., 2004; Timofeev and Steriade, 2004).

In sum, reduction of [Ca²⁺]_o from 1.2 mM to 1 mM significantly reduces synaptic transmission (Dingledine and Somjen, 1981). Additionally, [Ca²⁺]_o drops during seizure discharges from about 1.2 mM to 0.6 mM (Heinemann and Lux, 1977; Pumain et al., 1983). At such low levels of [Ca²⁺]_o the synaptic transmission becomes greatly impaired (Crochet et al., 2005; Seigneur and Timofeev, 2010; Somjen, 2002) despite the fact that reduction of [Ca²⁺]_o is known to drive seizure generation (Haas and Jefferys, 1984; Taylor and Dudek, 1982). Several hypotheses have been put forward to account for this seemingly paradoxical situation (Somjen, 2002). Hyperpolarizing Ca²⁺-dependent K⁺ currents such as the BK and the after-hyperpolarization (AHP) currents display reduced activations in low [Ca²⁺]_o conditions, resulting in enhanced neuronal excitability, and multiple regular spiking pyramidal neurons change firing pattern to bursting dynamics (Boucetta et al., 2013).

Under conditions of reduced efficiency of chemical synaptic transmission, local neuronal synchronization could be achieved via electrical coupling between different groups of neurons (Perez Velazquez and Carlen, 2000; Galarreta and Hestrin, 1999; Gibson et al., 1999; Schmitz et al., 2001), glial cells (Amzica et al., 2002), or ephaptic interactions (Grenier et al., 2003; Taylor and Dudek, 1982; Taylor and Dudek, 1984a; Taylor and Dudek, 1984b). Electrical coupling has a high efficacy for short-range synchronization (Galarreta and Hestrin, 2001), and it can be enhanced by low [Ca²⁺]_o (Thimm et al., 2005). At [Ca²⁺]_o below 1.0 mM, gap junction hemichannels open (Thimm et al., 2005), creating conditions for paroxysmal synchronization of neuronal activities via electrical synapses (Timofeev et al., 2012). It has been proposed that the presence of extracellular Ca²⁺ stabilizes the hemichannel closed state by disruption of salt-bridge interactions of charged residues present at the hemichannel pore (Lopez et al., 2016). Lowering [Ca²⁺]_o allows the formation of the salt-bridge interaction, thereby stabilizing the hemichannel open state and enhancing electrical coupling. The long-range synchrony mediated by electrical synapses could be achieved via axo-axonal coupling, which was shown in hippocampal formation (Schmitz et al., 2001). These results suggest possible strong involvement of [Ca²⁺]_o alternations in the development of epileptiform events.

Finally, increased neuronal excitability, as seen prior to seizure onset, in response to low [Ca²⁺]_o and [Mg²⁺]_o, may depend on their involvement in surface charge screening (Hille et al., 1975; Madeja, 2000). The extracellular portion of the neuronal membrane contains many negatively charged amino acid residues. The presence of these negatively charged residues effectively reduces the transmembrane voltage by increasing the net negative charge of the extracellular space. This increase in extracellular negativity results in the relative depolarization of the intracellular space of the neuron and increases neuronal excitability (Hille et al., 1975; Madeja, 2000). The negative charges of the amino acid residues are effectively neutralized by the presence of extracellular divalent Ca²⁺ and Mg²⁺ cations (Hille et al., 1975; Madeja, 2000). In doing so, they help maintain the polarization of the cellular membrane and reduce excitability by preventing activation of voltage-dependent ion channels (Hille et al., 1975; Madeja, 2000). Therefore, increased excitability driven by reduced surface charge screening in low [Ca²⁺]_o and [Mg²⁺]_o conditions can lead to increased activation of voltage-gated ion channels, resulting in the gradual accumulation of [K⁺]_o and ultimately seizure initiation.

Conclusion

The complex interactions between the various major ionic species in the brain, in conditions when normal regulatory mechanisms are impaired, may trigger and underlie dynamics of pathological epileptiform events. There is a functional loop between neuronal activities and ionic dynamics. Change in neuronal activity leads to a change in extra- and intracellular ion concentrations, which in turn modulates neuronal excitability and synaptic efficacy, modifying neuronal activity further. Here we highlighted and discussed the underlying dynamic and biophysical mechanisms by which changes in ion concentrations may lead to seizure initiation, mediate transitions between different voltage dynamics during seizures, and trigger termination of seizures. Though we discussed only major ionic species, Na⁺, K⁺, Ca²⁺, Cl⁻, Mg²⁺, several other ions (e.g., H⁺, HCO₃⁻, etc.) may also play prominent roles in seizure dynamics and would require their own extended discussion along with the role of astroglia, oxygen, volumetric dynamics, and neuromodulatory control of neural excitability.

Acknowledgments

References

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