Cellular and network mechanisms of electrographic seizures

Abstract

Epileptic seizures constitute a complex multiscale phenomenon that is characterized by synchronized hyperexcitation of neurons in neuronal networks. Recent progress in understanding pathological seizure dynamics provides crucial insights into underlying mechanisms and possible new avenues for the development of novel treatment modalities. Here we review some recent work that combines in vivo experiments and computational modeling to unravel the pathophysiology of seizures of cortical origin. We particularly focus on how activity-dependent changes in extracellular potassium concentration affects the intrinsic dynamics of neurons involved in cortical seizures characterized by spike/wave complexes and fast runs.

Introduction

It is widely accepted that the development of epileptiform activity can result from a shift in the balance between synaptic excitation and inhibition towards excitation (Dichter and Ayala 1987; Galarreta and Hestrin 1998; Nelson and Turrigiano 1998; Tasker and Dudek 1991). In fact, an easy way to elicit acute seizures experimentally is to block synaptic inhibition (Chagnac-Amitai and Connors 1989a; b; Gutnick et al. 1982; Matsumoto and Ajmone-Marsan 1964a; b; Prince 1978; Steriade et al. 1998). Accordingly, the traditional point of view is that the key intracellular correlate of epileptiform activity, the paroxysmal depolarizing shift (PDS), consists of a giant EPSP (Johnston and Brown 1981) enhanced by activation of voltage-regulated intrinsic currents (de Curtis et al. 1999; Dichter and Ayala 1987; Prince and Connors 1984; Timofeev et al. 2004; Westbrook and Lothman 1983; Wong and Prince 1978). It was therefore a surprise when more recent evidence showed that synaptic inhibition remains functional in many forms of paroxysmal activities (Cohen et al. 2002; Davenport et al. 1990; Engel et al. 2003; Esclapez et al. 1997; Higashima 1988; Prince and Jacobs 1998; Timofeev et al. 2002b; Topolnik et al. 2003; Traub et al. 1996). Also, disruption of inhibitory function does not affect neocortical kindling (Denslow et al. 2001), which is associated with an increases in synaptic strength that mediates recruitment of larger cortical areas (Teskey et al. 2002). Furthermore, the firing of fast-spiking inhibitory interneurons during cortically-generated seizures is much stronger than the activity of other types of cortical neurons (Timofeev et al. 2002b). Therefore, a decrease or even absence of synaptic inhibition in presence of synaptic excitation cannot serve as a general mechanism of cortical epileptic seizures.

Extracellular potassium concentration [K⁺]_o increases during neuronal activity. In presence of neuronal hyperexcitability, the [K⁺]_o apparatus fails to maintain [K⁺]_o homeostasis (Grafstein 1957, Somjen 2002, Frohlich 2007). The resulting increase in [K⁺]_o depolarizes the reversal potential of K⁺ currents and can also affect the maximal conductances of some depolarizing currents such as the hyperpolarization-activated depolarizing current (I_h) (Spain et al. 1987) and the persistent sodium current (I_Na(p)) (Somjen and Muller 2000). Thus, the overall effect of an increase in [K⁺]_o is an upregulation of neuronal excitability. Indeed, periodic bursting was found in vitro after increasing [K⁺]_o (Jensen and Yaari 1997; Leschinger et al. 1993; Pan and Stringer 1997). Thus, changes in [K⁺]_o may play a critical role in seizure dynamics.

The complexity of the interaction dynamics between neuronal networks and ion concentrations during epileptiform activity requires a combined approach of experimental work and computational models. Here, we discuss recent modeling results regarding mechanisms of epileptic seizures in cortex. We first present an analysis of the network and cellular mechanisms of electrographic seizures in vivo. Then, we discuss the results from computational models that incorporate extracellular K⁺ concentration dynamics based on experimental data. Our findings suggest that (1) changes in [K⁺]_o activate latent intrinsic burst dynamics that result in paroxysmal bursting and (2) the dynamic interaction between network activity and [K⁺]_o causes the emergence of a stable paroxysmal network state in the form of self-sustained oscillations. We conclude with specific predictions derived from our model and propose that molecular mechanisms responsible for [K⁺]_o regulation should be examined as novel targets for pharmacological intervention in patients suffering from epilepsy.

Cortical origin of paroxysmal oscillations generated within the thalamocortical system

The origin of electrical seizures that accompany various types of epilepsy is largely unknown, especially for cortically generated seizures. Recent experimental studies strongly implicate a neocortical origin of spike-wave (SW) electroencephalographic (EEG) complexes at ~3 Hz, as in petit-mal epilepsy and seizures with the EEG pattern of the Lennox-Gastaut syndrome (Pinault et al. 1998; Steriade 2003; Steriade et al. 1998; Steriade and Contreras 1998; Timofeev et al. 1998; Timofeev and Steriade 2004). The etiologies of cortically-generated seizures include cortical dysplasia, traumatic injury and other idiopathic/genetic forms (Stafstrom 2005). The cortical origin of these seizure types is supported by: (a) the presence of paroxysms in neuronal pools within the cortical depth, even without reflection at the cortical surface (Steriade 1974), and in isolated cortical slabs in vivo (Timofeev et al. 1998); (b) their induction by infusion of the GABA_A-receptor antagonist bicuculline in neocortex of ipsilaterally thalamectomized cats (Steriade and Contreras 1998); and (c) the absence of paroxysmal patterns after intrathalamic injections of bicuculline, which rather induce low-frequency, regularly recurring spindle sequences as previously described in ferret slices in vitro (Bal et al. 1995) and cat (Ajmone-Marsan and Ralston 1956; Steriade and Contreras 1998) or rat (Castro-Alamancos and Calcagnotto 1999) thalamus in vivo, (d) the vast majority of thalamocortical (TC) neurons is hyperpolarized and does not fire spikes during paroxysmal discharges recorded in corresponding cortical areas (Pinault et al. 1998; Steriade and Contreras 1995; Steriade and Timofeev 2001; Timofeev et al. 1998; Timofeev and Steriade 2004).

As in the slow oscillation, cortical neurons are depolarized and fire spikes during the depth-negative (EEG spike) and are hyperpolarized during the depth-positive (EEG wave) components of SW. A typical example of a seizure that consists of both SW – poly-SW (PSW) complexes recurring with frequencies of 1–3 Hz and fast runs with oscillation frequencies of 8–14 Hz is shown in the Fig. 1. The seizure starts with SW-PSW discharges. The duration of PSW discharges increases progressively and the seizure displays a prolonged period of fast run. After the fast run the seizure transforms again to PSW complexes, the number of EEG spikes during these complexes decreases and the seizure terminates with SW discharges. Usually, SW-PSW complexes of electrographic seizures correspond to the clonic component of seizures, while fast runs correspond to the tonic component of seizures (Niedermeyer 2005a; b). Similar to spike-wave discharges, fast runs originate in neocortex. Since the frequency and the duration of fast runs are similar to spindles, it could be supposed that the runs of fast paroxysmal spikes share mechanisms with spindles and thus originate in the thalamus. However, the experimental evidence demonstrated that (a) during fast runs TC neurons display EPSPs that only rarely lead to the generation of action potentials (Timofeev et al. 1998) and not IPSP-mediated rebound Ca²⁺ spikes as during spindles, (b) the thalamic Ca²⁺ spike bursts precede the cortical depolarizing potentials during spindles, but, in the same cortex to TC neuronal pairs, the TC EPSPs occurring during fast runs follow the cortical neurons (see Fig. 11 in (Timofeev et al. 1998)). Also, runs of fast paroxysmal EEG spikes were found in isolated neocortical slabs (Timofeev et al. 1998). These observations confirm the cortical origin of fast runs.

Fig. 1. Field potential and intracellular features of an idiopathic electographic seizure recorded from cortical area 5 of cat anesthetized with ketamine-xylazine.

Upper panel, five upper traces are the local field potentials recorded with an array of electrodes from cortical surface and different cortical depths. The distance between electrodes in the array was ~0.4 mm. Lower trace, intracellular recording from cortical regular-spiking neuron located at 1 mm depth and ~0.5 mm lateral to the array. A period of spike-wave discharges and fast runs is expanded in the lower panels as indicated. In the left lower panel the EEG-spike and the EEG-wave components are marked by grey rectangles.

Cellular mechanisms mediating spike and wave discharges

The EEG “spike” of SW complexes corresponds to the paroxysmal depolarizing shift (PDS) of the membrane voltage in intracellular recordings (reviewed in (McCormick and Contreras 2001; McNamara 1994; Traub et al. 1996)). Initially, PDSs have been regarded as giant EPSPs (Johnston and Brown 1981; 1984), enhanced by activation of voltage-gated intrinsic (high-threshold Ca²⁺ and persistent Na⁺) currents (de Curtis et al. 1999; Dichter and Ayala 1987; Timofeev et al. 2004; Wong and Prince 1978). Specifically, the EPSPs initiate the PDS by depolarizing the postsynaptic neurons to the level of activation of the persistent Na⁺ current that maintains and enhances the achieved depolarization. This proposed contribution of the persistent Na⁺ current to the generation of PDSs has been recently demonstrated by intracellular recordings from pairs of neurons, in which one of the neurons was recorded with a pipette containing QX-314, an intracellular blocker of voltage gated Na⁺ currents. In all cells tested, the inclusion of QX-314 in the recording pipette caused a reduction of the maximal depolarization during the PDS (Fig. 2 B). Also, the PDSs increased their duration upon intracellular injection of steady depolarizing current (see Fig. 5 in (Timofeev et al. 2002b)). Intracellular recordings with the Ca²⁺ buffer BAPTA in the pipette indicate the role of Ca²⁺-dependent potassium current to the generation of hyperpolarizing potentials during seizures and indirectly support a role of Ca²⁺ influx via Ca²⁺ channels (Fig. 2 A). Together, these findings suggest that high-threshold Ca²⁺ currents and the persistent Na⁺ current could contribute to those depolarizations because these currents are activated at depolarized voltages.

Fig. 2. Role of Ca²⁺-activated and persistent Na⁺ currents in the generation of paroxysmal depolarizing shifts.

(A) EEG and dual intracellular recordings during a paroxysmal depolarizing shift. Intracellular recording with BAPTA field pipette reveals much larger depolarization during the paroxysmal depolarizing shift as compared to control recording with K⁺ acetate filled pipette. (B) EEG and dual intracellular recordings during a fragment of a seizure. One of the pipettes contained QX-314. The neuron recorded with this pipette revealed much smaller depolarization during paroxysmal activities as shown in the trace “difference”. (Modified from (Timofeev et al. 2004)).

In recent studies, inhibitory processes have been observed during different types of seizure activity (Esclapez et al. 1997; Prince and Jacobs 1998; Prince et al. 1997; Timofeev et al. 2002b; Traub et al. 1996). Recordings from human and rat slices (Cohen et al. 2002; Fujiwara-Tsukamoto et al. 2003) as well in vivo experiments in cats (Timofeev et al. 2002b) have demonstrated that PDSs contain an important inhibitory component. During the depolarizing components of seizures, the fast-spiking inhibitory interneurons fire at high frequencies (Timofeev et al. 2002b). The activation of postsynaptic GABA_A receptors was substantial and caused the intracellular chloride concentration to increase (Timofeev et al. 2002b). This change in ion concentration gradient depolarized the reversal potential for GABA_A inhibitory currents and thus decreased IPSP amplitudes or even reversed the polarity of IPSPs (Thompson and Gähwiler 1989). Also, prolonged high-frequency stimulation (Kaila et al. 1997; Taira et al. 1997) or spontaneous high-frequency firing of inhibitory interneurons (Timofeev et al. 2002b) may induce a rapid GABA_A-mediated bicarbonate-dependent increase in the [K+]_o. An increase in [K⁺]_o in mature neocortical pyramidal neurons would result in further increase in [Cl⁻]_i (DeFazio et al. 2000). The seizure-related depolarizing GABA responses are likely mediated via cation-chloride co-transporters (Payne et al. 2003).

Earlier hypotheses proposed that the EEG “wave” component reflects summated IPSPs that were ascribed to GABAergic processes triggered in cortical pyramidal neurons by local-circuit inhibitory cells (Giaretta et al. 1987; Pollen 1964). In computational models, the “wave” was similarly regarded as produced by GABA_B-mediated IPSPs (Destexhe 1998). However, during the EEG “waves” associated with neuronal hyperpolarization, the input resistance increases relative to the “spike” component (Matsumoto et al. 1969; Neckelmann et al. 2000; Timofeev et al. 2002b). These and similar results reported in a genetic rat model of absence epilepsy (Charpier et al. 1999; Crunelli and Leresche 2002; Staak and Pape 2001) and in cat in vivo (Timofeev et al. 2002b), contradict the idea of a role played by inhibitory receptors in the generation of hyperpolarizations associated with the EEG “wave” component of SW complexes. Furthermore, intracellular recordings with Cl⁻ filled pipettes did not reveal chloride-mediated effects during ‘wave’ components of seizures (Timofeev et al. 2002b). As to the possibility that GABA_B-mediated IPSPs underlie the “wave” component of SW seizures, including QX-314 in the recording pipette to block the G-protein-coupled GABA_B-evoked K⁺ current (Deisz et al. 1997; Jensen et al. 1993) did not significantly affect the hyperpolarization in our experiments (Fig. 2 B) (Timofeev et al. 2004; Timofeev and Steriade 2004). Together, these data suggested that GABA-mediated currents are not important for the hyperpolarizations that occur during these cortically-generated seizures.

Another group of mechanisms that can mediate hyperpolarization during SW complexes depends on K⁺ currents (Halliwell 1986; Schwindt et al. 1988). In recordings with Cs⁺-filled pipettes to non-selectively block K⁺ currents, pyramidal neurons displayed depolarizing potentials during the “wave” component of SW seizures (Timofeev et al. 2002b). This indicates a leading role played by K⁺ currents in the generation of seizure-related hyperpolarizing potentials. A particularly important role is played by I_K(Ca) because in recordings with pipettes filled with BAPTA the “wave”-related hyperpolarizations were reduced and the apparent input resistance increased (Timofeev et al. 2004; Timofeev and Steriade 2004). The second factor that may contribute to the “wave”-related hyperpolarization during cortically generated SW seizures is disfacilitation (Charpier et al. 1999; Neckelmann et al. 2000). Indeed, during the EEG “wave” component of SW seizures, cortical and TC neurons do not fire, thus creating conditions for disfacilitation. All these results indicate that the hyperpolarizations during SW seizure may be due to the combined effect of K⁺ currents and disfacilitation.

What factors are implicated in the transition from neuronal hyperpolarization to depolarization during paroxysmal SW discharges? Intracellular recordings from glial cells and direct measurement of [K⁺]_o indicated an increase in [K+]_o during paroxysmal activities (Amzica et al. 2002; Amzica and Steriade 2000; Moody et al. 1974; Timofeev et al. 2002a), leading to a positive shift in the reversal potential of K⁺-mediated currents, including I_h (Spain et al. 1987). More than half of neocortical neurons display resonance within the frequency range of 1–3 Hz or higher, which is mediated by I_h and enhanced by the persistent Na⁺ current, I_Na(p) (Hutcheon et al. 1996a; b; Hutcheon and Yarom 2000; Ulrich 2002). In our experiments, 20% of neocortical neurons displayed depolarizing sags after application of hyperpolarizing current pulses, probably caused by activation of I_h. Also, models of isolated pyramidal neurons with I_h included in their dendritic compartment showed that rebound depolarization was sufficient to generate single action potentials or spike-bursts (Timofeev et al. 2002a). The increased excitability of pyramidal neurons after the prolonged hyperpolarizations during the EEG “wave” component of SW complexes may contribute to the generation of the subsequent paroxysmal depolarization (Timofeev et al. 2002a; Timofeev and Steriade 2004). It is also possible that the Ca²⁺-mediated low-threshold current (I_T), alone or in combination with I_h, contributes to the generation of the rebound overexcitation, as shown in cortical slices (de la Peña and Geijo-Barrientos 1996) and in computational studies (Destexhe et al. 2001). However, the generation of I_T in cortical neurons requires voltages much more hyperpolarized than those normally seen during spontaneously occurring network operations (Paré and Lang 1998). Thus, the next paroxysmal cycle likely originates from the excitation driven by I_h in conjunction with synaptic inputs.

The summary diagram in Figure 3 tentatively indicates the different synaptic and intrinsic currents activated by neocortical neurons during paroxysmal activity. The PDS consists of (a) summated EPSPs and IPSPs; and (b) an intrinsic current, I_Na(p), as revealed by diminished depolarization in recordings with QX-314 in the recording micropipette. The hyperpolarization related to the EEG depth-positive “wave” is a combination of K⁺ currents (mainly I_K(Ca) and I_leak) and synaptic disfacilitation. Finally, the hyperpolarization-activated depolarizing sag, due to I_h, leads to a new paroxysmal cycle.

Fig. 3. Tentative representation of different synaptic and intrinsic currents activated in neocortical neurons during paroxysmal activity.

See text for description of how these currents interact during paroxysmal activity. Modified from (Timofeev and Steriade 2004).

Changes in the extracellular milieu and epileptogenesis

Modulation of extracellular ionic concentrations has a profound impact on the excitability of neurons and neuronal networks. According to Grafstein’s hypothesis (Herreras and Somjen 1993), K⁺ released during intense neuronal firing may accumulate in the interstitial space, depolarize neurons and lead to spike inactivation. During seizures, the increase in [K⁺]_o reaches 16 mM in the case of 4-AP induced epileptiform discharges in hippocampus (Avoli et al. 1996) and 7–12 mM in case of spontaneous electrographic seizures in neocortex (Amzica et al. 2002; Moody et al. 1974; Prince et al. 1973). A recent computational study showed that K⁺-mediated increase in I_h may lead to periodic bursting in a cortical network model (Timofeev et al. 2002a). It was shown that a combination of I_h,, I_K(Ca) and I_Na(p) in pyramidal cells is sufficient to generate paroxysmal oscillations at a frequency of 2–3 Hz. These oscillations started when the I_K(leak) and I_h reversal potentials were depolarized and the maximal conductance for I_h was increased to model the increased [K⁺]_o in paroxysmal foci (Timofeev et al. 2002a). A single PY cell with these properties was sufficient to mediate activity in an entire cortical network.

Cellular and network periodic bursting occurs in vitro after increasing [K⁺]_o (Jensen and Yaari 1997; Leschinger et al. 1993; Pan and Stringer 1997). Traumatic brain injury leading to loss of K⁺ conductance in hippocampal glia can result in the failure of glial K⁺ homeostasis and abnormal neuronal function including seizures (D’Ambrosio et al. 1999). The role of elevated [K⁺]_o in producing synchronized neuronal bursts through the shift of the K⁺ reversal potential was previously studied in hippocampal slice models (Traub and Dingledine 1990). An initial computational model (Kager et al. 2000) exhibited periodic bursting after [K⁺]_o increase in a single model cell; however, the bursts occurred at a very low frequency (every 10–15 sec) which might be attributed to the lack of I_K(Ca) in that model. An important role for the low-threshold Ca²⁺ (T-type) current for generating spike-and-wave oscillations has also been recently suggested (Destexhe et al. 2001). In recordings from granule cells of the dentate gyrus in hippocampus at different levels of ionic concentrations in vitro, a simultaneous increase in [K⁺]_o and decrease in [Ca²⁺]_o caused cellular bursts to appear at K⁺/Ca²⁺ concentrations that were previously recorded in vivo before the onset of synchronized reverberatory seizure activity (Pan and Stringer 1997). Spontaneous nonsynaptic epileptiform activity was found in hippocampal slices after increasing neuronal excitability (by removing extracellular Mg²⁺ and increasing extracellular K⁺) in the presence of Cd²⁺, a nonselective Ca²⁺ channel antagonist, or veratridine, a persistent sodium conductance enhancer (Bikson et al. 2002). In recordings from rat hippocampal slices with high [K⁺]_o, population bursts in CA1 were generated locally by intrinsically bursting pyramidal cells, which recruited and synchronized other neurons (Jensen and Yaari 1997).

Increases in [K⁺]_o unmasked a latent intrinsic burst mechanism that mediated 2–3 Hz oscillations in cortical neuron models that incorporate extracellular K⁺ dynamics (Bazhenov et al. 2004). Such increases of [K⁺]_o can also lead to oscillations at the frequency of fast runs. An external stimulus (DC pulse of 10 sec duration) applied to a single cortical pyramidal (PY) neuron induced a high-frequency spiking in this model cell (Fig. 4). A flow of K⁺ ions to the extracellular milieu overpowered the effects of the K⁺ pump and glial buffering, and led to [K⁺]_o increase (see insert in Fig. 4B). After stimulus termination, the neuron exhibited sustained periodic bursting in the 2–4 Hz frequency range. For each oscillation cycle, the slow membrane potential depolarization (due to combined effects of I_h and high [K⁺]_o that depolarized the reversal potentials of all K⁺ currents) activated the persistent sodium current and led to the onset of a new burst (see details in (Bazhenov et al. 2004)). Each burst started with a few spikes followed by spike inactivation and a depolarizing plateau that lasted 50–100 msec (see insert in Fig. 4A). Progressive increase of the intracellular Ca²⁺ concentration during the depolarized state increased activation of the Ca²⁺ dependent K⁺ current until the neuron switched back to the hyperpolarized state. Deactivation of I_K(Ca) determined the length of the hyperpolarized state and ultimately the frequency of slow bursting. Since K⁺ reversal potentials remained below −80 mV in these simulations even when [K⁺]_o was elevated, the neuron stayed hyperpolarized below resting potential between bursts. During slow bursting, [K⁺]_o gradually decreased and 5–6 sec later, bursting was replaced by faster oscillations at 10–14 Hz range. Decrease of [K⁺]_o restored “normal” hyperpolarized K⁺ reversal potentials. This increased the “hyperpolarizing force” such that the neuron did not stay “locked” in the depolarized state but repolarized back to the resting potential after one or few spikes. It also led to only minimal activation of the Ca²⁺ dependent K⁺ current, so the next spike (or short burst of spikes) occurred with smaller delay. Therefore, the frequency of bursting increased and the neuron stayed at more depolarized level of membrane potential. Fast oscillations lasted 20–25 sec and eventually terminated when [K⁺]_o decreased below a level that was necessary to maintain spiking. Thus the change of the [K⁺]_o can account for transitions between slow and fast paroxysmal oscillations and silent state in the cortical neuron model.

Fig. 4. Oscillatory activity mediated by elevated [K⁺]_o.

DC pulse (10 sec in duration, bar) was applied to the silent PY cell. Following high frequency firing, [K⁺]_o increased and maintained oscillations in PY neuron after DC pulse was removed. (A) Single PY neuron. Insert shows typical burst of spikes. (B) Reciprocally connected PY-IN pair. Insert shows [K⁺]_o evolution for PY neuron. Change of the [K⁺]_o induced transition from slow (2–3 Hz) to fast (10–15 Hz) oscillations. Bursts of spikes (but not tonic spiking) in PY neuron induced spikes in the interneuron (see IN panel).

To study effect of inhibitory feedback on the circuit dynamics, we included an inhibitory interneuron (IN) that receives synaptic excitation (AMPA-type) from the PY cell and in turn inhibits the PY cell (GABA_A-type synapse). The strength of PY-IN synapse was adjusted so that IN remained silent during tonic firing of the PY neuron (Fig. 4B). When the PY neuron started to burst, the excitatory drive from PY to IN cell was sufficient to trigger periodic IN spiking. These inhibitory spikes reduced the duration of PY bursts and thus increased the oscillation frequency. In agreement with in vivo recordings (Timofeev et al. 2002b), the IN spiking stopped when the PY neuron switched from slow bursting to the tonic firing. Two main factors contributed to the absence of IN spiking during fast runs. First, steady-state depression of excitatory coupling between PY and IN neurons was stronger during fast runs since average frequency of PY spiking was higher due to the continuous firing. During slow bursting, short-term depression was significantly reduced by the end of hyperpolarized (interburst) state. Second, during slow bursting the first few spikes at the burst onset occurred at a higher frequency than the spikes during fast run, therefore promoting EPSP summation in the IN.

Effects of intrinsic conductances on K⁺-induced oscillations

In agreement with in vivo results (see Fig. 3), high-threshold Ca²⁺ and persistent Na⁺ currents were important in creating periodic bursting in our model of neocortical activity in moderately elevated [K⁺]_o (Fig. 5). After oscillations were induced by long DC stimulation, sufficiently high maximal conductances for I_Na(p) and I_Ca were required to maintain periodic bursting. On the g_Ca(g_Na(p)) plane (see Fig. 5A, left) the region for bursting was bounded by two curves. Below the bottom curve, no oscillations were observed. Above the top curve, strong I_Ca and/or I_Na(p) induced a transient “lock” of the membrane potential in a depolarized state (spike inactivation). All these regimes are illustrated in panel Fig. 5C, where the maximal change in [Ca²⁺]_i during a burst is plotted for a cell held at a constant elevated level of [K⁺]_o = 5.5 mM. In particular, region C corresponds to long bursts with spike inactivation. In region D, the membrane potential was permanently “locked” in a depolarized state, which occurred for high g_Na(p) and relatively low g_Ca. The latter condition ensured weak I_K(Ca) activation. Examples of different firing patterns are shown in Fig. 5B.

Fig. 5. Effect of intrinsic conductances on neuronal oscillations.

(A) Increase of [K⁺]_o during DC stimulation led to oscillations. Sufficiently high levels of persistent Na⁺ and high-threshold Ca²⁺ conductances were required to maintain periodic bursting (top left). Increase of Ca²⁺-dependent K⁺ current reduced both duration and frequency of oscillations (top right). (B) Examples of PY oscillations corresponding to different regimes indicated in panel A, left. (C) [Ca²⁺]_i increase during a burst as a function of parameters g_Na(p) and g_Ca for a cell held at a constant level of [K⁺]_o (5.5mM). Longer bursts (more spikes or spike inactivation) produced higher [Ca²⁺]_i change. Four different regions can be discerned: A – no oscillations; B – bursting; C – bursting with spike inactivation; D – membrane potential “locked” in depolarized state. (D) Effect of the intrinsic conductances on frequency of oscillations. The most significant frequency changes (1 to 3 Hz) occurred with variations of the I_h maximal conductance. (Modified from (Bazhenov et al. 2004)).

The value of the conductance that mediates I_K(Ca) significantly affected both frequency and duration of the post-stimulus oscillations (Fig. 5A, right). When g_K(Ca) was below about 2 mS/cm², only fast long-lasting oscillations were observed. For higher conductances 2–3 Hz periodic bursting was found. The frequency increased slightly for g_K(Ca) above 5 mS/cm², which was primary the result of reduced burst duration. Stronger I_K(Ca) was more effective in terminating the depolarized plateau. As a result, less Ca²⁺ entered during the depolarized state and therefore the repolarization from the hyperpolarized state was also faster.

Among all the currents, I_h was most effective in controlling the oscillation frequency. Decrease of g_h reduced the frequency to about 1 Hz and very small values of g_h eliminated bursting (Fig. 5D. left). This is consistent with the importance of I_h in maintaining paroxysmal oscillations as proposed previously (Timofeev et al. 2002a). Increase of the maximal conductances for I_Na(p) and I_Km had opposing effects on the oscillation frequency (Fig. 5D, middle and right). Changing maximal conductance for I_Ca had a relatively weak effect on the frequency, although the conductance value had to be above certain limit to maintain bursting. This limit depended on the maximal conductance for I_Na(p), as shown in Fig. 5A, left.

Synchronization during fast runs and slow bursting

We recently reported very low levels of both short- and long range synchronization during paroxysmal fast runs (Boucetta et al. 2008). To study synchrony of population oscillations during different oscillatory regimes, we used computer simulations of network models composed of 100 PY neurons and 25 INs. Without synaptic coupling, the model neurons fired independently because of random variability of the model parameters across neurons and different initial conditions. (Fig. 6A, top). Upon termination of a simulated DC stimulus, all neurons displayed slow bursting followed by fast spiking; in different neurons, these transitions between fast and slow oscillations occurred at different times. When excitatory/inhibitory coupling between neurons was included, slow paroxysmal bursting became synchronized across neurons (Fig. 6A, bottom). Fig. 6B shows the time-dependent cross-correlation between neighbor PY cells in the network; during slow paroxysmal oscillations PY neurons fired with minimal phase delays. Similar to the single neuron model (Fig. 4), progressive decrease in [K⁺]_o triggered a transition from slow to fast oscillations. In most cases, neighboring neurons displayed this transition nearly simultaneously; however we found a few large clusters with very different transition times (compare neurons #1–50 and #51–100 in Fig. 6A, bottom). We hypothesized that including long-range connections between PY neurons would increase the global synchrony of transitions between epochs of slow and fast oscillations. To test this hypothesis, we included random long-range connections between PY neurons and varied the probability of this long-range coupling P. Indeed, when P > 0.02–0.03, the transition from slow bursting to fast run occurred almost simultaneously (within a 200 msec time window). Including random long-range connections with such low probability did not produce any systematic effect on phase relations between closely-positioned neurons.

Fig. 6. Oscillations following DC stimulation in network (100 PY – 25 IN) model.

(A) Top, no synaptic coupling. Bottom, coupled network. (B) Time-dependent cross-correlations between one PY neuron (PY35) and its neighbors (PY36–PY39). Without synaptic coupling all PY neurons fired independently. Including excitatory/inhibitory connections synchronized the slow oscillations. During fast run, however, PY neurons remained desynchronized. Oscillations in the neighboring PY cells displayed phase shift (local activity propagation) with sudden phase changes. (Modified from (Boucetta et al. 2008))

In contrast to the slow bursting mode, the degree of synchrony between neurons (even in close proximity) was reduced during fast runs. Typically, neighboring neurons fired with a phase shift that was consistent for a few cycles of network oscillation thus suggesting local spike propagation. Different cell pairs displayed phase delays of different signs (propagation in different directions). Phase relations between neurons changed from in-phase to out-of-phase oscillations or vice versa either gradually (see, e.g., cross-correlation plot for PY35 and PY36 in Fig. 6B) or suddenly (see, e.g., cross-correlation plot for PY35 and PY38 in Fig. 6B). These modeling results suggest that during fast runs, local synaptic excitation controls phase relations between neighbor neurons but is not sufficient to arrange stable network synchronization. Furthermore, the synchronizing effect of feedback inhibition was absent during fast runs because of low spiking activity of inhibitory interneurons. Thus, random long-range connections may increase the synchrony of transitions between slow bursting and fast runs but do not affect the synchrony of oscillations on a cycle-to-cycle basis.

Self-sustained oscillations mediated by extracellular K⁺ dynamics

In our modeling studies, the occurrence of oscillatory patterns displayed by cortical neurons (slow bursting or fast run) depended on the absolute level of [K⁺]_o (Bazhenov et al. 2004; Frohlich et al. 2006). In the model of an isolated cortical neuron, fast runs were the only stable firing pattern in presence of moderately elevated levels of [K⁺]_o ([K⁺]_o < [K⁺]_o^cr1 ≅ 5.75 mM). For higher [K⁺]_o levels ([K⁺]_o > [K⁺]_o^cr2 ≅ 6.4 mM), slow bursting was the only stable firing pattern. Importantly, for an intermediate range of [K⁺]_o, these two different oscillatory states co-exist ([K⁺]_o^cr1 < [K⁺]_o < [K⁺]_o^cr2) (Frohlich and Bazhenov 2006; Frohlich et al. 2006) – a phenomenon called bistability. In this range of [K⁺]_o, the system could display either tonic spiking or slow bursting depending on the initial state of the cell. In the single cell model, however, this bistability does not play a significant role because of the progressive monotonic [K⁺]_o decay. In the network model, however, the same bistability leads to self-sustained oscillations shaped into an alternating sequence of slow bursting and fast run epochs, each lasting several seconds (Fig. 7A). Due to the lateral excitatory connections, the frequency of fast runs was higher in the network model compared to the isolated neuron. Thus, during fast runs, the activity-dependent K⁺ efflux overwhelmed the [K⁺]_o regulation mechanism and therefore the level of [K⁺]_o progressively increased. This further increased the network excitability (positive feedback) until the network switched to the slow bursting mode at [K⁺]_o^cr2 (Fig. 7B). During slow bursting, the average network activity was much lower since it was dominated by relatively long intervals of silence between bursts. Due to the relatively weak K⁺ efflux during slow bursting, the [K⁺]_o regulation apparatus was sufficiently strong to clear excess [K⁺]_o. As a result, [K⁺]_o decreased until it reached the point ([K⁺]_o^cr1) where the network could not sustain bursting anymore and the network switched back to fast run, thus starting a new cycle of slow state transitions between fast run and slow bursting. We also found that the persistence of this transient dynamics depended on the balance between synaptic inhibition and excitation in the network (Frohlich and Bazhenov 2006; Frohlich et al. 2006). An activity-dependent increase in intracellular chloride concentration mediated by inhibitory synaptic currents caused a depolarizing shift in the reversal potential of chloride leading to a decrease in inhibition. The resulting overall shift in the balance between synaptic excitation and inhibition favored the slow bursting state during which [K⁺]_o decreased to eventually return to baseline causing termination of the oscillatory activity (Fig. 8) (Frohlich et al. 2007). Our model shows that the hysteresis between slow and fast oscillations in a single neuron could serve as the basis for both the maintenance and termination of slow bursting and fast runs seen in cat neocortex in vivo.

Fig. 7. Self-sustained oscillations in globally connected network with five PY cells and one IN.

(A) Top, network activity of PY cells (40 seconds duration) shows alternating epochs of fast run and slow bursting. Bottom, membrane voltage time course of PY cell and of IN. (B) [K⁺]_o increased during fast run and decreased during slow bursting. Upper switching point for transition from fast run to slow bursting and lower switching point for transition from slow bursting to fast run correspond to the end points of the hysteresis region. From (Frohlich et al. 2006), with permission. Copyright 2006 Society for Neuroscience.

Fig. 8. [K⁺]_o controls transitions between fast runs and slow bursting.

Computational model showing hysteresis between regimes of fast and slow oscillations as a function of [K⁺]_o, leading to spatial patterning of slow bursting and fast runs in a cortical network model of 80 PYs and 16 INs. Transient increase in initial [K⁺]_o triggered oscillations in network which was previously silent. Activity-dependent increase in intracellular chloride concentration caused shift in balance between synaptic excitation and inhibition resulting termination of oscillatory activity. Top, network activity; bottom, membrane voltage of representative PY neuron (PY#20).

Conclusion

Epileptic seizures are commonly considered unstable runaway dynamics of neuronal networks. Specifically, it has been suggested that positive feedback interaction between extracellular potassium and neural activity mediates cortical seizures. In a series of studies, reviewed here, we showed that epileptic seizures may represent a stable (or quasi-stable) cortical state caused by extracellular potassium concentration dynamics. This pathological state consisted of alternating epochs of tonic firing and bursting and coexisted with another attractor representing normal (healthy) cortical dynamics. This novel and surprising finding is in contrast with the currently held belief that epileptic seizures represent runaway network instabilities.

The basin of attraction of the “pathological” brain state depends on the variety of factors including intrinsic and synaptic conductances, synaptic connectivity patterns and may vary between healthy and epileptic brains. An increase in the size of this basin in patients suffering from epilepsy would reduce the threshold for transitions from the physiological to the pathological state. It may also affect an average time the brain spends in the pathological state (i.e. duration of seizures). The proposed model may explain the relatively random occurrence of most seizures. In the epileptic brain, internal fluctuations or external inputs would more easily drive the network into the basin of attraction of the seizure state due to its increased size. In contrast, such transitions may never occur in the non-epileptic brain.

Current antiepileptic drugs mainly either enhance GABA_A inhibition or decrease sodium currents. Approximately one-third of patients with symptomatic localization-related epilepsy syndromes (e.g., trauma) are refractory to available antiepileptic medications (Kwan and Brodie 2000). In these patients, therapeutical agents that stabilize [K⁺]_o at physiological levels could block the epileptic activity. A promising target for such therapeutics may be the astroglial KIR channels, which play a role in the K⁺ reuptake and spatial buffering (Newman 1986; 1993). The successful development of such treatment modalities could eventually reduce the number of patients suffering from drug-resistant epilepsy.