Introduction

Almost all experimental models for seizure generation are based on a variety of external protocols, including the administration of drugs such as pilocarpine (e.g.1,2,3), artificial increase of extracellular potassium concentration, [K+]e (e.g.4), or direct electric stimulation (e.g.5). However, these approaches may not accurately reflect the in vivo conditions, where otherwise normal neuronal activity can generate occasional seizures through mechanisms that are not fully understood. For this reason, it is important to investigate the processes that may underlie seizures onset during behavioral activities.

In this work we focused on one of the possible mechanisms, a pathological change in [K+]e homeostasis. As demonstrated in animal models, increasing [K+]e can lead to prolonged membrane depolarization, increased neuronal excitability, and a higher susceptibility to seizures. During in vivo activities, this can happen when the astrocytic uptake is compromised6 or when the membrane mechanisms for [K+]e reuptake are altered7,8. However, it is not clear how and under which conditions synaptic inputs.

generated in vivo may lead to seizures like those experimentally induced by an artificial [K+]e increase (e.g.4), because a direct investigation at cellular level is practically impossible. This process has been studied in previous computational models (e.g.9,10,11,12,13,14,15,16) that provided some useful insight.

However, no model considered at the same time the peculiar characteristics of a CA1 pyramidal neuron, such as its morphological structure, the non-uniform ion channel dendritic distribution, and the response to typical synaptic inputs during normal in vivo behavior. These features are instrumental in reproducing and predicting the behavior of real neurons, because a model heavily informed by in vivo data can be used to provide key results that can help shape future in vivo experiments to improve our understanding of seizure activity and possible novel treatment pathways in epilepsy.

Results

We used the model to study the conditions under which a local [K+]e accumulation in response to in vivo-like synaptic inputs can give rise to seizure-like activity. For the purposes of this work, we define seizure-like events in a single neuron a sudden burst of action potentials lasting long enough to generate a depolarizing envelope in the neuronal membrane eventually bringing the neuron close or at a depolarization block. Although these events depend on electrical activity in a network (here modelled with a barrage of synaptic events), they have been recorded and studied in single neurons4. We have studied the emergence of these events by carrying out a series of simulations by stimulating 10 synaptic inputs, randomly distributed as schematically shown in Fig. 1a and activated by presynaptic spike times (Fig. 1b) recorded from 10 CA3 pyramidal neurons in vivo during 10 min of normal exploratory behavior17. To model the [K+]i,e dynamics we used four time constants (see Methods). Potassium extrusion through the ion channels was represented by τ1; we fixed it to the relatively small value of 2 ms (in the range experimentally observed for K channels activation). The rationale for this choice is that its change implies a mutation of the channel kinetics that, for larger values, would prevent the membrane to repolarize completely after an action potential with most likely fatal consequences and, for smaller values, would generate bursts of large [K+]e concentration that are not observed in vivo under control conditions. The mechanisms underlying the reuptake by the neuron, the intracellular diffusion, and the astrocytic activity, were represented by τ2, τ3, and τ4, respectively. In this work we were interested in the [K+]e dynamics, although we also added a [K+]i diffusion term (see Methods). However, there is practically no experimental information on its value. From a theoretical point of view, the intracellular ion flux depends on both the effective Diffusion coefficient (Deff) and on the local concentration gradient. Considering that in the cytoplasm Deff can be up to 20-fold lower18 than its ~ 2μm2/ms in water, and that ion pumps and the active and fast propagation of signals throughout the neuron membrane greatly reduce the local concentration gradient, we argued that a plausible choice for the intra- and extracellular diffusion time constants (τ3, and τ4, respectively) was to assume that at any given time they have the same value.

Under control conditions (i.e. τ1 = 2 ms, τ2,3,4 = 50 ms), the somatic response was a train of isolated action potentials with occasional short bursts (Fig. 1c). No seizure-like behavior was generated at the soma (Fig. 1d, green marker), although a flurry of activity was elicited in the dendrites (Fig. 1d, blue and pink markers), and the [K+] inside and outside over the entire neuron remained close to the resting levels of 150 and 5 mM, respectively (not shown). These results confirm that, under control conditions, even a strong barrage of synaptic activations, like those occasionally generated during in vivo activity, are not able to elicit seizure-like activity at the soma. It should be noted that action potentials were generated in the dendrites too and, according to the local passive and active conditions, they were or not forward-propagated to the soma. A particularly striking case is shown in Fig. 1d, where several dendritic APs in the pink dendrite caused only small EPSP-like events at the soma.

We then rerun the same simulation after increasing the decay time constants for [K+]e (τ2 = 900 and τ3,4 = 1150 ms). The somatic and dendritic traces are shown in Fig. 2a for the same time windows presented in Fig. 1d. Under this conditions, seizure-like events were observed at the soma (Fig. 2a, green marker) and in the dendrites (Fig. 2a, blue and pink markers); similarly to those experimentally recorded from CA1 neurons in animal models of epilepsy (e.g.19), they lasted a few seconds and the [K+]e during each event reached peaks of up to 25 mM (Fig. 2a, top plots), especially in the dendrite undergoing a large depolarizing envelope. We found that, in all cases, seizure-like events started in a localized dendritic location, quickly followed by the axon and the rest of the neuron. The local [K+]e increase is a direct consequence of the local membrane depolarization, which depend on a number of factors such as the morphology of the dendrite, the strength of the input, and the local expression of dendritic conductance. For these reasons, each dendrite may respond in different ways. In the particular case of the pink dendrite, the main reason was the intense synaptic input it received (corresponding to synaptic input #6 in Fig. 1b). The fast spreading of a seizure-like activity throughout the cell is illustrated in Fig. 2b, representing snapshots of the [K+]e distribution during a 1 s time window (from 578.5–579.5 s) of the simulation in Fig. 2a. The complete 10 min movie for this case is compared with control (Fig. 1c) in the Supplementary movie SM1. Essentially similar results were obtained by repeating the simulation after a random relocation of the synaptic inputs (not shown). These results strongly support the hypothesis that a fast [K+]e reuptake is essential for normal neuronal function, and that epileptic seizures can occur during normal in vivo activity, without any external intervention, in the presence of a pathologically [K+]e re-equilibration time (e.g. τ2 = 900 and τ3,4 = 1150 ms).

Fig. 1
figure 1

(a) Morphology of the CA1 pyramidal neuron used for all simulations and typical synaptic inputs. Green, blue, and pink circles represent recording locations (soma and two dendrites, respectively). The red circles represent the position of all other synapses. (b) Raster plot representing synaptic activation times recorded in vivo from CA3 pyramidal neurons for 10 min (600 s). (c) Somatic membrane potential under the control condition in response to the synaptic activations as in (b). (d) Enlargements of the somatic and typical dendritic membrane potential around 300 and 600 s under control condition. Colored markers represent recording locations. Note that dendritic spikes did not systematically propagate to the soma. Traces were truncated to improve readability. Dendritic action potentials have a typical peak membrane potential around 0 mV (i.e. an amplitude of ~ 50–60 mV), as in the experiments (e.g.33) Full traces are shown in Supplementary Figure SF2.

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Fig. 2
figure 2

(a) Somatic and typical dendritic membrane potential during two 6-s windows around 300 and 600 s, during a simulation using low peak synaptic weight (30 nS) and slower time constants for [K+]e decay (τ2 = 900 and τ3,4 = 1150 ms); membrane potential recording locations are marked as in Fig. 1, and the top plots show the corresponding local [K+]e concentration time course. (b) Selected snapshots from a movie recording the dendritic [K+]e dynamics over the entire neuron during a 10 min simulation (see Supplementary movie SM1).

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To figure out the range of time constants that can give rise to epilepsy-like behavior, we performed an extensive series of 10 min simulations to systematically explore a wide combination of τ2,3,4 values. Simulations were carried out using both low and high synaptic weight (30 and 60 nS, respectively), to mimic inputs eliciting an average firing frequency of ~ 0.5 and ~ 1 Hz, in the range observed in vivo during a circadian rhythm20 under control conditions. The results are summarized in Fig. 3, where for each simulation we represented the overall duration of epileptic behavior with the total time in which [K+]e > 12 mM during a given simulation. The [K+]e accumulation was within control levels for a rather wide range of values of time constants for both low and high synaptic conductance (Fig. 3, purple areas). Values up to several hundreds of milliseconds were not able to elicit seizure-like activity at the soma. Seizures began to appear rather sharply when at least one of the time constants modulating potassium decay 2,3,4) was slower than ~ 1 s, independently of the synaptic strength. It should be stressed that in a set of simulations carried out by fixing τ3 = τ1 = 2 ms, the results did not significantly change (not shown). Progressively higher values were leading to more and more events, until the neuron reached a depolarized block state (red areas) from which it was not able to return to rest. These results suggest that the [K+]e dynamics is an extremely robust process that can lead to seizure-like activity only following a substantial change from its control condition.

Fig. 3
figure 3

3D contour plots representing the total number of seconds in which [K+]e  > 12 mM, during a series of 10 min simulations carried out by exploring a wide combination of τ2,3,4 decay time constants at low (left plot) and high (right plot) synaptic weight (30 and 60 nS, respectively). Values in the Z axis are color coded: the red area represents simulations reaching a depolarization block at any time during the 10 min stimulation, and dark purple represents simulations where the [K+]e never reached the 12 mM value. The white marker indicates the values used for the simulations shown in Fig. 4.

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To study in more detail the cellular conditions under which seizures can be elicited, we compared somatic and dendritic membrane potential in the same time windows, during simulations of different possible pathological configurations for synaptic input locations and altered [K+]e dynamics. Spike events were determined by detecting membrane potential upstroke above a -10 mV threshold; a depolarization block condition (which is around -40 mV) does not contribute to the spike count.

With strong synaptic weights in the Stratum Radiatum (Fig. 4a) and τ2 = 900 and τ3,4 = 1150 ms in the entire neuron (pink area in Fig. 4a, right), most of the dendritic spikes propagated to the soma, and had different bursts number, duration, and time course (see Supplementary movie SM2, and Supplementary Figure SF1a). Many additional independent mechanisms may modulate these properties in different ways; however, we did not explore in more detail this aspect here where we focused on demonstrating a proof of principle. With the synaptic inputs in the Stratum Lacunosum Moleculare (Fig. 4b), the cell underwent more and stronger seizure-like events (see also Supplementary Figure SF1b). Restricting the area with τ2 = 900 and τ3,4 = 1150 ms to the Stratum Radiatum (Fig. 4c, compare the schemes on the right with Fig. 3), the soma did not show any seizure-like events, although it exhibited more spikes and a significant [K+]e accumulation (not shown).

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Fig. 4
figure 4

Typical somatic and dendritic recordings from simulations under different conditions. Colored areas in the middle panels represent region with τ2 = 900 ms and τ3,4 = 1150 ms (pink), synaptic input locations (yellow), and area with shifted IA (green). a) Somatic (top) and apical dendrite (bottom) membrane potential with synaptic inputs in the Stratum Radiatum (yellow area) with high synaptic weights (60 nS) and using τ2 = 900 ms and τ3,4 = 1150 ms as [K+]e decay time constant (see white marker in Fig. 3, right) for the entire neuron (pink area). b) Soma (top) and basal dendrite (bottom) membrane potential with synaptic input in the Stratum Lacunosum Moleculare (yellow area); peak synaptic weight was reduced by ~ 30% (43 nS) to consider the lower number of synaptic inputs in this area compared to the apical dendrites34; [K+]e decay time constants as in (b) for entire neuron (pink area). (c) Soma (top) and apical dendrite (bottom) membrane potential with synaptic inputs in the Stratum Radiatum (yellow area, right) with high synaptic weights (60 nS), but restricting the area with slow [K+]e decay to the Stratum Radiatum (pink area, right). (d) Soma (top) and apical dendrite (bottom) membrane potential after a -7 mV shift of the A-type K+ current activation curve (green area) over the somatodendritic region; simulation conditions as in Fig. 4a (pink area). e) Number of somatic spikes elicited as function of time during simulations under the different conditions considered in this work (the caption for each plot indicates the relative figure and simulation panel, with “SF1” corresponding to the traces shown in Figure SF1).

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With this model we can also make experimentally testable predictions on the pharmacological actions that could reduce/prevent seizure events. In general, there could be three different types of modulations: 1) acting on the mechanisms able to speed-up [K+]e uptake; however, these mechanisms are uniformly expressed in all neurons, and their pharmacological manipulation can thus be expected to generate substantial collateral effects. 2) upregulation of the I-h current; in CA1 pyramidal neurons this current can reduce the temporal summation of synaptic inputs21 and is peculiarly expressed at an increasing density with distance from the soma. However, it is inactivated by depolarization and it thus cannot be effective during the large depolarizing envelope that underlies a seizure onset. 3) upregulation of the IA current, which is also expressed at an increasing density with distance from the soma in CA1 neurons only22; we argued that it can be used to reduce seizures occurrence without significantly affecting other neuronal populations. We tested this hypothesis by carrying out a simulation using the pathological conditions of Fig. 4a but applying a -7 mV shift of its activation curve, a process known to also occur through biochemical pathways23. The shift was applied to the soma and all dendrites. Under this condition (Fig. 4d), seizures were not elicited and the neuron exhibited control behavior (see also Supplementary Figure SF2). These results suggest that basal dendrites can be more prone to induce epileptic activity, that a substantial portion of the dendritic area should be affected by a pathological change in order for the neuron to exhibit seizure-like activity, and that a pharmacological modulation of the IA current can restore control conditions in the presence of a pathological [K+]e dynamics.

The different conditions are summarized and compared in Fig. 4e, where we report the number of somatic spikes generated under different conditions. Under control conditions (Fig. 4e “control”, see Figure SF1 for somatic and dendritic trace) a total number of approximately 600 somatic spikes were elicited during a 10 min simulation, without seizure-like activity. This increased to ~ 1400 after altering [K+]e decay in the entire cell (Fig. 4e “all”), resulting in an average frequency consistent with experimental findings for baseline activity during interictal discharges (2.7 Hz24). The average frequency was still much higher than control even limiting the affected area to the Stratum Radiatum (Fig. 4e “apic”). It further greatly increased to ~ 12 Hz (~ 7500 spikes) for synaptic inputs on basal dendrites (Fig. 4e “basal”), with an average frequency in the range of experimental findings during interictal discharges (9.4 ± 19 Hz23). Finally, firing was restored to a value consistent with control conditions after a -7 mV shift of the IA activation curve (Fig. 4e “shifting IA”), even with a slower potassium dynamics (τ2 = 900 and τ3,4 = 1150 ms) affecting the entire cell.

These results suggest that the probability and the electrophysiological profile of epileptic events, occurring during normal behavioral activities, can depend on a combination of factors such as the extent of the dendritic tree involved in the pathological change and the location and strength of synaptic inputs.

Discussion

In this work, we have shown how, and under which conditions, a prolonged decay in extracellular potassium concentration to its resting level can bring an otherwise normal neuron into a hyperexcitable state. In this state, seizure-like activity emerges in response to occasional bursts of in vivo-like synaptic inputs—stimuli that would typically be involved in cognitive functions under control conditions25. These findings highlight that, in the absence of additional pathological mechanisms, the disruption of potassium homeostasis must be rather severe before a normal neuron reaches a state capable of catalyzing seizures’ onset.

We investigated one potential underlying mechanism: the abnormal accumulation of extracellular potassium, as it could result from a slower reuptake or diffusion processes. One of the primary mechanisms responsible for this effect is a pathological change in the Na+/K+ pump, and there is ample experimental evidence indicating that a malfunction in potassium extrusion contributes to epileptic behavior8,26. However, the model also revealed that the same effect could independently arise due to impairments in astrocytic activity, as suggested by experimental findings linking astrocyte depletion or mutations in Kir channels to epilepsy27,28.

Our results underscore the critical role of potassium channels. Approximately 10% of the 80 potassium channel types—encoded by more than 70 genes—are associated with epilepsy29,30,31,32, often triggered by activity-dependent changes or genetic mutations that increase neuronal excitability. In this work we have restricted our analysis to changes in the reuptake/diffusion terms that, as we have shown in this work, can generate occasional and temporally restricted epileptic-like events, like those observed experimentally, without affecting normal neuron behaviour. Additional mechanisms such as mutations of Potassium, but also Sodium, channel kinetics could underlie epileptic events. However, these mutations would more drastically alter the firing properties even during moderate synaptic activity, with most likely fatal consequences already at postnatal days. The model also revealed that this crucial role of potassium channels could be leveraged to develop pharmacological strategies aimed at reducing epileptic behavior.

In conclusion, our model can serve as a versatile framework to study in more realistic details the processes underlying the onset of epileptic behavior, and it can be readily adapted to include additional mechanisms that may be involved. This enables a deeper exploration of individual components’ contribution and dynamic interaction in seizure initiation and progression. Notably, the results suggested the experimentally testable predictions that basal dendrites exhibit higher susceptibility to alterations in extracellular potassium dynamics, making them a potential focal point for early seizure activity, and that a pharmacological modulation of the A-type potassium current could be used to restore normal neuronal function by reducing the pathological hyperexcitation.

Methods

All simulations were carried out using the NEURON simulation environment35, with a previously published model validated against several experimental findings36 and the mpg141208_B_idA CA1 pyramidal cell morphology (downloaded from https://www.hippocampushub.eu/build/data/morphology). The neuron’s morphology is composed of a soma, axon, 52 basal dendrites, and 89 oblique dendrites, and includes all the typical ionic currents that characterize a CA1 pyramidal neuron, i.e. Na+ and KDR, two A-type (IA, for proximal and distal dendrites), M-type potassium current (KM), and the non-specific Ih current. The IA and Ih peak conductance increased linearly with distance from the soma21,22,37). For the purpose of this work, 10 AMPA and 10 NMDA synapses were randomly distributed over the basal or apical oblique dendrites and activated by replaying presynaptic spike times recorded from 10 CA3 neurons in vivo17 for 10 min during normal exploratory behavior. No synapses were located on the main apical trunk, where only a small minority of excitatory inputs are found in the proximal and medial region34. To keep the model as simple as possible we did not explicitly include also inhibitory inputs. Even if they can significantly modulate a neuron’s signal integration (e.g.38) and have a fundamental role in generating oscillations (e.g.39), their action cannot change the overall effect discussed in this work. The AMPA component was implemented as a double-exponential conductance equation, with 1 and 5 ms for the rise and decay time, respectively, and a reversal potential of 0 mV. The NMDA conductance was implemented as in Gasparini et al. (2004)33, with an external Mg2+ concentration of 1 mM and a reversal potential of 0 mV. The peak synaptic conductance used in this work (30 or 60 nS) was chosen in such a way that the average firing frequency of the neuron during a 10 min simulation was in the range experimentally observed during daily behavioral activities20.

In this work, we did not use a random background activity on top of the input signals, since we were interested in demonstrating a proof of principle rather than explore the neuron behaviour under different membrane conductance states (reviewed in40).

Although the result could be quantitatively different in the presence of a more or less balanced excitatory/inhibitory background activity, it can be expected that the qualitative result will remain the same, i.e. a pathological slower [K+]e reuptake dynamics can generate seizure-like events under normal in vivo inputs. From this point of view, here we are in a worst case scenario for seizure-like events generation. Considering that individual CA3-CA1 synapses have a peak conductance of ~ 1 nS, our setup corresponds to the activation of ~ 300–600 actual synapses. We believe that this number is consistent with the actual in vivo condition, considering that 50–200 synchronously activated synapses are sufficient to generate a dendritic AP41 and that only a fraction of dendritic branches can be involved in a typical in vivo activity, such as that observed for place cells42.

Intra- and extra-cellular potassium concentration

The [K+]i and [K+]e accumulation and reuptake during the neuron’s activity, was implemented with the following ordinary differential equations:

where.

$$\frac{{d[K^{ + } ]i}}{dt} = - B \cdot \frac{iK - iKrest}{{\tau_{1} }} + \frac{{[K^{ + } ]e - [K^{ + } ]e0}}{{\tau_{2} }} - \frac{{[K^{ + } ]i - [K^{ + } ]i0}}{{\tau_{3} }}$$
$$\frac{{d[K^{ + } ]e}}{dt} = B \cdot \frac{iK - iKrest}{{\tau_{1} }} - \frac{{[K^{ + } ]e - [K^{ + } ]e0}}{{\tau_{2} }} - \frac{{[K^{ + } ]e - [K^{ + } ]e0}}{{\tau_{4} }}$$

B = 1/depth/F*(1e4).

depth = 0.1 μm, volume beneath the membrane considered to calculate the instantaneous concentrations (in mM);

F = Faraday constant (C*mol-1);

iK = total K+ current density (mA*cm-2); iKrest = resting K+ current (mA*cm-2);

[K+]x0 = intra- extra-cellular concentration at rest (mM).

The time constants (in ms) represent: potassium extrusion through the ion channels (τ1), reuptake by the neuron (τ2), intracellular diffusion (τ3), and uptake due to astrocytes activity (τ4). The absolute [K+]i,e change caused by the current flux through a fixed membrane area depends on the volume just outside or beneath the membrane, which is controlled by the B factor. For both sides of the membrane we have chosen a depth value of 0.1 μm, which is a physiologically plausible value for the neuron-astrocyte intercellular space43.