The Na+/K+-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure.

Slow brain rhythms, for example during slow-wave sleep or pathological conditions like seizures and spreading depolarization, can be accompanied by oscillations in extracellular potassium concentration. Such slow brain rhythms typically have a lower frequency than tonic action-potential firing. They are assumed to arise from network-level mechanisms, involving synaptic interactions and delays, or from intrinsically bursting neurons. Neuronal burst generation is commonly attributed to ion channels with slow kinetics. Here, we explore an alternative mechanism generically available to all neurons with class I excitability. It is based on the interplay of fast-spiking voltage dynamics with a one-dimensional slow dynamics of the extracellular potassium concentration, mediated by the activity of the Na+/K+-ATPase. We use bifurcation analysis of the complete system as well as the slow-fast method to reveal that this coupling suffices to generate a hysteresis loop organized around a bistable region that emerges from a saddle-node loop bifurcation-a common feature of class I excitable neurons. Depending on the strength of the Na+/K+-ATPase, bursts are generated from pump-induced shearing the bifurcation structure, spiking is tonic, or cells are silenced via depolarization block. We suggest that transitions between these dynamics can result from disturbances in extracellular potassium regulation, such as glial malfunction or hypoxia affecting the Na+/K+-ATPase activity. The identified minimal mechanistic model outlining the sodium-potassium pump's generic contribution to burst dynamics can, therefore, contribute to a better mechanistic understanding of pathologies such as epilepsy syndromes and, potentially, inform therapeutic strategies.

Idealized multiple-timescale model of cortical spreading depolarization initiation and pre-epileptic hyperexcitability caused by NaV1.1/SCN1A mutations.

NaV1.1 (SCN1A) is a voltage-gated sodium channel mainly expressed in GABAergic neurons. Loss of function mutations of NaV1.1 lead to epileptic disorders, while gain of function mutations cause a migraine in which cortical spreading depolarizations (CSDs) are involved. It is still debated how these opposite effects initiate two different manifestations of neuronal hyperactivity: epileptic seizures and CSD. To investigate this question, we previously built a conductance-based model of two neurons (GABAergic and pyramidal), with dynamic ion concentrations (Lemaire et al. in PLoS Comput Biol 17(7):e1009239, 2021. https://doi.org/10.1371/journal.pcbi.1009239 ). When implementing either NaV1.1 migraine or epileptogenic mutations, ion concentration modifications acted as slow processes driving the system to the corresponding pathological firing regime. However, the large dimensionality of the model complicated the exploitation of its implicit multi-timescale structure. Here, we substantially simplify our biophysical model to a minimal version more suitable for bifurcation analysis. The explicit timescale separation allows us to apply slow-fast theory, where slow variables are treated as parameters in the fast singular limit. In this setting, we reproduce both pathological transitions as dynamic bifurcations in the full system. In the epilepsy condition, we shift the spike-terminating bifurcation to lower inputs for the GABAergic neuron, to model an increased susceptibility to depolarization block. The resulting failure of synaptic inhibition triggers hyperactivity of the pyramidal neuron. In the migraine scenario, spiking-induced release of potassium leads to the abrupt increase of the extracellular potassium concentration. This causes a dynamic spike-terminating bifurcation of both neurons, which we interpret as CSD initiation.

Modeling NaV1.1/SCN1A sodium channel mutations in a microcircuit with realistic ion concentration dynamics suggests differential GABAergic mechanisms leading to hyperexcitability in epilepsy and hemiplegic migraine.

Loss of function mutations of SCN1A, the gene coding for the voltage-gated sodium channel NaV1.1, cause different types of epilepsy, whereas gain of function mutations cause sporadic and familial hemiplegic migraine type 3 (FHM-3). However, it is not clear yet how these opposite effects can induce paroxysmal pathological activities involving neuronal networks' hyperexcitability that are specific of epilepsy (seizures) or migraine (cortical spreading depolarization, CSD). To better understand differential mechanisms leading to the initiation of these pathological activities, we used a two-neuron conductance-based model of interconnected GABAergic and pyramidal glutamatergic neurons, in which we incorporated ionic concentration dynamics in both neurons. We modeled FHM-3 mutations by increasing the persistent sodium current in the interneuron and epileptogenic mutations by decreasing the sodium conductance in the interneuron. Therefore, we studied both FHM-3 and epileptogenic mutations within the same framework, modifying only two parameters. In our model, the key effect of gain of function FHM-3 mutations is ion fluxes modification at each action potential (in particular the larger activation of voltage-gated potassium channels induced by the NaV1.1 gain of function), and the resulting CSD-triggering extracellular potassium accumulation, which is not caused only by modifications of firing frequency. Loss of function epileptogenic mutations, on the other hand, increase GABAergic neurons' susceptibility to depolarization block, without major modifications of firing frequency before it. Our modeling results connect qualitatively to experimental data: potassium accumulation in the case of FHM-3 mutations and facilitated depolarization block of the GABAergic neuron in the case of epileptogenic mutations. Both these effects can lead to pyramidal neuron hyperexcitability, inducing in the migraine condition depolarization block of both the GABAergic and the pyramidal neuron. Overall, our findings suggest different mechanisms of network hyperexcitability for migraine and epileptogenic NaV1.1 mutations, implying that the modifications of firing frequency may not be the only relevant pathological mechanism.

Initiation of migraine-related cortical spreading depolarization by hyperactivity of GABAergic neurons and NaV1.1 channels.

Spreading depolarizations (SDs) are involved in migraine, epilepsy, stroke, traumatic brain injury, and subarachnoid hemorrhage. However, the cellular origin and specific differential mechanisms are not clear. Increased glutamatergic activity is thought to be the key factor for generating cortical spreading depression (CSD), a pathological mechanism of migraine. Here, we show that acute pharmacological activation of NaV1.1 (the main Na+ channel of interneurons) or optogenetic-induced hyperactivity of GABAergic interneurons is sufficient to ignite CSD in the neocortex by spiking-generated extracellular K+ build-up. Neither GABAergic nor glutamatergic synaptic transmission were required for CSD initiation. CSD was not generated in other brain areas, suggesting that this is a neocortex-specific mechanism of CSD initiation. Gain-of-function mutations of NaV1.1 (SCN1A) cause familial hemiplegic migraine type-3 (FHM3), a subtype of migraine with aura, of which CSD is the neurophysiological correlate. Our results provide the mechanism linking NaV1.1 gain of function to CSD generation in FHM3. Thus, we reveal the key role of hyperactivity of GABAergic interneurons in a mechanism of CSD initiation, which is relevant as a pathological mechanism of Nav1.1 FHM3 mutations, and possibly also for other types of migraine and diseases in which SDs are involved.