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- Title
The Na<sup>+</sup>/K<sup>+</sup>-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure.
- Authors
Behbood, Mahraz; Lemaire, Louisiane; Schleimer, Jan-Hendrik; Schreiber, Susanne
- Abstract
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. Author summary: The brain can produce slow rhythms, such as those observed during sleep or epilepsy. These rhythms are much slower than the neuronal electrical signals, and their origins are still under debate. Mechanisms discussed so far are often based on the connection delays in neural networks or on neuronal ion channels with particularly slow kinetics. We show that neurons with specific spiking dynamics–allowing them to fire at arbitrarily low frequencies (so-called class I neurons) can produce slow rhythmic patterns without requiring synaptic connectivity or special ion channels. In these cells, slow rhythmic activity arises from the interplay of slow changes in extracellular potassium concentration and the cell's voltage dynamics, mediated by the Na+/K+-ATPase pump. The latter, found in all neurons, regulates the concentrations of sodium and potassium ions across the cell membrane. The core mechanism is not idiosyncratic, rather mathematical analysis shows under which conditions slow rhythmic activity can arise generically from the pump-based coupling in a broad class of neurons. We demonstrate that the pump is relevant for the creation of different firing patterns, some of which have been associated with pathologies of the brain. A better mechanistic understanding of these complex, concentration-dependent dynamics can therefore be relevant for therapeutic approaches.
- Subjects
BRAIN waves; NEURAL circuitry; SLOW wave sleep; ION channels; POTASSIUM ions; SODIUM channels; HEART
- Publication
PLoS Computational Biology, 2024, Vol 20, Issue 8, p1
- ISSN
1553-734X
- Publication type
Article
- DOI
10.1371/journal.pcbi.1011751