Non-trivial dynamics in a model of glial membrane voltage driven by open potassium pores.

Despite the molecular evidence that a nearly linear steady-state current-voltage relationship in mammalian astrocytes reflects a total current resulting from more than one differentially regulated K ⁺ conductance, detailed ordinary differential equation (ODE) models of membrane voltage V _m are still lacking. Various experimental results reporting altered rectification of the major Kir currents in glia, dominated by Kir4.1, have motivated us to develop a detailed model of V _m dynamics incorporating the weaker potassium K2P-TREK1 current in addition to Kir4.1, and study the stability of the resting state V _r . The main question is whether, with the loss of monotonicity in glial I-V curve resulting from altered Kir rectification, the nominal resting state V _r remains stable, and the cell retains the trivial, potassium electrode behavior with V _m after E _K . The minimal two-dimensional model of V _m near V _r showed that an N-shape deformed Kir I-V curve induces multistability of V _m in a model that incorporates K2P activation kinetics, and nonspecific K ⁺ leak currents. More specifically, an asymmetrical, nonlinear decrease of outward Kir4.1 conductance, turning the channels into inward rectifiers, introduces instability of V _r . That happens through a robust bifurcation giving birth to a second, more depolarized stable resting state V _dr  > -10 mV. Realistic recordings from electrographic seizures were used to perturb the model. Simulations of the model perturbed by constant current through gap junctions and seizure-like discharges as local field potentials led to depolarization and switching of V _m between the two stable states, in a downstate-upstate manner. In the event of prolonged depolarizations near V _dr , such catastrophic instability would affect all aspects of the glial function, from metabolic support to membrane transport, and practically all neuromodulatory roles assigned to glia.
Competing Interests: Declaration of interests The authors declare no competing interests.
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