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 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 dynamics incorporating the weaker potassium K2P-TREK1 current in addition to Kir4.1, and study the stability of the resting state V. 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 remains stable, and the cell retains the trivial, potassium electrode behavior with V after E. The minimal two-dimensional model of V near V showed that an N-shape deformed Kir I-V curve induces multistability of V 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. That happens through a robust bifurcation giving birth to a second, more depolarized stable resting state V > -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 between the two stable states, in a downstate-upstate manner. In the event of prolonged depolarizations near V, 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.