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

Despite the molecular evidence that the nearly linear steady-state current-voltage relationship in mammalian astrocytes reflects a total current resulting from more than one differently regulated K+ conductances, detailed ODE models of membrane voltage Vm are still lacking. Repeated experimental results of deregulated expressions of major K+ channels in glia, Kir4.1, in models of neurodegenerative disease, as well as their altered rectification when assembling heteromeric Kir4.1/Kir5.1 channels have motivated us to attempt a detailed model incorporating the weaker potassium K2P-TREK1 current, in addition to Kir4.1, and study the stability of the resting state Vr. The main question is whether with a deregulated Kir conductivity the nominal resting state Vr remains stable, and the cell retains a trivial, potassium electrode behavior with Vm following EK. The minimal 2-dimensional model near Vr showed that certain alterations of Kir4.1 current may result in multistability of Vm if the typically observed K+ currents - Kir, K2P, and non-specific potassium leak are present. More specifically, a decrease or loss of outward Kir4.1 conductance (turning the channels into inwardly rectifying) introduces instability of Vr, near EK. That happens through robustly observed fold bifurcation giving birth to a second, much more depolarized stable resting state Vdr > -10 mV. Realistic time series were used to perturb the membrane model, from recordings of glial Vm during electrographic seizures. Simulations of the perturbed system by constant currents through gap-junctions and transient seizure-like discharges as local field potentials led to depolarization of the astrocyte and switching of Vm between the two stable states, in a downstate - upstate manner. If the prolonged depolarizations near Vdr prove experimentally plausible, such catastrophic instability would impact all aspects of the glial function, from metabolic support to membrane transport and practically all neuromodulatory roles assigned to glia. Statement of SignificanceThe almost linear current-voltage relationship of most glial membranes results from multiple non-linear potassium leaky-pore, or background conductances. The corresponding channel types develop and deregulate independently, some of them asymmetrically - deregulate differently in different Vm ranges. Effect of those deregulations on whole-cell voltage responses has not been treated. We developed a minimal ODE model of voltage dynamics incorporating detailed models of the different potassium currents based on electrophysiological recordings. Parametrically inducing some of the reported deregulations of Kir current in glia resulted in instability of the nominal resting membrane potential and appearence of a second much more depolarized resting state. If prolonged glial depolarizations prove plausible such bistability would change the present beliefs about glial Vm dynamics.