  Despite the molecular evidence that close to linear steady state I-V
relationship in mammalian astrocytes reflects a total current resulting from
more than one differently regulated K+ conductances, detailed ODE models of
membrane voltage Vm incorporating multiple conductances are lacking. Repeated
results of deregulated expressions of major K+ channels in glia, Kir4.1, in
models of disease, as well as their altered rectification when assembling
heteromeric Kir4.1/Kir5.1 channels have motivated us to attempt a detailed
model adding the weaker potassium K2P current, in addition to Kir4.1, and study
the stability of the resting state Vr. We ask whether with a deregulated Kir
conductivity the nominal resting state Vr remains stable, and the cell retains
a potassium electrode behavior with Vm following E_K. The minimal 2-dimensional
model near Vr showed that certain alterations of Kir4.1 current may result in
multistability of Vm if the model incorporates the typically observed K+
currents: Kir, K2P, and non-specific potassium leak. More specifically, a
decrease or loss of outward Kir4.1 conductance introduces instability of Vr,
near E_K. That happens through a fold bifurcation giving birth to a much more
depolarized second, stable resting state Vdr>-10 mV. Realistic timeseries were
used to perturb the membrane model, from recordings at the glial membrane
during electrographic seizures. Simulations of the perturbed system by constant
current through GJCs 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 down-state / up-state 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.
