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

Abstract: 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.