Slow Ionic Dynamics Reshape Bistability in a Biophysical Mean-Field Model of Brain Activity

Abstract

Brain states such as sleep, seizures, and resting wakefulness are often described in terms of transitions between distinct population states. Biophysically inspired mean-field models that couple neuronal firing statistics to slow ionic homeostasis provide a mechanistic bridge between detailed single-neuron physiology and macroscopic brain activity. Here we examine this issue in a biophysical mean-field model of cortical populations driven by potassium exchange and compare its dynamical repertoire with a matched spiking network across six physiological and pathological regimes. The fast subsystem contains a substantial region in which low- and high-activity fixed points coexist, but this conditional bistability is not inherited by the physiological resting branch of the complete slow-fast system. A generic fast-slow calculation identifies how feedback through a dynamical ionic variable changes the stability conditions of the fast subsystem, and an exact equilibrium reduction of the KIonEx-MF equations yields a single equilibrium on the physiological resting branch over the range examined. This resting state is excitable: perturbations generate intermittent synchronized events in both the mean-field and spiking-network descriptions. The results show how slow ionic dynamics can reshape conclusions drawn from a frozen fast subsystem and provide noise-driven excitability as an alternative route to spontaneous population transitions.