Abstract

Epileptic seizures emerge from complex interactions between neuronal excitability, ionic homeostasis, and cellular metabolism. Although the Na+-K+-ATPase pump is known to play a central role in restoring ionic gradients during neuronal activity, the influence of ATP availability on seizure dynamics remains poorly understood. Here, we extend the Epileptor-2 model by introducing an energy-dependent formulation of Na+-K+-ATPase pump activity coupled to intracellular ATP dynamics. ATP production and consumption are modeled through phenomenological kinetic equations linking metabolic state to ionic regulation.

Using experimentally inspired ATP-related fluorescence signals, we calibrate the ATP production parameters to reproduce realistic depletion and recovery timescales during seizure-like events (SLEs). Within this framework, we show that ATP production acts as a critical control parameter governing transitions between distinct pathological regimes. Reduced ATP production capacity prolongs seizures and induces transitions from periodic SLEs to status epilepticus-like events (SELEs), characterized by sustained elevations of extracellular potassium and persistent neuronal firing. Severe metabolic impairment further traps the system in depolarized pathological states.

We additionally investigate the influence of astrocytic potassium buffering through bifurcation analysis of the glial uptake parameter $G_{glia}$. The analysis reveals transitions between stable resting states, periodic seizure activity, SELEs, and spreading depression-like events (SDLEs). In SDLE regimes, ATP transiently decreases during the onset of depolarization before recovering as neuronal firing collapses and pump activity diminishes.

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