Bistability of silence and seizure-like bursting

Neuronal circuits exhibiting seizure episodes have been shown to be prone to multistability. The coexistence of normal and pathological regimes could explain why seizures suddenly start and stop. Methods developed in dynamical systems theory are powerful tools for determining the cellular mechanisms that underlie multistable seizure dynamics. Here, we present two different approaches to assess multistability in a model neuron. In this model, we identified a bursting regime and a silent regime. First, we investigated properties of a square pulse of injected current which produced a switch from seizure-like bursting into silence. By systematically varying the phase and amplitude of the pulse, we found contiguous pulse parameter sets, so-called windows, that satisfied this criterion, and we determined the dependence of these windows on the parameter gleak. As gleak increased, the size of each window scaled according to the same law as the amplitude of the saddle orbit. Second, we examined the role of each current in supporting bistability of bursting and silence. We defined the index of propensity for multistability as the range of gleak for which bursting and silence coexisted. We computed this quantity while iteratively varying the maximal conductance of each voltage-gated current one at a time. Increasing the maximal conductance of the slow potassium current or the hyperpolarization-activated current increased the range of bistability. In contrast, decreasing the maximal conductance of the persistent sodium current increased the range of bistability.