Multiple modes of a conditional neural oscillator

Abstract

We present a model for a conditional bursting neuron consisting of five conductances: Hodgkin-Huxley type time- and voltage-dependent Na+ and K+ conductances, a calcium activated voltage-dependent K+ conductance, a calcium-inhibited time- and voltage-dependent Ca++ conductance, and a leakage Cl- conductance. With an initial set of parameters (version S), the model shows a hyperpolarized steady-state membrane potential at which the neuron is silent. Increasing gNa and decreasing gCl, where gi is the maximal conductance for species i, produces bursts of action potentials (Burster N). Alternatively, an increase in gCa produces a different bursting state (Burster C). The two bursting states differ in the periods and amplitudes of their bursting pacemaker potentials. They show different steady-state I-V curves under simulated voltage-clamp conditions; in simulations that mimic a steady-state I-V curve taken under experimental conditions only Burster N shows a negative slope resistance region. Model C continues to burst in the presence of TTX, while bursting in Model N is suppressed in TTX. Hybrid models show a smooth transition between the two states.