A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Botzinger complex (pre-BotC) in mammals. Two minimal models of these neurons are proposed. In model I, bursting arises via fast activation and slow inactivation of a persistent Na+ current I(NaP-h). In model 2, bursting arises via a fast-activating persistent Na+ current I(NaP) and slow activation of a K+ current I(KS). In both models, action potentials are generated via fast Na+ and K+ currents. The two models have few differences in parameters to facilitate a rigorous comparison of the two different burst- generating mechanisms. Both models are consistent with many of the dynamic features of electrophysiological recordings from pre-BotC oscillatory bursting neurons in vitro, including voltage-dependent activity modes (silence, bursting, and beating), a voltage-dependent burst frequency that can vary from 0.05 to > 1 Hz, and a decaying spike frequency during bursting. These results are robust and persist across a wide range of parameter values for both models. However, the dynamics of model 1 are more consistent with experimental data in that the burst duration decreases as the baseline membrane potential is depolarized and the model has a relatively flat membrane potential trajectory during the interburst interval. We propose interval. We propose several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.
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