A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Bötzinger complex (pre-BötC) in mammals. Two minimal models of these neurons are proposed. In model 1, bursting arises via fast activation and slow inactivation of a persistent Na+ current INaP-h. In model 2, bursting arises via a fast-activating persistent Na+ current INaP and slow activation of a K+ current IKS. 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-BötC 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 several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.

We have proposed models for the ionic basis of oscillatory bursting of respiratory pacemaker neurons in the pre-Bötzinger complex. In this paper, we investigate the frequency control and synchronization of these model neurons when coupled by excitatory amino-acid-mediated synapses and controlled by convergent synaptic inputs modeled as tonic excitation. Simulations of pairs of identical cells reveal that increasing tonic excitation increases the frequency of synchronous bursting, while increasing the strength of excitatory coupling between the neurons decreases the frequency of synchronous bursting. Low levels of coupling extend the range of values of tonic excitation where synchronous bursting is found. Simulations of a heterogeneous population of 50-500 bursting neurons reveal coupling effects similar to those found experimentally in vitro: coupling increases the mean burst duration and decreases the mean burst frequency. Burst synchronization occurred over a wide range of intrinsic frequencies (0.1-1 Hz) and even in populations where as few as 10% of the cells were intrinsically bursting. Weak coupling, extreme parameter heterogeneity, and low levels of depolarizing input could contribute to the desynchronization of the population and give rise to quasiperiodic states. The introduction of sparse coupling did not affect the burst synchrony, although it did make the interburst intervals more irregular from cycle to cycle. At a population level, both parameter heterogeneity and excitatory coupling synergistically combine to increase the dynamic input range: robust synchronous bursting persisted across a much greater range of parameter space (in terms of mean depolarizing input) than that of a single model cell. This extended dynamic range for the bursting cell population indicates that cellular heterogeneity is functionally advantageous. Our modeled system accounts for the range of intrinsic frequencies and spiking patterns of inspiratory (I) bursting cells found in the pre-Bötzinger complex in neonatal rat brain stem slices in vitro. There is a temporal dispersion in the spiking onset times of neurons in the population, predicted to be due to heterogeneity in intrinsic neuronal properties, with neurons starting to spike before (pre-I), with (I), or after (late-I) the onset of the population burst. Experimental tests for a number of the model's predictions are proposed.