Quantal slowing in coupled rhythmogenic neural networks: Applications to breathing

The preBötzinger Complex is a neuronal central pattern generator of about 1000 neurons that produces a metronomic signal setting the inspiratory rhythm in mammals. This circuit is coupled to a separate rhythmogenic one driving exhalation. The excitability of the inhalation circuit can be reduced using opiates, while the exhalation circuit does not respond to these drugs. Under the influence of opiates, the interacting system of the inhalation/exhalation pattern generators exhibits quantal slowing – the system falls into one of few dynamical phases characterized by integer numbers of exhalations between inhalations. We examine this phenomenon using leaky integrate-and-fire neuron models of both central pattern generators with synaptic coupling between them. We demonstrate that this model produces quantal slowing. We explore which of the postulated forms of the interconnections between these circuits is consistent with experiment. Finally, we comment on the relation of this system to other examples of nonlinear, coupled oscillators.