Nonlinear synchronization of neuronal firing on a random graph: Application to breathing rhythm formation in the preBötzinger complex.

The preBötzinger complex is a network of a few thousands of neurons that produces the rhythmic signal controlling mammalian breathing (inspiration). In vitro experiments demonstrated that the activation of small group of neurons in this network results in a “burstlet” of neuronal firing that propagates through the network after some delay (Kam et al., 2013). We consider a simple model burstlet dynamics based on the nonlinear synchronization of imprecise neuronal oscillators interacting on a random graph. The numerical simulations based on this model reproduce features observed in the experiment, such as (i) the probability of systemic synchronization in response to a given number of stimulated neurons, and (ii) the time lag between stimulation and systemic synchronization as a function of the number of stimulated neurons. We conclude by discussing how the topology of the neuronal connectivity affects the robustness of the emergent rhythm dynamics of the network in response to local damage (cell death).