Bifurcations underlying sigh and eupnea rhythmic transition in a pre-Botzinger complex model

Neuronal networks control motor output through multi-rhythmic electrical activities with different frequencies and amplitudes of different neurons. For example, the pre-Botzinger complex related to respiratory function exhibits sigh (slow frequency and large amplitude) and eupnea (fast frequency and small amplitude) rhythms. In the present paper, rhythm transitions modulated by several physiological factors are simulated in a coupling model composed of sigh and eupnea compartments, and the roles of ionic currents and the underlying bifurcation mechanism of the rhythm transitions are acquired. The transition from sigh- and eupnea-rhythm to the eupnea rhythm induced by the blockage of calcium or hyperpolarization-activated channels is related to supercritical Hopf bifurcation of the sigh compartment, and to the sigh rhythm caused by the blockage of persistent sodium channel or change of extracellular potassium concentration is associated with subcritical Hopf/fold limit cycle bifurcation of the eupnea compartment. The parameter regions of ionic currents and dynamical mechanism of rhythm transitions in the pre-Botzinger complex are helpful for the modulation to the respiratory rhythms.