Dynamics Analysis of Firing Patterns in Pre-Bötzinger Complex Neurons Model

Dynamics of antiphase bursting modulated by the inhibitory synaptic and hyperpolarization-activated cation currents

Antiphase bursting related to the rhythmic motor behavior exhibits complex dynamics modulated by the inhibitory synaptic current (Isyn), especially in the presence of the hyperpolarization-activated cation current (Ih). In the present paper, the dynamics of antiphase bursting modulated by the Ih and Isyn is studied in three aspects with a theoretical model. Firstly, the Isyn and the slow Ih with strong strength are the identified to be the necessary conditions for the antiphase bursting. The dependence of the antiphase bursting on the two currents is different for low (escape mode) and high (release mode) threshold voltages (Vth) of the inhibitory synapse. Secondly, more detailed co-regulations of the two currents to induce opposite changes of the bursting period are obtained. For the escape mode, increase of the Ih induces elevated membrane potential of the silence inhibited by a strong Isyn and shortened silence duration to go beyond Vth, resulting in reduced bursting period. For the release mode, increase of the Ih induces elevated tough value of the former part of the burst modulated by a nearly zero Isyn and lengthen burst duration to fall below Vth, resulting in prolonged bursting period. Finally, the fast-slow dynamics of the antiphase bursting are acquired. Using one-and two-parameter bifurcations of the fast subsystem of a single neuron, the burst of the antiphase bursting is related to the stable limit cycle, and the silence modulated by a strong Isyn to the stable equilibrium to a certain extent. The Ih mainly modulates the dynamics within the burst and quiescent state. Furthermore, with the fast subsystem of the coupled neurons, the silence is associated with the unstable equilibrium point. The results present theoretical explanations to the changes in the bursting period and fast-slow dynamics of the antiphase bursting modulated by the Isyn and Ih, which is helpful for understanding the antiphase bursting and modulating rhythmic motor patterns.

Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network

Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.