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

Abstract

Antiphase bursting related to the rhythmic motor behavior exhibits complex dynamics modulated by the inhibitory synaptic current (I_syn), especially in the presence of the hyperpolarization-activated cation current (I_h). In the present paper, the dynamics of antiphase bursting modulated by the I_h and I_syn is studied in three aspects with a theoretical model. Firstly, the I_syn and the slow I_h 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 (V_th) 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 I_h induces elevated membrane potential of the silence inhibited by a strong I_syn and shortened silence duration to go beyond V_th, resulting in reduced bursting period. For the release mode, increase of the I_h induces elevated tough value of the former part of the burst modulated by a nearly zero I_syn and lengthen burst duration to fall below V_th, 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 I_syn to the stable equilibrium to a certain extent. The I_h 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 I_syn and I_h, which is helpful for understanding the antiphase bursting and modulating rhythmic motor patterns.

Keywords: Ih current; antiphase bursting; bifurcation; fast-slow dissection method; inhibitory synaptic current.