Bursting Synchronization Dynamics In Complex Nonlinear Respiratory System

Respiratory rhythm is a complex physiological movement.Pre-Botzinger complex is the key site for the generation of respiratory rhythm.In normal state,respiratory rhythm is uniform and orderly.However,respiratory rhythm will change to pathological state.Therefore,the mechanism of respiratory rhythm and their control have been an important scientific issue in related research areas.The coupled neuron model in the pre-Botzinger complex is studied in this paper.The effect of the intrinsic currents on the rhythm patterns of the neuronal system are investigated from the point of view nonlinear dynamics.Experiments show that calcium-activated non-specific cationic current(I_CAN)and persistent sodium current(I_NaP)are prevalent in the pre-Botzinger complex,and they play an important role in the generation of bursting,especially the mixed bursting.By multiple time-scale analysis,bifurcation analysis and other dynamic theories,we investigate the effect of calcium-activated non-specific cationic current(I_CAN)on the respiratory rhythm under conditions of the persistent sodium current(I_NaP)activation and deactivation respectively.The paper includes four parts.The first section introduces the biological background and the basic knowledge of nonlinear dynamics use in this paper.In the section 2,we investigate how the persistent sodium conductance(g_NaP)make the system produce more complex bursting pattern—depolarization block bursting?DB-bursting?,of which the persistent sodium current(I_NaP)and the calcium activated non-specific cationic current(I_CAN)are both in the activated state.By the multiple time scale,fast-slow decomposition and two parameter bifurcation analysis,we explain the generation mechanisms of mixed depolarization block bursting?mixed DB-bursting?.In the Section 3,the effects of two intrinsic parameters of calcium conductance(g_CAN)and inositol 1,4,5-triphosphate?[IP3]?on respiratory rhythm are studied with the persistent sodium current being in the deactivation state.The firing patterns of respiratory rhythm in each parameter region are given.The phase plane analysis,bifurcation analysis and the fast and slow decomposition are used to explain the transition mechanism between different firing patterns.In the last section,we give the conclusions and prospects of this paper.The results in this paper show that the combination effects of persistent sodium current and calcium activated non-specific cationic current as well as the action of single current will make the system show more complex firing patterns,such as depolarization blocking bursting and dendrite bursting,and so on.The results in this paper are of great significance to understand the dynamic behavior of large-scale networks.The revealing of the effects of physiological parameters on the rhythm dynamics will help us to understand the mechanisms of pathological respiratory rhythm in the pre-Botzinger complex.