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Dynamical analysis of dendritic mixed bursting within the pre-Bötzinger complex

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Abstract

A special class of neurons within the brainstem pre-Bötzinger complex (pre-BötC) may perform diversified electrical actions, which are closely related to the generation of mammalian respiratory rhythm. Researches on electrical activities of those neurons are of highly interest and have been conducted both experimentally and computationally. One interesting firing activity observed experimentally is the so-called mixed bursting (MB), which exhibits more than one type of short bursts within a periodic cycle and is believed to be generated by the joint action of persistent sodium current and intracellular calcium oscillations. In this paper, based on Park and Rubin’s model for single pre-BötC neuron, we numerically find that MB can also be driven by the sole action of intracellular calcium oscillations originating from the dendrite. We call such MB the dendritic mixed bursting (DMB). We show several special DMBs one after another and interpret their dynamical mechanisms via fast–slow decomposition and bifurcation analysis. In addition, we show how calcium-activated nonspecific cationic conductance (\(g_{\text{ CAN }}\)) affects certain DMB activities. This work may provide significant insights for comprehending compound kinetics scenarios within the pre-BötC.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (11872003, 11772069), Cultivation Plan for “Yujie” Team of North China University of Technology (No. 107051360019XN137/002).

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China

    Zhuosheng Lü & Meiru Liu

  2. School of Science, North China University of Technology, Beijing, 100144, People’s Republic of China

    Lixia Duan

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  1. Zhuosheng Lü
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  2. Meiru Liu
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Appendix

Appendix

See Tables 1, 2 and 3.

Table 3 Specific parameter values of ion conductances and [IP3] used in Sects. 4.1, 5 and 6
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Lü, Z., Liu, M. & Duan, L. Dynamical analysis of dendritic mixed bursting within the pre-Bötzinger complex. Nonlinear Dyn 103, 897–912 (2021). https://doi.org/10.1007/s11071-020-06097-1

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