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Journal of Computational Neuroscience

, Volume 34, Issue 2, pp 345–366 | Cite as

Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons

  • Choongseok Park
  • Jonathan E. Rubin
Article

Abstract

Activity of neurons in the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem drives the inspiratory phase of the respiratory rhythm. Experimental results have suggested that multiple bursting mechanisms based on a calcium-activated nonspecific cationic (CAN) current, a persistent sodium (NaP) current, and calcium dynamics may be incorporated within the pre-BötC. Previous modeling works have incorporated representations of some or all of these mechanisms. In this study, we consider a single-compartment model of a pre-BötC inspiratory neuron that encompasses particular aspects of all of these features. We present a novel mathematical analysis of the interaction of the corresponding rhythmic mechanisms arising in the model, including square-wave bursting and autonomous calcium oscillations, which requires treatment of a system of differential equations incorporating three slow variables.

Keywords

Respiration Pre-Bötzinger complex Multiple bursting mechanisms Bifurcation analysis 

Notes

Acknowledgements

This work was partially supported by the National Science Foundation award DMS 1021701. The authors thank Natalia Toporikova for many helpful conversations relating to this work.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Center for the Neural Basis of CognitionUniversity of PittsburghPittsburghUSA

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