Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons
- 448 Downloads
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.
KeywordsRespiration Pre-Bötzinger complex Multiple bursting mechanisms Bifurcation analysis
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.
- Butera, R., Rubin, J., Terman, D., Smith, J. (2005). Oscillatory bursting mechanisms in respiratory pacemaker neurons and networks. In S. Coombes & P. Bressloff (Eds.), Bursting: the genesis of rhythm in the nervous system. Singapore: World Scientific.Google Scholar
- Butera, R.J. Jr., Clark, J.W. Jr., Canavier, C.C., Baxter, D.A., Byrne, J.H. (1995). Analysis of the efects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems. Journal of Computational Neuroscience, 2(1), 19–44.CrossRefPubMedGoogle Scholar
- Butera, R.J. Jr., Rinzel, J., Smith, J.C. (1999). Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology, 82(1), 382–397.Google Scholar
- Peña, F., & Ramirez, J.M. (2002). Endogenous activation of serotonin-2a receptors is required for respiratory rhythm generation in vitro. The Journal of Neuroscience, 22(24), 11,055–11,064.Google Scholar
- Rinzel, J. (1987). A formal classification of bursting mechanisms in excitable systems. In Gleason, A. (Ed.), In: Proceedings of the international congress of mathematicians. Providence, RI: American Mathematical Society.Google Scholar
- Rubin, J.E., Hayes, J.A., Mendenhall, J.L., Del Negro, C.A. (2009). Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations. Proceedings of the National Academy of Sciences of the United States of America, 106(8), 2939–2944.CrossRefPubMedGoogle Scholar
- Viemari, J.C., Garcia, A.J. 3rd, Doi, A., Ramirez, J.M. (2011). Activation of alpha-2 noradrenergic receptors is critical for the generation of fictive eupnea and fictive gasping inspiratory activities in mammals in vitro. The European Journal of Neuroscience, 33(12), 2228–2237.CrossRefPubMedGoogle Scholar