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 ParkEmail author
  • Jonathan E. Rubin


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.


Respiration 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.


  1. Adams, W.B., & Benson, J.A. (1985). The generation and modulation of endogenous rhythmicity in the aplysia bursting pacemaker neurone r15. Progress in Biophysics and Molecular Biology, 46(1), 1–49.CrossRefPubMedGoogle Scholar
  2. Bertram, R., Sherman, A., Satin, L.S. (2010). Electrical bursting, calcium oscillations, and synchronization of pancreatic islets. Advances in Experimental Medicine and Biology, 654, 261–279.CrossRefPubMedGoogle Scholar
  3. Best, J., Borisyuk, A., Rubin, J., Terman, D., Wechselberger, M. (2005). The dynamic range of bursting in a model respiratory pacemaker network. SIAM Journal on Applied Dynamical Systems, 4(4), 1107–1139.CrossRefGoogle Scholar
  4. 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
  5. 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
  6. 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
  7. Chay, T.R., & Keizer, J. (1983). Minimal model for membrane oscillations in the pancreatic beta-cell. Biophysical Journal, 42(2), 181–190.CrossRefPubMedGoogle Scholar
  8. Crowder, E.A., Saha, M.S., Pace, R.W., Zhang, H., Prestwich, G.D., Del Negro, C.A. (2007). Phosphatidylinositol 4,5-bisphosphate regulates inspiratory burst activity in the neonatal mouse pre-Bötzinger complex. The Journal of Physiology 582(3), 1047–1058.CrossRefPubMedGoogle Scholar
  9. Csercsik, D., Farkas, I., Hrabovszky, E., Liposits, Z. (2012). A simple integrative electrophysiological model of bursting GnRH neurons. Journal of Computational Neuroscience, 32(1), 119–136.CrossRefPubMedGoogle Scholar
  10. Del Negro, C.A., Hayes, J.A., Rekling, J.C. (2011). Dendritic calcium activity precedes inspiratory bursts in pre-Bötzinger complex neurons. The Journal of Neuroscience, 31(3), 1017–1022.CrossRefPubMedGoogle Scholar
  11. Del Negro, C.A., Koshiya, N., Butera, R.J., Smith, J.C. (2002a). Persistent sodium current, membrane properties and bursting behavior of pre-Bötzinger complex inspiratory neurons in vitro. Journal of Neurophysiology, 88(5), 2242–2250.CrossRefPubMedGoogle Scholar
  12. Del Negro, C.A., Morgado-Valle, C., Feldman, J.L. (2002b). Respiratory rhythm: an emergent network property? Neuron, 34(5), 821–830.CrossRefPubMedGoogle Scholar
  13. Del Negro, C.A., Morgado-Valle, C., Hayes, J.A., Mackay, D.D., Pace, R.W., Crowder, E.A., Feldman, J.L. (2005). Sodium and calcium current-mediated pacemaker neurons and respiratory rhythm generation. The Journal of Neuroscience, 25(2), 446–453.CrossRefPubMedGoogle Scholar
  14. Doi, A., & Ramirez, J.M. (2008). Neuromodulation and the orchestration of the respiratory rhythm. Respiratory Physiology & Neurobiology, 164(1–2), 96–104.CrossRefGoogle Scholar
  15. Doi, A., & Ramirez, J.M. (2010). State-dependent interactions between excitatory neuromodulators in the neuronal control of breathing. The Journal of Neuroscience, 30(24), 8251–8262.CrossRefPubMedGoogle Scholar
  16. Duan, W., Lee, K., Herbison, A.E., Sneyd, J. (2011). A mathematical model of adult gnrh neurons in mouse brain and its bifurcation analysis. Journal of Theoretical Biology, 276(1), 22–34.CrossRefPubMedGoogle Scholar
  17. Dunmyre, J.R., Del Negro, C.A., Rubin, J.E. (2011). Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons. Journal of Computational Neuroscience, 31(2), 305–328.CrossRefPubMedGoogle Scholar
  18. Errington, A.C., Renger, J.J., Uebele, V.N., Crunelli, V. (2010). State-dependent firing determines intrinsic dendritic ca2+ signaling in thalamocortical neurons. The Journal of Neuroscience 30(44), 14843–14853.CrossRefPubMedGoogle Scholar
  19. Feldman, J.L., & Del Negro, C.A. (2006). Looking for inspiration: new perspectives on respiratory rhythm. Nature Reviews Neuroscience, 7(3), 232–242.CrossRefPubMedGoogle Scholar
  20. Feldman, J.L., & Smith, J.C. (1989). Cellular mechanisms underlying modulation of breathing pattern in mammals. Annals of the New York Academy of Sciences, 563, 114–130.CrossRefPubMedGoogle Scholar
  21. Fletcher, P.A., & Li, Y.X. (2009). An integrated model of electrical spiking, bursting, and calcium oscillations in gnrh neurons. Biophysical Journal, 96(11), 4514–4524.CrossRefPubMedGoogle Scholar
  22. Hughes, S.W., Errington, A., Lorincz, M.L., Kékesi, K.A., Juhász, G., Orbán, G., Cope, D.W., Crunelli, V. (2008). Novel modes of rhythmic burst firing at cognitively-relevant frequencies in thalamocortical neurons. Brain Research, 1235, 12–20.CrossRefPubMedGoogle Scholar
  23. Johnson, S.M., Smith, J.C., Funk, G.D., Feldman, J.L. (1994). Pacemaker behavior of respiratory neurons in medullary slices from neonatal rat. Journal of Neurophysiology, 72(6), 2598–2608.PubMedGoogle Scholar
  24. Koizumi, H., & Smith, J.C. (2008). Persistent Na+ and K+ - dominated leak currents contribute to respiratory rhythm generation in the pre-Bötzinger complex in vitro. The Journal of Neuroscience, 28(7), 1773–1785.CrossRefPubMedGoogle Scholar
  25. Mironov, S.L. (2008). Metabotropic glutamate receptors activate dendritic calcium waves and trpm channels which drive rhythmic respiratory patterns in mice. The Journal of Physiology, 586(9), 2277–2291.CrossRefPubMedGoogle Scholar
  26. Pace, R.W., Mackay, D.D., Feldman, J.L., Del Negro, C.A. (2007a). Inspiratory bursts in the pre-Bözinger complex depend on a calcium-activated non-specific cation current linked to glutamate receptors in neonatal mice. The Journal of Physiology 582(1), 113–125.CrossRefPubMedGoogle Scholar
  27. Pace, R.W., Mackay, D.D., Feldman, J.L., Del Negro, C.A. (2007b). Role of persistent sodium current in mouse pre-Bötzinger complex neurons and respiratory rhythm generation. The Journal of Physiology, 580(2), 485–496.CrossRefPubMedGoogle Scholar
  28. Paton, J.F., Abdala, A.P., Koizumi, H., Smith, J.C., St-John, W.M. (2006). Respiratory rhythm generation during gasping depends on persistent sodium current. Nature Neuroscience, 9(3), 311–313.CrossRefPubMedGoogle Scholar
  29. Peña, F., Parkis, M.A., Tryba, A.K., Ramirez, J.M. (2004). Differential contribution of pacemaker properties to the generation of respiratory rhythms during normoxia and hypoxia. Neuron, 43(1), 105–117.CrossRefPubMedGoogle Scholar
  30. 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
  31. Ptak, K., Zummo, G.G., Alheid, G.F., Tkatch, T., Surmeier, D.J., McCrimmon, D.R. (2005). Sodium currents in medullary neurons isolated from the pre-Bötzinger complex region. The Journal of Neuroscience, 25(21), 5159–5170.CrossRefPubMedGoogle Scholar
  32. Ramirez, J.M., Koch, H., Garcia, A.J., Doi, A., Zanella, S. (2011). The role of spiking and bursting pacemakers in the neuronal control of breathing. Journal of Biological Physics, 37(3), 241–261.CrossRefPubMedGoogle Scholar
  33. Rekling, J.C., & Feldman, J.L. (1998). PreBötzinger complex and pacemaker neurons: hypothesized site and kernel for respiratory rhythm generation. Annual Review of Physiology, 60, 385–405.CrossRefPubMedGoogle Scholar
  34. 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
  35. 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
  36. Rybak, I.A., Abdala, A.P., Markin, S.N., Paton, J.F., Smith, J.C. (2007). Spatial organization and state-dependent mechanisms for respiratory rhythm and pattern generation. Progress in Brain Research, 165, 201–220.CrossRefPubMedGoogle Scholar
  37. Saftenku, E.E. (2012). Models of calcium dynamics in cerebellar granule cells. Cerebellum, 11(1), 85–101.CrossRefPubMedGoogle Scholar
  38. Shao, X.M., & Feldman, J.L. (2000). Acetylcholine modulates respiratory pattern: effects mediated by m3-like receptors in preBötzinger complex inspiratory neurons. Journal of Neurophysiology, 83(3), 1243–1252.PubMedGoogle Scholar
  39. Smith, J.C., Butera, R.J., Koshiya, N., Del Negro, C., Wilson, C.G., Johnson, S.M. (2000). Respiratory rhythm generation in neonatal and adult mammals: the hybrid pacemaker-network model. Respiration Physiology, 122(2–3), 131–147.CrossRefPubMedGoogle Scholar
  40. Smith, J.C., Ellenberger, H.H., Ballanyi, K., Richter, D.W., Feldman, J.L. (1991). Pre-Bötzinger complex: a brainstem region that may generate respiratory rhythm in mammals. Science, 254(5032), 726–729.CrossRefPubMedGoogle Scholar
  41. Terman, D. (1992). The transition from bursting to continuous spiking in excitable membrane models. Journal of Nonlinear Science, 2(2), 135–182.CrossRefGoogle Scholar
  42. Thoby-Brisson, M., & Ramirez, J.M. (2001). Identification of two types of inspiratory pacemaker neurons in the isolated respiratory neural network of mice. Journal of Neurophysiology, 86(1), 104–112.PubMedGoogle Scholar
  43. Topolnik, L. (2012). Dendritic calcium mechanisms and long-term potentiation in cortical inhibitory interneurons. The European Journal of Neuroscience, 35(4), 496–506.CrossRefPubMedGoogle Scholar
  44. Toporikova, N., & Butera, R.J. (2011). Two types of independent bursting mechanisms in inspiratory neurons: an integrative model. Journal of Computational Neuroscience, 30(3), 515–528.CrossRefPubMedGoogle Scholar
  45. 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
  46. Viemari, J.C., & Ramirez, J.M. (2006). Norepinephrine differentially modulates different types of respiratory pacemaker and nonpacemaker neurons. Journal of Neurophysiology, 95(4), 2070–2082.CrossRefPubMedGoogle Scholar

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

Personalised recommendations