Journal of Computational Neuroscience

, Volume 30, Issue 3, pp 607–632 | Cite as

Interacting oscillations in neural control of breathing: modeling and qualitative analysis

  • Jonathan E. Rubin
  • Bartholomew J. Bacak
  • Yaroslav I. Molkov
  • Natalia A. Shevtsova
  • Jeffrey C. Smith
  • Ilya A. Rybak


In mammalian respiration, late-expiratory (late-E, or pre-inspiratory) oscillations emerge in abdominal motor output with increasing metabolic demands (e.g., during hypercapnia, hypoxia, etc.). These oscillations originate in the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) and couple with the respiratory oscillations generated by the interacting neural populations of the Bötzinger (BötC) and pre-Bötzinger (pre-BötC) complexes, representing the kernel of the respiratory central pattern generator. Recently, we analyzed experimental data on the generation of late-E oscillations and proposed a large-scale computational model that simulates the possible interactions between the BötC/pre-BötC and RTN/pFRG oscillations under different conditions. Here we describe a reduced model that maintains the essential features and architecture of the large-scale model, but relies on simplified activity-based descriptions of neural populations. This simplification allowed us to use methods of dynamical systems theory, such as fast-slow decomposition, bifurcation analysis, and phase plane analysis, to elucidate the mechanisms and dynamics of synchronization between the RTN/pFRG and BötC/pre-BötC oscillations. Three physiologically relevant behaviors have been analyzed: emergence and quantal acceleration of late-E oscillations during hypercapnia, transformation of the late-E activity into a biphasic-E activity during hypercapnic hypoxia, and quantal slowing of BötC/pre-BötC oscillations with the reduction of pre-BötC excitability. Each behavior is elicited by gradual changes in excitatory drives or other model parameters, reflecting specific changes in metabolic and/or physiological conditions. Our results provide important theoretical insights into interactions between RTN/pFRG and BötC/pre-BötC oscillations and the role of these interactions in the control of breathing under different metabolic conditions.


Neural oscillations Respiratory central pattern generator Pre-Bötzinger Complex Parafacial respiratory group Coupled oscillators Phase plane analysis 



This study was supported by National Institute of Neurological Disorders and Stroke (NINDS), NIH grant R01 NS057815 (I.A. Rybak), NSF grant DMS 0716936 (J. E. Rubin) and in part by the Intramural Research Program of the NIH, NINDS (J.C. Smith).


  1. Abbott, S. B., Burke, P. G., & Pilowsky, P. M. (2009). Galanin microinjection into the preBötzinger or the Bötzinger complex terminates central inspiratory activity and reduces responses to hypoxia and hypercapnia in rat. Respiratory Physiology & Neurobiology, 167(3), 299–306.CrossRefGoogle Scholar
  2. Abdala, A. P., Rybak, I. A., Smith, J. C., & Paton, J. F. (2009a). Abdominal expiratory activity in the rat brainstem-spinal cord in situ: Patterns, origins and implications for respiratory rhythm generation. Journal de Physiologie, 587(Pt 14), 3539–3559.CrossRefGoogle Scholar
  3. Abdala, A. P., Rybak, I. A., Smith, J. C., Zoccal, D. B., Machado, B. H., St-John, W. M., et al. (2009b). Multiple pontomedullary mechanisms of respiratory rhythmogenesis. Respiratory Physiology & Neurobiology, 168(1–2), 19–25.CrossRefGoogle Scholar
  4. Baker, S. N., Kilner, J. M., Pinches, E. M., & Lemon, R. N. (1999). The role of synchrony and oscillations in the motor output. Experimental Brain Research, 128(1–2), 109–117.CrossRefGoogle Scholar
  5. Ballanyi, K., Onimaru, H., & Homma, K. (1999). Respiratory network function in the isolated brainstem-spinal cord of newborn rats. Progress in Neurobiology, 59(6), 583–634.PubMedCrossRefGoogle Scholar
  6. Bauer, M., Oostenveld, R., Peeters, M., & Fries, P. (2006). Tactile spatial attention enhances gamma-band activity in somatosensory cortex and reduces low-frequency activity in parieto-occipital areas. The Journal of Neuroscience, 26(2), 490–501.PubMedCrossRefGoogle Scholar
  7. Bazhenov, M., Timofeev, I., Steriade, M., & Sejnowski, T. J. (1999). Self-sustained rhythmic activity in the thalamic reticular nucleus mediated by depolarizing GABAA receptor potentials. Nature Neuroscience, 2(2), 168–174.PubMedCrossRefGoogle Scholar
  8. Bianchi, A. L., Denavitsaubie, M., & Champagnat, J. (1995). Central control of breathing in mammals - neuronal circuitry, membrane-properties, and neurotransmitters. Physiological Reviews, 75(1), 1–45.PubMedGoogle Scholar
  9. Burke, P. G., Abbott, S. B., McMullan, S., Goodchild, A. K., & Pilowsky, P. M. (2010). Somatostatin selectively ablates post-inspiratory activity after injection into the Bötzinger complex. Neuroscience, 167, 528–539.Google Scholar
  10. Butera, R. J., Rinzel, J., & Smith, J. C. (1999a). Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology, 82(1), 382–397.PubMedGoogle Scholar
  11. Butera, R. J., Rinzel, J., & Smith, J. C. (1999b). Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations of coupled pacemaker neurons. Journal of Neurophysiology, 82(1), 398–415.PubMedGoogle Scholar
  12. Cohen, M. I. (1979). Neurogenesis of respiratory rhythm in the mammal. Physiological Reviews, 59(4), 1105–1173.PubMedGoogle Scholar
  13. Daun, S., Rubin, J. E., & Rybak, I. A. (2009). Control of oscillation periods and phase durations in half-center central pattern generators: A comparative mechanistic analysis. Journal of Computational Neuroscience, 27(1), 3–36.PubMedCrossRefGoogle Scholar
  14. Dutschmann, M., & Herbert, H. (2006). The Kölliker-Fuse nucleus gates the postinspiratory phase of the respiratory cycle to control inspiratory off-switch and upper airway resistance in rat. The European Journal of Neuroscience, 24(4), 1071–1084.PubMedCrossRefGoogle Scholar
  15. Ermentrout, B. (2002). Simulating, Analyzing, and Animating Dynamical Systems. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
  16. Feldman, J. L. (1986). Neurophysiology of breathing in mammals. In F. E. Bloom (Ed.), Handbook of physiology (Vol. 4, pp. 463–524). Bethesda, MD: Am Physiol SocGoogle Scholar
  17. Feldman, J. L., & Del Negro, C. A. (2006). Looking for inspiration: new perspectives on respiratory rhythm. Nature Reviews. Neuroscience, 7(3), 232–242.PubMedCrossRefGoogle Scholar
  18. Fortin, G., & Thoby-Brisson, M. (2009). Embryonic emergence of the respiratory rhythm generator. Respiratory Physiology & Neurobiology, 168, 86–91.Google Scholar
  19. Fortuna, M. G., West, G. H., Stornetta, R. L., & Guyenet, P. G. (2008). Bötzinger expiratory-augmenting neurons and the parafacial respiratory group. The Journal of Neuroscience, 28(10), 2506–2515.PubMedCrossRefGoogle Scholar
  20. Grillner, S. (2006). Biological pattern generation: the cellular and computational logic of networks in motion. Neuron, 52(5), 751–766.PubMedCrossRefGoogle Scholar
  21. Guyenet, P. G. (2008). The 2008 Carl Ludwig lecture: retrotrapezoid nucleus, CO2 homeostasis, and breathing automaticity. Journal of Applied Physiology, 105(2), 404–416.PubMedCrossRefGoogle Scholar
  22. Guyenet, P. G. & Mulkey, D. K. (2010). Retrotrapezoid nucleus and parafacial respiratory group. Respir Physiol Neurobiol (Epub ahead of print, Feb 25).Google Scholar
  23. Guyenet, P. G., Mulkey, D. K., Stornetta, R. L., & Bayliss, D. A. (2005). Regulation of ventral surface chemoreceptors by the central respiratory pattern generator. The Journal of Neuroscience, 25(39), 8938–8947.PubMedCrossRefGoogle Scholar
  24. Guyenet, P. G., Stornetta, R. L., & Bayliss, D. A. (2008). Retrotrapezoid nucleus and central chemoreception. Journal de Physiologie, 586(8), 2043–2048.CrossRefGoogle Scholar
  25. Guyenet, P. G., Bayliss, D. A., Stornetta, R. L., Fortuna, M. G., Abbott, S. B., & DePuy, S. D. (2009). Retrotrapezoid nucleus, respiratory chemosensitivity and breathing automaticity. Respiratory Physiology & Neurobiology, 168(1–2), 59–68.CrossRefGoogle Scholar
  26. Hegger, R., Kantz, H., & Schreiber, T. (1999). Practical implementation of nonlinear time series methods: The TISEAN package. Chaos, 9, 413.PubMedCrossRefGoogle Scholar
  27. Iizuka, M., & Fregosi, R. F. (2007). Influence of hypercapnic acidosis and hypoxia on abdominal expiratory nerve activity in the rat. Respiratory Physiology & Neurobiology, 157(2–3), 196–205.CrossRefGoogle Scholar
  28. Izhikevich E. M. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT PressGoogle Scholar
  29. Janczewski, W. A., & Feldman, J. L. (2006a). Distinct rhythm generators for inspiration and expiration in the juvenile rat. Journal of Physiology-London, 570(2), 407–420.Google Scholar
  30. Janczewski, W. A., & Feldman, J. L. (2006b). Novel data supporting the two respiratory rhythm oscillator hypothesis. Focus on "respiration-related rhythmic activity in the rostral medulla of newborn rats". Journal of Neurophysiology, 96(1), 1–2.PubMedCrossRefGoogle Scholar
  31. Janczewski, W. A., Onimaru, H., Homma, I., & Feldman, J. L. (2002). Opioid-resistant respiratory pathway from the preinspiratory neurones to abdominal muscles: In vivo and in vitro study in the newborn rat. Journal de Physiologie, 545(Pt 3), 1017–1026.CrossRefGoogle Scholar
  32. Joseph, I. M., & Butera, R. J. (2005). A simple model of dynamic interactions between respiratory centers. Conference Proceedings IEEE Engineering in Medicine & Biology Society, 6, 5840–5842.Google Scholar
  33. Kantz, H., & Schreiber, T. (2004). Nonlinear time series analysis (2nd ed.). Cambridge: Cambridge University Press.Google Scholar
  34. Kay, L. M., Beshel, J., Brea, J., Martin, C., Rojas-Libano, D., & Kopell, N. (2009). Olfactory oscillations: the what, how and what for. Trends in Neurosciences, 32(4), 207–214.PubMedCrossRefGoogle Scholar
  35. Lal, A.,Oku, Y., Hülsmann, S., Okada, Y., Miwakeichi, F., Kawai, S., Tamura, Y. & Ishiguro, M. (2010) Dual oscillator model of the respiratory neuronal network generating quantal slowing of respiratory rhythm. Journal of Computational Neuroscience [Epub ahead of print].Google Scholar
  36. Mellen, N. M., Janczewski, W. A., Bocchiaro, C. M., & Feldman, J. L. (2003). Opioid-induced quantal slowing reveals dual networks for respiratory rhythm generation. Neuron, 37(5), 821–826.PubMedCrossRefGoogle Scholar
  37. Molkov, Y. I., Abdala, A. P. L., Bacak, B. J., Smith, J. C., Paton, J. F. R., & Rybak, I. A. (2010). Late-expiratory activity: emergence and interactions with the respiratory CPG. Journal of Neurophysiology, doi: 10.1152/jn.00334.2010.
  38. Monnier, A., Alheid, G. F., & McCrimmon, D. R. (2003). Defining ventral medullary respiratory compartments with a glutamate receptor agonist in the rat. Journal de Physiologie, 548(Pt 3), 859–874.CrossRefGoogle Scholar
  39. Onimaru, H., & Homma, I. (1987). Respiratory rhythm generator neurons in medulla of brainstem-spinal cord preparation from newborn rat. Brain Research, 403(2), 380–384.PubMedCrossRefGoogle Scholar
  40. Onimaru, H., & Homma, I. (2003). A novel functional neuron group for respiratory rhythm generation in the ventral medulla. The Journal of Neuroscience, 23(4), 1478–1486.PubMedGoogle Scholar
  41. Onimaru, H., Arata, A., & Homma, I. (1988). Primary respiratory rhythm generator in the medulla of brainstem-spinal cord preparation from newborn rat. Brain Research, 445(2), 314–324.PubMedCrossRefGoogle Scholar
  42. Onimaru, H., Arata, A., & Homma, I. (1990). Inhibitory synaptic inputs to the respiratory rhythm generator in the medulla isolated from newborn rats. Pflugers Archiv, 417(4), 425–432.PubMedCrossRefGoogle Scholar
  43. Onimaru, H., Ikeda, K., & Kawakami, K. (2009). Phox2b, RTN/pFRG neurons and respiratory rhythmogenesis. Respiratory Physiology & Neurobiology, 168(1–2), 13–18.CrossRefGoogle Scholar
  44. Pagliardini, S., Tan, W., Janczewski, W. A., & Feldman, J. L. (2009). Excitation and disinhibition of RTN/pFRG neurons induce active expiration in adult rats. In The XI-th Oxford Conference on Modeling and Control of Breathing: New Frontiers in Respiratory Control, Program and Abstracts, Nara, Japan (pp. 101).Google Scholar
  45. Paton, J. F., & Dutschmann, M. (2002). Central control of upper airway resistance regulating respiratory airflow in mammals. Journal of Anatomy, 201(4), 319–323.PubMedCrossRefGoogle Scholar
  46. Pikovsky, A., Rosenblum, M., & Kurths, J. (2003). Synchronization: A universal concept in nonlinear sciences (Cambridge Nonlinear Science Series): Cambridge University Press.Google Scholar
  47. Richter, D. W. (1996). Neural regulation of respiration: Rhythmogenesis and afferent control. In R. Greger & U. Windhorst (Eds.), Comprehensive Human Physiology. From Cellular Mechanisms to Integration, Vol. 2 (pp. 2079–2095). Berlin: Springer-Verlag.Google Scholar
  48. Rubin, J. E., Hayes, J. A., Mendenhall, J. L., & Del Negro, C. A. (2009a). 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, 2939–2944.CrossRefGoogle Scholar
  49. Rubin, J. E., Shevtsova, N. A., Ermentrout, G. B., Smith, J. C., & Rybak, I. A. (2009b). Multiple rhythmic states in a model of the respiratory central pattern generator. Journal of Neurophysiology, 101(4), 2146–2165.CrossRefGoogle Scholar
  50. Rybak, I. A., Shevtsova, N. A., St-John, W. M., Paton, J. F., & Pierrefiche, O. (2003). Endogenous rhythm generation in the pre-Bötzinger complex and ionic currents: Modelling and in vitro studies. The European Journal of Neuroscience, 18(2), 239–257.PubMedCrossRefGoogle Scholar
  51. Rybak, I. A., Shevtsova, N. A., Paton, J. F., Dick, T. E., St-John, W. M., Morschel, M., et al. (2004a). Modeling the ponto-medullary respiratory network. Respiratory Physiology & Neurobiology, 143(2–3), 307–319.CrossRefGoogle Scholar
  52. Rybak, I. A., Shevtsova, N. A., Ptak, K., & McCrimmon, D. R. (2004b). Intrinsic bursting activity in the pre-Bötzinger complex: Role of persistent sodium and potassium currents. Biological Cybernetics, 90(1), 59–74.CrossRefGoogle Scholar
  53. 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.PubMedCrossRefGoogle Scholar
  54. Rybak, I. A., O'Connor, R., Ross, A., Shevtsova, N. A., Nuding, S. C., Segers, L. S., et al. (2008). Reconfiguration of the pontomedullary respiratory network: a computational modeling study with coordinated in vivo experiments. Journal of Neurophysiology, 100(4), 1770–1799.PubMedCrossRefGoogle Scholar
  55. Singer, W. (1993). Synchronization of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349–374.PubMedCrossRefGoogle Scholar
  56. Skinner, F. K., Kopell, N., & Marder, E. (1994). Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. Journal of Computational Neuroscience, 1(1–2), 69–87.PubMedCrossRefGoogle Scholar
  57. 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.PubMedCrossRefGoogle Scholar
  58. 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.PubMedCrossRefGoogle Scholar
  59. Smith, J. C., Abdala, A. P., Koizumi, H., Rybak, I. A., & Paton, J. F. (2007). Spatial and functional architecture of the mammalian brain stem respiratory network: A hierarchy of three oscillatory mechanisms. Journal of Neurophysiology, 98(6), 3370–3387.PubMedCrossRefGoogle Scholar
  60. Smith, J. C., Abdala, A. P., Rybak, I. A., & Paton, J. F. (2009). Structural and functional architecture of respiratory networks in the mammalian brainstem. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 364(1529), 2577–2587.PubMedCrossRefGoogle Scholar
  61. Thoby-Brisson, M., Karlen., M, Wu, N., Charnay, P., Champagnat, J., & Fortin G. (2009). Genetic identification of an embryonic parafacial oscillator coupling to the preBötzinger complex. Nature Neuroscience, 12, 1028–U1100.Google Scholar
  62. Tort, A. B., Kramer, M. A., Thorn, C., Gibson, D. J., Kubota, Y., Graybiel, A. M., et al. (2008). Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a t-maze task. Proceedings of the National Academy of Sciences of the United States of America, 105(51), 20517–20522.PubMedCrossRefGoogle Scholar
  63. Wang, X. J., & Rinzel, J. (1992). Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Computation, 4(1), 84–97.CrossRefGoogle Scholar
  64. Wittmeier, S., Song, G., Duffin, J., & Poon, C. S. (2008). Pacemakers handshake synchronization mechanism of mammalian respiratory rhythmogenesis. Proceedings of the National Academy of Sciences of the United States of America, 105(46), 18000–18005.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jonathan E. Rubin
    • 1
  • Bartholomew J. Bacak
    • 2
  • Yaroslav I. Molkov
    • 2
  • Natalia A. Shevtsova
    • 2
  • Jeffrey C. Smith
    • 3
  • Ilya A. Rybak
    • 2
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Department of Neurobiology and AnatomyDrexel University College of MedicinePhiladelphiaUSA
  3. 3.Cellular and Systems Neurobiology Section, National Institute of Neurological Disorders and StrokeNational Institutes of HealthBethesdaUSA

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