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

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Abstract

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.

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References

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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 

  • 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.

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • Cohen, M. I. (1979). Neurogenesis of respiratory rhythm in the mammal. Physiological Reviews, 59(4), 1105–1173.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • Ermentrout, B. (2002). Simulating, Analyzing, and Animating Dynamical Systems. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  Google Scholar 

  • 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 Soc

  • Feldman, J. L., & Del Negro, C. A. (2006). Looking for inspiration: new perspectives on respiratory rhythm. Nature Reviews. Neuroscience, 7(3), 232–242.

    Article  PubMed  CAS  Google Scholar 

  • Fortin, G., & Thoby-Brisson, M. (2009). Embryonic emergence of the respiratory rhythm generator. Respiratory Physiology & Neurobiology, 168, 86–91.

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Grillner, S. (2006). Biological pattern generation: the cellular and computational logic of networks in motion. Neuron, 52(5), 751–766.

    Article  PubMed  CAS  Google Scholar 

  • Guyenet, P. G. (2008). The 2008 Carl Ludwig lecture: retrotrapezoid nucleus, CO2 homeostasis, and breathing automaticity. Journal of Applied Physiology, 105(2), 404–416.

    Article  PubMed  Google Scholar 

  • Guyenet, P. G. & Mulkey, D. K. (2010). Retrotrapezoid nucleus and parafacial respiratory group. Respir Physiol Neurobiol (Epub ahead of print, Feb 25).

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Guyenet, P. G., Stornetta, R. L., & Bayliss, D. A. (2008). Retrotrapezoid nucleus and central chemoreception. Journal de Physiologie, 586(8), 2043–2048.

    Article  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hegger, R., Kantz, H., & Schreiber, T. (1999). Practical implementation of nonlinear time series methods: The TISEAN package. Chaos, 9, 413.

    Article  PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • Izhikevich E. M. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press

  • 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.

    CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    CAS  Google Scholar 

  • Kantz, H., & Schreiber, T. (2004). Nonlinear time series analysis (2nd ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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].

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Onimaru, H., Ikeda, K., & Kawakami, K. (2009). Phox2b, RTN/pFRG neurons and respiratory rhythmogenesis. Respiratory Physiology & Neurobiology, 168(1–2), 13–18.

    Article  CAS  Google Scholar 

  • 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).

  • Paton, J. F., & Dutschmann, M. (2002). Central control of upper airway resistance regulating respiratory airflow in mammals. Journal of Anatomy, 201(4), 319–323.

    Article  PubMed  Google Scholar 

  • Pikovsky, A., Rosenblum, M., & Kurths, J. (2003). Synchronization: A universal concept in nonlinear sciences (Cambridge Nonlinear Science Series): Cambridge University Press.

  • 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 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Singer, W. (1993). Synchronization of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349–374.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Wang, X. J., & Rinzel, J. (1992). Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Computation, 4(1), 84–97.

    Article  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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Acknowledgements

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).

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA

    Jonathan E. Rubin

  2. Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, 19129, USA

    Bartholomew J. Bacak, Yaroslav I. Molkov, Natalia A. Shevtsova & Ilya A. Rybak

  3. Cellular and Systems Neurobiology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD, 20892, USA

    Jeffrey C. Smith

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  1. Jonathan E. Rubin
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  2. Bartholomew J. Bacak
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  3. Yaroslav I. Molkov
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  4. Natalia A. Shevtsova
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  5. Jeffrey C. Smith
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  6. Ilya A. Rybak
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Correspondence to Jonathan E. Rubin.

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Rubin, J.E., Bacak, B.J., Molkov, Y.I. et al. Interacting oscillations in neural control of breathing: modeling and qualitative analysis. J Comput Neurosci 30, 607–632 (2011). https://doi.org/10.1007/s10827-010-0281-0

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