Abstract
The preBötzinger complex (preBötC) is a heterogeneous neuronal network within the mammalian brainstem that has been experimentally found to generate robust, synchronous bursts that drive the inspiratory phase of the respiratory rhythm. The persistent sodium (NaP) current is observed in every preBötC neuron, and significant modeling effort has characterized its contribution to square-wave bursting in the preBötC. Recent experimental work demonstrated that neurons within the preBötC are endowed with a calcium-activated nonspecific cationic (CAN) current that is activated by a signaling cascade initiated by glutamate. In a preBötC model, the CAN current was shown to promote robust bursts that experience depolarization block (DB bursts). We consider a self-coupled model neuron, which we represent as a single compartment based on our experimental finding of electrotonic compactness, under variation of g NaP, the conductance of the NaP current, and g CAN, the conductance of the CAN current. Varying these two conductances yields a spectrum of activity patterns, including quiescence, tonic activity, square-wave bursting, DB bursting, and a novel mixture of square-wave and DB bursts, which match well with activity that we observe in experimental preparations. We elucidate the mechanisms underlying these dynamics, as well as the transitions between these regimes and the occurrence of bistability, by applying the mathematical tools of bifurcation analysis and slow-fast decomposition. Based on the prevalence of NaP and CAN currents, we expect that the generalizable framework for modeling their interactions that we present may be relevant to the rhythmicity of other brain areas beyond the preBötC as well.
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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.
Brockhaus, J., & Ballanyi, K. (1998). Synaptic inhibition in the isolated respiratory network of neonatal rats. European Journal of Neuroscience, 10(12), 3823–3839.
Butera, R., Rinzel, J., & Smith, J. (1999a). Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology, 82(1), 382–397.
Butera, R., Rinzel, J., & Smith, J. (1999b). Models of respiratory rhythm generation in the pre-Botzinger complex. II. Populations of coupled pacemaker neurons. Journal of Neurophysiology, 82(1), 398–415.
Crowder, E., Saha, M., Pace, R., Zhang, H., Prestwich, G., & Del Negro, C. (2007). Phosphatidylinositol 4, 5-bisphosphate regulates inspiratory burst activity in the neonatal mouse preBötzinger complex. The Journal of Physiology, 582(3), 1047–1058.
Del Negro, C., Hayes, J., & Rekling, J. (2010). Dendritic calcium activity in preBötzinger complex neurons in neonatal mice studied in vitro. Journal of Neuroscience (submitted).
Del Negro, C., Johnson, S., Butera, R., & Smith, J. (2001). Models of respiratory rhythm generation in the pre-Botzinger complex. III. Experimental tests of model predictions. Journal of Neurophysiology, 86(1), 59–74.
Del Negro, C., Koshiya, N., Butera Jr., R., & Smith, J. (2002a). Persistent sodium current, membrane properties and bursting behavior of pre-botzinger complex inspiratory neurons in vitro. Journal of Neurophysiology, 88(5), 2242–2250.
Del Negro, C., Morgado-Valle, C., & Feldman, J. (2002b). Respiratory rhythm: An emergent network property? Neuron, 34(5), 821–830.
Del Negro, C., Morgado-Valle, C., Hayes, J., Mackay, D., Pace, R., Crowder, E., et al. (2005). Sodium and calcium current-mediated pacemaker neurons and respiratory rhythm generation. Journal of Neuroscience, 25(2), 446–453.
Dhooge, A., Govaerts, W., & Kuznetsov, Y. (2003). MATCONT: A MATLAB package for numerical bifurcation analysis of O.D.E.s. ACM Transactions on Mathematical Software (TOMS), 29(2), 164.
Dunmyre, J. R., & Rubin, J. E. (2010). Optimal intrinsic dynamics for bursting in a three-cell network. SIAM Journal on Applied Dynamical Systems, 9, 154–187. doi:10.1137/090765808, http://link.aip.org/link/?SJA/9/154/1.
Egorov, A., Hamam, B., Fransén, E., Hasselmo, M., & Alonso, A. (2002). Graded persistent activity in entorhinal cortex neurons. Nature, 420(6912), 173–178.
Ermentrout, G. (2002). Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. Society for Industrial Mathematics.
Feldman, J., & Del Negro, C. (2006). Looking for inspiration: New perspectives on respiratory rhythm. Nature Reviews Neuroscience, 7(3), 232–241.
Feldman, J., & Smith, J. (1989). Cellular mechanisms underlying modulation of breathing pattern in mammals. Annals of the New York Academy of Sciences, 563(Modulation of Defined Vertebrate Neural Circuits), 114–130.
Fenichel, N. (1979). Geometric singular perturbation theory for ordinary differential equations. Journal of Differential Equations, 31(1), 53–98. doi:10.1016/0022-0396(79)90152-9, http://www.sciencedirect.com/science/article/B6WJ2-4KF75DG-5/%2/759c4cfb4dfa51704c3b8edb0e864f48.
Fransén, E., Tahvildari, B., Egorov, A., Hasselmo, M., & Alonso, A. (2006). Mechanism of graded persistent cellular activity of entorhinal cortex layer v neurons. Neuron, 49(5), 735–746.
Hindmarsh, A., Brown, P., Grant, K., Lee, S., Serban, R., Shumaker, D., et al. (2005). SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software (TOMS), 31(3), 363–396.
Jones, C. (1994). Geometric singular perturbation theory. Dynamical Systems (Montecatini Terme, 1994), 1609, 44–118.
Koizumi, H., & Smith, J. (2008). Persistent Na+ and K+-dominated leak currents contribute to respiratory rhythm generation in the pre-Botzinger complex in vitro. Journal of Neuroscience, 28(7), 1773–1785.
Lee, R., & Heckman, C. (2001). Essential role of a fast persistent inward current in action potential initiation and control of rhythmic firing. Journal of Neurophysiology, 85(1), 472–427.
Liu, D., & Liman, E. (2003). Intracellular Ca2+ and the phospholipid P.I.P.2 regulate the taste transduction ion channel TRPM5. Proceedings of the National Academy of Sciences of the United States of America, 100(25), 15160–15165.
Mironov, S. (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.
Morgado-Valle, C., Beltran-Parrazal, L., DiFranco, M., Vergara, J., & Feldman, J. (2008). Somatic Ca2+ transients do not contribute to inspiratory drive in preBötzinger complex neurons. The Journal of Physiology, 586(18), 4531.
Nilius, B., Mahieu, F., Prenen, J., Janssens, A., Owsianik, G., & Vennekens, R. (2006). The Ca2+-activated cation channel TRPM4 is regulated by phosphatidylinositol 4, 5-biphosphate. The EMBO Journal, 25(3), 467–478.
Pace, R., & Del Negro, C. (2008). A.M.P.A. and metabotropic glutamate receptors cooperatively generate inspiratory-like depolarization in mouse respiratory neurons in vitro. European Journal of Neuroscience, 28(12), 2434–2442.
Pace, R., Mackay, D., Feldman, J., & Del Negro, C. (2007a). Inspiratory bursts in the preBötzinger 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.
Pace, R., Mackay, D., Feldman, J., & Del Negro, C. (2007b). Role of persistent sodium current in mouse preBötzinger complex neurons and respiratory rhythm generation. The Journal of Physiology, 580(2), 485–496.
Paton, J., Abdala, A., Koizumi, H., Smith, J., & St-John, W. (2006). Respiratory rhythm generation during gasping depends on persistent sodium current. Nature Neuroscience, 9(3), 311–313.
Ptak, K., Zummo, G., Alheid, G., Tkatch, T., Surmeier, D., & McCrimmon, D. (2005). Sodium currents in medullary neurons isolated from the pre-Botzinger complex region. Journal of Neuroscience, 25(21), 5159–5170.
Purvis, L. K., Smith, J. C., Koizumi, H., & Butera, R. J. (2007). Intrinsic bursters increase the robustness of rhythm generation in an excitatory network. Journal of Neurophysiology, 97(2), 1515–1526. doi:10.1152/jn.00908.2006, http://jn.physiology.org/cgi/content/abstract/97/2/1515, http://jn.physiology.org/cgi/reprint/97/2/1515.pdf.
Ren, J., & Greer, J. (2006). Modulation of respiratory rhythmogenesis by chloride-mediated conductances during the perinatal period. Journal of Neuroscience, 26(14), 3721–3730.
Rubin, J., & Terman, D. (2002). Synchronized activity and loss of synchrony among heterogeneous conditional oscillators. SIAM Journal on Applied Dynamical Systems, 1(1), 146–174.
Rubin, J., Shevtsova, N., Ermentrout, B., Smith, J., & Rybak, I. (2009a). Multiple rhythmic states in a model of the respiratory cpg. Journal of Neurophysiology, 101, 2146–2165.
Rubin, J. E. (2006). Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters. Physical Review E. (Statistical, Nonlinear, and Soft Matter Physics), 74(2), 021917. doi:10.1103/PRE.74.021917, http://link.aps.org/abstract/PRE/v74/e021917.
Rubin, J. E., Hayes, J., Mendenhall, J., & Del Negro, C. (2009b). Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations. Proceedings of the National Academy of Sciences, 106(8), 2939–2944. doi:10.1073/pnas.0808776106, http://www.pnas.org/content/106/8/2939.abstract, http://www.pnas.org/content/106/8/2939.full.pdf+html.
Rybak, I., Abdala, A., Markin, S., Paton, J., & Smith, J. (2007). Spatial organization and state-dependent mechanisms for respiratory rhythm and pattern generation. Progress in Brain Research, 165, 201–220.
Rybak, I., Shevtsova, N., St-John, W., Paton, J., & Pierrefiche, O. (2003). Endogenous rhythm generation in the pre-Botzinger complex and ionic currents: Modelling and in vitro studies. European Journal of Neuroscience, 18(2), 239–257.
Rybak, I., Shevtsova, N., Ptak, K., & McCrimmon, D. (2004). Intrinsic bursting activity in the pre-Botzinger complex: Role of persistent sodium and potassium currents. Biological Cybernetics, 90(1), 59–74.
Shao, X., & Feldman, J. (1997). Respiratory rhythm generation and inhibition of expiratory neurons in pre-Botzinger complex: Differential roles of glycinergic and G.A.B.A.ergic neuronal transmission. Journal of Neurophysiology, 77, 1853–1860.
Smith, J., Abdala, A., Koizumi, H., Rybak, I., & Paton, J. (2007). Spatial and functional architecture of the mammalian brainstem respiratory network: A hierarchy of three oscillatory mechanisms. Journal of Neurophysiology, 98, 3370–3387.
Smith, J., Ellenberger, H., Ballanyi, K., Richter, D., & Feldman, J. (1991). Pre-Botzinger complex: A brainstem region that may generate respiratory rhythm in mammals. Science, 254(5032), 726.
Tazerart, S., Viemari, J., Darbon, P., Vinay, L., & Brocard, F. (2007). Contribution of persistent sodium current to locomotor pattern generation in neonatal rats. Journal of Neurophysiology, 98(2), 613–628.
Tazerart, S., Vinay, L., & Brocard, F. (2008). The persistent sodium current generates pacemaker activities in the central pattern generator for locomotion and regulates the locomotor rhythm. Journal of Neuroscience, 28(34), 8577–8589.
Toporikova, N., & Butera, R. (2010). Two types of independent bursting mechanisms in inspiratory neurons: An integrative model. Journal of Computational Neuroscience, 1–14. doi:10.1007/s10827-010-0274-z.
Tsuruyama, K., Hsiao, C.-F., Nguyen, V. T., Chandler, S. H. (2008). Intracellular calcium signaling modulates rhythmical burst activity in rat trigeminal principal sensory neurons. Program No. 575.17. 2008 Neuroscience Meeting Planner. Washington, DC: Society for Neuroscience.
Wu, N., Enomoto, A., Tanaka, S., Hsiao, C., Nykamp, D., Izhikevich, E., et al. (2005). Persistent sodium currents in mesencephalic v neurons participate in burst generation and control of membrane excitability. Journal of Neurophysiology, 93(5), 2710–2722.
Zhong, G., Masino, M., & Harris-Warrick, R. (2007). Persistent sodium currents participate in fictive locomotion generation in neonatal mouse spinal cord. Journal of Neuroscience, 27(17), 4507–4518.
Acknowledgements
We thank John Hayes for assistance in collecting experimental data. This work was partially supported by National Science Foundation awards DMS-0716936, DMS-1021701 and EMSW21-RTG 0739261, and National Institute of Health grants 1R01HL104127-01 and 1R21NS070056-01.
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Dunmyre, J.R., Del Negro, C.A. & Rubin, J.E. Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons. J Comput Neurosci 31, 305–328 (2011). https://doi.org/10.1007/s10827-010-0311-y
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DOI: https://doi.org/10.1007/s10827-010-0311-y