Skip to main content
Erschienen in: Journal of Computational Neuroscience 2/2008

01.10.2008

Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation

verfasst von: William H. Nesse, Alla Borisyuk, Paul C. Bressloff

Erschienen in: Journal of Computational Neuroscience | Ausgabe 2/2008

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N → ∞. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Brockhaus, J., & Ballanyi, K. (1998). Synaptic inhibition in the isolated respiratory network of neonatal rats. European Journal of Neuroscience, 10, 3823–3839.PubMedCrossRef Brockhaus, J., & Ballanyi, K. (1998). Synaptic inhibition in the isolated respiratory network of neonatal rats. European Journal of Neuroscience, 10, 3823–3839.PubMedCrossRef
Zurück zum Zitat Butera, R. J., Rinzel, J., & Smith, J. C. (1999a). Models of respiratory rthythm generation in the pre-bötzinger complex. I. bursting pacemaker neurons. Journal of Neurophysiology, 81, 382–397. Butera, R. J., Rinzel, J., & Smith, J. C. (1999a). Models of respiratory rthythm generation in the pre-bötzinger complex. I. bursting pacemaker neurons. Journal of Neurophysiology, 81, 382–397.
Zurück zum Zitat Butera, R. J., Rinzel, J., & Smith, J. C. (1999b). Models of respiratory rthythm generation in the pre-bötzinger complex. II. Populations of coupled pacemaker neurons. Journal of Neurophysiology, 81, 398–415. Butera, R. J., Rinzel, J., & Smith, J. C. (1999b). Models of respiratory rthythm generation in the pre-bötzinger complex. II. Populations of coupled pacemaker neurons. Journal of Neurophysiology, 81, 398–415.
Zurück zum Zitat Buzaki, G. (2007). Rhythms in the brain. Oxford: Oxford University Press. Buzaki, G. (2007). Rhythms in the brain. Oxford: Oxford University Press.
Zurück zum Zitat Chub, N., & O’Donovan, M. J. (2001). Post-episode depression of GABAergic transmission in spinal neurons of the chick embryo. Journal of Neurophysiology, 85, 2166–2176.PubMed Chub, N., & O’Donovan, M. J. (2001). Post-episode depression of GABAergic transmission in spinal neurons of the chick embryo. Journal of Neurophysiology, 85, 2166–2176.PubMed
Zurück zum Zitat Cupello, A. (2003). Neuronal transmembrane chloride electrochemical gradient: A key player in GABAA receptor activation physiological effect. Amino Acids, 24, 335–346.PubMedCrossRef Cupello, A. (2003). Neuronal transmembrane chloride electrochemical gradient: A key player in GABAA receptor activation physiological effect. Amino Acids, 24, 335–346.PubMedCrossRef
Zurück zum Zitat Del Negro, C. A., Johnson, S. M., Butera, R. J., & Smith, J. C. (2001). Models of respiratory rthythm generation in the pre-bötzinger complex. III. Experimental tests of model predictions. Journal of Neurophysiology, 86, 59–74.PubMed Del Negro, C. A., Johnson, S. M., Butera, R. J., & Smith, J. C. (2001). Models of respiratory rthythm generation in the pre-bötzinger complex. III. Experimental tests of model predictions. Journal of Neurophysiology, 86, 59–74.PubMed
Zurück zum Zitat Del Negro, C. A., Morgado-Valle, C., & Feldman, J. L. (2002). Respiratory rhythm: An emergent network property? Neuron, 34, 821–830.PubMedCrossRef Del Negro, C. A., Morgado-Valle, C., & Feldman, J. L. (2002). Respiratory rhythm: An emergent network property? Neuron, 34, 821–830.PubMedCrossRef
Zurück zum Zitat Destexhe, A., Rudolph, M., Fellous, J. M., & Sejnowski, T. J. (2001). Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience, 107, 13–24.PubMedCrossRef Destexhe, A., Rudolph, M., Fellous, J. M., & Sejnowski, T. J. (2001). Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience, 107, 13–24.PubMedCrossRef
Zurück zum Zitat Feldman, J. L., & Del Negro, C. A. (2006). Looking for inspiration: New perspectives on respiratory rhythm. Naturalist Reviews in Neuroscience, 7, 232–242, March.CrossRef Feldman, J. L., & Del Negro, C. A. (2006). Looking for inspiration: New perspectives on respiratory rhythm. Naturalist Reviews in Neuroscience, 7, 232–242, March.CrossRef
Zurück zum Zitat Funk, G. D., & Feldman, J. L. (1995). Generation of respiratory rhythm and pattern in mammals: Insights from developmental studies. Current Opinion in Neurobiology, 5, 778–785.PubMedCrossRef Funk, G. D., & Feldman, J. L. (1995). Generation of respiratory rhythm and pattern in mammals: Insights from developmental studies. Current Opinion in Neurobiology, 5, 778–785.PubMedCrossRef
Zurück zum Zitat Gang, H., Ditzinger, T., Ning, C. Z., & Haken, H. (1993). Stochastic resonance without external periodic force. Physical Review Letters, 71, 807–810.PubMedCrossRef Gang, H., Ditzinger, T., Ning, C. Z., & Haken, H. (1993). Stochastic resonance without external periodic force. Physical Review Letters, 71, 807–810.PubMedCrossRef
Zurück zum Zitat Gardiner, C. W. (2004). Handbook of stochastic methods. New York: Springer. Gardiner, C. W. (2004). Handbook of stochastic methods. New York: Springer.
Zurück zum Zitat Ge, Q., & Feldman, J. L. (1998). AMPA receptor activation and phosphatase inhibition affect neonatal rat respiratory rhythm generation. Journal of Physiology, 509, 255–266.PubMedCrossRef Ge, Q., & Feldman, J. L. (1998). AMPA receptor activation and phosphatase inhibition affect neonatal rat respiratory rhythm generation. Journal of Physiology, 509, 255–266.PubMedCrossRef
Zurück zum Zitat Gigante, G., Mattia, M., & Giudice, P. D. (2007). Diverse population-bursting modes of adapting spiking neurons. Physical Review Letters, 98, 148101.PubMedCrossRef Gigante, G., Mattia, M., & Giudice, P. D. (2007). Diverse population-bursting modes of adapting spiking neurons. Physical Review Letters, 98, 148101.PubMedCrossRef
Zurück zum Zitat Gutkin, B. S., Ermentrout, B. G. (1998). Dynamics of membrane excitability determine inter-spike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Computation, 10, 1047–1065.PubMedCrossRef Gutkin, B. S., Ermentrout, B. G. (1998). Dynamics of membrane excitability determine inter-spike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Computation, 10, 1047–1065.PubMedCrossRef
Zurück zum Zitat Han, S. K., Yim, T. G., Postnov, D. E., & Sosnovtseva, O. V. (1999). Interacting coherence resonance oscillators. Physical Review Letters, 83, 1771.CrossRef Han, S. K., Yim, T. G., Postnov, D. E., & Sosnovtseva, O. V. (1999). Interacting coherence resonance oscillators. Physical Review Letters, 83, 1771.CrossRef
Zurück zum Zitat Hille, B. (2001). Ion channels of excitable membranes, 3rd edition. Sunderland, MA: Sinauer. Hille, B. (2001). Ion channels of excitable membranes, 3rd edition. Sunderland, MA: Sinauer.
Zurück zum Zitat Holcman, D., & Tsodyks, M. (2006). The emergence of up and down states in cortical networks. PLoS Computational Biology, 2(3), 0714–0181.CrossRef Holcman, D., & Tsodyks, M. (2006). The emergence of up and down states in cortical networks. PLoS Computational Biology, 2(3), 0714–0181.CrossRef
Zurück zum Zitat Izhikevich, E. M. (2007). Dynamical systems in Neuroscience: The geometry of excitability and bursting. Cambridge: MIT. Izhikevich, E. M. (2007). Dynamical systems in Neuroscience: The geometry of excitability and bursting. Cambridge: MIT.
Zurück zum Zitat Johnson, S. M., Wilkerson, J. E., Wenninger, M. R., Henderson, D. R., & Mitchell, G. S. (2002). Role of synaptic inhibition in turtle respiratory rhythm generation. Journal of Physiology, 544, 253–265.PubMedCrossRef Johnson, S. M., Wilkerson, J. E., Wenninger, M. R., Henderson, D. R., & Mitchell, G. S. (2002). Role of synaptic inhibition in turtle respiratory rhythm generation. Journal of Physiology, 544, 253–265.PubMedCrossRef
Zurück zum Zitat Jonas, E., & Kaczmarek, L. K. (1999). The inside story: Subcellular mechanisms of neuromodulation. In P. S. Katz (Ed.), Beyond neurotransmission: Neuromodulation and its importance for information processing (pp. 83–120). Oxford: Oxford University Press. Jonas, E., & Kaczmarek, L. K. (1999). The inside story: Subcellular mechanisms of neuromodulation. In P. S. Katz (Ed.), Beyond neurotransmission: Neuromodulation and its importance for information processing (pp. 83–120). Oxford: Oxford University Press.
Zurück zum Zitat Kosmidis, E. K., Pierrefiche, O., & Vibert, J. F. (2004). Respiratory-like rhythmic activity can be produced by an excitatory network of non-pacemaker neuron models. Journal of Neurophysiology, 92, 686–699.PubMedCrossRef Kosmidis, E. K., Pierrefiche, O., & Vibert, J. F. (2004). Respiratory-like rhythmic activity can be produced by an excitatory network of non-pacemaker neuron models. Journal of Neurophysiology, 92, 686–699.PubMedCrossRef
Zurück zum Zitat Kurrer, C., & Schulten, K. (1995). Noise-induced synchronous neural oscillations. Physical Review E, 51, 6213.CrossRef Kurrer, C., & Schulten, K. (1995). Noise-induced synchronous neural oscillations. Physical Review E, 51, 6213.CrossRef
Zurück zum Zitat Kuznetsov, Y. A. (2004). Elements of Applied Bifurcation Theory, 3rd edition. New York: Springer-Verlag. Kuznetsov, Y. A. (2004). Elements of Applied Bifurcation Theory, 3rd edition. New York: Springer-Verlag.
Zurück zum Zitat Lindner, B., Garcia-Ojalvo, J., Neiman, A., & Schimansky-Geier, L. (2004). Effects of noise in excitable systems. Physics Reports, 392, 321–424.CrossRef Lindner, B., Garcia-Ojalvo, J., Neiman, A., & Schimansky-Geier, L. (2004). Effects of noise in excitable systems. Physics Reports, 392, 321–424.CrossRef
Zurück zum Zitat Loebel, A., & Tsodyks, M. (2002). Computation by ensemble synchronization in recurrent networks with synaptic depression. Journal of Comparative Neuroscience, 13, 111–124.CrossRef Loebel, A., & Tsodyks, M. (2002). Computation by ensemble synchronization in recurrent networks with synaptic depression. Journal of Comparative Neuroscience, 13, 111–124.CrossRef
Zurück zum Zitat Mattia, M., & Giudice, P. D. (2002). Population dynamics of interacting spiking neurons. Physical Review E, 66, 051917.CrossRef Mattia, M., & Giudice, P. D. (2002). Population dynamics of interacting spiking neurons. Physical Review E, 66, 051917.CrossRef
Zurück zum Zitat McCormick, D. A., & Yuste, R. (2006). Up states and cortical dynamics. In G. Grillner (Ed.), Microcircuits: The interface between neurons and global brain function. Cambridge: MIT. McCormick, D. A., & Yuste, R. (2006). Up states and cortical dynamics. In G. Grillner (Ed.), Microcircuits: The interface between neurons and global brain function. Cambridge: MIT.
Zurück zum Zitat O’Donovan, M. J. (1999). The origin of spontaneous activity in developing networks of the vertebrate nervous system. Current Opinion in Neurobiology, 9, 94–104.PubMedCrossRef O’Donovan, M. J. (1999). The origin of spontaneous activity in developing networks of the vertebrate nervous system. Current Opinion in Neurobiology, 9, 94–104.PubMedCrossRef
Zurück zum Zitat Pace, R. W., Mackay, D. D., Feldman, J. L., & Del Negro, C. A. (2007). Role of persistent sodium current in mouse preBötzinger complex neurons and respiratory rhythm generation. Journal of Physiology, 582, 485–496.CrossRef Pace, R. W., Mackay, D. D., Feldman, J. L., & Del Negro, C. A. (2007). Role of persistent sodium current in mouse preBötzinger complex neurons and respiratory rhythm generation. Journal of Physiology, 582, 485–496.CrossRef
Zurück zum Zitat Pham, J., Pakdaman, K., & Vibert, J. F. (1998). Noise-induced coherent oscillations in randomly connected neural networks. Physical Review E, 58, 3610.CrossRef Pham, J., Pakdaman, K., & Vibert, J. F. (1998). Noise-induced coherent oscillations in randomly connected neural networks. Physical Review E, 58, 3610.CrossRef
Zurück zum Zitat Pikovisky, A., & Ruffo, S. (1999). Finite-size effects in a population of interacting oscillators. Physical Review E, 59, 1633.CrossRef Pikovisky, A., & Ruffo, S. (1999). Finite-size effects in a population of interacting oscillators. Physical Review E, 59, 1633.CrossRef
Zurück zum Zitat Pradines, J. R., Osipov, G. V., & Collins, J. J. (1999). Coherence resonance in excitable and oscilatory systems: The essential role of slow and fast dynamics. Physical Review E, 60, 6407.CrossRef Pradines, J. R., Osipov, G. V., & Collins, J. J. (1999). Coherence resonance in excitable and oscilatory systems: The essential role of slow and fast dynamics. Physical Review E, 60, 6407.CrossRef
Zurück zum Zitat Rappel, W. J., & Karma, A. (1996). Noise-induced coherence in neural networks. Physical Review Letters, 77, 3256.PubMedCrossRef Rappel, W. J., & Karma, A. (1996). Noise-induced coherence in neural networks. Physical Review Letters, 77, 3256.PubMedCrossRef
Zurück zum Zitat Rappel, W. J., & Strogatz, S. (1994). Stochastic resonance in an autonomous system with a nonuniform limit cycle. Physical Review E, 50, 3249–3250.CrossRef Rappel, W. J., & Strogatz, S. (1994). Stochastic resonance in an autonomous system with a nonuniform limit cycle. Physical Review E, 50, 3249–3250.CrossRef
Zurück zum Zitat Rinzel, J., & Ermentrout, B. (1998). Analysis of neural excitability and oscillations. In C. Koch, I. Segev (Eds.), Methods of neuronal modeling: From synapses to networks, 2nd Ed. (pp. 252–291). Cambridge: Bradford. Rinzel, J., & Ermentrout, B. (1998). Analysis of neural excitability and oscillations. In C. Koch, I. Segev (Eds.), Methods of neuronal modeling: From synapses to networks, 2nd Ed. (pp. 252–291). Cambridge: Bradford.
Zurück zum Zitat Sernagor, E., Chub, N., Ritter, A., & O’Donovan, M. J. (1995). Pharmacological characterization of the rhythmic synaptic drive onto lumbosacral motoneurons in the chick embryo spinal cord. Journal of Neuroscience, 15, 7452–7464.PubMed Sernagor, E., Chub, N., Ritter, A., & O’Donovan, M. J. (1995). Pharmacological characterization of the rhythmic synaptic drive onto lumbosacral motoneurons in the chick embryo spinal cord. Journal of Neuroscience, 15, 7452–7464.PubMed
Zurück zum Zitat Shelly, M. J., & Tao, L. (2001). Effidient and accurate time-stepping schemes for integrate-and-fire neuronal networks. Journal of Comparative Neuroscience, 11, 11–119. Shelly, M. J., & Tao, L. (2001). Effidient and accurate time-stepping schemes for integrate-and-fire neuronal networks. Journal of Comparative Neuroscience, 11, 11–119.
Zurück zum Zitat 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, 726–729.PubMedCrossRef 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, 726–729.PubMedCrossRef
Zurück zum Zitat Tabak, J., O’Donovan, M. J., Rinzel, J. (2006). Differential control of active and silent phases in relaxation models of neuronal rhythms. Journal of Comparative Neuroscience, 21, 307–328.CrossRef Tabak, J., O’Donovan, M. J., Rinzel, J. (2006). Differential control of active and silent phases in relaxation models of neuronal rhythms. Journal of Comparative Neuroscience, 21, 307–328.CrossRef
Zurück zum Zitat Tabak, J., & Rinzel, J. (2005). Bursting in excitatory neural networks. In S. Coombes & P. C. Bressloff (Eds.), Bursting: The genesis of rhythm in the nervous system (pp. 273–301). Hackensack: World Scientific. Tabak, J., & Rinzel, J. (2005). Bursting in excitatory neural networks. In S. Coombes & P. C. Bressloff (Eds.), Bursting: The genesis of rhythm in the nervous system (pp. 273–301). Hackensack: World Scientific.
Zurück zum Zitat Tabak, J., Rinzel, J., & O’Donovan, J. (2001). The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord. Journal of Neuroscience, 21, 8966–8978.PubMed Tabak, J., Rinzel, J., & O’Donovan, J. (2001). The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord. Journal of Neuroscience, 21, 8966–8978.PubMed
Zurück zum Zitat Tabak, J., Senn, W., O’Donovan, J., & Rinzel, J. (2000). Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. Journal of Neuroscience, 20, 3041–3056.PubMed Tabak, J., Senn, W., O’Donovan, J., & Rinzel, J. (2000). Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. Journal of Neuroscience, 20, 3041–3056.PubMed
Zurück zum Zitat Tryba, A. K., Peña, F., & Ramirez, J. M. (2003). Stabilization of bursting in respiratory pacemaker neurons. Journal of Neuroscience, 23, 3538–3546.PubMed Tryba, A. K., Peña, F., & Ramirez, J. M. (2003). Stabilization of bursting in respiratory pacemaker neurons. Journal of Neuroscience, 23, 3538–3546.PubMed
Zurück zum Zitat Tsodyks, M., Uziel, A., & Markram, H. (2000). Synchrony generation in recurrent networks with frequency-dependent synapses. Journal of Neuroscience, 20, RC50.PubMed Tsodyks, M., Uziel, A., & Markram, H. (2000). Synchrony generation in recurrent networks with frequency-dependent synapses. Journal of Neuroscience, 20, RC50.PubMed
Zurück zum Zitat Van Vreeswijk, C., & Hansel, D. (2001). Patterns of synchrony in neural networks with spike adaptation. Neural Computation, 13, 959–992.PubMedCrossRef Van Vreeswijk, C., & Hansel, D. (2001). Patterns of synchrony in neural networks with spike adaptation. Neural Computation, 13, 959–992.PubMedCrossRef
Zurück zum Zitat Vladimirski, B. B., Tabak, J., O’Donovan, M. J., & Rinzel, J. (in press). Episodic activity in a heterogenious excitatory network, from spiking neurons to mean field. Journal of Comparative Neuroscience. Vladimirski, B. B., Tabak, J., O’Donovan, M. J., & Rinzel, J. (in press). Episodic activity in a heterogenious excitatory network, from spiking neurons to mean field. Journal of Comparative Neuroscience.
Zurück zum Zitat Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1–22.PubMedCrossRef Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1–22.PubMedCrossRef
Metadaten
Titel
Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation
verfasst von
William H. Nesse
Alla Borisyuk
Paul C. Bressloff
Publikationsdatum
01.10.2008
Verlag
Springer US
Erschienen in
Journal of Computational Neuroscience / Ausgabe 2/2008
Print ISSN: 0929-5313
Elektronische ISSN: 1573-6873
DOI
https://doi.org/10.1007/s10827-008-0081-y

Weitere Artikel der Ausgabe 2/2008

Journal of Computational Neuroscience 2/2008 Zur Ausgabe

Premium Partner