Advertisement

Emergent Bursting in Small Networks of Model Conditional Pacemakers in the pre-Bötzinger Complex

  • Jonathan E. Rubin
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 605)

This paper summarizes some lessons learned from the computational study of bursting oscillations in small networks of model pre-Bötzinger complex (pBC) neurons. Dynamical systems analysis explains the mechanisms through which synaptic coupling enhances the dynamic range of bursting and predicts the existence of multiple forms of busting and tonic spiking solutions. This analysis also demonstrates that intrinsically bursting cells are not required for network bursting and suggests possible roles for cells with different intrinsic behaviors in enhancing the robustness of bursting.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Best, J., Borisyuk, A., Rubin, J., Terman, D. and Wechselberger, M. (2005) The dynamic range of bursting in a model respiratory pacemaker network. SIAM J. Appl. Dyn. Syst. 4, 1107–1139.CrossRefGoogle Scholar
  2. Butera, R.J., Rinzel, J. and Smith, J.C. (1999a) Models of respiratory rhythm generation in the pre-Bötzinger complex: I. Bursting pacemaker neurons. J. Neurophysiol. 81, 382–397.Google Scholar
  3. Butera, R.J., Rinzel, J. and Smith, J.C. (1999b) Models of respiratory rhythm generation in the pre-Bötzinger complex: II. Populations of coupled pacemakers. J. Neurophysiol. 81, 398–415.Google Scholar
  4. Butera, R., Rubin, J., Terman, D. and Smith, J. (2005) Oscillatory bursting mechanisms in respiratory pacemaker neurons and networks. In: S. Coombes and P.C. Bressloff (Eds.), Bursting: The Genesis of Rhythm in the Nervous System. World Scientific, Singapore, pp. 303–346.Google Scholar
  5. Rinzel, J. (1987) A formal classification of bursting mechanisms in excitable systems. In: A.M. Gleason (Ed.), Proceedings of the International Congress of Mathematics. AMS, Providence, pp. 1578–1593.Google Scholar
  6. Rubin, J. and Terman, D. (2002) Synchronized bursts and loss of synchrony among heterogeneous conditional oscillators. SIAM J. Appl. Dyn. Syst. 1, 146–174.CrossRefGoogle Scholar
  7. Rubin, J. (2006) Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters. Phys. Rev. E 74, 021917.CrossRefGoogle Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  • Jonathan E. Rubin
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghUSA

Personalised recommendations