Advertisement

Dynamic-Clamp pp 261-273 | Cite as

Dynamic-Clamp-Constructed Hybrid Circuits for the Study of Synchronization Phenomena in Networks of Bursting Neurons

  • Carmen C Canavier
  • Fred H Sieling
  • Astrid A Prinz
Chapter
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 1)

Abstract

Hybrid circuits comprised of one biological bursting neuron and one model bursting neuron were constructed using the dynamic clamp to create artificial synaptic conductances in both neurons. The strength and duration of reciprocal inhibitory and excitatory synaptic inputs were varied in a number of such circuits. The phase resetting curves (PRCs) for each component neuron were constructed for each isolated neuron using a pulse in postsynaptic conductance elicited by a single burst in the other neuron. The PRCs from the two component neurons were then used to predict whether a one to one phase-locked mode would be observed in the hybrid network, and if so, to predict the phase angle and network period. The predictions were qualitatively correct for 161 of 164 inhibitory networks and for 64 of 86 excitatory networks. The failures in the case of inhibition resulted from very weak coupling and in the case of excitation from two special cases, one in which the coupling becomes effectively continuous and another in which complex behavior results from a discontinuous PRC. The firing intervals and network period predictions were generally accurate within 10% of the values actually observed in the hybrid networks, a level similar to the level of variability observed in the measurement of the PRC and of the intrinsic period in the biological neuron.

Keywords

Model Neuron Stimulus Interval Synaptic Conductance Biological Neuron Recovery Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

Some of the work presented here was supported by NIH NS54281 grant which was awarded under the CRCNS program. Sorinel Oprisan performed some of the analyses presented herein. We also acknowledge Eve Marder for her support.

References

  1. Acker CD, Kopell N, White JA (2003) Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J Comput Neurosci 15:71–90PubMedCrossRefGoogle Scholar
  2. Arshavsky Y, Grillner S, Orlovsky G et al. (1991) Central pattern generators and the spatiotemporal pattern of movements. In: Fagard J and Wolff P (eds) The Development of Timing Control, Elsevier, Amsterdam, pp 93–115Google Scholar
  3. Canavier CC, Butera RJ, Dror RO et al. (1997) Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation. Biol Cybernetics 77:367–380CrossRefGoogle Scholar
  4. Canavier CC, Baxter DA, Clark JW et al. (1999) Control of multistability in ring circuits of oscillators. Biol Cybernetics 80:87–102CrossRefGoogle Scholar
  5. Canavier CC (2005) The application of phase resetting curves to the analysis of pattern generating circuits containing bursting neurons. In: Coombes S and Bressloff P (eds) Bursting: The Genesis of Rhythm in the Nervous System. Series in Mathematical Neuroscience, World Scientific, Singapore, pp 175–200CrossRefGoogle Scholar
  6. Ermentrout B (2002) Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM, PhiladelphiaCrossRefGoogle Scholar
  7. Liu Z, Golowasch J, Marder E et al. (1998) A model neuron with activity-dependent conductances regulated by multiple calcium sensors. J Neurosci 18:2309–2320PubMedGoogle Scholar
  8. Luo C, Canavier CC, Baxter DA et al. (2004) Multimodal behavior in a four neuron ring circuit: mode switching. IEEE Trans Biomed Eng 51:205–218PubMedCrossRefGoogle Scholar
  9. Oprisan SA, Canavier CC (2001) Stability analysis of rings of pulse-coupled oscillators: The effect of phase resetting in the second cycle after the pulse is important at synchrony and for long pulses. Differ Equations Dyn Syst 9:242–259.Google Scholar
  10. Oprisan SA, Canavier CC (2005) Stability criterion for a two-neuron reciprocally coupled network based on the phase and burst resetting curves. Neurocomputing 65–66:733–739CrossRefGoogle Scholar
  11. Oprisan SA, Prinz AA, Canavier, CC (2004) Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. Biophysical J 87:2283–2298CrossRefGoogle Scholar
  12. Oprisan SA, Thirumalai V, and Canavier CC (2003) Dynamics from a time series: Can we extract the phase resetting curve from a time series? Biophysical J 84:2919–2928CrossRefGoogle Scholar
  13. Preyer AJ, Butera RJ (2007) The effect of residual electrode resistance and sampling delay on transient instability in the dynamic clamp system. Conf Proc IEEE Eng Med Biol Soc 2007:430–433PubMedGoogle Scholar
  14. Ramirez J, Pearson K (1991) Octopominergic modulation of interneurons in the flight system of the locust. J Neurophys 66:1522–1537Google Scholar
  15. Prinz AA, Thirumalai V, Marder E (2003) The functional consequences of changes in the strength and duration of synaptic inputs to oscillatory neurons. J. Neurosci 23:943–954PubMedGoogle Scholar
  16. Selverston A, Panchin YV, Arshavsky et al. (1997) Shared features of invertebrate pattern generators. In Stein SG, Grillner S, Selverston AI and Stuart DG (eds) Neurons, Networks, and Motor Behavior. MIT Press, Cambridge, pp 105–117.Google Scholar
  17. Sharp AA, O’Neil MB, Abbott LF et al. (1993) Dynamic clamp – computer-generated conductances in real neurons. J Neurophysiol 69:992–995PubMedGoogle Scholar
  18. Sieling FH, Canavier CC, Prinz AA (2008). Predicting phase-locking in excitatory hybrid circuits, BMC Neurosci 9: P133.CrossRefGoogle Scholar
  19. Smith J, Ellenberger H, Ballanyi K et al. (1991) PreBotzinger complex: A brainstem region that may generate respiratory rhythm in mammals. Science 254:726–729PubMedCrossRefGoogle Scholar
  20. Tasaki K, Cooke M (1990) Characterization of Ca current underlying burst formation in lobster cardiac ganglion motorneurons. J Neurophysiol 63:370–364Google Scholar
  21. Wallen P and Grillner S (1987) N-methyl D-aspartate receptor-induced, inherent oscillatory activity in neurons active during fictive locomotion in the lamprey. J Neurosci 7:2745–2755PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Carmen C Canavier
    • 1
  • Fred H Sieling
  • Astrid A Prinz
  1. 1.Neuroscience Center of Excellence, Louisiana State University Health Sciences CenterNew OrleansUSA

Personalised recommendations