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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Acker CD, Kopell N, White JA (2003) Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J Comput Neurosci 15:71–90
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 93–115
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 77:367–380
Canavier CC, Baxter DA, Clark JW et al. (1999) Control of multistability in ring circuits of oscillators. Biol Cybernetics 80:87–102
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 175–200
Ermentrout B (2002) Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM, Philadelphia
Liu Z, Golowasch J, Marder E et al. (1998) A model neuron with activity-dependent conductances regulated by multiple calcium sensors. J Neurosci 18:2309–2320
Luo C, Canavier CC, Baxter DA et al. (2004) Multimodal behavior in a four neuron ring circuit: mode switching. IEEE Trans Biomed Eng 51:205–218
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.
Oprisan SA, Canavier CC (2005) Stability criterion for a two-neuron reciprocally coupled network based on the phase and burst resetting curves. Neurocomputing 65–66:733–739
Oprisan SA, Prinz AA, Canavier, CC (2004) Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. Biophysical J 87:2283–2298
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 84:2919–2928
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 2007:430–433
Ramirez J, Pearson K (1991) Octopominergic modulation of interneurons in the flight system of the locust. J Neurophys 66:1522–1537
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 23:943–954
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.
Sharp AA, O’Neil MB, Abbott LF et al. (1993) Dynamic clamp – computer-generated conductances in real neurons. J Neurophysiol 69:992–995
Sieling FH, Canavier CC, Prinz AA (2008). Predicting phase-locking in excitatory hybrid circuits, BMC Neurosci 9: P133.
Smith J, Ellenberger H, Ballanyi K et al. (1991) PreBotzinger complex: A brainstem region that may generate respiratory rhythm in mammals. Science 254:726–729
Tasaki K, Cooke M (1990) Characterization of Ca current underlying burst formation in lobster cardiac ganglion motorneurons. J Neurophysiol 63:370–364
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 7:2745–2755
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Canavier, C.C., Sieling, F.H., Prinz, A.A. (2009). Dynamic-Clamp-Constructed Hybrid Circuits for the Study of Synchronization Phenomena in Networks of Bursting Neurons. In: Bal, T., Destexhe, A. (eds) Dynamic-Clamp. Springer Series in Computational Neuroscience, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89279-5_12
Download citation
DOI: https://doi.org/10.1007/978-0-387-89279-5_12
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-89278-8
Online ISBN: 978-0-387-89279-5
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)