Skip to main content
Log in

Relationship between burst properties and sensitivity to input: A theoretical analysis

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

This paper examines the sensitivity of endogenous bursters to a brief input pulse. The interneurons of the lobster cardiac ganglion were selected as a case study.

Using a mathematical model specifically developed for the neurons in the cardiac ganglion of the lobster (Av-Ron et al., 1993), we show a tight link between burst characteristics and certain other parameters. We show that cells with different burst properties differ in their sensitivity to an input of a brief pulse.

Irrespective of these differences, all cells display a bimodal response to a brief pulse applied during the quiescent period. During the first three-quarters of the quiescent period, they respond by producing a single spike at most. During the remaining one-quarter, the brief pulse can initiate the cells' intrinsic burst. Our predictions fit experimental results obtained by Tazaki and Cooke (1979).

The results obtained herein are discussed with respect to fault tolerance considerations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Akaike N, Lee KS, Brown AM (1978) The calcium current of the Helix neuron. J. Gen. Physiol. 71:509–531.

    Google Scholar 

  • Av-Ron E (1992) Ph.D. thesis Weizmann Institute. Rehovot, Israel.

    Google Scholar 

  • Av-Ron E, Parnas H, Segel LA (1991) A minimal biophysical model for an excitable and oscillatory neuron. Biol. Cybern. 65:487–500.

    Google Scholar 

  • Av-Ron E, Parnas H, Segel LA (1993) A basic biophysical model for bursting neurons. Biol. Cybern. 69:87–95.

    Google Scholar 

  • Bertram R (1993a) A computational study of the effects of serotonin on a molluscan burster neuron. Biol. Cybern. 69:257–267.

    Google Scholar 

  • Bertram R (1993b) Reduced-system analysis of the effects of serotonin on a molluscan burster neuron. Biol. Cybern. 70:359–368.

    Google Scholar 

  • Friesen WO (1975a) Physiological anatomy and burst pattern in the cardiac ganglion of the spiny lobster Panulirus interuptus. J. Comp. Physiol. 101:173–189.

    Google Scholar 

  • Friesen WO (1975b) Synaptic interaction in the cardiac ganglion of the spiny lobster Panulirus interuptus. J. Comp. Physiol. 10(1):191–205.

    Google Scholar 

  • Hagiwara S, Takahashi K (1967) Surface density of calcium ions and calcium spikes in the Barnacle muscle fiber membrane. J. Gen. Physiol. 50:583–601.

    Google Scholar 

  • Hartline DK (1967) Impulse identification and axon mapping of the nine neurons in the cardiac ganglion of the lobster, Homarus americanus. J. Exp. Biol. 47:327–340.

    Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in the nerve. J. Physiol. (London) 117:500–544.

    Google Scholar 

  • Llinas R, Steinberg IZ, Walton K (1981) Relationship between presynaptic calcium current and postsynaptic potentiation in squid synapse. Biophys. J. 33:322–351.

    Google Scholar 

  • Lustig C, Parnas H, Segel LA (1989) Neurotransmitter release: Development of a theory for total release based on kinetics. J. Theor. Biol. 136:151–170.

    Google Scholar 

  • Mayeri E (1973) A relaxation oscillator description of the burst-generation mechanism in the cardiac ganglion of the lobster, Homarus americanus. J. Gen. Physiol. 62:473–488.

    Google Scholar 

  • Parnas H, Rudolph L (1991) Representation of synapses in neuronal networks. Technical Report, The Leibniz Center for Research in Computer Science, Hebrew University, Jerusalem, Israel.

    Google Scholar 

  • Parnas H, Segel LA (1989) Facilitation as a tool to study the entry of calcium and the mechanism of neurotransmitter release. Prog. Neur. (Kerkut GA, Phillis JW) 32:1–9.

    Google Scholar 

  • Rinzel J (1984) Excitation dynamics: Insights from simplified membrane models. Proc. of 68th Annual Meeting of Fed. Am. Soc. Exp. Bio. St. Louis, MO.

  • Rinzel J (1985) Bursting oscillations in an excitable membrane model. In: RJ Jarvis, BD Sleeman, eds. Ordinary and partial differential equations. Springer-Verlag, New York. pp. 304–316.

    Google Scholar 

  • Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: E Teramoto, M Yamaguti, eds. Mathematical topics in population biology, morphogenesis and neurosciences. Lecture notes in biomathematics, Vol. 71, Springer, Heidelberg, New York, pp 267–281.

    Google Scholar 

  • Rinzel J, Lee YS (1987) Dissection of a model for neuronal parabolic bursting. J. Math. Bio. 25:653–675.

    Google Scholar 

  • Sivan E, Segel LA, Parnas H (1995) Modulated excitability: A new way to obtain bursting neurons. Biol. Cybern. 72:455–461.

    Google Scholar 

  • Tazaki K, Cooke IM (1979) Spontaneous electrical activity and interaction of large and small cells in cardiac ganglion of the crab Portunus sanguinolentus. J. Neurophysiol. 42:975–999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sivan, E., Parnas, H. & Dolev, D. Relationship between burst properties and sensitivity to input: A theoretical analysis. J Comput Neurosci 3, 35–50 (1996). https://doi.org/10.1007/BF00158336

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00158336

Keywords

Navigation