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Electrophysiology of a leaky cable model for coupled neurons

Published online by Cambridge University Press:  17 February 2009

Roman R. Poznanski
Affiliation:
Department of Information Sciences, Toho University, 2–2–1 Miyama, Funabashi-shi, Tokyo 274, Japan.
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Abstract

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An analytical expression for the voltage response to current stimulation at relatively short and long times is used to obtain estimates of the passive electrical constants of a neuron that is electrotonically coupled at the soma and dendritic terminals to other neurons in a neural network.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Cole, K. S., Membranes, ions and impulses, (Univ. of California Press, Berkeley, 1968).CrossRefGoogle Scholar
[2]Coombs, J. S., Curtis, D. R. and Eccles, J. C., “The electrical constants of the motoneurone membrane”, J Physiol. (Lond.) 145 (1959) 505528.CrossRefGoogle ScholarPubMed
[3]Deakin, M. A. B., Bywater, R. A. R. and Redman, S. J., “Determination of time-constants in cables of finite length”, Bull. Math. Biol. 54 (1992) 673686.CrossRefGoogle Scholar
[4]Jack, J. J. B., Noble, D. and Tsien, R. W., Electric current flow in excitable cells (Clarendon Press, Oxford, 1975).Google Scholar
[5]Jack, J. J. B. and Redman, S. J., “The propagation of transient potentials in some linear cable structures”, J. Physiol. (Lond.) 215 (1971) 283320.CrossRefGoogle ScholarPubMed
[6]Jackson, M. B., “Cable analysis with the whole-cell patch clamp: theory and experiment”, Biophys. J. 61 (1992) 756766.CrossRefGoogle ScholarPubMed
[7]Major, G., Evans, J. D. and Jack, J. J. B., “Solutions for transients in arbitrarily branching cables”, Biophys. J. 65 (1993) 423491.CrossRefGoogle ScholarPubMed
[8]McMachlan, N. W., Complex variable theory and transform calculus (2nd ed.) (Cambridge University Press, Cambridge, 1963).Google Scholar
[9]Poznanski, R. R., “Transient response in a somatic shunt cable model for synaptic input activated at the terminal”, J. Theoret. Biol. 127 (1987) 3150.CrossRefGoogle Scholar
[10]Poznanski, R. R., Modeling in the neurosciences: from ionic channels to neural networks (Harwood Academic Publishers, New York, 1998).Google Scholar
[11]Poznanski, R. R., Gibson, W. G. and Bennett, M. R., “Electrotonic coupling between two CA3 hippocampal pyramidal neurons: a distributed cable model with somatic gap-junction”, Bull. Math. Biol. 57 (1995) 865881.CrossRefGoogle ScholarPubMed
[12]Rall, W., “Time constants and electrotonic length of membrane cylinders and neurons”, Biophys. J. 9 (1969) 14831508.CrossRefGoogle ScholarPubMed
[13]Rall, W., “Core conductor theory and cable properties of neurons”, in Handbook of physiology, the nervous system, (ed. Kandal, I.), (MD: American Physiological Society, Bethesda, 1977) 3997.Google Scholar
[14]Redman, S. J., McLachlan, E. M., and Hirst, G. D. S., “Nonuniform passive membrane properties of rat lumbar sympathetic ganglion cells”, J. Neurophysiol. 57 (1987) 633644.CrossRefGoogle ScholarPubMed
[15]Rorig, B., Klausa, G. and Sutor, B., “Intracellular acidification reduced gap junction coupling between immature rat neocortical pyramidal neurones”, J. Physiol. (Lond.) 490 (1996) 3149.CrossRefGoogle ScholarPubMed
[16]Schanne, O. F., “Measurement of cytoplasmic resistivity by means of the glass microelectrode”, in Glass Microelectrodes (eds. Lavallee, M., Schanne, O. F. and Herbert, N. C.) (John Wiley and Sons, New York, 1969) 299321.Google Scholar
[17]Spray, D. C. and Dermietzel, R., Gap junctions in the nervous system (R. G. Landes Publisher, Austin, 1996).CrossRefGoogle Scholar
[18]Tuckwell, H. C., Introduction to theoretical neurobiology. Vol. I, linear cable theory and dendritic structure (Cambridge University Press, New York, 1988).Google Scholar
[19]Winslow, R. L. and Miller, R. F., “A theoretical and experimental study of the effects of non-uniform membrane resistance on the shape of single-cell charging curves”, Neurosci. 29 (1989) 761771.CrossRefGoogle ScholarPubMed