Abstract
A mathematical model of the neurone has been developed using the method of subdivision of the neurone into a number of equivalent circuit compartments. Compartmental characteristics have been investigated by calculating the shape indices of the output produced in response to a given somatic input conductance change. A generalised form of compartmental chain has been chosen to allow calculation of the shape indices produced by a variety of geometrical configurations including the straight and tapering chain forms. Equations have been deduced from the computations made on a CDC 6600 computer relating the peak amplitude of the output response to the compartmental diameter for both the straight and tapering chain forms. The effect of variation in the location of the input conductance injection site has also been related to the peak amplitude of the somatic response. The optimum characteristics of the input conductance pulse shape have been computed initially using a rectangular pulse and later the more physiologically relevant double exponential shape. The effect of alteration in the end compartmental terminal impedances over the range from open to short circuit conditions was also calculated. The establishment of optimum single compartmental chain criteria allows the future investigation of multiple chain and pyramidal cell configurations.
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Barrett, J.N., Crill, W.E.: Specific membrane resistivity of dye injected cat motoneurones. Brain Res. 28, 556–561 (1971)
Barrett, J.N., Crill, W.E.: Specific membrane properties of cat motoneurones. J. Physiol. 239, 301–324 (1974a)
Barrett, J.N., Crill, W.E.: Influence of dendritic location and membrane properties on the effectiveness of synapses on cat motoneurones. J. Physiol. 239, 325–345 (1974b)
Fitzhugh, R.: Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol. 43, 867–896 (1960)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–545 (1952)
Jack, J.J.B., Redman, S.J.: The propagation of transient potentials in some linean cable structure. J. Physiol. 215, 283–320 (1971)
McLennan, H.: Synaptic transmission. 2nd Ed., Chap. 3, p. 41. Philadelphia: Saunders and Co. 1970
Rall, W.: Branching dendritic trees and motoneuron membrane resistivity. Exp. Neurol. 1, 491–527 (1959)
Rall, W.: Membrane potential transients and membrane time constant of motoneurons. Exp. Neurol. 2, 503–532 (1960)
Rall, W.: Theory of physiological properties of dendrites. Ann. N.Y. Acad. Sci. 96, 1071–1092 (1962)
Rall, W.: Theoretical significance of dendritic trees for neuronal input-output relations. In: Neural theory and modeling. pp. 73–97. Ed.: Reiss, R.F., Stanford, Stanford University Press 1964
Rall, W.: Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. J. Neurophysiol. 30, 1138–1168 (1967)
Rall, W.: Time constants and electrotonic length of membrane cylinders and neurons. Biophys. J. 9, 1483–1508 (1969)
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Keller, D.J., Lal, S. Membrane voltage changes in a compartmental chain model of a neurone. Biol. Cybernetics 24, 211–217 (1976). https://doi.org/10.1007/BF00335981
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DOI: https://doi.org/10.1007/BF00335981