Abstract
A both simple and efficient algorithm is presented that yields the voltages and currents in an arbitrary cable structure. The algorithm consists of the following steps: 1. The cable structure is divided into homogeneous cable segments; 2. Each cable segment is considered as a two-port, and replaced by an equivalent circuit consisting of discrete elements; 3. The resulting equivalent scheme of the whole cable structure is solved with an algorithm for ladder networks (or, if the structure is not tree-like, with a network analysis program), which yields the input and output voltages and currents of each cable segment; and if required 4. The voltage and current distribution in each segment is determined from the input and output voltages and currents. The algorithm is applied to blowfly photoreceptor cells that are electrically coupled, and to blowfly Large Monopolar Cells. For LMC's it is shown that the loads at the input and output sides of the axon determine whether unidirectional or bidirectional signal transmission occurs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Braitenberg V (1967), Patterns of projection in the visual system of the fly. I. Retina-lamina projections. Exp Brain Res 16:184–209
Bunow B, Segev I, Fleshman JW (1985) Modelling the electrical behavior of anatomically complex neurons using a network analysis program: excitable membrane. Biol Cybern 53:41–56
Butz EG, Cowan JD (1974) Transient potentials in dendritic systems of arbitrary geometry. Biophys J 14:661–689
Chi C, Carlson SD (1976) Close apposition of photoreceptor cell axons in the housefly. J Insect Physiol 22:1153–1157
Hardie RC, Franceschini N, Ribi W, Kirschfeld K (1981) Distribution and properties of sex-specific photoreceptors in the fly Musca domestica. J Comp Physiol 145:139–152
Hateren JH van (1986) Electrical coupling of neuro-ommatidial photoreceptor cells in the blowfly. J Comp Physiol (in press)
Jack JJB, Noble D, Tsien RW (1975) Electric current flow in excitable cells. Clarendon Press, Oxford
Kinariwala B, Kno FF, Tsao N (1973) Linear circuits and computation. Wiley, New York
Kirschfeld K, Franceschini N (1968) Optische Eigenschaften der Ommatidien im Komplexauge von Musca. Kybernetik 5:47–52
Koch C (1984) Cable theory in neurons with active, linearized membranes. Biol Cybern 50:15–33
Koch C, Poggio T (1985) Asimple algorithm for solving the cable equation in dendritic trees of arbitrary geometry. J Neurosci Methods 12:303–315
Koch C, Poggio T, Torre V (1982) Retinal ganglion cells: a functional interpretation of dendritic morphology. Philos Trans R Soc Lond Ser B 298:227–264
Rall W (1959) Branching dendritic trees and motoneuron membrane resistivity. Exp Neurol 1:491–527
Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Reiss RF (ed) Neural theory and modelling. Stanford University Press, Stanford
Ribi WA (1978) Gap junctions coupling photoreceptor axons in the first optic ganglion of the fly. Cell Tissue Res 195:299–308
Scholes J (1969) The electrical responses of the retinal receptors and the lamina in the visual system of the fly Musca. Kybernetik 6:149–162
Scott A (1970) Active and nonlinear wave propagation in electronics. Wiley, New York
Segev I, Fleshman JW, Miller JP, Bunow B (1985) Modelling the electrical behavior of anatomically complex neurons using a network analysis program: passive membrane. Biol Cybern 53:27–40
Shaw SR (1975) Retinal resistance barriers and electrical lateral inhibition. Nature 255:480–483
Shaw SR (1981) Anatomy and physiology of identified nonspiking cells in the photoreceptor-lamina complex of the compound eye of insects, especially Diptera. In: Roberts A, Bush BMH (eds) Neurons without impulses. Cambridge University Press, Cambridge, pp 61–116
Shaw SR (1984a) Asymmetric distribution of gap junctions amongst identified photoreceptor axons of lucilia cuprina (Diptera). J Cell Sci 66:65–80
Shaw SR (1984b) Early visual processing in insects. J Exp Biol 112:225–251
Shaw SR, Stowe S (1982) Freeze-fracture evidence for gap junctions connecting the axon terminals of dipteran photoreceptors. J Cell Sci 53:115–141
Strausfeld NJ, Nässel DR (1980) Neuroarchitecture of brain regions that subserve the compound eyes of crustancea and insects. In: Autrum H (ed) Handbook of sensory physiology, Vol. VII/6B. Springer, Berlin Heidelberg New York, pp 1–133
Wilson M (1978) Generation of graded potential signals in the second order cells of locust ocellus. J Comp Physiol 124:317–331
Zettler F, Järvilehto M (1973) Active and passive axonal propagation of non-spike signals in the retina of Calliphora. J Comp Physiol 85:89–104
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Hateren, J.H. An efficient algorithm for cable theory, applied to blowfly photoreceptor cells and LMC's. Biol. Cybern. 54, 301–311 (1986). https://doi.org/10.1007/BF00318426
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00318426