A simple analytical method for determining the steady-state potential in models of geometrically complex neurons

Journal of Neuroscience Methods

Volumn 82, Issue 2, 1998, Pages 123-133

  Vermeulen, Arthur ^a,b   Rospars, Jean Pierre ^a  

^a CEMAGREF   (France)

^b GRENOBLE INSTITUTE OF TECHNOLOGY   (France)

Author keywords

Cable equation; Dendritic tree; Olfactory neuron; Single neuron modelling; Thevenin's equivalent

Indexed keywords

ANALYTIC METHOD; ARTICLE; COMPARTMENT MODEL; DENDRITE; GEOMETRY; MATHEMATICAL MODEL; NERVE CELL; NERVE CELL MEMBRANE POTENTIAL; NERVOUS SYSTEM ELECTROPHYSIOLOGY; OLFACTORY NERVOUS SYSTEM; PRIORITY JOURNAL; SENSORY RECEPTOR; STEADY STATE;

ALGORITHMS; DATA INTERPRETATION, STATISTICAL; DENDRITES; ELECTROPHYSIOLOGY; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEURONS;

EID: 0032146597     PISSN: 01650270     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0270(98)00040-5     Document Type: Article

References (27)

1. Abbott L.F. Simple diagrammatic rules for solving dendritic cable problems. Phys A. 185:1992;343-356.
2. Abbott L.F., Farhi E., Gutmann S. The path integral for dendritic trees. Biol Cybern. 66:1991;49-60.
3. Bressloff P.C., Taylor J.G. Compartmental-model response function for dendritic trees. Biol Cybern. 70:1993;199-207.
4. Butz E.G., Cowan J.D. Transient potentials in dendritic systems for arbitrary geometry. Biophys J. 14:1974;661-689.
5. Carnevale N.T., Johnston D. Electrophysiological characterization of remote chemical synapses. J Neurophysiol. 47:1982;606-621.
6. De Schutter E. A consumer guide to neural modeling software. Trends Neurosci. 15:1992;414-421.
7. Getchell T.V., Getchell M.L. Peripheral mechanisms of olfaction: biochemistry and neurophysiology. Finger T.E., Silver W.L. Neurobiology of Taste and Smell. 1991;91-123 Krieger, Malabar, FL.
8. Kaissling K.-E. Insect olfaction. Beidler L.M. Handbook of Sensory Physiology. Chemical Senses, Part. I, Olfaction. IV:1971;351-431 Springer, Berlin.
9. Kaissling K-E. R.H. Wright Lectures on Insect Olfaction. In: Colbow K, editor. Simon Fraser University, Burnady, 1987:1-75.
10. Koch C., Poggio T. A simple algorithm for solving the cable equation in dendritic trees of arbitrary geometry. J Neurosci Methods. 12:1985;303-315.
11. Koch C., Poggio T., Torre V. Retinal ganglion cells: a functional interpretation of dendritic morphology. Philos Trans R Soc Lond B. 2998:1982;227-264.
12. Lumbroso H. Problemes Resolus Sur Les Circuits Electriques. 1985;1-375 Dunod, Paris.
13. Neerhoff FL. Theorie van het elektrische netwerk, Deel A, Technische Hogeschool Delft, Delft, 1985:1-176.
14. Perkel D.H., Mulloney B., Budelli R.I. Quantitative methods for predicting neuronal behavior. Neuroscience. 6:1981;823-837.
15. Pongrácz F., McClintock T.S., Ache B.W., Shepherd G.M. Signal transmission in lobster olfactory receptor cells: functional significance of electrotonic structure analysed by a compartmental model. Neuroscience. 55:1993;325-338.
16. Rall W. Membrane potential transients and membrane time constant of motoneurons. Exp Neurol. 2:1960;503-532.
17. Rall W. Theoretical significance of dendritic trees for neuronal input-output relations. Reiss R.F. Neural Theory and Modeling. 1964;73-97 Stanford University Press, Stanford.
18. Rall W. The Theoretical Foundation of Dendritic Function. Segev I., Rinzel J., Shepherd G.M. Selected Papers of Wilfrid Rall with Commentaries. 1995;1-456 MIT Press, Cambridge, MA.
19. Rospars J.-P., Lansky P., Tuckwell H.C., Vermeulen A. Coding of odor intensity in a steady-state deterministic model of the olfactory receptor neuron. J Comput Neurosci. 3:1996;51-72.
20. Segev I. Single neurone models: oversimple, complex and reduced. Trends Neurosci. 15:1992;414-421.
21. Segev I., Fleshman J.W., Burke R.E. Compartmental models of complex neurons. Koch C., Segev I. Methods in Neuronal Modeling; From Synapses to Networks. 1989;63-96 MIT Press, Cambridge, MA.
22. Segev I., Rinzel J., Shepherd G.M. Overview of Wilfrid Rall's contributions to understanding dendritic function. Segev I., Rinzel J., Shepherd G.M. The Theoretical Foundation of Dendritic Function: Selected Papers of Wilfrid Rall with Commentaries. 1995;3-23 MIT Press, Cambridge, MA.
23. Tuckwell H.C. Introduction to Theoretical Neurobiology. I:1988;1-291 Cambridge University Press, Cambridge.
24. Tuckwell H.C., Rospars J-P., Vermeulen A., Lánský P. Time-dependent solutions for a cable model of an olfactory receptor neuron. J Theor Biol. 181:1996;25-31.
25. Vermeulen A., Rospars J-P., Lánský P., Tuckwell H.C. Coding of stimulus intensity in an olfactory receptor neuron: role of neuron spatial extension and dendritic backpropagation of action potentials. Bull Math Biol. 58:1996;493-512.
26. Vermeulen A, Rospars J-P Dendritic integration in olfactory sensory neurons: A steady state analysis of how the neuron structure and neuron environment influence the coding of odor intensity. J Comput Neurosci. 5:1998;243-266.
27. Walsh J.B., Tuckwell H.C. Determination of the electrical potential over dendritic trees by mapping onto a nerve cylinder. J Theor Neurobiol. 4:1985;27-46.