Encyclopedia of Computational Neuroscience

2015 Edition
| Editors: Dieter Jaeger, Ranu Jung

Electrotonic Length, Formulas and Estimates

Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6675-8_480

Definition

The electrotonic length of a cylindrical neurite is its physical length divided by its space constant. The electrotonic length of a dendritic tree is estimated with formulas that assume the dendritic tree can be approximated as an equivalent cylinder.

Detailed Description

Rall showed that the complex branched morphology of a dendritic tree can be reduced to an equivalent cylinder given a certain set of assumptions (see entry “ Equivalent Cylinder Model (Rall)”). An important property of the equivalent cylinder is its electrotonic length, L, which equals the physical length of the cylinder, ℓ, divided by λ, the space constant. An estimate of L will tell us how far distal synapses are electrotonically from the soma, and this will tell us whether these synapses can be effective in driving the cell to threshold.

For a cell represented as an equivalent cylinder, Rall ( 1969) used separation of variables to derive the transient solution for voltage in the cylinder as
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References

  1. Holmes WR, Rall W (1992) Electrotonic length estimates in neurons with tapering or somatic shunt. J Neurophysiol 68:1421–1437PubMedGoogle Scholar
  2. Holmes WR, Segev I, Rall W (1992) Interpretation of time constant and electrotonic length estimates in multicylinder or branched neuronal structures. J Neurophysiol 68:1401–1420PubMedGoogle Scholar
  3. Major G, Evans JD, Jack JJB (1993a) Solutions for transients in arbitrary branching cables: I. Voltage recording with a somatic shunt. Biophys J 65:423–449PubMedCentralPubMedGoogle Scholar
  4. Major G, Evans JD, Jack JJB (1993b) Solutions for transients in arbitrarily branching cables: II. Voltage clamp theory. Biophys J 65:450–468PubMedCentralPubMedGoogle Scholar
  5. Rall W (1969) Time constants and electrotonic length of membrane cylinders and neurons. Biophys J 9:1483–1508PubMedCentralPubMedGoogle Scholar
  6. Rall W (1977) Core conductor theory and cable properties of neurons, chap 3. In: Handbook of physiology. The nervous system. Cellular biology of neurons, Sect 1, vol I, parts 1 & 2. American Physiology Society, Bethesda, pp 39–97Google Scholar

Further Reading

  1. Rall W, Burke RE, Holmes WR, Jack JJB, Redman SJ, Segev I (1992) Matching dendritic neuron models to experimental data. Physiol Rev 72:S159–S186PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Biological SciencesOhio UniversityAthensUSA