Definition
The space (length) constant λ with λ = (Rmd/(4Ra))1/2 is a measure of steady-state voltage decay with distance in a cell. Quantitatively λ is the distance over which the steady-state voltage decays to 1/e or 37 % of its value at the origin in a semi-infinite cable.
Detailed Description
As given in the definition above, the space constant λ with λ = (Rmd/(4Ra))1/2 is a measure of steady-state voltage decay in a cell. Quantitatively λ is the distance (usually expressed in cm or μm) over which the steady-state voltage decays to 1/e or 37 % of its value at the origin in a semi-infinite cable. This can be seen by solving the steady-state cable equation (Rall 1977)
with boundary conditions of voltage clamp to V0 at the origin and voltage bounded at x = ∞ to get
The above equation is useful to describe...
Reference
Rall W (1977) Core conductor theory and cable properties of neurons. In: Handbook of physiology. The nervous system. Cellular biology of neurons, sect 1, vol I, pt 1, chap 3. American Physiological Society, Bethesda, pp 39–97
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Holmes, W.R. (2014). Space (Length) Constant, Lambda, in Neuronal Signaling. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_36-1
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_36-1
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