Time Constant, τ, in Neuronal Signaling
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_37-1
Definition
The membrane time constant τ with τ = RmCm is a measure of the rate of voltage decay (or charging) in a cell (Rall 1977). Quantitatively τ is the time it takes for the voltage to decay to 1/e or 37 % of its initial value in an isopotential or uniformly polarized cell.
Detailed Description
As given in the definition above, the membrane time constant τ with τ = R
mC
m is a measure of the rate of voltage decay (or charging) in a cell. Quantitatively τ is the time it takes for the voltage to decay to 1/e or 37 % of its initial value in an isopotential or uniformly polarized cell. This can be seen from the solution of the differential equation for a uniformly polarized cell,
$$ {\mathrm{C}}_{\mathrm{m}}\mathrm{dV}/\mathrm{dt}+\mathrm{V}/{\mathrm{R}}_{\mathrm{m}}=0 $$
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References
- 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 39–97Google Scholar
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© Springer Science+Business Media New York 2014