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Length constant is a constant used in neurobiology signified by the Greek letter lambda (λ).
Additional recommended knowledge
In an action potential (or in a passive spread of signal) in a neuron, the constant λ is
The resistance across the membrane is a function of the number of open ion channels and the resistance inside the membrane is generally a function of the diameter of the axon. A large diameter is related to a lower ri.
The length constant is used to describe the rise of potential difference across the membrane
The fall of voltage is described by
Where voltage is typically in millivolts, x is distance in millimeters, and λ is in millimeters.
Vmax is defined as the maximum voltage attained in the action potential, where
where rm is the resistance across the membrane and I is the current flow.
Setting for x= λ for the rise of voltage sets V(x) equal to .63 Vmax. This means that the length constant is the distance at which 63% of Vmax has been reached during the rise of voltage.
Setting for x= λ for the fall of voltage sets V(x) equal to .37 Vmax, meaning that the length constant is the distance at which 37% of Vmax has been reached during the fall of voltage.
The longer a length constant is, the bigger the effect of a potential (either an action potential or a current injected at the site) will have along the cell. A long length constant can result in spatial summation, or the algebraic summation of one potential with other potentials from other areas of the cell.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Length_constant". A list of authors is available in Wikipedia.|