Space (Length) Constant, Lambda, in Neuronal Signaling

Definition

The space (length) constant λ with λ = (R_md/(4R_a))^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 = (R_md/(4R_a))^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)

$$ {\uplambda}^2{\mathrm{d}}^2\mathrm{V}/{\mathrm{d}\mathrm{x}}^2-\mathrm{V}=0 $$

with boundary conditions of voltage clamp to V₀ at the origin and voltage bounded at x = ∞ to get

$$ \mathrm{V}\left(\mathrm{x}\right)={\mathrm{V}}_0 \exp \left(-\mathrm{x}/\uplambda \right). $$

The above equation is useful to describe...