Hille equation

The Hille equation relates the maximum ionic conductance of an ion channel to its length and radius (or diameter), with the commonly used version implicitly takes into account a hemispherical cap.{{cite book | title=Ion channels of excitable membranes' | publisher=Sinauer Associates | author=Hille, Bertil | year=2001 | location=Sunderland, MA | isbn=978-0-87893-321-1 }} As it is ultimately based on a macroscopic continuum model, it does not take into account molecular interactions, and real conductances are often several times less than the predicted maximal flux.

Assumptions and Derivations

Equation

File:HilleEqnParameters.svg

The Hille equation predicts the following maximum conductance $g$ for a pore with length $l$ , radius $a$ , in a solvent with resistivity $\rho$ :

$\frac{1}{g} = (l+\pi\frac{a}{2}) \times{} \frac{\rho}{\pi{}a^2}$

Rearranging the terms, the maximal flux based on length $l$ and diameter $d$ can be shown to be:

$\frac{1}{g} = \frac{l\rho}{(\pi{}(\frac{d}{2})^2)} + \frac{\rho}{d}$

Physical Implications

References

Category:Ion channels

Category:Electrophysiology