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.[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

Parameters in the Hille equation.

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

gollark: I think the school also has some sort of PCB production equipment extant.

gollark: Actually, the time per unit time increases asymptotically as you approach 1970.

gollark: Yes. Barely.

gollark: Imagine CRT monitors.

gollark: But they do talk about this cohort being better than the previous one somehow.

References

Hille, Bertil (2001). Ion channels of excitable membranes'. Sunderland, MA: Sinauer Associates. ISBN 978-0-87893-321-1.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[Hille_book_2001-1] Hille, Bertil (2001). Ion channels of excitable membranes'. Sunderland, MA: Sinauer Associates. ISBN 978-0-87893-321-1.