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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. 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

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Equation

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

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

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

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

Physical Implications

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References

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

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