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[]

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Equation[]

Parameters in the Hille 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[]