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The '''Hille equation''' relates the maximum ionic [[Electrical conductance|conductance]] of an [[ion channel]] to its length and [[radius]] (or [[diameter]]), with the commonly used version implicitly takes into account a hemispherical cap.<ref name="Hille book 2001">{{cite book | title=Ion channels of excitable membranes' | publisher=Sinauer Associates | author=Hille, Bertil | year=2001 | location=Sunderland, MA | isbn=0-88214-320-2 {{Please check ISBN|reason=Check digit (2) does not correspond to calculated figure.}}}}</ref> 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==
 
[[File:HilleEqnParameters.svg|thumb|right|Parameters in the Hille equation.]]
 
The Hille equation predicts the following maximum conductance <math>g</math> for a pore with length <math>l</math>, radius <math>a</math>, in a solvent with resistivity <math>\rho</math>:
 
<math>\frac{1}{g} = (l+\pi\frac{a}{2}) \times{} \frac{\rho}{\pi{}a^2}</math>
 
Rearranging the terms, the maximal flux based on length <math>l</math> and diameter <math>d</math> can be shown to be:
 
<math>\frac{1}{g} = \frac{l\rho}{(\pi{}(\frac{d}{2})^2)} + \frac{\rho}{d}</math>
 
==Physical Implications==
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==References==
{{reflist}}
 
{{DEFAULTSORT:Hille Equation}}
[[Category:Ion channels]]
[[Category:Electrophysiology]]

Revision as of 21:48, 21 February 2013

Template:Orphan

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 for a pore with length , radius , in a solvent with resistivity :

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

Physical Implications

Template:Empty section

References

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