Hille equation

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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.[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 ρ: 1g=(l+πa2)×ρπa2 Rearranging the terms, the maximal flux based on length l and diameter d can be shown to be: 1g=lρ(π(d2)2)+ρd

Physical Implications

References

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