%0 Journal Article %1 Pesk_1988_863 %A Peskoff, A. %A Bers, D. M. %D 1988 %J Biophys. J. %K Biological Channels; Diffusion; Ion Ions; Mathematics; Membrane Models, Potentials; %N 6 %P 863--875 %T Electrodiffusion of ions approaching the mouth of a conducting membrane channel. %U http://www.biophysj.org/cgi/reprint/53/6/863 %V 53 %X The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (L�uger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50\% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/2 (a + lambda) times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.

@article{Pesk_1988_863, abstract = {The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (L�uger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50\% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/[2 (a + lambda)] times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.}, added-at = {2009-06-03T11:20:58.000+0200}, author = {Peskoff, A. and Bers, D. M.}, biburl = {https://www.bibsonomy.org/bibtex/2ade416557e0454555ba4421d6f523f39/hake}, description = {The whole bibliography file I use.}, file = {Pesk_1988_863.pdf:Pesk_1988_863.pdf:PDF;Pesk_1988_863.pdf:Pesk_1988_863.pdf:PDF}, institution = {Department of Biomathematics and Physiology, University of California, Los Angeles 90024-1766.}, interhash = {47659c3e6b20e704c739127380d6c9ee}, intrahash = {ade416557e0454555ba4421d6f523f39}, journal = {Biophys. J.}, keywords = {Biological Channels; Diffusion; Ion Ions; Mathematics; Membrane Models, Potentials;}, month = Jun, number = 6, pages = {863--875}, pmid = {2456103}, timestamp = {2009-06-03T11:21:25.000+0200}, title = {Electrodiffusion of ions approaching the mouth of a conducting membrane channel.}, url = {http://www.biophysj.org/cgi/reprint/53/6/863}, volume = 53, year = 1988 }