Abstract
In this work, we examine effects of large permanent charges on ionic flow through ion channels based on a quasi-one-dimensional Poisson–Nernst–Planck model. It turns out that large positive permanent charges inhibit the flux of cation as expected, but strikingly, as the transmembrane electrochemical potential for anion increases in a particular way, the flux of anion decreases. The latter phenomenon was observed experimentally but the cause seemed to be unclear. The mechanisms for these phenomena are examined with the help of the profiles of the ionic concentrations, electric fields and electrochemical potentials. The underlying reasons for the near zero flux of cation and for the decreasing flux of anion with the increasing of its transmembrane electrochemical potential are shown to be significantly different over different regions of the permanent charge. Our model is oversimplified. More structural detail and more correlations between ions can and should be included. But the basic finding seems striking and important and deserving of further investigation.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
References
J.N. Abelson, M.I. Simon, S.V. Ambudkar, M.M. Gottesman, ABC Transporters: Biochemical, Cellular, and Molecular Aspects (Academic Press, 1998)
P.F. Baker, M.P. Blaustein, A.L. Hodgkin, R.A. Steinhardt, J. Physiol. 200, 431 (1969)
M.P. Blaustein, W.J. Lederer, Physiol. Rev. 79, 763 (1999)
P. Chlanda, E. Mekhedov, H. Waters, C.L. Schwartz, E.R. Fischer, R.J. Ryham, F.S. Cohen, P.S. Blank, J. Zimmerberg, Nat. Microbiol. 1, 16050 (2016)
B. Eisenberg, W. Liu, Mol. Based Math. Biol. 5, 125 (2017)
B. Eisenberg, ASBMB Today 13, 36 (2014)
B. Eisenberg, Fluct. Noise Lett. 11, 1240001 (2012)
B. Eisenberg, Crowded charges in ion channels, in Advances in Chemical Physics, edited by S.A. Rice, A.R. Dinner (John Wiley & Sons, Inc., 2012), Vol. 148, pp. 77–223
R.S. Eisenberg, J. Memb. Biol. 150, 1 (1996)
R.S. Eisenberg, Atomic biology, electrostatics and ionic channels, in New Developments and Theoretical Studies of Proteins, edited by R. Elber (World Scientific, Philadelphia, 1996), pp. 269–357
R.S. Eisenberg, J. Memb. Biol. 115, 1 (1990)
B. Eisenberg, W. Liu, SIAM J. Math. Anal. 38, 1932 (2007)
B. Eisenberg, W. Liu, H. Xu, Nonlinearity 28, 103 (2015)
O. Frohlich, R.B. Gunn, Biochem. Biophys. Acta 864, 169 (1986)
D. Gillespie, A singular perturbation analysis of the Poisson–Nernst–Planck system: Applications to Ionic Channels, Ph.D. Dissertation, Rush University at Chicago, 1999
J. Griffiths, C. Sansom, The Transporter Facts Book (Academic Press, 1997)
F. Helfferich, Ion Exchange (1995 Reprint) (McGraw Hill reprinted by Dover, 1962)
B. Hille, Ion Channels of Excitable Membranes, 3rd edn. (Sinauer Associates Inc., 2001)
B. Hille, Transport Across Cell Membranes: Carrier Mechanisms, in Textbook of Physiology, edited by H.D. Patton et al. (Saunders, 1989), Vol. 1, Chap. 2, pp. 24–47
A.L. Hodgkin, Biol. Rev. 26, 339 (1951)
S. Ji, B. Eisenberg, W. Liu, J. Dyn. Differ. Equ. (2017), https://doi.org/10.1007/s10884-017-9607-1
S. Ji, W. Liu, J. Dyn. Differ. Equ. 24, 955 (2012)
S. Ji, W. Liu, M. Zhang, SIAM J. Appl. Math. 75, 114 (2015)
R.D. Keynes, R.C. Swan, J. Physiol. 147, 591 (1959)
G. Lin, W. Liu, Y. Yi, M. Zhang, SIAM J. Appl. Dyn. Syst. 12, 1613 (2013)
W. Liu, SIAM J. Appl. Math. 65, 754 (2005)
W. Liu, J. Differ. Equ. 246, 428 (2009)
W. Liu, B. Wang, J. Dyn. Differ. Equ. 22, 413 (2010)
W. Liu, X. Tu, M. Zhang, J. Dyn. Differ. Equ. 24, 985 (2012)
W. Liu, H. Xu, J. Differ. Equ. 258, 1192 (2015)
M. Lu, J. Symersky, M. Radchenko, A. Koide, Y. Guo, R. Nie, S. Koide, Proc. Natl. Acad. Sci. U. S. A. 110, 2099 (2013)
H. Miedema, M. Vrouenraets, J. Wierenga, W. Meijberg, G. Robillard, B. Eisenberg, Nano Lett. 7, 2886 (2007)
W. Nonner, R.S. Eisenberg, Biophys. J. 75, 1287 (1998)
R.F. Pierret, Semiconductor Device Fundamentals (Addison Wesley, 1996)
I. Rubinstein, Electro-Diffusion of Ions, in SIAM Studies in Applied Mathematics (SIAM, Philadelphia, PA, 1990), Vol. 11
B. Sakmann, E. Neher, Single Channel Recording, 2nd edn. (Plenum, 1995)
W.D. Stein, T. Litman, Channels, carriers, and pumps: an introduction to membrane transport (Elsevier, 2014)
R.B. Stockbridge, L. Kolmakova-Partensky, T. Shane, A. Koide, A. Koide, C. Miller, S. Newstead, Nature 525, 548 (2015)
S.M. Sze, Physics of Semiconductor Devices (John Wiley & Sons, 1981)
F.L. Theodoulou, I.D. Kerr, Biochem. Soc. Trans. 43, 1033 (2015)
D. Tosteson, Membrane Transport: People and Ideas (American Physiological Society, 1989)
H.H. Ussing, Acta Physiolog. Scand. 19, 43 (1949)
H.H. Ussing, Nature 160, 262 (1947)
D. Vasileska, S.M. Goodnick, G. Klimeck, in Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation (CRC Press, 2010), Vol. 764
W. Wang, R. MacKinnon, Cell 169, 422 (2017)
L. Zhang, W. Liu, Poisson–Nernst–Planck systems for ion channels with large permanent charges. Preprint.
J. Zheng, M.C. Trudeau, Handbook of ion channels (CRC Press, 2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, L., Eisenberg, B. & Liu, W. An effect of large permanent charge: decreasing flux with increasing transmembrane potential. Eur. Phys. J. Spec. Top. 227, 2575–2601 (2019). https://doi.org/10.1140/epjst/e2019-700134-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2019-700134-7