Cespe UnB

Editorial Assistants:
W. Abrahão
G. Oliveira
L. Salgueiro

Editorial Technical Support:
D. H. Diaz
M. A. Gomez
J. Barbosa

Editorial management and production:
SOLGRAF Editora
solgraf@gmail.com






95/105= 0.91


1,1

Numerical solutions of the full set of the time-dependent Nernst-Planck and Poisson equations modeling electrodiffusion in a simple ion channel.

doi: 10.6062/jcis.2012.03.02.0052(Free PDF)

Authors

Valent I., Neogrády P., Schreiber I., and Marek M.

Abstract

The concept of electrodiffusion based on the Nernst-Planck equations for ionic fluxes coupled with the Poisson equation expressing relation between gradient of the electric field and the charge density is widely used in many areas of natural sciences and engineering. In contrast to the steady-state solutions of the Nernst-Planck-Poisson (abbreviated as NPP or PNP) equations, little is known about the time-dependent behavior of electrodiffusion systems. We present numerical solutions of an NPP system modeling dynamics in the interior of a membrane channel containing an electrolyte after a potential jump at one side of the membrane (voltage-clamp). The NPP equations were solved using the VLUGR2 solver based on an adaptive-grid finite-difference method with an implicit timestepping. The used approach allows for solving the full set of the NPP equations without approximations such as the electroneutrality or constant-field assumptions. Calculations reveal interesting nonlinear time evolution of the ionic concentrations and potential.

Keywords

time-dependent Nernst-Planck and Poisson equations, electrodiffusion, PNP theory, nonlinear dynamics, membrane, ion channel, voltage-clamp.

References

[1] PLANCK M. 1889. Ann. Physik. Chem. N.F., 39: 161.

[2] GOLDMAN DE. 1943. Journal of General Physiology, 27: 37-60.

[3] ́MAFE S, PELLICER J & AGUILELLA VM. 1986. Journal of Physical Chemistry, 90: 6045-6050.

[4] BARCILON V, CHEN D-P & EISENBERG RS. 1992. SIAM Journal on Applied Mathematics, 52: 1405-1425.

[5] KURNIKOVA MG, COALSON RD, GRAF P & NITZAN A. 1999. Biophysical Journal, 76: 642-656.

[6] RAMIREZ P, MAFE S, AGUILELLA VM & ALCARAZ A. 2003. Physical Review E, 68: 011910.

[7] LIU Q, WANG Y, GUO W, JI H, XUE J & OUYANG Q. 2007. Physical Review E, 75: 051201.

[8] HELFFERICH F & PLESSET MS. 1958. Journal of Chemical Physics 418-424.

[9] COHEN H & COOLEY JW. 1965. Biophysical Journal, 5: 145-162.

[10] HAFEMANN DR. 1965. Journal of Physical Chemistry, 69: 4226-4231.

[11] MacGILLIVRAY AD. 1970. Journal of Chemical Physics, 52:3126-3132.

[12] OFFNER F. 1974. Journal of Theoretical Biology, 45: 81-91.

[13] BRUMLEVE TR & BUCK RP. 1978. Journal of Electroanalytical Chemistry, 90: 1-13.

[14] MURPHY WD, MANZANARES JA, MAFE S & REISS H. 1992. Journal of Physical Chemistry, 96: 9983-9991.

[15] MANZANARES JA, MURPHY WD, MAFE S & REISS H. 1993. Journal of Physical Chemistry, 97: 8524-8530.

[16] RUDOLPH M. 1994. Journal of Electroanalytical Chemistry, 375:89-99.

[17] SOKALSKI T, LINGENFELTER P & LEWENSTAM A. 2003. Journal of Physical Chemistry, 107: 2443-2452.

[18] BIENIASZ LK. 2004. Journal of Electroanalytical Chemistry, 565:251-271.

[19] LIM J, WHITCOMB J, BOYD J & VARGHESE J. 2007. Journal of Colloid and Interface Science, 305: 159-174.

[20] DAS S, DUBSKY P, BERG A & EIJKEL JCT. 2012. Physical Review Letters, 108: 138101.

[21] WANG H & PILON L. 2012. Electrochimica Acta, 64: 130-139.

[22] GRYSAKOWSKI B, JASIELEC JJ, WIERZBA B, SOKALSKI T, LEWENSTAM A & DANIELEWSKI M. 2011. Journal of Electroanalytical Chemistry, 662: 143-149.

[23] SAMSON E & MARCHAND J. 1999. Journal of Colloid and Interface Science, 215: 1-8.

[24] OLESEN LH, BAZANT MZ & BRUUS H. 2010. Physical Review E, 82: 011501.

[25] PAZ-GARCIA JM, JOHANNESSON B, OTTOSEN LM, RIBEIRO AB IA & RODRIGUES-MAROTO JM. 2011. Separation and Purification Technology, 79: 183-192.

[26] HORNO J, CASTILLA J & GONZALES-FERNANDES CF. 1992. Journal of Physical Chemistry, 96: 854-858.

[27] SAMSON E, MARCHAND J, ROBERT J-L & BOURNAZEL J-P. 1999. International Journal for Numerical Methods in Engineering, 46: 2043-2060.

[28] BAZANT MZ, THORNTON K & AJDARI A. 2004. Physical Review E, 70: 021506.

[29] SOESTBERGEN M, BIESHEUVEL PM & BAZANT MZ. 2010. Physical Review E, 81: 021503.

[30] BEUNIS F, STRUBBE F, MARESCAUX M, BEECKMAN J, NEYTS K & VERSCHUEREN ARM. 2008. Physical Review E, 78: 011502.

[31] GOLOVNEV A & TRIMPER S. 2009. Journal of Chemical Physics,131: 114903.

[32] BLOM JG, TROMPERT RA & VERWER JG. 1996. ACM Transactions on Mathematical Software, 22: 302-328.

[33] ZHOU SA & UESAKA M. 2009. International Journal of Applied Electromagnetics and Mechanics, 29: 25-36.

[34] HERAS JA. 2011. American Journal of Physics, 79: 409-416.

[35] KEENER J & SNEYD J. 1998. Mathematical Physiology, 82-87. Springer-Verlag, New York.

[36] CORRY B, KUYUCAK S & CHUNG S-H. 2000. Biophysical Journal, 78: 2364-2381.

[37] ARNDT RA & ROPER LD. 1973. Mathematical Biosciences, 16: 103-117.

[38] BAXTER BJC & ISERLES A. 2003. In: CUCKER F (Ed.) Special Volume: Foundations of Computational Mathematics, 3-34. Elsevier Science B.V.

Search










Combining wavelets and linear spectral mixture model for MODIS satellite sensor time-series analysis
doi: 10.6062/jcis.2008.01.01.0005
Freitas and Shimabukuro(Free PDF)

Riddled basins in complex physical and biological systems
doi: 10.6062/jcis.2009.01.02.0009
Viana et al.(Free PDF)

Use of ordinary Kriging algorithm and wavelet analysis to understanding the turbidity behavior in an Amazon floodplain
doi: 10.6062/jcis.2008.01.01.0006
Alcantara.(Free PDF)

A new multi-particle collision algorithm for optimization in a high performance environment
doi: 10.6062/jcis.2008.01.01.0001
Luz et al.((Free PDF)

Reviewer Guidelines
(Under Construction)
Advertisers/Sponsors
Advertises Media Information