Skip to main content
SpringerLink
Log in

Simulating Ion Permeation Through the ompF Porin Ion Channel Using Three-Dimensional Drift-Diffusion Theory

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

Ionic channels, natural nanotubes found in biological cells, are interesting to the electronics community because they display a range of device-like functions. The purpose of this paper is to illustrate how the solution methodology, developed for 3-D drift-diffusion models of semiconductor devices, can be applied to ion permeation in ionic channels. For this study we select the ompF porin channel, found in the membrane of the E. coli bacterium. The self-consistent 3-D model is based on the simultaneous solution of Poisson's equation, which captures Coulomb interactions, and a current continuity equation for each ion species, describing permeation down an electrochemical gradient. Water is treated as a uniform background medium with a specific dielectric constant. For demonstration, a simple model is assumed for the mobility/diffusivity of each ionic species and we compute the current-voltage relations for ompF porin in a wide range of conditions. Agreement with experimental measurements is surprisingly good given that the model uses the ion diffusivity as the only calibrated parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alder B.J. 1992. In M. Mareschal and B. L. Holian (Ed.), Microscopic Simulations of Complex Hydrodynamic Phenomena. Plenum Press, New York, p. 425–430.

    Google Scholar 

  • Antosiewicz J., Gilson M.K., Lee I.H., and McCammon J.A., 1995. Acetylcholinesterase: Diffusional encounter rate constants for dumbbell models of ligand. Biophysical Journal 68: 62.

    Google Scholar 

  • Antosiewicz J., McCammon J.A., and Gilson M.K. 1994. Prediction of pH-dependent properties of proteins. Journal of Molecular Biology 238: 415.

    Google Scholar 

  • Ashcroft F.M. 1999. Ion Channels and Disease. Academic Press, New York, p. 481.

    Google Scholar 

  • Bagchi B. and Biswas R. 1998. Ionic mobility and ultrafast solvation: Control of a slow phenomenon by fast dynamic. Accounts of Chemical Research 31: 181.

    Google Scholar 

  • Bank R.E., Burgler J., Coughran W.M., Jr., Fichtner W., and Smith R.K. 1990. Recent progress in algorithms for semiconductor device simulation. International Series on Numerical Mathematics 93: 125.

    Google Scholar 

  • Bank R.E., Rose D.J., and Fichtner W. 1983. Numerical methods for semiconductor device simulation. IEEE Transactions on Electron Devices ED-30(9): 1031.

    Google Scholar 

  • Barcilon V. 1992. Ion flow through narrow membrane channels: Part I. SIAM Journal on Applied Mathematics 52: 1391.

    Google Scholar 

  • Barcilon V., Chen D., Eisenberg R.S., and Ratner M. 1993. Barrier crossing with concentration boundary conditions in biological channels and chemical reactions. Journal of Chemical Physics 98: 1193.

    Google Scholar 

  • Barcilon V., Chen D.P., and Eisenberg R.S. 1992. Ion flow through narrow membranes channels: Part II. SIAM Journal on Applied Mathematics 52: 1405.

    Google Scholar 

  • Barcilon V., Cole J., and Eisenberg R.S. 1971.Asingular perturbation analysis of induced electric fields in nerve cells. SIAM Journal on Applied Mathematics 21(2): 339.

    Google Scholar 

  • Barthel J., Buchner R., and Münsterer M. 1995. Electrolyte Data Collection Vol. 12, Part 2: Dielectric Properties ofWater and Aqueous Electrolyte Solutions. DECHEMA, Frankfurt am Main.

    Google Scholar 

  • Barthel J., Krienke H., and Kunz W. 1998. Physical Chemistry of Electrolyte Solutions: Modern Aspects. Springer, New York.

    Google Scholar 

  • Berry S.R., Rice S.A., and Ross J. 2000. Physical Chemistry. Oxford University Press, New York, Oxford, p. 1064.

    Google Scholar 

  • Cardenas A.E., Coalson R.D., and Kurnikova M.G. 2000. Three-dimensional Poisson-Nernst-Planck studies: Influence of membrane electrostatics on gramicidin a channel conductance. Biophysical Journal 79: 80.

    Google Scholar 

  • Chen D., Eisenberg R., Jerome J., and Shu C. 1995. Hydrodynamic model of temperature change in open ionic channels. Biophysical Journal 69: 2304.

    Google Scholar 

  • Chen D.P. and Eisenberg R.S. 1993. Charges, currents and potentials in ionic channels of one conformation. Biophysical Journal. 64: 1405.

    Google Scholar 

  • Ciccotti G. and Hoover W.G. (eds.). 1990. Molecular-Dynamics Simulations of Statistical-Mechanical Systems. North Holland, New York, p. 326.

    Google Scholar 

  • Conway B.E. 1969. Electrochemical Data. Greenwood Press Publishers, Westport CT, p. 374.

    Google Scholar 

  • Conway B.E., Bockris J.O.M., and Yaeger E. (eds.). 1983. Comprehensive Treatise of Electrochemistry. Plenum, New York, p. 472.

    Google Scholar 

  • Cowan S.W., Schirmer T., Rummel G., Steiert M., Ghosh R., Pauptit R.A., Jansonius J.N., and Rosenbusch J.P. 1992. Crystal structures explain functional properties of two E. coli porins. Nature 358: 727.

    Google Scholar 

  • Davis H.T. 1996. Statistical Mechanics of Phases, Interfaces, and Thin Films. Wiley-VCH, New York, p. 712.

    Google Scholar 

  • Durand-Vidal S., Simonin J.-P., and Turq P. 2000. Electrolytes at Interfaces. Kluwer, Boston.

    Google Scholar 

  • Eisenberg R.S. 1986. Impedance measurements as estimators of the properties of the extracellular space. Annals of the New York Academy of Science 481: 116.

    Google Scholar 

  • Eisenberg R.S. 1996. Computing the field in proteins and channels. Journal of Membrane Biology 150: 1.

    Google Scholar 

  • Eisenberg R.S. 1999. From structure to function in open ionic channels. Journal of Membrane Biology 171: 1.

    Google Scholar 

  • Eisenberg R.S. and Mathias R.T. 1980. Structural analysis of electrical properties of cells and tissues. CRC Critical Reviews in Bioengineering 4(3): 203.

    Google Scholar 

  • Eisenberg R.S., Barcilon V., and Mathias R.T. 1979. Electrical properties of spherical syncytia. Biophysical Journal 25(1): 151.

    Google Scholar 

  • Eisenberg R.S., Klosek M.M., and Schuss Z. 1995. Diffusion as a chemical reaction: Stochastic trajectories between fixed concentrations. Journal of Chemical Physics 102: 1767.

    Google Scholar 

  • Evans D.J. and Morriss G.P. 1990. Statistical Mechanics of Nonequilibrium Liquids. Academic Press, New York, p. 302.

    Google Scholar 

  • Ferry D.K. 1991. Semiconductors. McMillan Publishing Company, New York.

    Google Scholar 

  • Gillespie D. and Eisenberg R.S. 2002. Physical descriptions of experimental selectivity measurements in ion channels. European Biophysics Journal 31: 454.

    Google Scholar 

  • Harned H.S. and Owen B.B. 1958. The Physical Chemistry of Electrolytic Solutions. Reinhold Publishing Corporation, New York.

    Google Scholar 

  • Hess K. 2000. Advanced Theory of Semiconductor Devices. IEEE Press, New York, p. 350.

    Google Scholar 

  • Hille B. 2001. Ionic Channels of Excitable Membranes. Sinauer Associates Inc., Sunderland, p. 388.

    Google Scholar 

  • Hodgkin A.L. 1937. Evidence for electrical transmission in nerve. I. Journal of Physiology 90: 183.

    Google Scholar 

  • Hodgkin A.L. 1992. Chance and Design. Cambridge University Press, New York, p. 401.

    Google Scholar 

  • Hollerbach U., Chen D., Nonner W., and Eisenberg B. 1999. Three-dimensional Poisson-Nernst-Planck theory of open channels. Biophysical Journal 76: A205.

    Google Scholar 

  • Honig B. and Nichols A. 1995. Classical electrostatics in biology and chemistry. Science 268: 1144.

    Google Scholar 

  • Hoover W. 1986. Molecular Dynamics. Springer-Verlag, New York, p. 138.

    Google Scholar 

  • Hoover W.G. 1991. Computational Statistical Mechanics. Elsevier, New York, p. 313. http://hoshi-o.physiology.uiowa.edu/Mutations/Home.html

    Google Scholar 

  • Im W. and Roux B. 2001. Brownian dynamics simulations of ions channels: A general treatment of electrostatic reaction fields for molecular pores of arbitrary geometry. Biophysical Journal 115(10): 4850.

    Google Scholar 

  • ISE Integrated System Engineering TCAD software (http://www.ise.ch).

  • Jack J.J.B., Noble D., and Tsien R.W. 1975. Electric Current Flow in Excitable Cells. Clarendon Press, New York, Oxford.

    Google Scholar 

  • Jorgensen W.L. 1998. OPLS force fields. In P.v.R. Schleyer (Ed.), The Encyclopedia of Computational Chemistry, John Wiley & Sons Ltd., Athens, USA.

    Google Scholar 

  • Jorgensen W.L. and Tirado-Rives J. 1988. The OPLS (Optimized Potentials for Liquid Simulations) potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. Journal of the American Chemical Society 110: 1657.

    Google Scholar 

  • Kurnikova M.G., Coalson R.D., Graf P., and Nitzan A. 1999. A lattice relaxation algorithm for 3-D Poisson-Nernst-Planck theory with application to ion transport through the gramicidin a channel. Biophysical Journal 76: 642.

    Google Scholar 

  • Kurnikova M.G., Waldeck D.H., and Coalson R.D. 1996. A molecular dynamics study of the dielectric friction. Journal of Chemical Physics 105(2), 628.

    Google Scholar 

  • Lide D.R. 1994. (editor-in-chief), CRC Handbook of Chemistry and Physics. CRC press, Boca Raton, p. 5–90.

    Google Scholar 

  • Lundstrom M. 1992. Fundamentals of Carrier Transport. Addison-Wesley, New York.

    Google Scholar 

  • Mareschal M. and Holian B.L. (eds.). 1992. Microscopic Simulations of Complex Hydrodynamic Phenomena. Plenum Press, NewYork.

    Google Scholar 

  • Mathias R.T., Levis R.A., and Eisenberg R.S. 1980. Electrical models of excitation-contraction coupling and charge movement in skeletal muscle. Journal of General Physiology 76(1): 1.

    Google Scholar 

  • Mauro A., Blake M., and Labarca P. 1988. Voltage gating of conductance in lipid bilayers induced by porin from outer membrane of Neisseria Gonorrhoease. Proceedings of the National Academy of Science 85: 1071.

    Google Scholar 

  • Nee T.-w. and Zwanzig R. 1970. Theory of dielectric relaxation in polar liquids. Journal of Chemical Physics 52: 6353.

    Google Scholar 

  • Newman J.S. 1991. Electrochemical Systems. Prentice-Hall, Englewood Cliffs, NJ, p. 560.

    Google Scholar 

  • Nonner W., Catacuzzeno L., and Eisenberg B. 2000. Binding and selectivity in L-type Ca channels: A mean spherical approximation. Biophysical Journal 79: 1976.

    Google Scholar 

  • Nonner W., Gillespie D., and Eisenberg B. 2002. Flux and selectivity in the Ca channel: A density functional approach. Biophysical Journal 82: 340a.

    Google Scholar 

  • Nonner W., Gillespie D., Henderson D., and Eisenberg B. 2001. Ion accumulation in a biological calcium channel: Effects of solvent and confining pressure. Journal of Physical Chemistry B 105: 6427.

    Google Scholar 

  • Phale P.S., Philippsen A., Widmer C., Phale V.P., Rosenbusch J.P., and Schirmer T. 2001. Role of charged residues at the OmpF porin channel constriction probed by mutatgenesis and simulation. Biochemistry 40: 6319.

    Google Scholar 

  • Philippsen A., Im W., Engel A., Schirmer T., Roux B., and Muller D.J. 2002. Imaging the electrostatic potential of transmembrane channels: Atomic probe microscopy of Ompf porin. Biophysical Journal 82(3): 1667.

    Google Scholar 

  • PROPHET Web site at Stanford University (http://wwwtcad. stanford.edu/~prophet/).

  • Ravaioli U. 1998. Hierarchy of simulation approaches for hot carrier transport in deep submicron devices. Semiconductor Science and Technology 3: 1–10.

    Google Scholar 

  • Robinson R.A. and Stokes R.H. 1959. Electrolyte Solution. Butterworths Scientific Publications, London.

    Google Scholar 

  • Roux B. 1999. Statistical mechanical equilibrium theory of selective ion channels. Biophysical Journal 77: 139.

    Google Scholar 

  • Roux B. and Karplus M. 1991. Ion transport in a gramicidin-like channel: Dynamics and mobility. Journal of Physical Chemistry 95: 4856.

    Google Scholar 

  • Roux B. and Karplus M. 1991. Ion transport in a model gramicidin channel. Structure and thermodynamics. Biophysical Journal 59: 961.

    Google Scholar 

  • Saint N., Lou K.-L., Widmer C., Luckey M., Schirmer T., and Rosenbusch J.P. 1996. Structural and functional characterization of Ompf porin mutants selected for large pore size. II. Functional characterization. Journal of Biological Chemistry 271(34): 20676.

    Google Scholar 

  • Saint N., Prilipov A., Hardmeyer A., Lou K.-L., Schirmer T., and Rosenbusch J. 1996. Replacement of the Sole Hisdinyl Residue in Ompf Porin from E. coli by threonine (H21t) does not affect channel structure and function. Biochemical and Biophysical Research Communications 223: 118.

    Google Scholar 

  • Schindler H. and Rosenbusch J.P. 1978. Matrix protein from Escherichia coli outer membranes form voltage controlled channels in lipid bilayers. Proceedings of the National Academy of Science USA 75: 3751.

    Google Scholar 

  • Schirmer T. 1998. General and specific porins from bacterial outer membranes. Journal of Structural Biology 121: 101.

    Google Scholar 

  • Schirmer T. and Phale P.S. 1999. Brownian dynamics simulation of ion flow through porin channels. Journal of Molecular Biology 294: 1159.

    Google Scholar 

  • Schmickler W.1996. Interfacial Electrochemistry. Oxford University Press, New York.

  • Schuss Z., Nadler B., and Eisenberg R.S. 2001. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model. Physical Review E 64: 036116-1.

    Google Scholar 

  • Selberherr S. 1984. Analysis and Simulation of Semiconductor Devices. Springer-Verlag, Vienna.

    Google Scholar 

  • Sharp K. and Honig B. 1990. Electrostatic interactions in macromolecules: Theory and applications. Annual Reviewof Biophysics and Bioengineering 19:301.

    Google Scholar 

  • Shockley W. 1950. Electrons and holes in semiconductors. Van Nostrand, Princeton, NJ. Silvaco TCAD (http://www.silvaco.com).

    Google Scholar 

  • Simonin J.-P. 1997. Real ionic solutions in the mean spherical approximation. 2. Pure strong electrolytes up to very high concentrations and mixtures, in the primitive model. Journal of Physical Chemistry B 101: 4313.

    Google Scholar 

  • Simonin J.-P. and Blum L. 1996. Departures from ideality in pure ionic solutions using the mean spherical approximation. Journal of the Chemical Society, Faraday Transactions 92: 1533.

    Google Scholar 

  • Simonin J.-P., Bernard O., and Blum L. 1998. Real ionic solutions in the mean spherical approximation. 3. Osmotic and activity coefficients for associating electrolytes in the primitive model. Journal of Physical Chemistry B 102: 4411.

    Google Scholar 

  • Simonin J.-P., Bernard O., and Blum L. 1999. Ionic solutions in the binding mean spherical approximation: Thermodynamic properties of mixtures of associating electrolytes. Journal of Physical Chemistry B 103: 699.

    Google Scholar 

  • Simonin J.-P., Blum L., and Turq P. 1996. Real ionic solutions in the mean spherical approximation. 1. Simple salts in the primitive model. Journal of Physical Chemistry 100: 7704.

    Google Scholar 

  • Synopsis TCAD (http://www.synopsys.com).

  • Tieleman D.P. and Berendsen H.J.C. 1998. A molecular dynamics study of the pores formed by Escherichia Coli Ompf Porin in a fully hydrated palmitoyloleoylphosphatidylcholine bilayer. Biophysical Journal 74: 2786.

    Google Scholar 

  • Tieleman D.P., Biggin P.C., Smith G.R., and Sansom M.S.P. 2001. Simulation approaches to ion channel structure-function relationships. Quarterly Reviews of Biophysics 34: 473.

    Google Scholar 

  • Tyrrell H.J.V. and Harris K.R. 1984. Diffusion in Liquids. Butterworths Monographs in Chemistry, Boston.

  • Valdiosera R., Clausen C., and Eisenberg R.S. 1974. Circuit models of the passive electrical properties of frog skeletal muscle fibers. Journal of General Physiology 63: 432.

    Google Scholar 

  • van der Straaten T., Varma S., Chiu S.-W., Tang J., Aluru N., Eisenberg R., Ravaioli U., and Jakobsson E. 2002. Combining computational chemistry and computational electronics to understand protein ion channels. In The Technical Proceedings of the Second International Conference on Computational Nanoscience and Nanotechnology, pp. 60–63.

  • Waisman E. and Lebowitz J.L. 1972. Mean spherical model integral equation for charged hard spheres. I. Method of solution. Journal of Chemical Physics 56: 3086.

    Google Scholar 

  • Waisman E. and Lebowitz J.L. 1972. Mean spherical model integral equation for charged hard spheres. II. Spheres. Journal of Chemical Physics 56: 3093.

    Google Scholar 

  • Warshel A. and Russell S.T. 1984. Calculations of electrostatic interactions in biological systems and in solutions. Quarterly Review of Biophysics 17: 283.

    Google Scholar 

  • Weiss M.S. and Schulz G.E. 1992. Structure of porin refined at 1.8 Å resolution. Journal of Molecular Biology 227: 493.

    Google Scholar 

  • Wolynes P. 1980. Dynamics of electrolyte solutions. Annual Reviews Physical Chemistry 31: 345.

    Google Scholar 

  • Young J.D., Blake M., Mauro A., and Cohn Z.A. 1983. Properties of the major outer membrane protein from Neisseria Gonorrhoeae incorporated into model lipid membranes. Proceedings of the National Academy of Science 80: 3831.

    Google Scholar 

  • Zematis Jr., J.F., Clark D.M., Rafal M., and Scrivner N.C. 1986. Handbook of Aqueous Electrolyte Thermodynamics. Design Institute for Physical Property Data, American Institute of Chemical Engineers, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N Mathews Ave., Urbana, IL, 61801, USA

    T.A. van der Straaten, U. Ravaioli & N.R. Aluru

  2. Department of Molecular Biophysics and Physiology, Rush Medical College, 1750 W Harrison St., Chicago, IL, 60612, USA

    T.A. van der Straaten, J.M. Tang & R.S. Eisenberg

Authors
  1. T.A. van der Straaten
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J.M. Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. U. Ravaioli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R.S. Eisenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. N.R. Aluru
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

van der Straaten, T., Tang, J., Ravaioli, U. et al. Simulating Ion Permeation Through the ompF Porin Ion Channel Using Three-Dimensional Drift-Diffusion Theory. Journal of Computational Electronics 2, 29–47 (2003). https://doi.org/10.1023/A:1026212825047

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026212825047

Search

Navigation