Skip to main content
Biophysical Journal logoLink to Biophysical Journal
. 1998 Dec;75(6):2767–2782. doi: 10.1016/S0006-3495(98)77720-3

Dynamic properties of Na+ ions in models of ion channels: a molecular dynamics study.

G R Smith 1, M S Sansom 1
PMCID: PMC1299950  PMID: 9826599

Abstract

We present simulation results for the effective diffusion coefficients of a sodium ion in a series of model ion channels of different diameters and hydrophobicities, including models of alamethicin, a leucine-serine peptide, and the M2 helix bundle of the nicotinic acetylcholine receptor. The diffusion coefficient, which in the simulations has a value of 0.15(2) A2ps-1 in bulk water, is found to be reduced to as little as 0.02(1) A2ps-1 in the narrower channels, and to about 0.10(5) A2ps-1 in wider channels such as the nicotinic acetylcholine receptor. It is anticipated that this work will be useful in connection with calculations of channel conductivity using such techniques as the Poisson-Nernst-Planck equation, Eyring rate theory, or Brownian dynamics.

Full Text

The Full Text of this article is available as a PDF (319.2 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Adcock C., Smith G. R., Sansom M. S. Electrostatics and the ion selectivity of ligand-gated channels. Biophys J. 1998 Sep;75(3):1211–1222. doi: 10.1016/S0006-3495(98)74040-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Akabas M. H., Kaufmann C., Cook T. A., Archdeacon P. Amino acid residues lining the chloride channel of the cystic fibrosis transmembrane conductance regulator. J Biol Chem. 1994 May 27;269(21):14865–14868. [PubMed] [Google Scholar]
  3. Akabas M. H., Stauffer D. A., Xu M., Karlin A. Acetylcholine receptor channel structure probed in cysteine-substitution mutants. Science. 1992 Oct 9;258(5080):307–310. doi: 10.1126/science.1384130. [DOI] [PubMed] [Google Scholar]
  4. Bertrand D., Devillers-Thiéry A., Revah F., Galzi J. L., Hussy N., Mulle C., Bertrand S., Ballivet M., Changeux J. P. Unconventional pharmacology of a neuronal nicotinic receptor mutated in the channel domain. Proc Natl Acad Sci U S A. 1992 Feb 15;89(4):1261–1265. doi: 10.1073/pnas.89.4.1261. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Breed J., Biggin P. C., Kerr I. D., Smart O. S., Sansom M. S. Alamethicin channels - modelling via restrained molecular dynamics simulations. Biochim Biophys Acta. 1997 Apr 26;1325(2):235–249. doi: 10.1016/s0005-2736(96)00262-3. [DOI] [PubMed] [Google Scholar]
  6. Breed J., Sankararamakrishnan R., Kerr I. D., Sansom M. S. Molecular dynamics simulations of water within models of ion channels. Biophys J. 1996 Apr;70(4):1643–1661. doi: 10.1016/S0006-3495(96)79727-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Cafiso D. S. Alamethicin: a peptide model for voltage gating and protein-membrane interactions. Annu Rev Biophys Biomol Struct. 1994;23:141–165. doi: 10.1146/annurev.bb.23.060194.001041. [DOI] [PubMed] [Google Scholar]
  8. Changeux J. P., Galzi J. L., Devillers-Thiéry A., Bertrand D. The functional architecture of the acetylcholine nicotinic receptor explored by affinity labelling and site-directed mutagenesis. Q Rev Biophys. 1992 Nov;25(4):395–432. doi: 10.1017/s0033583500004352. [DOI] [PubMed] [Google Scholar]
  9. Chen D., Lear J., Eisenberg B. Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel. Biophys J. 1997 Jan;72(1):97–116. doi: 10.1016/S0006-3495(97)78650-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Chen D., Xu L., Tripathy A., Meissner G., Eisenberg B. Permeation through the calcium release channel of cardiac muscle. Biophys J. 1997 Sep;73(3):1337–1354. doi: 10.1016/S0006-3495(97)78167-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Chiu S. W., Jakobsson E. Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath. Biophys J. 1989 Jan;55(1):147–157. doi: 10.1016/S0006-3495(89)82786-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Chiu S. W., Jakobsson E., Subramaniam S., McCammon J. A. Time-correlation analysis of simulated water motion in flexible and rigid gramicidin channels. Biophys J. 1991 Jul;60(1):273–285. doi: 10.1016/S0006-3495(91)82049-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Chiu S. W., Novotny J. A., Jakobsson E. The nature of ion and water barrier crossings in a simulated ion channel. Biophys J. 1993 Jan;64(1):98–109. doi: 10.1016/S0006-3495(93)81344-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Cohen B. N., Labarca C., Czyzyk L., Davidson N., Lester H. A. Tris+/Na+ permeability ratios of nicotinic acetylcholine receptors are reduced by mutations near the intracellular end of the M2 region. J Gen Physiol. 1992 Apr;99(4):545–572. doi: 10.1085/jgp.99.4.545. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Cooper K., Jakobsson E., Wolynes P. The theory of ion transport through membrane channels. Prog Biophys Mol Biol. 1985;46(1):51–96. doi: 10.1016/0079-6107(85)90012-4. [DOI] [PubMed] [Google Scholar]
  16. Cowan S. W., Schirmer T., Rummel G., Steiert M., Ghosh R., Pauptit R. A., Jansonius J. N., Rosenbusch J. P. Crystal structures explain functional properties of two E. coli porins. Nature. 1992 Aug 27;358(6389):727–733. doi: 10.1038/358727a0. [DOI] [PubMed] [Google Scholar]
  17. Doyle D. A., Morais Cabral J., Pfuetzner R. A., Kuo A., Gulbis J. M., Cohen S. L., Chait B. T., MacKinnon R. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science. 1998 Apr 3;280(5360):69–77. doi: 10.1126/science.280.5360.69. [DOI] [PubMed] [Google Scholar]
  18. Doyle D. A., Wallace B. A. Crystal structure of the gramicidin/potassium thiocyanate complex. J Mol Biol. 1997 Mar 14;266(5):963–977. doi: 10.1006/jmbi.1996.0837. [DOI] [PubMed] [Google Scholar]
  19. Dwyer T. M., Adams D. J., Hille B. The permeability of the endplate channel to organic cations in frog muscle. J Gen Physiol. 1980 May;75(5):469–492. doi: 10.1085/jgp.75.5.469. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Fox R. O., Jr, Richards F. M. A voltage-gated ion channel model inferred from the crystal structure of alamethicin at 1.5-A resolution. Nature. 1982 Nov 25;300(5890):325–330. doi: 10.1038/300325a0. [DOI] [PubMed] [Google Scholar]
  21. Galzi J. L., Devillers-Thiéry A., Hussy N., Bertrand S., Changeux J. P., Bertrand D. Mutations in the channel domain of a neuronal nicotinic receptor convert ion selectivity from cationic to anionic. Nature. 1992 Oct 8;359(6395):500–505. doi: 10.1038/359500a0. [DOI] [PubMed] [Google Scholar]
  22. Gutman M., Tsfadia Y., Masad A., Nachliel E. Quantitation of physical-chemical properties of the aqueous phase inside the phoE ionic channel. Biochim Biophys Acta. 1992 Aug 24;1109(2):141–148. doi: 10.1016/0005-2736(92)90077-y. [DOI] [PubMed] [Google Scholar]
  23. Hucho F., Oberthür W., Lottspeich F. The ion channel of the nicotinic acetylcholine receptor is formed by the homologous helices M II of the receptor subunits. FEBS Lett. 1986 Sep 1;205(1):137–142. doi: 10.1016/0014-5793(86)80881-x. [DOI] [PubMed] [Google Scholar]
  24. Hucho F., Tsetlin V. I., Machold J. The emerging three-dimensional structure of a receptor. The nicotinic acetylcholine receptor. Eur J Biochem. 1996 Aug 1;239(3):539–557. doi: 10.1111/j.1432-1033.1996.0539u.x. [DOI] [PubMed] [Google Scholar]
  25. Jakobsson E., Chiu S. W. Stochastic theory of ion movement in channels with single-ion occupancy. Application to sodium permeation of gramicidin channels. Biophys J. 1987 Jul;52(1):33–45. doi: 10.1016/S0006-3495(87)83186-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Jordan P. C. Electrostatic modeling of ion pores. Energy barriers and electric field profiles. Biophys J. 1982 Aug;39(2):157–164. doi: 10.1016/S0006-3495(82)84503-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Karlin A., Akabas M. H. Toward a structural basis for the function of nicotinic acetylcholine receptors and their cousins. Neuron. 1995 Dec;15(6):1231–1244. doi: 10.1016/0896-6273(95)90004-7. [DOI] [PubMed] [Google Scholar]
  28. Kerr I. D., Sankararamakrishnan R., Smart O. S., Sansom M. S. Parallel helix bundles and ion channels: molecular modeling via simulated annealing and restrained molecular dynamics. Biophys J. 1994 Oct;67(4):1501–1515. doi: 10.1016/S0006-3495(94)80624-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Kienker P. K., DeGrado W. F., Lear J. D. A helical-dipole model describes the single-channel current rectification of an uncharged peptide ion channel. Proc Natl Acad Sci U S A. 1994 May 24;91(11):4859–4863. doi: 10.1073/pnas.91.11.4859. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Kienker P. K., Lear J. D. Charge selectivity of the designed uncharged peptide ion channel Ac-(LSSLLSL)3-CONH2. Biophys J. 1995 Apr;68(4):1347–1358. doi: 10.1016/S0006-3495(95)80307-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Kreusch A., Neubüser A., Schiltz E., Weckesser J., Schulz G. E. Structure of the membrane channel porin from Rhodopseudomonas blastica at 2.0 A resolution. Protein Sci. 1994 Jan;3(1):58–63. doi: 10.1002/pro.5560030108. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Kuyucak S., Hoyles M., Chung S. H. Analytical solutions of Poisson's equation for realistic geometrical shapes of membrane ion channels. Biophys J. 1998 Jan;74(1):22–36. doi: 10.1016/S0006-3495(98)77763-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Lear J. D., Wasserman Z. R., DeGrado W. F. Synthetic amphiphilic peptide models for protein ion channels. Science. 1988 May 27;240(4856):1177–1181. doi: 10.1126/science.2453923. [DOI] [PubMed] [Google Scholar]
  34. Li S. C., Hoyles M., Kuyucak S., Chung S. H. Brownian dynamics study of ion transport in the vestibule of membrane channels. Biophys J. 1998 Jan;74(1):37–47. doi: 10.1016/S0006-3495(98)77764-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Nicholson L. K., Teng Q., Cross T. A. Solid-state nuclear magnetic resonance derived model for dynamics in the polypeptide backbone of the gramicidin A channel. J Mol Biol. 1991 Apr 5;218(3):621–637. doi: 10.1016/0022-2836(91)90706-c. [DOI] [PubMed] [Google Scholar]
  36. Nutter T. J., Adams D. J. Monovalent and divalent cation permeability and block of neuronal nicotinic receptor channels in rat parasympathetic ganglia. J Gen Physiol. 1995 Jun;105(6):701–723. doi: 10.1085/jgp.105.6.701. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Ortells M. O., Lunt G. G. A mixed helix-beta-sheet model of the transmembrane region of the nicotinic acetylcholine receptor. Protein Eng. 1996 Jan;9(1):51–59. doi: 10.1093/protein/9.1.51. [DOI] [PubMed] [Google Scholar]
  38. Roux B., Karplus M. Ion transport in a model gramicidin channel. Structure and thermodynamics. Biophys J. 1991 May;59(5):961–981. doi: 10.1016/S0006-3495(91)82311-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Roux B., Karplus M. Molecular dynamics simulations of the gramicidin channel. Annu Rev Biophys Biomol Struct. 1994;23:731–761. doi: 10.1146/annurev.bb.23.060194.003503. [DOI] [PubMed] [Google Scholar]
  40. Roux B., Prod'hom B., Karplus M. Ion transport in the gramicidin channel: molecular dynamics study of single and double occupancy. Biophys J. 1995 Mar;68(3):876–892. doi: 10.1016/S0006-3495(95)80264-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Sancho M., Partenskii M. B., Dorman V., Jordan P. C. Extended dipolar chain model for ion channels: electrostriction effects and the translocational energy barrier. Biophys J. 1995 Feb;68(2):427–433. doi: 10.1016/S0006-3495(95)80204-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Sankararamakrishnan R., Adcock C., Sansom M. S. The pore domain of the nicotinic acetylcholine receptor: molecular modeling, pore dimensions, and electrostatics. Biophys J. 1996 Oct;71(4):1659–1671. doi: 10.1016/S0006-3495(96)79370-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Sansom M. S., Sankararamakrishnan R., Kerr I. D. Modelling membrane proteins using structural restraints. Nat Struct Biol. 1995 Aug;2(8):624–631. doi: 10.1038/nsb0895-624. [DOI] [PubMed] [Google Scholar]
  44. Sansom M. S., Smith G. R., Adcock C., Biggin P. C. The dielectric properties of water within model transbilayer pores. Biophys J. 1997 Nov;73(5):2404–2415. doi: 10.1016/S0006-3495(97)78269-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  45. Sansom M. S. Structure and function of channel-forming peptaibols. Q Rev Biophys. 1993 Nov;26(4):365–421. doi: 10.1017/s0033583500002833. [DOI] [PubMed] [Google Scholar]
  46. Skerra A., Brickmann J. Simulation of voltage-driven hydrated cation transport through narrow transmembrane channels. Biophys J. 1987 Jun;51(6):977–983. doi: 10.1016/S0006-3495(87)83425-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Smart O. S., Breed J., Smith G. R., Sansom M. S. A novel method for structure-based prediction of ion channel conductance properties. Biophys J. 1997 Mar;72(3):1109–1126. doi: 10.1016/S0006-3495(97)78760-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  48. Smart O. S., Goodfellow J. M., Wallace B. A. The pore dimensions of gramicidin A. Biophys J. 1993 Dec;65(6):2455–2460. doi: 10.1016/S0006-3495(93)81293-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Smith G. R., Sansom M. S. Molecular dynamics study of water and Na+ ions in models of the pore region of the nicotinic acetylcholine receptor. Biophys J. 1997 Sep;73(3):1364–1381. doi: 10.1016/S0006-3495(97)78169-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Song L., Hobaugh M. R., Shustak C., Cheley S., Bayley H., Gouaux J. E. Structure of staphylococcal alpha-hemolysin, a heptameric transmembrane pore. Science. 1996 Dec 13;274(5294):1859–1866. doi: 10.1126/science.274.5294.1859. [DOI] [PubMed] [Google Scholar]
  51. Tikhonov D. B., Zhorov B. S. Kinked-helices model of the nicotinic acetylcholine receptor ion channel and its complexes with blockers: simulation by the Monte Carlo minimization method. Biophys J. 1998 Jan;74(1):242–255. doi: 10.1016/S0006-3495(98)77783-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  52. Unwin N. Acetylcholine receptor channel imaged in the open state. Nature. 1995 Jan 5;373(6509):37–43. doi: 10.1038/373037a0. [DOI] [PubMed] [Google Scholar]
  53. Unwin N. Nicotinic acetylcholine receptor at 9 A resolution. J Mol Biol. 1993 Feb 20;229(4):1101–1124. doi: 10.1006/jmbi.1993.1107. [DOI] [PubMed] [Google Scholar]
  54. Urry D. W. The gramicidin A transmembrane channel: a proposed pi(L,D) helix. Proc Natl Acad Sci U S A. 1971 Mar;68(3):672–676. doi: 10.1073/pnas.68.3.672. [DOI] [PMC free article] [PubMed] [Google Scholar]
  55. Villarroel A., Herlitze S., Koenen M., Sakmann B. Location of a threonine residue in the alpha-subunit M2 transmembrane segment that determines the ion flow through the acetylcholine receptor channel. Proc Biol Sci. 1991 Jan 22;243(1306):69–74. doi: 10.1098/rspb.1991.0012. [DOI] [PubMed] [Google Scholar]
  56. Wallace B. A. Structure of gramicidin A. Biophys J. 1986 Jan;49(1):295–306. doi: 10.1016/S0006-3495(86)83642-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  57. Woolley G. A., Biggin P. C., Schultz A., Lien L., Jaikaran D. C., Breed J., Crowhurst K., Sansom M. S. Intrinsic rectification of ion flux in alamethicin channels: studies with an alamethicin dimer. Biophys J. 1997 Aug;73(2):770–778. doi: 10.1016/S0006-3495(97)78109-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  58. Woolley G. A., Wallace B. A. Model ion channels: gramicidin and alamethicin. J Membr Biol. 1992 Aug;129(2):109–136. doi: 10.1007/BF00219508. [DOI] [PubMed] [Google Scholar]
  59. You S., Peng S., Lien L., Breed J., Sansom M. S., Woolley G. A. Engineering stabilized ion channels: covalent dimers of alamethicin. Biochemistry. 1996 May 21;35(20):6225–6232. doi: 10.1021/bi9529216. [DOI] [PubMed] [Google Scholar]
  60. Zhong Q., Jiang Q., Moore P. B., Newns D. M., Klein M. L. Molecular dynamics simulation of a synthetic ion channel. Biophys J. 1998 Jan;74(1):3–10. doi: 10.1016/S0006-3495(98)77761-6. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES