European Biophysics Journal

, Volume 40, Issue 6, pp 775–782 | Cite as

Selectivity sequences in a model calcium channel: role of electrostatic field strength

  • Daniel Krauss
  • Bob Eisenberg
  • Dirk GillespieEmail author
Original Paper


The energetics that give rise to selectivity sequences of ionic binding selectivity of Li+, Na+, K+, Rb+, and Cs+ in a model of a calcium channel are considered. This work generalizes Eisenman’s classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres). The selectivity filter of the model calcium channel allows the carboxyl terminal groups of glutamate and aspartate side chains to directly interact with and coordinate the permeating ions. Ion dehydration effects are represented with a Born energy between the dielectric coefficients of the selectivity filter and the bath. High oxygen concentration creates a high field strength site that prefers small ions, as in Eisenman’s model. On the other hand, a low filter dielectric constant also creates a high field strength site, but this site prefers large ions, contrary to Eisenman’s model. These results indicate that field strength does not have a unique effect on ionic binding selectivity sequences once entropic, electrostatic, and dehydration forces are included in the model. Thus, Eisenman’s classic relationship between field strength and selectivity sequences must be supplemented with additional information about selectivity filters such as the calcium channel that has amino acid side chains mixing with ions to make a crowded permeation pathway.


Eisenman selectivity sequences Calcium channels Selectivity Modeling 



D.G. and D.K. were supported by NIH grant R01-AR054098. B.E. was supported in part by NIH grant GM076013. We thank Sameer Varma for very useful discussions about potassium channels and how they relate to our work.


  1. Armstrong CM (1989) Reflections on selectivity. In: Tosteson DC (ed) Membrane transport: people and ideas. American Physiological Society, Bethesda, pp 261–273Google Scholar
  2. Barthel JMG, Krienke H, Kunz W (1998) Physical chemistry of electrolyte solutions: modern aspects. Springer, New YorkGoogle Scholar
  3. Blum L (1975) Mean spherical model for asymmetric electrolytes I: method of solution. Mol Phys 30:1529–1535CrossRefGoogle Scholar
  4. Blum L (1980) Solution of the Ornstein-Zernike equation for a mixture of hard ions and Yukawa closure. J Stat Phys 22:661–672CrossRefGoogle Scholar
  5. Boda D, Busath DD, Henderson D, Sokołowski S (2000) Monte Carlo simulations of the mechanism of channel selectivity: the competition between volume exclusion and charge neutrality. J Phys Chem B 104:8903–8910CrossRefGoogle Scholar
  6. Boda D, Henderson D, Busath DD (2001) Monte Carlo study of the effect of ion and channel size on the selectivity of a model calcium channel. J Phys Chem B 105:11574–11577CrossRefGoogle Scholar
  7. Boda D, Henderson D, Busath DD (2002) Monte Carlo study of the selectivity of calcium channels: improved geometry. Mol Phys 100:2361–2368CrossRefGoogle Scholar
  8. Boda D, Valiskó M, Eisenberg B, Nonner W, Henderson D, Gillespie D (2006) The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel. J Chem Phys 125:034901CrossRefGoogle Scholar
  9. Boda D, Valiskó M, Eisenberg B, Nonner W, Henderson D, Gillespie D (2007) Combined effect of pore radius and protein dielectric coefficient on the selectivity of a calcium channel. Phys Rev Lett 98:168102PubMedCrossRefGoogle Scholar
  10. Boda D, Nonner W, Henderson D, Eisenberg B, Gillespie D (2008) Volume exclusion in calcium selective channels. Biophys J 94:3486–3496PubMedCrossRefGoogle Scholar
  11. Boda D, Valiskó M, Henderson D, Eisenberg B, Gillespie D, Nonner W (2009) Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion. J Gen Physiol 133:497–509PubMedCrossRefGoogle Scholar
  12. Bostick D, Brooks CL III (2007) Selectivity in K+ channels is due to topological control of the permeant ion’s coordinated state. Proc Natl Acad Sci USA 104:9260–9265PubMedCrossRefGoogle Scholar
  13. Doyle DA, Morais Cabral J, Pfuetzner RA, Kuo A, Gulbis JM, Cohen SL, Chait BT, MacKinnon R (1998) The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 280:69–77PubMedCrossRefGoogle Scholar
  14. Dzidic I, Kebarle P (1970) Hydration of the alkali ions in the gas phase: enthalpies and entropies of reactions M + (H2O)n−1 + H2O = M + (H2O)n. J Phys Chem 74:1466–1474CrossRefGoogle Scholar
  15. Eisenman G (1962) Cation selective glass electrodes and their mode of operation. Biophys J 2(Suppl. 2):259–323PubMedCrossRefGoogle Scholar
  16. Eisenman G, Alvarez O (1991) Structure and function of channels and channelogs as studied by computational chemistry. J Membr Biol 119:109–132PubMedCrossRefGoogle Scholar
  17. Eisenman G, Horn R (1983) Ionic selectivity revisited: the role of kinetic and equlibrium processes in ion permeation through channels. J Membr Biol 76:197–225PubMedCrossRefGoogle Scholar
  18. Fawcett WR (1999) Thermodynamic parameters for the solvation of monatomic ions in water. J Phys Chem B 103:11181–11185CrossRefGoogle Scholar
  19. Fowler PW, Tai K, Sansom MSP (2008) The selectivity of K+ ion channels: testing the hypotheses. Biophys J 95:5062–5072PubMedCrossRefGoogle Scholar
  20. Gillespie D (2008) Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study. Biophys J 94:1169–1184PubMedCrossRefGoogle Scholar
  21. Gillespie D, Boda D (2008) The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity. Biophys J 95:2658–2672PubMedCrossRefGoogle Scholar
  22. Gillespie D, Fill M (2008) Intracellular calcium release channels mediate their own countercurrent: the ryanodine receptor case study. Biophys J 95:3706–3714PubMedCrossRefGoogle Scholar
  23. Gillespie D, Xu L, Wang Y, Meissner G (2005) (De)constructing the ryanodine receptor: modeling ion permeation and selectivity of the calcium release channel. J Phys Chem B 109:15598–15610PubMedCrossRefGoogle Scholar
  24. Gillespie D, Boda D, He Y, Apel P, Siwy ZS (2008) Synthetic nanopores as a test case for ion channel theories: the anomalous mole fraction effect without single filing. Biophys J 95:609–619PubMedCrossRefGoogle Scholar
  25. Gillespie D, Giri J, Fill M (2009) Reinterpreting the anomalous mole fraction effect: the ryanodine receptor case study. Biophys J 97:2212–2221PubMedCrossRefGoogle Scholar
  26. Hille B (2001) Ion channels of excitable membranes, 3rd edn. Sinauer Associates, SunderlandGoogle Scholar
  27. Koch SE, Bodi I, Schwartz A, Varadi G (2000) Architecture of Ca2+ channel pore-lining segments revealed by covalent modification of substituted cysteines. J Biol Chem 275:34493–34500PubMedCrossRefGoogle Scholar
  28. Krasne S, Eisenman G (1973) The molecular basis of ion selectivity. In: Eisenman G (ed) Membranes: a series of advances: lipid bilayers and antibiotics, vol 2. Marcel Dekker, New YorkGoogle Scholar
  29. Krauss D, Gillespie D (2010) Sieving experiments and pore diameter: it’s not a simple relationship. Eur Biophys J 39:1513–1521PubMedCrossRefGoogle Scholar
  30. Malasics A, Gillespie D, Nonner W, Henderson D, Eisenberg B, Boda D (2009) Protein structure and ionic selectivity in calcium channels: selectivity filter size, not shape, matters. Biochim Biophys Acta Biomembr 1788:2471–2480CrossRefGoogle Scholar
  31. Miedema H, Meter-Arkema A, Wierenga J, Tang J, Eisenberg B, Nonner W, Hektor H, Gillespie D, Meijberg W (2004) Permeation properties of an engineered bacterial OmpF porin containing the EEEE-locus of Ca2+ channels. Biophys J 87:3137–3147PubMedCrossRefGoogle Scholar
  32. Miedema H, Vrouenraets M, Wierenga J, Gillespie D, Eisenberg B, Meijberg W, Nonner W (2006) Ca2+ selectivity of a chemically modified OmpF with reduced pore volume. Biophys J 91:4392–4400PubMedCrossRefGoogle Scholar
  33. Nonner W, Eisenberg B (1998) Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels. Biophys J 75:1287–1305PubMedCrossRefGoogle Scholar
  34. Nonner W, Catacuzzeno L, Eisenberg B (2000) Binding and selectivity in L-type calcium channels: a mean spherical approximation. Biophys J 79:1976–1992PubMedCrossRefGoogle Scholar
  35. Nonner W, Gillespie D, Henderson D, Eisenberg B (2001) Ion accumulation in a biological calcium channel: effects of solvent and confining pressure. J Phys Chem B 105:6427–6436CrossRefGoogle Scholar
  36. Rodriguez-Contreras A, Nonner W, Yamoah EN (2002) Ca2+ transport properties and determinants of anomalous mole fraction effects of single voltage-gated Ca2+ channels in hair cells from bullfrog saccule. J Physiol 538:729–745PubMedCrossRefGoogle Scholar
  37. Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Crystallogr B25:925–946Google Scholar
  38. Thomas M, Jayatilaka D, Corry B (2007) The predominant role of coordination number in potassium channel selectivity. Biophys J 93:2635–2643PubMedCrossRefGoogle Scholar
  39. Varma S, Rempe S (2007) Tuning ion coordination architectures to enable selective partitioning. Biophys J 93:1093–1099PubMedCrossRefGoogle Scholar
  40. Varma S, Sabo D, Rempe SB (2008) K+/Na+ selectivity in K channels and valinomycin: over-coordination versus cavity-size constraints. J Mol Biol 376:13–22PubMedCrossRefGoogle Scholar
  41. Waisman E, Lebowitz JL (1970) Exact solution of an integral equation for the structure of a primitive model of an electrolyte. J Chem Phys 52:4307–4309CrossRefGoogle Scholar

Copyright information

© European Biophysical Societies' Association 2011

Authors and Affiliations

  1. 1.Department of Molecular Biophysics and PhysiologyRush University Medical CenterChicagoUSA
  2. 2.Grinnell CollegeGrinnellUSA

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