Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-13T09:03:53.293Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical perspectives on ion-channel electrostatics: continuum and microscopic approaches

Published online by Cambridge University Press:  17 March 2009

Michael B. Partenskii  and
Peter C. Jordan
Peter C. Jordan
Affiliation:
Department of Chemistry, Brandeis University, Waltham, MA 02254–9110
Get access Rights & Permissions [Opens in a new window]

Extract

Peter Läuger introduced me (P.C.J.) to the field of ion-channel electrostatics while I was a sabbatical visitor at Konstanz in 1978–79. Läuger pointed out that the relative conductance of hydrophobic ions through phosphatidyl choline (PC) and glyceryl monooleate (GMO) membranes differed by a factor of about 100 (Hladky & Haydon, 1973), quite consistent with the difference in the water-membrane potential differences in the two systems (Pickar & Benz, 1978). However, cation conductance through gramicidin channels spanning these membranes only differs by a factor of 2–3 (Bamberg et al. 1976). Why? It is the pursuit of an answer to this question which led me into my researches in this field.

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 25 , Issue 4 , November 1992 , pp. 477 - 510
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abe, T. (1986). A modification of the Born equation. J. Phys. Chem., 90, 713–715.CrossRefGoogle Scholar
Abraham, M. H. & Liszi, J. (1978). Calculations of ionic solvation. Part 1. Free energies of solvation of gaseous univalent ions using a one-layer continuum model. J. Chem. Soc, Farad. Trans. I. 74, 1604–1614.CrossRefGoogle Scholar
Abraham, M. H. & Liszi, J. (1980). Calculations of ionic solvation. Part 4. Further calculations in solvation of gaseous univalent ions using a one-layer and two-layer continuum models. J. Chem. Soc. Farad. Trans. I. 76, 1219–1231.Google Scholar
Alper, H. E. & Levy, R. M. (1989). Computer simulations of the dielectric properties of water: Studies of the simple point charge and transferrable intermolecular potential models. J. Chem. Phys. 91, 1242–1251.CrossRefGoogle Scholar
Andersen, O. S. (1983). Ion movement through gramicidin A channels. Single channel measurements at very high potentials. Biophys. J. 41, 119–133.CrossRefGoogle ScholarPubMed
Andersen, O. S. (1984). Gramicidin channels. Ann. Rev. Physiol. 46, 531–548.CrossRefGoogle ScholarPubMed
Ashcroft, R. G., Coster, H. G. L. & Smith, J. R. (1981). The molecular organisation of bimolecular lipid membranes. The dielectric structure of the hydrophilic/hydrophobic interface. Biochim. Biophys. Acta. 643, 191–204.CrossRefGoogle ScholarPubMed
Ashcroft, R. G., Coster, H. G. L., Laver, D. R. & Smith, J. R. (1983). The effects of cholesterol inclusion on the molecular organisation of bimolecular lipid membranes. Biochim. Biophys. Acta. 730, 231–238.CrossRefGoogle Scholar
Bamberg, E., Noda, K., Gross, E. & Läuger, P. (1976). Single channel parameters of gramicidin A, B and C. Biochim. Biophys. Acta. 418, 223–228.Google Scholar
Berkowitz, M. L. & Raghavan, K. (1991). Computer simulation of a water membrane interface. Langmuir. 7, 1042–1044.CrossRefGoogle Scholar
Bockris, J. O'M. & Reddy, A. K. N. (1977). Modern Electrochemistry, Vol. 1. New York: Plenum Press, Inc.Google Scholar
Bogusz, S. & Busath, D. (1992). Is a β-barrel model of the K+ channel energetically feasible? Biophys. J. 62, 19–21.CrossRefGoogle Scholar
Bottcher, C. J. F. (1973). Theory of Electric Polarization, Vol. I. Amsterdam: Elsevier.Google Scholar
Brooks, C. L. III, Karplus, M. & Pettitt, B. M. (1988). Proteins: A theoretical perspective of dynamics, structure and thermodynamics. Adv. Chem. Phys. 71, 1–259.Google Scholar
Brown, W. F. (1956). Dielectrics. Berlin: Springer.CrossRefGoogle Scholar
Bucher, M. & Porter, T. L. (1986). Analysis of the Born model for the hydration of ions. J. Phys. Chem. 90, 3406–3411.Google Scholar
Cai, M. & Jordan, P. C. (1990). How does vestibule surface charge affect ion conduction and toxin binding in a sodium channel? Biophys. J. 57, 883–891.CrossRefGoogle Scholar
Cevc, G., Watts, A. & Marsh, D. (1981). Titration of phase transition of phosphatidylserine bilayer membranes. Effects of pH, surface electrostatics, ion binding and head-group hydration. Biochemistry. 20, 4955–4965.CrossRefGoogle ScholarPubMed
Chiu, S. W., Jakobsson, E., McCammon, J. A. & Subramaniam, S. (1989). Water and polypeptide conformations in the gramicidin channel. A molecular dynamics study. Biophys. J. 56, 253–261.CrossRefGoogle Scholar
Colombini, M. (1980). Pore size and properties of channels from mitochondria isolated from Neuraspora crassa. J. Membr. Biol. 53, 79–84.CrossRefGoogle Scholar
Colombini, M., Konig, T., Tung, J. & Yeung, C. L. (1987). The mitochondrial outer membrane channel, VDAC, is regulated by a synthetic polyanion. Biochim. Biophys. Acta. 905, 279–286.Google Scholar
Conway, B. E. (1984). Electrochemical surface science: The study of monolayers of adatoms and solvent molecules at charged metal interfaces. Prog. Surf. Sci. 56, 1–138.Google Scholar
Dani, J. A. (1986). Ion channel entrances influence permeation. Net charge, size, shape, and binding considerations. Biophys. J. 49, 607–618.CrossRefGoogle ScholarPubMed
Dani, J. A. (1989). Open channel structure and ion binding sites of the nicotinic acetylcholine receptor channel. J. Neurosci. 9, 884–892.Google Scholar
Daumas, P., Lazaro, R., Heitz, F. & Ranjalahyrasoloarijao, L. (1989). Gramicidin A Analogs. Influence of the Substitution of the Tryptophans by Naphthylalanines. Biochimie. 71, 77–81.CrossRefGoogle ScholarPubMed
Davidson, N. (1962). Statistical Mechanics. New York: McGraw-Hill Book Co. pp. 394–427.Google Scholar
Demchenko, A. P., Kositsky, N. N. & Teslenko, V. I. (1990). The influence of dynamics of ionic channel protein on its selectivity function. Biophys. Chem. 35, 25–35.Google Scholar
Dogonadze, R. R. & Kornyshev, A. A. (1974). Polar solvent structure in the theory of ionic solvation. J. Chem. Soc. Far. Trans. II. 70, 1121–1132.CrossRefGoogle Scholar
Dolgov, O. V., Kirzhnits, D. A. & Maximov, E. G. (1981). On the admissable sign of the static dielectric constant of matter. Rev. Mod. Phys. 53, 81–93.CrossRefGoogle Scholar
Eherson, S. (1987). Boundary continuity and analytical potential in continuum solvation models. Implications for the Born model. J. Phys. Chem. 91, 1868–1873.Google Scholar
Fawcett, W. R. (1979). Molecular models for solvent structure at polarizable interfaces. Isr.J. Chem., 18, 3–16.CrossRefGoogle Scholar
Feldman, V. I., Partenskii, M. B. & Vorobjev, M. M. (1986 a). Surface electron screening theory and its application to metal-electrolyte interfaces. Prog. Surf. Sci. 23, 1–153.CrossRefGoogle Scholar
Feldman, V. I., Partenskii, M. B. & Vorobjev, M. M. (1986 b). Density functional approach to the metal-solid electrolyte interface: electron relaxation effect, equilibrium electrical properties and bilayer stability problem. Electrochim. Acta. 31, 291–297.CrossRefGoogle Scholar
Fernandez, M. S. & Fromherz, P. (1977). Lipoid pH indicators as probes of electrical potential and polarity in micelles. J. Phys. Chem. 81, 1755–1761.CrossRefGoogle Scholar
Flagg-Newton, J., Simpson, I. & Loewenstein, W. R. (1979). Permeability of the cell-to-cell membrane channels in mammalian cell junction. Science (Wash. D.C.). 204, 404–407.CrossRefGoogle Scholar
Flewelling, R. F. & Hubbell, W. L. (1986). The membrane dipole potential in a total membrane potential model. Applications to hydrophobic interactions with membranes. Biophys. J. 49, 541–552.Google Scholar
Fröhlich, H. (1958). Theory of Dielectrics. Oxford: Clarendon Press.Google Scholar
Garavito, R. M., Jenckins, J., Jansonius, J. N., Karlsson, R. & Rosenbusch, J. P. (1983). X-ray diffraction analysis of matrix porin, an integral membrane protein from Escherichia Coli. J. Mol. Biol. 164, 313–327.Google Scholar
Gilson, M. K. & Honig, B. H. (1986). Dielectric constant of a folded protein. Biopolymers. 25, 2097–2119.Google Scholar
Guidelli, R. (1990). General features of lattices of point dipoles against a charged wall. J. Chem. Phys. 92, 6152–6160.Google Scholar
Glueckauf, E. (1964). Heats and entropies of ions in aqueous solutions. Trans. Far. Soc., 60, 572–577.CrossRefGoogle Scholar
Grahame, D. C. (1950). Effects of dielectric saturation upon the diffuse double layer and the free energy of hydration of ions. J. Chem. Phys. 18, 903–909.Google Scholar
Grahame, D. C. (1953). Diffuse double layer theory for electrolytes of unsymmetrical valence types. J. Chem. Phys. 21, 1054–1060.CrossRefGoogle Scholar
Green, M. E. & Lewis, J. (1991). Monte Carlo simulation of the water in a channel with charges. Biophys. J., 59, 419–426.CrossRefGoogle Scholar
Green, W. N.Andersen, O. S. & Weiss, L. B. (1987 a). Batrachotoxin-modifled sodium channels in planar lipid bilayers. Ion permeation and block. J. Gen. Physiol. 89, 841–872.CrossRefGoogle ScholarPubMed
Green, W. N.Andersen, O. S. & Weiss, L. B. (1987 b). Batrachotoxin-modified sodium channels in planar lipid bilayers. Characterization of saxitoxin-induced and tetrodotoxin-induced channel closures. J. Gen. Physiol. 89, 873–903.CrossRefGoogle Scholar
Harrison, W. (1970). Solid State Theory. New York: McGraw Hill.Google Scholar
Harvey, S.C. (1989). Treatment of electrostatic effects in macromolecular modeling. Proteins, 5, 78–92.CrossRefGoogle ScholarPubMed
Heitz, F., Spach, F. & Trudelle, Y. (1984). Single channels of various gramicidins. Voltage effects. Biophys. J. 45, 97–99.CrossRefGoogle ScholarPubMed
Heitz, F., Daumas, P., Van Mau, N., Lazaro, R., Trudelle, Y., Etchebest, C. & Pullman, A. (1988). Linear gramicidins: Influence of the nature of the aromatic side chains on conductance. In Transport through Membranes: Carriers, Channels and Pumps (Ed. Pullman, A., Jortner, J. & Pullman, B.), pp. 147–165, Dordrecht, Netherlands: Kluwer Academic Pub.CrossRefGoogle Scholar
Hille, B. (1984). Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer Associates.Google Scholar
Hladky, S. B. & Haydon, D. A. (1973). Membrane conductance and surface potential. Biochim. Biophys. Acta. 318, 464–468.Google Scholar
Hush, N. S. (1948). Free energies of hydration of gaseous ions. Aust. J. Sci. Res. A. 1, 480–493.Google Scholar
Jayaram, B., Honig, B., Sharp, K. & Fine, R. (1989 a). Free-Energy Calculations of Ion Hydration. An Analysis of the Born Model in Terms of Microscopic Simulations. J. Phys. Chem. 93, 4320–4327.CrossRefGoogle Scholar
Jayaram, B., Sharp, K. A. & Honig, B. (1989 b). The electrostatic potential of B-DNA. Biopolymers. 28, 975–993.CrossRefGoogle ScholarPubMed
Jordan, P. C. (1979). Chemical Kinetics and Transport. New York: Plenum Publishing Co.CrossRefGoogle Scholar
Jordan, P. C. (1981). Energy barriers for the passage of ion through channels. Exact solution of two electrostatic problems. Biophys. Chem. 13, 203–212.Google Scholar
Jordan, P. C. (1982). Electrostatic modeling of ion pores. Energy barriers and electric field profiles. Biophys. J., 39, 157–164.CrossRefGoogle ScholarPubMed
Jordan, P. C. (1983). Electrostatic modeling of ion pores. II. Effects attributable to the membrane dipole potential. Biophys. J. 41, 189–195.CrossRefGoogle Scholar
Jordan, P. C. (1984). The total electrostatic potential in a gramicidin channel. J. Membr. Biol. 78, 91–102.CrossRefGoogle Scholar
Jordan, P. C. (1986). Ion channel electrostatics and the shape of channel proteins. In Ion Channel Reconstitution (ed. Miller, C.), pp. 37–55, New York: Plenum Publ. Corp.CrossRefGoogle Scholar
Jordan, P. C. (1987). How pore mouth charge distributions alter the permeability of transmembrane ionic channels. Biophys. J. 51, 297–311.Google Scholar
Jordan, P. C. (1990). Ion-water and ion-polypeptide correlations in a gramicidin-like channel. A molecular dynamics study. Biophys. J. 58, 1133–1156.Google Scholar
Jordan, P. C. (1991). Effects of cation variation on ion-water-polypeptide correlations in a gramicidinlike channel. Biophys. J. 59, 320a.Google Scholar
Jordan, P. C. (1992). Interactions of ions with membrane proteins. In Thermodynamics of Cell Surface Receptors (ed. Jackson, M.), pp. 0000, Boca Raton, FL: CRC Press, Inc.Google Scholar
Jordan, P. C., McCammon, J. A., Bacquet, R. J. & Tran, P. (1989). How electrolyte shielding influences the electrical potential in transmembrane ion channels. Biophys. J. 55, 1041–1052.Google Scholar
Kharkats, Y. I. & Ulstrup, J. (1991). The electrostatic Gibbs energy of finite-size ions near a planar boundary between two dielectric media. J. Electroanal. Chem. 308, 17–26.CrossRefGoogle Scholar
Kim, Z. B., Kornyshev, A. A. & Partenskii, M. B. (1989). On the anomalously high and negative values of the compact layer capacity in some new models of the metal/electrolyte interface. J. Electroanal. Chem. 265, 1–9.CrossRefGoogle Scholar
King, G., Lee, F. S. & Warshel, A. (1992). Microscopic simulations of macroscopic dielectric constants of solvated proteins. J. Chem. Phys. 95, 4366–4377.CrossRefGoogle Scholar
Kirkwood, J G. (1939). The dielectric polarization of polar liquids. J. Chem. Phys. 7, 911–921.CrossRefGoogle Scholar
Kistler, J. & Stroud, R. M. (1981). Crystalline arrays of membrane-bound acetylcholine receptor. Proc. Nat. Acad. Sci. U.S.A. 78, 3678–3682.CrossRefGoogle ScholarPubMed
Kistler, J., Stroud, R. M., Klymkowsky, M. W., Lalancette, R. A. & Fairclough, R. H. (1981). Structure and function of an acetylcholine receptor. Biophys. J. 37, 371–383.Google Scholar
Kjellendar, R. & Marcelja, S. (1985). Polarization of water between molecular surfaces: A molecular dynamics study. Chem. Scr. 25, 73–80.Google Scholar
Klapper, I., Hagstrom, R., Fine, R., Sharp, K. & Honig, B. (1986). Focusing of electric fields in the active site of Cu-Zn superoxide dismutase: effects of ionic strength and amino-acid modification. Proteins Struc. Func. Gen., 1, 47–59.CrossRefGoogle ScholarPubMed
Koeppe, R. E. II, & Kimura, M. (1984). Computer building of β-helical polypeptide models. Biopolymers. 23, 23–38.CrossRefGoogle Scholar
Kornyshev, A. A. (1985). Nonlocal electrostatics of solvents. In The chemical physics of solvation (ed. Dogonadze, R. R., Kalman, E., Kornyshev, A. A. and Ulstrup, J.), pp. 77–141, Amsterdam: Elsevier.Google Scholar
Kornyshev, A. A. & Ulstrup, J. (1986). Polar solvent structural parameters from absorption bands of mixed-valence transition metal complexes and from protonation equilibria of aliphatic and alicyclic diamines. Chem. Phys. Lett., 126, 74–80.Google Scholar
Leikin, S. & Kornyshev, A. A. (1991). Theory of hydration forces. Nonlocal electrostatic interaction of neutral surfaces. J. Chem. Phys. 92, 6890–6897.Google Scholar
Levitt, D. G. (1978). Electrostatic calculations for an ion channel. I. Energy and potential profiles and interaction between ions. Biophys. J. 22, 202–219.CrossRefGoogle ScholarPubMed
Levitt, D. G. (1984). Kinetics of movement in narrow channels. Curr. Top. Membr. Transp. 21, 181–197.Google Scholar
Levitt, D. G. (1991). General theory for multiion channel. I. Application to acetylcholine channel. Biophys. J. 59, 278–288.Google Scholar
Levitt, D. G. & Decker, E. R. (1988). Electrostatic radius of the gramicidin channel determined from voltage dependence of H+ ion conductance. Biophys. J. 53, 33–38.Google Scholar
Liszi, J. & Ruff, I. (1985). Semi-macroscopic models of ionic solvation. In The chemical physics of solvation (ed. Dogonadze, R. R., Kalman, E., Kornyshev, A. A. and Ulstrup, J.), pp. 119–142, Amsterdam: Elsevier.Google Scholar
Mackay, D. H. J., Berens, P. H., Hagler, A. T. & Wilson, K. R. (1984). Structure and dynamics of ion-transport through gramicidin A. Biophys. J. 46, 229–248.Google Scholar
Martinez, G., Sancho, M. & Fonseca, V. (1992). Study of the influence of the side chain dipoles on the conductance of ion channels formed by gramicidin analogues. In Charge and Field Effects in Biosystems, Vol. 3 (ed. Allen, M. J., Cleary, S. F., Sowers, A. E. & Shillady, D. D.), pp. 139–151, Boston: Birkhauser.CrossRefGoogle Scholar
Millen, W. A. & Watts, D. W. (1967). Theoretical calculations of thermodynamic functions of solvation of ions. J. Am. Chem. Soc. 89, 6051–6056.Google Scholar
Monoi, H. (1991). Effective pore radius of the gramicidin channel. Electrostatic energies of ions calculated by a three dielectric model. Biophys. J. 59, 786–794.CrossRefGoogle ScholarPubMed
Morro, A. (1991). The Born model in terms of microscopic simulations. Phys. Rev. A. 43, 6970–6974.Google Scholar
Nakamura, H. & Nishida, S. (1987). Numerical calculations of electrostatic potentials of protein-solvent systems by the self-consistent boundary method. J. Phys. Soc. Jap. 56, 1609–1622.Google Scholar
Neumann, M. (1983). Dipole moment fluctuation formulas in computer simulations of polar systems. Mol. Phys. 50, 841–858.Google Scholar
Neumann, M. (1986). Dielectric relaxation in water. Computer simulations with the TIP4P potential. J. Chem. Phys. 85, 1567–1580.CrossRefGoogle Scholar
Neumann, M. & Steinhauser, O. (1980). The influence of boundary conditions used in machine simulations on the structure of polar systems. Mol. Phys. 39, 437–454.CrossRefGoogle Scholar
Parsegian, V. A. (1969). Energy of an ion crossing a low dielectric membrane: solution to four relevant electrostatic problems. Nature (Lond.). 221, 844–846.CrossRefGoogle Scholar
Partenskii, M. B. & Feldman, V. J. (1989). Electron and molecular effects in the double layer for the metal electrode/solution interface. J. Electroanal. Chem. 273, 57–68.CrossRefGoogle Scholar
Partenskii, M. & Jordan, P. C. (1992). Nonlinear dielectric behavior of water in transmembrane ion channels: Ion energy barriers and the channel dielectric constant. J. Phys. Chem. 96, 3906–3910.CrossRefGoogle Scholar
Partenskii, M. B. & Vorobjev, M. M. (1984). Influence of metal electrode on the capacitance of the double layer in a metal/solid electrolyte system. Sov. Phys. Dokl. 29, 746–748.Google Scholar
Partenskii, M. B., Cai, M. & Jordan, P. C. (1991 a). A dipolar chain model for the electrostatics of transmembrane ion channels. Chem. Phys. 153, 125–131.CrossRefGoogle Scholar
Partenskii, M. B., Cai, M. & Jordan, P. C. (1991 b). A dipolar chain model for the electrostatics of transmembrane ion channels. (Erratum), Chem. Phys. 154, 197.Google Scholar
Partenskii, M. B., Cai, M. & Jordan, P. C. (1991 c). Influence of the pore-former Charge distribution on the electrostatic properties of dipolar water chains in transmembrane ion channels. Electrochim. Acta. 36, 1753–1756.Google Scholar
Partenskii, M. B., Cai, M. & Jordan, P. C. (1992). Influence of the pore former on the ion free energy in the dipolar chain model of ion channels. Biophys. J. 61, A514.Google Scholar
Pickar, A. D. & Benz, R. (1978). Transport of oppositely charged lipophilic ion probes in lipid bilayers having various structures. J. Membr. Biol. 44, 353–376.CrossRefGoogle Scholar
Raghavan, K., Reddy, M. R. & Berkowitz, M. L. (1992). A molecular dynamics study of the structure and dynamics of water between dilaurylphosphatidylethanolamine bilayers. Langmuir. 8, 233–240.Google Scholar
Ramachandran, G. N. & Sasisekharan, V. (1968). Conformations of polypeptides and proteins. Adv. Prot. Chem. 23, 283–437.Google ScholarPubMed
Rand, R. P., Fuller, N., Parsegian, V. A. & Rau, D. C. (1988). Variation in hydration forces between neutral phospholipid bilayers: Evidence of hydration attraction. Biochemistry 27, 7711–7722.Google Scholar
Raudino, A. & Mauzerell, D. (1986). Dielectric properties of the polar head group region of zwitterionic lipid bilayers. Biophys. J. 50, 441–449.CrossRefGoogle ScholarPubMed
Ravindran, A. & Moczydlowski, E. (1989). Influence of negative surface charge on toxin binding to canine heart Na+ channels in planar bilayers. Biophys. J. 55, 359–365.Google Scholar
Rodgers, K. K. & Sugar, S. G. (1991). Surface electrostatics, reduction potentials, and the internal dielectric constant of proteins. J. Amer. Chem. Soc. 113, 9419–9421.Google Scholar
Rosen, D. (1963). Dielectric properties of protein powders with adsorbed water. Trans. Far. Soc. 59, 2178–2191.Google Scholar
Roux, B. (1990). Theoretical study of ion transport in the gramicidin A channel. Harvard University, Thesis.Google Scholar
Roux, B. & Karplus, M. (1991). Ion transport in a model gramicidin channel. Structure and thermodynamics. Biophys. J. 59, 961–981.Google Scholar
Sancho, M. & Martinez, G. (1991). Electrostatic modeling of dipole-ion interactions in gramicidinlike channels. Biophys. J. 60, 81–88.Google Scholar
Schnitzer, J. E. & Lambrakis, K. C. (1991). Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes. J. Theor. Biol. 152, 203–222.Google Scholar
Schnuelle, G. D. & Beveridge, D. L. (1975). A statistical thermodynamic supermolecule-continuum study of ion hydration. J. Phys. Chem. 79, 2566–2573.CrossRefGoogle Scholar
Schwartzman, G., Weigandt, H., Rose, B., Zimmerman, A., Ben-Haim, D. & Loewenstein, W. R. (1982). Diameter of cell-to-cell junctional membrane channels as probed with neutral molecules. Science 213, 551–553.Google Scholar
Sharp, K. A. & Honig, B. (1990). Electrostatic interactions in macromolecules. Theory and applications. Ann. Rev. Biophys. Biophys. Chem. 19, 301–332.Google Scholar
Simonson, T., Perahia, D. & Brunger, A. (1991). Microscopic theory of the dielectric properties of proteins. Biophys. J. 59, 670–690.Google Scholar
Sung, S. S. & Jordan, P. C. (1987). Why is gramicidin valence selective? A theoretical study. Biophys. J. 51, 661–672.Google Scholar
Takashima, S. & Schwan, H. P. (1965). Dielectric dispersion of crystalline powders of amino acids, peptides and proteins, J. Phys. Chem. 69, 4176–4182.Google Scholar
Takeuchi, H., Nemoto, Y. & Harada, I. (1990). Environments and conformations of tryptophan side chains of gramicidin A in phospholipid bilayers studied by raman spectroscopy. Biochemistry 29, 1572–1579.Google Scholar
Tredgold, R. H. & Hole, P. N. (1976). Dielectric behavior of dry synthetic polypeptides. Biochim. Biophys. Acta. 443, 137–142.CrossRefGoogle ScholarPubMed
Unwin, P. N. T. & Zampighi, G. (1980). Structure of the junction between communicating cells. Nature 283, 545–549.Google Scholar
Urbakh, M. & Klafter, J. (1992). Dipole relaxation near boundaries. J. Phys. Chem. 96, 3480–3485.Google Scholar
Wallace, B. A. (1990). Gramicidin Channels and Pores. Ann. Rev. Biophys. Biophys. Chem. 19, 127–157.Google Scholar
Warshel, A. & Russell, S. T. (1984). Calculations of electrostatic interactions in biological systems and in solutions. Q. Rev. Biophys. 17, 283–422.CrossRefGoogle ScholarPubMed
Warshel, A. & Åqvist, J. (1991). Electrostatic energy and macromolecular function. Ann. Rev. Biophys. Biophys. Chem. 20, 267–298.Google Scholar
Warwicker, J. & Watson, J. C. (1982). Calculations of electric potentials in the active site cleft due to a-helix dipoles. J. Mol. Biol. 157, 671–679.Google Scholar