Role of nonlocal electrostatic effects in the stabilization of monovalent cations in an aqueous cavity surrounded by a weakly polar environment

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

We developed earlier (Russ. J. Electrochem., 2018, vol. 54, p. 879), a new nonlocal electrostatic (NE) method for calculating electric field distributions in systems where there are spatially limited regions filled with polar media with nonlocal dielectric properties. This method was used for NE analysis of the stabilization of a monovalent cation in a spherical cavity filled with water and surrounded by a local dielectric. For one- and three-mode models of the dielectric function, NE formulas were obtained for the field distribution inside such a cavity, provided that the ion is located at its center. NE relations have been derived for the change in cation solvation energy ΔW during its transition from solution to the center of such a cavity. It is shown that when the correlation length of water in the cavity decreases compared to the solution (at the same values of the dielectric constant of water in the cavity and in the volume of the solution), the amount of work to transfer an ion from the solution into the cavity (–ΔW) decreases significantly compared to the calculation using the local theory used in the work (B. Roux, R. MacKinnon, Science, 1999, vol. 285, p. 100).

Full Text

Restricted Access

About the authors

A. A. Rubashkin

Institute of Cytology RAS

Author for correspondence.
Email: andrey.rubashkin@gmail.com
Russian Federation, St. Petersburg

V. A. Vigont

Institute of Cytology RAS

Email: andrey.rubashkin@gmail.com
Russian Federation, St. Petersburg

M. A. Vorotyntsev

Institute of Physical Chemistry and Electrochemistry named after A.N. Frumkin RAS

Email: mivo2010@yandex.com
Russian Federation, Moscow

References

  1. Hille, B. Ion Channels of Excitable Membrane, Sunderland, MA: Sinauer, 3rd Ed., 2001. 814 p.
  2. Roux, B. and MacKinnon, R., The cavity and pore helices in the KcsA K+ Channel: Electrostatic stabilization of monovalent cations, Science, 1999, vol. 285, p. 100.
  3. Doyle, D.A., Cabral, J.M., Pfuetzner, R.A., Kuo A., Gulbis, J.M., Cohen, S.L., Chait, B.T., and MacKinnon, R., The structure of the potassium channel: molecular basis of K+ conduction and selectivity, Science, 1998, vol. 280, p. 69.
  4. Bichet, D., Grabe, M., Jan, Y.N., and Jan, L.Y., Electrostatic interactions in the channel cavity as an important determinant of potassium channel selectivity, PNAS, 2006, vol. 103, p. 14355.
  5. Zhou, Y. and MacKinnon, R., Ion binding affinity in the cavity of the KcsA potassium channel, Biochemistry, 2004, vol. 43, p. 4978.
  6. Kariev, A. and Green, M.E., Quantum calculations on water in the KcsA channel cavity with permeant and nonpermeant ions, Biochim. Biophys. Acta – Biomembranes, 2009, vol. 1788, p. 1188.
  7. Yao, Z., Qiao, B., and de la Cruz, M.O., Potassium ions in the cavity of a KcsA channel model, Phys. Rev. E, 2013, vol. 88, p. 062712.
  8. Song, Z., Cao, X., Horng, T.-L., and Huang, H., Selectivity of the KcsA potassium channel: Analysis and computation, Phys. Rev. E, 2019, vol. 100, p. 022406.
  9. Kariev, A.M. and Green, M.E., The pore of the KcsA channel, including the entire cavity up to the selectivity filter, participates in selectivity, rectification, and ion transport, Biophys. J., 2023, vol. 122, SUPPLEMENT 1, p. 525A.
  10. Israelachvili, J.N. Intermolecular and Surface Forces, Academic Press, 3rd Ed., 2011. 674 p.
  11. Israelachvili, J.N. and Pashley, R.M., Molecular layering of water at surfaces and origin of repulsive hydration forces, Nature, 1983, vol. 306, p. 249.
  12. Toney, M., Howard, J., Richer, J., Borges, G.L., Gordon, J., Melroy, O., Wiesler, D., Yee, D., and Sorensen, L., Voltage-Dependent Ordering of Water Molecules at an Electrode-Electrolyte Interface, Nature, 1994, vol. 368, p. 444.
  13. Velasco-Velez, J.-J., Wu, C.H., Pascal, T.A., Wan, L.F., Guo, J., Prendergast, D., and Salmeron, M., The structure of interfacial water on gold electrodes studied by x-ray absorption spectroscopy, Science, 2014, vol. 346, p. 831.
  14. Fumagalli, L., Esfandiar, A., Fabregas, R., Hu, S., Ares, P., Janardanan, A., Yang, Q., Radha, B., Taniguchi, T., Watanabe, K., Gomila, G., Novoselov, K.S., and Geim, A. K., Anomalously low dielectric constant of confined water, Science, 2018, vol. 360, p. 1339.
  15. Рубашкин, А.А., Исерович П. Новый подход к селективности ионных каналов. Нелокально электростатическое расмотрение. Докл. Акад. наук. 2007. Т. 417. С. 121. [Rubashkin, A.A. and Iserovich, P., A new approach to the selectivity of ion channels: Nonlocal electrostatic consideration, Dokl. Biochem. and Biophys., 2007, vol. 417, p. 302.]
  16. Bardhan, J.P., Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins, J. Chem. Phys., 2011, vol. 135, p. 104113–1.
  17. Рубашкин, А.А. Роль пространственной дисперсии диэлектрической проницаемости сферической водной полости в уменьшении свободной энергии переноса иона в полость. Электрохимия. 2014. Т. 50. С. 1212. [Rubashkin, A.A., The role of spatial dispersion of the dielectric constant of spherical water cavity in the lowering of the free energy of ion transfer to the cavity, Russ. J. Electrochem., 2014, vol. 50, p. 1090.]
  18. Корнышев, А.А., Цицуашвили, Г.И., Ярощук, А.Э. Эффект структуры полярного растворителя в теории диэлектрического исключения ионов из пор полимерных мембран. Постановка задачи. Расчет потенциала. Электрохимия. 1989. Т. 25. С. 1027. [Kornyshev, A.A., Tsitsuashvili, G.I., and Yaroschuk, A.E., The effect of polar solvent structure in the theory of dielectric exclusion of ions from polymermembrane pores. Setting of the problem. Calculation of potential, Sov. Electrochem., 1989, vol 25, p. 923.]
  19. Корнышев, А.А., Цицуашвили, Г.И., Ярощук, А.Э. Эффект структуры полярного растворителя в теории диэлектрического исключения ионов из пор полимерных мембран. Расчет свободной энергии переноса заряда из объема растворителя в пору. Электрохимия. 1989. Т. 25. С. 1037. [Kornyshev, A.A., Tsitsuashvili, G.I., and Yaroschuk, A.E., The effect of polar solvent structure in the theory of dielectric exclusion of ions from polymermembrane pores. Calculation of free energy of charge transfer from the solvent into a pore, Sov. Electrochem., 1989, vol 25, p. 932.]
  20. Kornyshev, A.A., Nonlocal screening of ions in a structurized polar liquid – new aspects of solvent description in electrolyte theory, Electrochim. Acta, 1981, vol. 26, p. 1.
  21. Воротынцев, М.А., Корнышев, А.А., Электростатика сред с пространственной дисперсией. М.: Наука., 1993. 240 с. [Vorotyntsev, M. A. and Kornyshev, A.A., Electrostatics of Media with Spatial Dispersion (in Russian), Moscow: Nauka, 1993. 240 p.]
  22. Kornyshev, A.A., Rubinshtein, A.I., and Vorotyntsev, M.A., Model nonlocal electrostatics: 1, J. Phys. C: Solid State Phys., 1978, vol. 11, p. 3307.
  23. Vorotyntsev, M.A., Model nonlocal electrostatics: II. Spherical interface, J. Phys. C: Solid State Phys., 1978, vol. 11, p. 3323.
  24. Hildebrandt, A., Blossey, R., Rjasanow, S., Kohlbacher, O., and Lenhof, H.-P., Novel Formulation of Nonlocal Electrostatics, Phys. Rev. Lett., 2004, vol. 93, p. 108104–1.
  25. Rubinstein, A. and Sherman, S., Influence of the Solvent Structure on the Electrostatic Interactions in Proteins, Biophys. J., 2004, vol. 87, p. 1544.
  26. Rubinstein, A.I., Sabirianov, R.F., and Namavar, F., Effects of the dielectric properties of the ceramic-solvent interface on the binding of proteins to oxide ceramics: a non-local electrostatic approach, Nanotechnology, 2016, vol. 27, p. 415703.
  27. Rubinstein, A., Sabirianov, R.F., Mei, W.N., Namavar, F., and Khoynezhad, A., Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach, Phys. Rev. E, 2010, vol. 82, p. 021915.
  28. Paillusson, F. and Blossey, R., Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics, Phys. Rev. E, 2010, vol. 82, p. 052501–1.
  29. Kornyshev, A.A. and Sutmann, G., The shape of the nonlocal dielectric function of polar liquids and the implications for thermodynamic properties of electrolytes: a comparative study, J. Chem. Phys., 1996, vol. 104, p. 1524.
  30. Kornyshev, A.A., Leikin, S., and Sutmann, G., “Overscreening” in a polar liquid as a result of coupling between polarization and density fluctuations, Electrochim. Acta, 1997, vol. 42, p. 849.
  31. Bopp, P.A., Kornyshev, A.A., and Sutmann, G., Static nonlocal dielectric function of liquid water, Phys. Rev. Lett., 1996, vol. 76, p. 1280.
  32. Fedorov, M.V. and Kornyshev, A.A., Unravelling the solvent response to neutral and charged solutes, Mol. Phys., 2007, vol. 105, p. 1.
  33. Holub, K. and Kornyshev, A.A., Comment on the solvent structure in thermodynamics of electrolytes: anomalous behaviour of activity coefficients at low concentrations, J. Electroanal. Chem., 1982, vol. 142, p. 57.
  34. Kornyshev, A.A., Non-local dielectric response of a polar-solvent and Debye screening in ionic solution, J. Chem. Soc. Faraday Trans.II, 1983, vol. 79, p. 651.
  35. Kornyshev, A.A., Nonlocal electrostatics of solvation, in: R.R. Dogonadze, E. Kalman, A.A. Kornyshev, J. Ulstrup (Eds.), The Chemical Physics of Solvation. Amsterdam: Elsevier Science Ltd, 1985, p. 268.
  36. Basilevsky, M.V. and Parsons, D.F., An advanced continuum medium model for treating solvation effects: nonlocal electrostatics with a cavity, an advanced continuum medium model for treating solvation effects: nonlocal electrostatics with a cavity, J. Chem. Phys., 1996, vol. 105, p. 3734.
  37. Basilevsky, M.V. and Parsons, D.F. Nonlocal continuum solvation model with exponential susceptibility kernels, J. Chem. Phys., 1998, vol. 108, p. 9107.
  38. Воротынцев, М.А., Рубашкин, А.А., Антипов, А.Е. Новый подход в теории ограниченных в пространстве нелокальных диэлектрических сред. Электрохимия. 2018. Т. 54. № 10 ПРИЛОЖЕНИЕ. С. S54–S61. [Vorotyntsev, M.A., Rubashkin, A.A., and Antipov, A.E., A new approach in the theory of space-confined nonlocal dielectric media, Russ. J. Electrochem., 2018, vol. 54, p. 879.]
  39. Vorotyntsev, M.A. and Rubashkin, A.A., Uniformity ansatz for inverse dielectric function of spatially restricted nonlocal polar medium as a novel approach for calculation of electric characteristics of ion–solvent system, Chem. Phys., 2019, vol. 521, p. 14.
  40. Rubashkin, A.A., Iserovich, P., and Vorotyntsev, M.A., Physical origin of Na+/Cl- selectivity of tight junctions between epithelial cells. Nonlocal electrostatic approach, J. Mol. Liq., 2020, 317, p. 113884–1.
  41. Dogonadze, R.R. and Kornyshev, A.A., Polar solvent structure in the theory of ionic salvation, J. Chem. Soc. Faraday Trans. II, 1974, vol. 70, p. 1121.
  42. Kornyshev, A.A. and Volkov, A.G., On the evaluation of standard Gibbs energies of ion transfer between 2 solvents, J. Electroanal. Chem., 1984, vol. 180, p. 363.
  43. Зубарев, Д.Н. Неравновесная статистическая термодинамика. М.: Наука, 1971. 416 с. [Zubarev, D.N., Non-Equilibrium Statistical Thermodynamics (in Russian), Moscow: Nauka, 1971. 416 p.]

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Appendix 1
Download (119KB)
Indexing metadata
3. Appendix 2
Download (129KB)
Indexing metadata
4. Fig. 1. (a) Schematic representation of the system: an ion of radius a in the center of a spherical cavity of radius R (its permittivity is indicated – in the general case described by the nonlocal permittivity function εcav(k)), surrounded by a dielectric medium with permittivity εp. (b) Change in the Gibbs free energy (ΔG = –ΔW, in units of kT) upon the transition of a K+ ion from solution to the center of the cavity depending on the permittivity of the protein environment of the aqueous cavity εp. Calculation (ΔG = ΔGLE) using formulas (1.1)–(1.2) of the local electrostatics model. The permittivity inside the cavity εcav is equal to 80 (curve 1) or 4.9 (curve 2). The radius of the cavity R = 5Å. The radius of the K+ cation (a = 1.49Å) is taken according to the Gurary and Adrian scale.

Download (86KB)
Indexing metadata
5. Fig. 2. Change in the Gibbs free energy (ΔG = –ΔW, in kT units) during the transition of a K+ ion to the center of the cavity depending on the permittivity of the protein environment of the aqueous cavity. All calculations were performed using nonlocal electrostatics (NE) and a single-mode model of the dielectric function of water. Solid curves 1 and 2 were calculated using NE formulas (23)–(24), derived in accordance with the inverse dielectric approximation (IDA) [38]. Circles and rectangles are calculations using NE formulas (14)–(16), obtained based on the dielectric approximation (DA) approach [23]. For curve 2 and rectangles, the permittivity in the cavity is εcav = 4.9, for curve 1 and circles εcav = 80. For all cases, the parameter εo = 4.9, the correlation lengths in the free solution (Λ) and in the cavity (Λcav) are equal to each other: Λ = Λcav = 5 Å; the radius of the cavity R = 5Å.

Download (66KB)
Indexing metadata
6. Fig. 3. Change in the Gibbs free energy (ΔG = –ΔW, in kT units) upon the transition of a K+ ion to the center of the cavity depending on the permittivity of the protein environment of the aqueous cavity. Solid curves 1 and 2 are calculations using formulas (23)–(24) of the single-mode model (1M) of nonlocal electrostatics (NE), dashed curves 3 and 4 are calculations (ΔG = ΔGLE) using formulas (1.1)–(1.2) of local electrostatics (LE). For curves 1 and 3, the value εcav = ε = 80, for curves 2 and 4 εcav = εo = 4.9. The cavity radius R = 5Å, other parameters are given in Table 1.

Download (71KB)
Indexing metadata
7. Fig. 4. Nonlocal electrostatic (NE) calculations of the change in Gibbs free energy (ΔG = –ΔW, in kT units) during the transition of a K+ ion to the center of the cavity, depending on the permittivity of the protein environment of the aqueous cavity. Curves 2 and 4 are calculations using formulas (23)–(24) of the single-mode (1M) NE model. Curves 1 and 3 are calculations using formulas (34.1)–(37) of the three-mode (3M) NE model. For solid curves 1 and 2, the correlation length of water in the cavity is equal to λ3(cav) = 5Å, for dashed curves 3 and 4, the value λ3(cav) = 2Å. The cavity radius R = 5Å, other parameters are given in Table 2.

Download (77KB)
Indexing metadata
8. Fig. 5. Change in free energy (ΔG = –ΔW, in kT units) during the transition of a K+ ion to the center of the cavity depending on the correlation length λ3(cav) in the aqueous cavity. Curves 1, 1' – calculation using the formulas of the single-mode model (1M) of nonlocal electrostatics (NE). Curves 2, 2' – calculation using the formulas of the three-mode model (3M) of NE. Horizontal straight lines 3, 3' – calculation using local electrostatics (LE). For solid curves 1, 2, 3 the cavity radius R = 5Å, for dashed curves 1', 2', 3' the cavity radius R = 6Å, other parameters are given in Table 3.

Download (86KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences