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Counterion vibrations in the DNA low-frequency spectra

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Abstract.

The vibrations of univalent metal cations with respect to phosphate groups of the DNA backbone are described using the four-mass model approach (S.N. Volkov, S.N. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991)) extended in this paper. The force constant of the counterion-phosphate interaction is determined by considering the DNA with counterions as a lattice of ion crystal. For such ion-phosphate lattice the Madelung constant and the dielectric constant are estimated. The obtained value of the Madelung constant is lower than for the NaCl crystal, and its value is about 1.3. The dielectric constant is within 2.3-2.7 depending on the counterion type and form of the double helix. The calculations of the low-frequency spectra show that for the DNA with metal cations Na+ , K+ , Rb+ and Cs+ the frequency of ion-phosphate vibrations decreases from 174 to 96cm^-1 as the counterion mass increases. The obtained frequencies agree well with the vibrational spectra of polynucleotides in a dry state which prove our suggestion about the existence of the ion-phosphate lattice around the DNA double helix. The amplitudes of conformational vibrations for DNA in B -form are calculated as well. The results demonstrate that light counterions ( Na+ do not disturb the internal dynamics of the DNA. However, heavy counterions ( Cs+ have effect on the internal vibrations of the DNA structural elements.

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References

  1. W. Saenger, Principles of Nucleic Acid Structure (Springer, New York, 1984).

  2. Yu.P. Blagoi, V.L. Galkin, G.O. Gladchenko, The Complexes of Nucleic Acids and Metals in the Solutions (Naukova Dumka, Kiev, 1991).

  3. Y. Levin, Rep. Prog. Phys. 65, 1577 (2002).

    Article  ADS  Google Scholar 

  4. A.A. Kornyshev, D.J. Lee, S. Leikin, A. Wynveen, Rev. Mod. Phys. 79, 943 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  5. V.I. Ivanov, Biopolymers 12, 89 (1973).

    Article  Google Scholar 

  6. C.G. Baumann, Proc. Natl. Acad. Sci. U.S.A. 94, 6185 (1997).

    Article  ADS  Google Scholar 

  7. L.D. Williams, L.J. Maher, Annu. Rev. Biophys. Biomol. Struct. 29, 497 (2000).

    Article  Google Scholar 

  8. I.Ya. Skuratovskii, L.I. Volkova, K. Kapitonova, V.N. Bartenev, J. Mol. Biol. 134, 369 (1979).

    Article  Google Scholar 

  9. V. Tereshko, G. Minasov, M. Egli, Nucl. Acids Res. 29, 1208 (2001).

    Article  Google Scholar 

  10. V. Tereshko, G. Minasov, M. Egli, J. Am. Chem. Soc. 121, 3590 (1999).

    Article  Google Scholar 

  11. R. Das, T.T. Mills, L.W. Kwok, Phys. Rev. Lett. 90, 188103 (2003).

    Article  ADS  Google Scholar 

  12. G.S. Manning, Q. Rev. Biophys. 11, 179 (1978).

    Article  Google Scholar 

  13. M.D. Frank-Kamenetskii, V.V. Anshelevich, A.V. Lukashin, Sov. Phys. Usp. 151, 595 (1987).

    Google Scholar 

  14. P. Varnai, K. Zakrzewska, Nucl. Acids Res. 32, 4269 (2004).

    Article  Google Scholar 

  15. S.Y. Ponomarev, K.M. Thayer, D.L. Beveridge, Proc. Natl. Acad. Sci. U.S.A. 101, 14771 (2004).

    Article  ADS  Google Scholar 

  16. C. Kittel, Introduction to Solid State Physics (John Wiley and Sons, Inc., New York, 1954).

  17. L. Young, V.V. Prabhu, E.W. Prohofsky, Phys. Rev. A 39, 3173 (1989).

    Article  ADS  Google Scholar 

  18. S.N. Volkov, A.M. Kosevich, Mol. Biol. 21, 797 (1987) (Moscow).

    Google Scholar 

  19. S.N. Volkov, A.M. Kosevich, G.E. Weinreb, Biopolimery i Kletka 5, 32 (1989) (Kiev).

    Google Scholar 

  20. S.N. Volkov, A.M. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991).

    Google Scholar 

  21. A.M. Kosevich, S.N. Volkov, in Nonlinear Excitations in Biomolecules, edited by M. Peyrard (Springer, 1995).

  22. S. Cocco, R. Monasson, J. Chem. Phys. 112, 10017 (2000).

    Article  ADS  Google Scholar 

  23. A. Wittlin, Phys. Rev. A 34, 493 (1986).

    Article  ADS  Google Scholar 

  24. J.W. Powell, Phys. Rev. A 35, 3929 (1987).

    Article  ADS  Google Scholar 

  25. T. Weidlich, S.M. Lindsay, A. Rupprecht, Phys. Rev. Lett. 61, 1674 (1988).

    Article  ADS  Google Scholar 

  26. Om P. Lamba, A.H.-J. Wang, G.J. Thomas jr., Biopolymers 28, 667 (1989).

    Article  Google Scholar 

  27. H. Urabe, J. Chem. Phys. 92, 768 (1990).

    Article  ADS  Google Scholar 

  28. T. Weidlich, J. Biomol. Struct. Dyn. 8, 139 (1990).

    Google Scholar 

  29. T. Weidlich, Biopolymers 30, 477 (1990).

    Article  Google Scholar 

  30. L. Genzel, T.P. Martin, Surf. Sci. 34, 33 (1973).

    Article  ADS  Google Scholar 

  31. S.M. Perepelytsya, S.N. Volkov, Ukr. J. Phys. 49, 1072 (2004) arXiv: q-bio.BM/0412022.

    Google Scholar 

  32. B.E Hingerty, Biopolymers 24, 427 (1985).

    Article  Google Scholar 

  33. J. Ramstein, R. Lavery, Proc. Natl. Acad. Sci. U.S.A. 85, 7231 (1988).

    Article  ADS  Google Scholar 

  34. A.K. Mazur, L. Jernigan, Biopolymers 31, 1615 (1991).

    Article  Google Scholar 

  35. T. Schlick, Molecular Modeling and Simulation (Springer, New York, 2002).

  36. S. Arnott, D.W.I. Hukins, Biochem. Biophys. Res. Commun. 47, 1504 (1972).

    Article  Google Scholar 

  37. B. Schnider, M. Kabelac, J. Am. Chem. Soc. 120, 161 (1998).

    Article  Google Scholar 

  38. M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954).

  39. V.Ya. Maleev, M.A. Semenov, A.I. Gasan, V.A. Kashpur, Biophysics 38, 768 (1993) (Moscow).

    Google Scholar 

  40. H. Urabe, Biophys. J. 74, 1533 (1998).

    ADS  Google Scholar 

  41. T. Weidlich, S.M. Lidsay, A. Rupprecht, Biopolymers 26, 439 (1987).

    Article  Google Scholar 

  42. P.J. Adams, M.L. VanSteenberg, S.A. Lee, A. Rupprecht, J. Biomol. Struct. Dyn. 11, 1277 (1994).

    Google Scholar 

  43. N. Lavalle, S.A. Lee, A. Rupprecht, Biopolymers 30, 877 (1990).

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Taras Shevchenko National University, 64 Volodymyrska St., 01033, Kiev, Ukraine

    S. M. Perepelytsya

  2. Bogolyubov Institute for Theoretical Physics, NAS of Ukraine, 14-b Metrologichna St., 03680, Kiev, Ukraine

    S. N. Volkov

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  1. S. M. Perepelytsya
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  2. S. N. Volkov
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Perepelytsya, S.M., Volkov, S.N. Counterion vibrations in the DNA low-frequency spectra. Eur. Phys. J. E 24, 261–269 (2007). https://doi.org/10.1140/epje/i2007-10236-x

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