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DNA molecule as an elastic Heisenberg chain

  • V. L. Golo
  • E. I. Kats
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Abstract

A DNA molecule is simulated by an anisotropic elastic fiber which defines the configuration of the molecule central line and is supplemented with a chain of quantum two-level systems imitating hydrogen bonds between two polynucleotide chains in the DNA double helix. The system Hamiltonian consists of Kirchhoff’s classical elastic energy and the energy of a quantum anisotropic chain of “spins” 1/2. The two-level systems and macroscopic vector variables which determine the conformation of the central line are coupled by a classical vector field q, which is introduced to take into account the existence of two polynucleotide strands. Averaging over fast (microscopic) variables yields an effective potential U(q). In the approximation of weak coupling between the systems, the spectrum of elementary excitations and effective potential U(q) have been calculated in explicit form. The relation between elementary excitations in the “magnetic” subsystem and so-called breathing modes [C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. Biol. 135, 391 (1980); G. Manning, Biopolymers 22, 689 (1983)] corresponding to low-frequency excitations in DNA molecules is discussed.

Keywords

Central Line Mandel Elastic Fiber Double Helix Polynucleotide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. Biol. 135, 391 (1980).Google Scholar
  2. 2.
    G. Manning, Biopolymers 22, 689 (1983).CrossRefGoogle Scholar
  3. 3.
    B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. Watson, Molecular Biology of the Cell, Garland Publishers, New York (1989).Google Scholar
  4. 4.
    A. V. Vologodskii, S. D. Leven, K. V. Klenin et al., Ann. Rev. Biophys. Biomol. Struct. 23, 609 (1992).Google Scholar
  5. 5.
    B. Fain, J. Rudnik, and S. Ostlund, E-prints Archive, Cond. Mat./96 10 126.Google Scholar
  6. 6.
    P. G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University, Ithaca (1979).Google Scholar
  7. 7.
    T. Dauxois, M. Peyrard, and A. R. Bishop, Phys. Rev. E 47, R44 (1993).CrossRefADSGoogle Scholar
  8. 8.
    T. Dauxois, M. Peyrard, and A. R. Bishop, Phys. Rev. E 47, 684 (1993).CrossRefADSGoogle Scholar
  9. 9.
    T. Dauxois and M. Peyrard, Phys. Rev. E 51, 4027 (1995).CrossRefADSGoogle Scholar
  10. 10.
    N. L. Marky and G. S. Manning, Biopolymers 31, 1543 (1991).CrossRefGoogle Scholar
  11. 11.
    V. L. Golo and E. I. Kats, JETP Lett. 62, 627 (1995).ADSGoogle Scholar
  12. 12.
    J. F. Marko and E. D. Siggia, Phys. Rev. E 52, 2912 (1995).ADSMathSciNetGoogle Scholar
  13. 13.
    V. L. Golo and E. I. Kats, JETP Lett. 60, 679 (1994).ADSGoogle Scholar
  14. 14.
    G. Kirchhoff, Mechanik, Tenbnir, Berlin (1897).Google Scholar
  15. 15.
    B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Contemporary Geometry [in Russian], Nauka, Moscow (1979).Google Scholar
  16. 16.
    L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon Press, New York (1980).Google Scholar
  17. 17.
    K. V. Klenin, H. D. Frank-Kamenetskii, and J. Langowski, Biophys. J. 68, 81 (1995).Google Scholar
  18. 18.
    G. Chirico and J. Langowski, Biopolymers 34, 415 (1994).CrossRefGoogle Scholar
  19. 19.
    Yu. A. Izyumov and Yu. N. Skryabin, Statistical Mechanics of Magnetically Ordered Systems [in Russian], Nauka, Moscow (1987).Google Scholar
  20. 20.
    H. Bethe, Z. Phys. 71, 205 (1931).ADSzbMATHGoogle Scholar
  21. 21.
    S. V. Tyablikov, Methods in the Quantum Theory of Magnetism [in Russian], Nauka, Moscow (1965).Google Scholar
  22. 22.
    V. M. Agranovich, Theory of Excitons [in Russian], Nauka, Moscow (1968).Google Scholar

Copyright information

© American Institute of Physics 1997

Authors and Affiliations

  • V. L. Golo
    • 1
  • E. I. Kats
    • 2
  1. 1.Department of Mechanics and MathematicsM. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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