DNA molecule as an elastic Heisenberg chain |
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Authors: | V L Golo E I Kats |
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Institution: | (1) Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, 119899 Moscow, Russia;(2) L. D. Landau Institute of Theoretical Physics, Russian Academy of Sciences, 117940 Moscow, Russia |
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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.
Zh. éksp. Teor. Fiz. 111, 1833–1844 (May 1997) |
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