DNA MOLECULE AS AN ELASTIC HEISENBERG CHAIN

A DNA molecule is simulated by an anisotropic elastic fiber which defi nes the configuration of the molecule central line and is supplemented with a chain of quantum two-level systems imitating hydrogen bonds be tween two polynucleotide chains in the DNA double helix. The system Ha miltonian consists of Kirchhoff's classical elastic energy and the ene rgy of a quantum anisotropic chain of ''spins'' 1/2. The two-level sys tems 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 effect ive potential U(q). In the approximation of weak coupling between the systems, the spectrum of elementary excitations and effective potentia l U(q) have been calculated in explicit form. The relation between ele mentary excitations in the ''magnetic'' subsystem and so-called breath ing modes [C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. B iol. 135, 391 (1980); G. Manning, Biopolymers 22, 689 (1983)] correspo nding to low-frequency excitations in DNA molecules is discussed. (C) 1997 American Institute of Physics.