Abstract
We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.
Similar content being viewed by others
References
S. B. Smith, L. Finzi, and C. Bustamante, Science 258, 1122 (1992).
G. V. Shivashankar, M. Feingold, O. Krichevsky, and A. Libchaber, Proc. Nat. Acad. Sci. USA 96, 7916 (1999).
C. G. Baumann, V. A. Bloomfeld, S. B. Smith, C. Bustamante, M. D. Wang, and S. M. Block, Biophys. J. 78, 1965 (2000).
D. G. Grier, Nature (London) 424, 810 (2003).
T. R. Strick, J. F. Allemand, D. Bensimon, and V. Croquette, Ann. Rev. Biophys. Biomol. Struct. 29, 523 (2000).
M. C. Williams and I. Rouzina, Curr. Opin. Struct. Biol. 12, 330 (2002).
L. P. Eisenhart, Riemannian Geometry (Princeton Univ. Press, Princeton, 1964).
M. P. DoCarmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976).
M. M. Postnikov, Lectures on Geometry, Semester III: Smooth Manifolds (Nauka, Moscow, 1987) [in Russian].
S. L. Zhang, X. J. Zuo, M. G. Xia, S. M. Zhao, and E. H. Zhang, Phys. Rev. E 70, 051902 (2004).
N. Thamwattana, J. A. McCoy, and J. M. Hill, Q. J. Mech. Appl. Math. 61, 431 (2008).
A. Feoli, V. V. Nesterenko, and G. Scarpetta, Nucl. Phys. B 705, 577 (2005).
V. V. Nesterenko, J. Math. Phys. 32, 3315 (1991).
V. V. Nesterenko, Phys. Lett. B 327, 50 (1994).
S. A. Gogilidze and Yu. S. Surovtsev, arXiv: hepth/9809191.
P. Ramon, Field Theory: A Modern Primer (Benjamin, London, 1981).
V. L. Golo and E. I. Kats, J. Exp. Theor. Phys. 84, 1003 (1997).
V. V. Nesterenko, A. Feoli, and G. Scarpetta, J. Math. Phys. 36, 5552 (1995).
M. V. Ostrogradsky, Mem. Acad. Imper. Sci. SPb. 4, 385 (1850).
D. M. Gitman and I. V. Tyutin, Quantizationof Fields with Constraints (Springer, Berlin, 1991).
V. V. Nesterenko, J. Phys. A: Math. Gen. 22, 1673 (1989).
V. V. Nesterenko, arXiv: hep-th/9309021v1.
A. J. Hanson, T. Regge, and C. Teitelboim, Constraints Hamiltonian Systems (Academia Nazionale dei Lincei, Rome, 1976).
J. Govaerts, Hamiltonian Quantisation and Constrained Dynamics (Leuven Univ. Press, Leuven, 1991).
G. M. Malacinski and D. Freifelder, Essentials of Molecular Biology (Jones and Bartlett, Boston, 1998).
B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walters, Molecular Biology of the Cell, 4th ed. (Garland Science, New York, 2002).
R. R. Sinden, DNA Structure and Function (Academic, New York, 1994).
J. D. Watson and F. H. C. Crick, Nature (London) 171, 737 (1953).
S. Neidle, Principles of Nucleic Acid Structure (Academic, New York, 2008).
A. H.-J. Wang, G. J. Quigley, F. J. Kolpak, J. L. Crawford, J. H. van Boom, G. van der Marel, and A. Rich, Nature (London) 282, 680 (1979).
A. Rich, A. Norheim, and A. H. J. Wang, Ann. Rev. Biochem. 53, 791 (1984).
M. A. Kastenholz, T. U. Schwartz, and P. H. Hunenberger, Biophys. J. 91, 2976 (2006).
F. M. Pohl and T. M. Jovin, J. Mol. Biol. 67, 375 (1972).
T. M. Jovin, D. M. Soumpasis, and L. P. McIntosh, Ann. Rev. Phys. Chem. 38, 521 (1987).
F. M. Pohl, Cold Spring Harbor Symp. Quant. Biol. 47, 113 (1983).
D. M. Soumpasis and T. M. Jovin, in Nucleic Acids and Molecular Biology, Ed. by F. Eckstein and D. M. J. Lilley (Springer, Berlin, 1987), p.85.
M. Behe and G. Felsenfeld, Proc. Nat. Acad. Sci. USA 78, 1619 (1981).
T. M. Jovin, L. P. McIntosh, D. J. Arndt-Jovin, D. A. Zarling, M. Robert-Nicoud, J. H. van de Sande, K. F. Jorgenson, and F. Eckstein, J. Biomol. Struct. Dynam. 1, 21 (1983).
J. B. Chaires and J. M. Sturtevant, Proc. Nat. Acad. Sci. USA 83, 5479 (1986).
R. F. Weaver, Molecular Biology, 2nd ed (McGraw-Hill, New York, 2004).
L. J. Peck and J. C. Wang, Proc. Nat. Acad. Sci. USA 80, 6206 (1983).
T. R. O’Connor, D. S. Kang, and R. D. Wells, J. Biol. Chem. 261, 13302 (1986).
J. M. Ferreira and R. D. Sheardy, Biophys. J. 91, 3383 (2006).
M. Yavari, Commun. Theor. Phys. 59, 125 (2013).
M. Yavari, Int. J. Mod. Phys. B 27, 1350121 (2013).
M. Yavari, Eur. Phys. J. Plus 129, 21 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Yavari, M. A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism. J. Exp. Theor. Phys. 122, 1104–1110 (2016). https://doi.org/10.1134/S1063776116050137
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776116050137