Abstract—Conformational mobility is one of the most important properties of the DNA molecule. A striking example of this mobility is provided by the formation of regions where the double helix is locally unwound. The resulting so-called open DNA states play an important role in transcription, replication, and denaturation. In a “nonrelativistic” approximation, the open DNA states are often modeled as quasiparticles, or kinks, with a certain mass (mk), velocity (uk), and rest energy (E0 k). When more than one open state forms in a DNA molecule, statistics can be considered for an ensemble of N DNA kinks. The statistical properties of the ensemble are still poorly understood. In this paper the properties were investigated on the basis of recent data on the dynamic characteristics of DNA kinks. It was assumed that the interaction between the kinks is weak, all kinks are identical and the number N of DNA kinks is fixed. The statistical sum Zk, the free energy Fk, the velocity distribution function ρ1(vk), the average energy εk, the heat capacity Cv, k, and the entropy Sk were calculated for the ensemble of N DNA kinks. Temperature dependence curves of these characteristics were obtained and compared for four homogeneous sequences (poly(A), poly(T), poly(G), and poly(C)) and the pBR322 plasmid sequence.
Similar content being viewed by others
REFERENCES
L. V. Yakushevich, Methods of Theoretical Physics in Studies on the Properties of Biopolymers (Pushchino, 1990) [in Russian].
M. Peyrard, Nonlinearity 17 (2), 1 (2004). https://doi.org/10.1088/0951-7715/17/2/R01
Nonlinear Excitations in Biomolecules, Ed. by M. Peyrard (Springer, Berlin, 1995).
A. Scott, Encyclopedia of Nonlinear Science (Frances and Taylor, New York, 2005).
M. Peyrard and A. R. Bishop, Phys. Rev. Lett. 62 (23), 2755 (1989).
T. Dauxois, M. Peyrard and A. R. Bishop, Phys. Rev. E 47 (1), 684 (1993). https://doi.org/10.1103/PhysRevE.47.684
S. W. Englander, N. R. Kallenbach, A. J. Heeger, et al., Proc. Natl. Acad. Sci. U. S. A. 77 (12), 7222 (1980).
A. A. Grinevich, A. A. Ryasik, and L. V. Yakushevich, Chaos Solit. Fract. 75, 62 (2015). https://doi.org/10.1016/j.chaos.2015.02.009
L. V. Yakushevich, J. Biol. Phys. 24 (2–4), 131 (1999). https://doi.org/10.1023/A:1005143428994
G. A. Wildes, M. Marty-Roda, S. Cuesta-Lopez, et al., J. Phys. Chem. B 122 (9), 2504 (2018). https://doi.org/10.1021/acs.jpcb.7b11608
A. S. Shigaev, O. A. Ponomarev, and V. D. Lakhno, Mat. Biol. Bioinform. 8 (2), 553 (2013). https://doi.org/10.17537/2018.13.t162
L. V. Yakushevich, Nonlinear Physics of DNA (RKhD, Moscow—Izhevsk, 2007) [in Russian].
L. V. Yakushevich, L. A. Krasnobaev, A. V. Shapovalov, and N. R. Quintero, Biophysics (Moscow) 50 (3), 404 (2005).
L. V. Yakushevich and L. A. Krasnobaeva, Biophysics (Moscow) 61 (2), 241 (2016). https://doi.org/10.1134/S0006350908010041
M. Cadoni, R. De Leo, S. Demelio, and G. Gaeta, J. Nonlinear Math. Phys. 17 (4), 557 (2010). https://doi.org/10.1142/S1402925110001069
S. Vedad and A. Heidari, Progr. Appl. Math. 4 (2), 1 (2012). https://doi.org/10.3968/j.pam.19252502820120402.1520
S. Zdravković, M. V. Satarić, and M. Daniel, Int. J. Modern Phys. B 27 (31), 1350184 (2013). https://doi.org/10.1142/S0217979213501841
A. Di Garbo, Biophys. Chem. 208 (1), 76 (2016). https://doi.org/10.1016/j.bpc.2015.09.006
L. Liu and Ch. Li, Adv. Math. Phys. 2018, 1–7 (2018). https://doi.org/10.1155/2018/4676281
L. V. Yakushevich and L. A. Krasnobaeva, Math. Biol. Bioinform. 12 (1), 1 (2017). https://doi.org/10.17537/2017.12.1
L. V. Yakushevich and L. A. Krasnobaeva, Biophysics (Moscow) 63 (1) 31 (2018). https://doi.org/10.1134/S0006350918010190
F. Bolivar, R. L. Rodriguez, P. J. Greene, et al., Gene 2 (2), 95 (1977).
G. F. Karavaev, Basic Principles of Statistical Physics (Tomsk. State Univ., Tomsk, 1993) [in Russian].
I. A. Kvasnikov, Thermodynamics and Staistical Physics (Editorial URSS, Moscow, 2010) [in Russian].
I. P. Bazarov, Thermodynamics (Vysshaya Shkola, Moscow, 1991) [in Russian].
A. V. Levanov and E. E. Antipenko, Determination of Thermodynamic Properties by Staistical Methods. Classic Perfect Gas (Moscow State Univ., Moscow, 2006) [in Russian].
A. Sommerfeld, Lectures in Theoretical Physics, Vol. 5: Thermodynamics and Statistical Mechanics (Academic, New York, 1964; Izd. Inostrannoi Literatury, Moscow, 1955).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflict of interest. This article does not contain any studies involving animals or human subjects performed by any of the authors.
Additional information
Translated by T. Tkacheva
Rights and permissions
About this article
Cite this article
Krasnobaeva, L.A., Yakushevich, L.V. The Dynamic and Statistical Properties of DNA Kinks. BIOPHYSICS 65, 22–27 (2020). https://doi.org/10.1134/S0006350920010091
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0006350920010091