Abstract
The dynamics of local deformations in DNA is studied in a simple mathematical model based on the sine-Gordon equation with two additional terms, one accounting for the effects of dissipation and the other for the action of an external field. The energy method is used to derive equations for the velocity of the local deformation as a function of time. Conditions are determined when dissipation and continuous external action are balanced, whereby the deformation can move along the DNA at a constant velocity. The velocity vs. time plots are shown for homopolynucleotide chains at model parameter values: initial velocity v 0 = 189 m/s, dissipation coefficient \(\overline \beta ^{DNA} \) = 4.25·10−34 J s, and generalized external force F DNA0 = = 3.12·10−22 J. The correspondence of these value with available experimental data is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. W. Englander, N. R. Kallenbach, A. J. Heeger, et al., Proc. Natl. Acad. Sci. USA 77, 7222 (1980).
L. V. Yakushevich, Quart. Rev. Biophys. 26, 201 (1993).
L. V. Yakushevich, Nonlinear Physics of DNA (Wiley, Weinheim, 2004).
L. V. Yakushevich, L. A. Krasnobaeva, A. V. Shapovalov, and N. R. Quintero, Biofizika 50, 450 (2005).
L. V. Yakushevich, Stud. Biophys. 121, 201 (1987).
N. R. Quintero, A. Sanchez, and F. G. Mertens, Phys. Rev. E 62, R60 (2000).
S. Cuenda and A. Sanchez, Fluctuation and Noise Lett. 4, L–571 (2004).
A. Sanchez and A. R. Bishop, SIAM Rev. 40, 579 (1998).
D. MacLaughlin and A. Scott, Solitons in Action, Ed. by K. Longren and A. Scott (Mir, Moscow, 1981), pp. 210–268 [in Russian].
L. D. Landau and E. M. Livshits, Mechanics (Nauka, Moscow, 1965) [in Russian].
D. A. Koster, V. Croquette, C. Dekker, et al., Nature 434, 671 (2005).
P. Nelson, Biophysics 96, 14342 (1999).
J. M. Schurr, B. S. Fujimoto, P. Wu, and L. Song, Fluorescence studies of nucleic acids. Dynamics, rigidities and structures, Preprint (Dept. Chem. University of Washington, Seattle, 1991).
L. F. Liu and J. C. Wang, Proc. Natl. Acad. Sci. USA 84, 7024 (1987).
Author information
Authors and Affiliations
Additional information
Original Russian Text © L.V. Yakushevich, L.A. Krasnobaeva, 2007, published in Biofizika, 2007, Vol. 52, No. 2, pp. 237–243.
Rights and permissions
About this article
Cite this article
Yakushevich, L.V., Krasnobaeva, L.A. Influence of dissipation and external field on the dynamics of local deformations in DNA. BIOPHYSICS 52, 179–184 (2007). https://doi.org/10.1134/S0006350907020066
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0006350907020066