Abstract
The motion of a transcription bubble under constant torque is investigated. The motion of the bubble was modeled by a modified sine-Gordon equation. Numerical solutions of this equation (kinks) were found. Trajectories of the kink motion in homogeneous and inhomogeneous sequences were calculated for different model values of the torque M τ and the initial velocity v 0. It was shown that a change in the torsion moment M τ has a significant impact on the character of the kink trajectory. At the same time, a change in the initial kink velocity v 0 in a rather wide range of values does not affect the character of the kink trajectory.
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References
S. Forth, M. Y. Sheinin, J. Inman, and M. D. Wang, Annu. Rev. Biophys. 42, 583 (2013).
A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. A 68, 033802 (2003).
A. La Porta and M. D. Wang, Phys. Rev. Lett. 92, 190801 (2004).
D. Klaue and R. Seidel, Phys. Rev. Lett. 102, 028302 (2009).
Y. Harada, O. Ohara, A. Takatsuki, et al., Nature 409 (6816), 113 (2001).
J. Lipfert, J. W. J. Kerssemakers, T. Jager, and N. H. Dekker, Nat. Methods 7 (12), 977 (2010).
L. V. Yakushevich, Nonlinear Physics of DNA (RKhD, Moscow, 2007) [in Russian].
S. W. Englander, N. R. Kallenbach, A. J. Heeger, et al., Proc. Natl. Acad. Sci. USA 77 (12), 7222 (1980).
S. Cuenda and A. Sánchez, Phys. Rev. E 70, 051903 (2004).
B. Barbi, C. Place, V. Popkov, and M. Salerno, Phys. Rev. E 70, 041901 (2004).
G. Gaeta, Phys. Rev. E 74, 021921 (2006).
J. A. González, S. Cuenda, and A. Sánchez, Phys. Rev. E 75, 036611 (2007).
G. Gaeta and L. Venier, Phys. Rev. E 78, 011901 (2008).
M. Cadoni, R. De Leo, S. Demelio, and G. Gaeta, J. Nonlin. Math. Phys. 17 (4), 557 (2010).
N. Theodorakopoulos, Phys. Rev. E 82, 021905 (2010).
S. Cuenda, N. R. Quintero, and A. Sánchez, Discrete Contin. Dyn. Syst. Ser. S 4 (5), 1047 (2011).
G. Derks and G. Gaeta, Physica D 240 (22), 1805 (2011).
N. Theodorakopoulos and M. Peyrard, Phys. Rev. Lett. 108, 078104 (2012).
L. V. Yakushevich and L. A. Krasnobaeva, Biophysics (Moscow) 52 (2), 179 (2007).
A. A. Grinevich and L. V. Yakushevich, Math. Biol. Bioinform. 10 (1), 164 (2015).
A. A. Grinevich, A. A. Ryasik, and L. V. Yakushevich, Chaos Solitons Fractals 75, 62 (2015).
L. V. Yakushevich, L. A. Krasnobaeva, A. V. Shapovalov, and N. R. Quintero, Biophysics (Moscow) 50 (3), 404 (2005).
D. W. McLaughlin and A. C. Scott, Phys. Rev. A 18 (4), 1652 (1978).
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Original Russian Text © A.A. Grinevich, L.V. Yakushevich, 2016, published in Biofizika, 2016, Vol. 61, No. 4, pp. 638–646.
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Grinevich, A.A., Yakushevich, L.V. On the modeling of the motion of a transcription bubble under constant torque. BIOPHYSICS 61, 539–546 (2016). https://doi.org/10.1134/S0006350916040126
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DOI: https://doi.org/10.1134/S0006350916040126