National Research Tomsk State University
Tomsk, Tomsk, Russian Federation
Pushchino, Moscow, Russian Federation
In this work, mathematical modeling methods are used to study the features of the dynamics of the nonlinear conformational perturbations, kinks, in the pPF1 plasmid. The motion of kinks is considered as the motion of quasiparticles in the potential field of the plasmid. The behavior of such quasiparticles is largely determined by the type and nature of this field. To simulate the movement of the kink along the pPF1 plasmid, the McLaughlin-Scott equation was used. Using the quasi-homogeneous approximation and the block method, the energy profile of the potential field of the pPF1 plasmid was calculated and 2D kink trajectories were constructed in the region located between the genes of the Egfp and mCherry fluorescent proteins, taking into account the effects of dissipation and exposure to a constant torsion field. It was shown that there are threshold values of the torsion field, below and above which the behavior of the kink changes significantly: there is a transition from the cyclic motion of the kink inside the region located between the genes of the fluorescent proteins Egfp and mCherry to the translational motion and exit from this region. Threshold values have been estimated. It was shown that they depend on the nature of the energy profile near the region located between the genes of the fluorescent proteins Egfp and mCherry.
DNA kinks, plasmid pPF1, energy profile, 2D trajectory, torsion moment
1. Masulis I.S., Babaeva Z.Sh., Chernyshov S.V., Ozoline O.N. Visualizing the activity of Escherichia coli divergent promoters and probing their dependence on superhelical density using dual-colour fluorescent reporter vector. Scientific Reports, 2015, vol. 5, pp. 11449, doi:https://doi.org/10.1038/srep11449.
2. Zdravkovic S., Satarić M.V., Daniel M. Kink solitons in DNA. International Journal of Modern Physics B., 2013, vol. 31, pp. 1350184.
3. Englander S.W., Kallenbach N.R., Heeger A.J., Krumhansl J.A., Litwin A. Nature of the open state in DNA structure. Proc. Natl. Acad. Sci., 1980, vol. 77, pp. 7222-7226.
4. Clark D., Pazdernik N. Biotechnology, 2nd Edition. Academic Cell, 2015.
5. Zuo Y., Steitz T.A. A structure-based kinetic model of transcription. Transcription, 2017, vol. 8, pp. 1-8, doi:https://doi.org/10.1080/21541264.2016.1234821.
6. He Y., Yan C., Fang J., Inouye C., Tjian R., Ivanov I., Nogales E. Near-atomic resolution visualization of human transcription promoter opening. Nature, 2016, vol. 533, pp. 359-365, doi:https://doi.org/10.1038/nature17970.
7. Bailey L.J., Doherty A.J. Mitochondrial DNA replication: a PrimPol perspective. Biochem Soc Trans, 2017, vol. 45, pp. 513-529, doi:https://doi.org/10.1042/BST20160162.
8. Bleichert F., Botchan M.R., Berger J.M. Mechanisms for initiating cellular DNA replication. Science, 2017, vol. 355, pp. 215-222, doi:https://doi.org/10.1126/science.aah6317.
9. Sicard F., Destainville N., Manghi M. DNA denaturation bubbles: Free-energy landscape and nucleation/closure rates. J. of Chemical Physics, 2015, vol. 142, pp. 903-910, doi:https://doi.org/10.1063/1.4905668.
10. Shi C., Shang F., Zhou M., Zhang P., Wang Y., Ma C. Triggered isothermal PCR by denaturation bubble-mediated strand exchange amplification. Chem. Commun., 2016, vol. 52, pp. 11551-11554, doi:https://doi.org/10.1039/C6CC05906F.
11. Singh A.R., Granek R. Manipulation of double-stranded DNA melting by force. Phys. Rev. E, 2017, vol. 96, pp. 032417-032422, doi:https://doi.org/10.1103/PhysRevE.96.032417.
12. Dwiputra D., Hidayat W., Zen F.P. Nonlinear dynamics of DNA bubble induced by site specific DNA-protein interaction. J. Phys.: Conf. Ser., 2017, vol. 856, pp. 012005-012009, doi:https://doi.org/10.1088/1742-6596/856/1/011001.
13. Yakushevich L.V., Krasnobaeva L.A. Double energy profile of pBR322 plasmid. AIMS Biophysics, 2021, vol. 8, no. 2, pp. 221-232, doi:https://doi.org/10.3934/biophy.2021016.
14. Yakushevich L.V., Krasnobaeva L.A. Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics. Biophysical Reviews, 2021, pp. 1-24, doi:https://doi.org/10.1007/s12551-021-00801-0.
15. Grinevich A.A., Masulis I.S., Yakushevich L.V. Mathematical modeling of transcription bubble behavior in the pPF1 plasmid and its modified versions: the link between the plasmid energy profile and the direction of transcription. Biophysics, 2021, vol. 66, no. 2, pp. 248-258, doi:https://doi.org/10.31857/S0006302921020058. (In Russ.)
16. McLaughlin D.W., Scott A.C. Perturbation analysis of fluxon dynamics. Phys Rev A, 1978, vol. 18, pp. 1652, doi:https://doi.org/10.1103/PhysRevA.18.1652.
17. Yakushevich L.V., Krasnobaeva L.A. Effects of dissipation and external fields on the dynamics of conformational distortions in DNA. Biophysics, 2007, vol. 52, pp. 237-243. (In Russ.)
18. Yakushevich L.V., Krasnobaeva L.A. A new approach to studies of nonlinear dynamics of kinks activated in inhomogeneous polynucleotide chains. Int. J. Nonl. Mech., 2008, vol. 43, pp. 1074-1081, doi: 10.1016/ j.ijnonlinmec.2008.05.00.b0100.
