Geodesic
Trajectories of solitons movement in the potential field of pPF1 plasmid with non-zero initial velocity
Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024) no. 1, pp. 232-247

Voir la notice de l'article provenant de la source Math-Net.Ru

Nonlinear conformational distortions, such as, for example, locally unwound regions of the DNA double helix, named open states, are considered in this work as solitons moving in the potential field of this molecule. It is believed that open states play an important role in the processes of transcription, replication, denaturation, as well as in the transmission of structural changes and information along the DNA molecule. This work examines the problem of the movement of kink- like solitons (kinks) in the potential field of the pPF1 plasmid, the sequence of which includes the genes of the fluorescent proteins Egfp and mCherry, separated by a small intermediate region. The results of calculations of energy profiles of the main and complementary sequences of the plasmid, as well as 2D and 3D trajectories of kinks with a non-zero initial velocity are presented. It has been shown that two types of kinks can be activated in the pPF1 plasmid, which can be considered as two types of quasiparticles that have their own energy, mass, velocity and move in the potential field of the plasmid. It was found that the lowest energy required to form these kinks is observed in the intermediate region located between the fluorescent protein genes. It was shown that the nature of the motion of kinks does not depend on the value of their initial velocity. It was shown that there are threshold values of the torsion field, upon reaching which the behavior of kinks changes sharply: from damped oscillations within the intermediate region to forward motion and penetration into neighboring regions. These values have been calculated. It turned out that for the first kink moving in the main sequence potential field, the threshold value is 4.95 $\times$ 10$^{-22}$ J, and for the second kink – 4.20 $\times$ 10$^{-22}$ J. 
@article{MBB_2024_19_1_a12,
     author = {L. V. Yakushevich and L. A. Krasnobaeva},
     title = {Trajectories of solitons movement in the potential field of {pPF1} plasmid with non-zero initial velocity},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {232--247},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2024_19_1_a12/}
}
TY  - JOUR
AU  - L. V. Yakushevich
AU  - L. A. Krasnobaeva
TI  - Trajectories of solitons movement in the potential field of pPF1 plasmid with non-zero initial velocity
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2024
SP  - 232
EP  - 247
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2024_19_1_a12/
LA  - ru
ID  - MBB_2024_19_1_a12
ER  - 
%0 Journal Article
%A L. V. Yakushevich
%A L. A. Krasnobaeva
%T Trajectories of solitons movement in the potential field of pPF1 plasmid with non-zero initial velocity
%J Matematičeskaâ biologiâ i bioinformatika
%D 2024
%P 232-247
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2024_19_1_a12/
%G ru
%F MBB_2024_19_1_a12
L. V. Yakushevich; L. A. Krasnobaeva. Trajectories of solitons movement in the potential field of pPF1 plasmid with non-zero initial velocity. Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024) no. 1, pp. 232-247. http://geodesic.mathdoc.fr/item/MBB_2024_19_1_a12/

[1] S. Zdravkovic, M. V. Sataric, M. Daniel, “Kink solitons in DNA”, International Journal of Modern Physics B, 27:31 (2013), 1350184 | DOI | Zbl | DOI | Zbl

[2] A. S. Shigaev, O. A. Ponomarev, V. D. Lakhno, “Teoreticheskie i eksperimentalnye issledovaniya otkrytykh sostoyanii DNK”, Matematicheskaya biologiya i bioinformatika, 8:2 (2013), 553–664 | DOI | MR | DOI | MR

[3] D. Clark, N. Pazdernik, Biotechnology, 2nd edn., Academic Cell, Amsterdam, 2015

[4] Y. He, C. Yan, J. Inouye C. Fang, R. Tjian, I. Ivanov, E. Nogalese, “Near-atomic resolution visualization of human transcription promoter opening”, Nature, 533 (2016), 359–365 | DOI | DOI

[5] L. J. Bailey, A. J. Doherty, “Mitochondrial DNA replication: a PrimPol perspective”, Biochem. Soc. Trans, 45 (2017), 513–529 | DOI | DOI

[6] F. Bleichert, M. R. Botchan, J. M. Berger, “Mechanisms for initiating cellular DNA replication”, Science, 355 (2017), 215–222 | DOI | DOI

[7] F. Sicard, N. Destainville, M. Manghi, “DNA denaturation bubbles:free-energy landscape and nucleation/closure rates”, J. Chem. Phys, 142 (2015), 903–910 | DOI | DOI

[8] C. Shi, F. Shang, M. Zhou, P. Zhang, Y. Wang, C. Ma, “Triggered isothermal PCR by denaturation bubble-mediated strand exchange amplification”, Chemical Communications, 52 (2016), 11551–11554 | DOI | DOI

[9] A. R. Singh, R. Granek, “Manipulation of double-stranded DNA melting by force”, Phys. Rev. E, 96 (2017), 032417–032422 | DOI | DOI

[10] D. Dwiputra, W. Hidayat, F. P. Zen, “Nonlinear dynamics of DNA bubble induced by site specific DNA-protein interaction”, J. Phys. Conf. Ser, 856 (2017), 012005–012009 | DOI | DOI

[11] S. W. Englander, N. R. Kallenbach, A. J. Heeger, J. A. Krumhansl, A. Litwin, “Nature of the open state in DNA structure”, Proc. Natl. Acad. Sci, 77 (1980), 7222–7226 | DOI | DOI

[12] A. Barone, F. Esposito, C. J. Magee, A. C. Scott, “Theory and Applications of the Sine Gordon Equation”, La Rivista del Nuovo Cimento, 1 (1971), 227–267 | DOI | DOI

[13] S. Yomosa, “Soliton excitations in deoxyribonucleic acid (DNA) double helices”, Phys. Rev. A, 27 (1983), 2120–2125 | DOI | MR | DOI | MR

[14] J. A. Krumhansl, D. M. Alexander, “Nonlinear dynamics and conformational excitations in biomolecular materials”, Structure and dynamics: nucleic acids and proteins, eds. Clementi E., Sarma R.H., Adenine Press, New York, 1983, 61–80

[15] S. Homma, S. Takeno, “A coupled base-rotator model for structure and dynamics of DNA”, Progress of Theoretical Physics, 72 (1984), 679–693 | DOI | MR | Zbl | DOI | MR | Zbl

[16] V. K. Fedyanin, I. Gochev, V. Lisy, “Nonlinear dynamics of bases in continual model of DNA double helices”, Stud. Biophys, 116 (1986), 59–64

[17] L. V. Yakushevich, Nonlinear physics of DNA, Wiley, Weinheim, 2004

[18] G. Gaeta, L. Venier, “Solitary waves in twistopening models of DNA dynamics”, Physical Review E, 78 (2008), 011901 | DOI | MR | DOI | MR

[19] M. Cadoni, R. De Leo, S. Demelio, “Soliton propagation in homogeneous and inhomogeneous models for DNA torsion dynamics”, Journal of Nonlinear Mathematical Physics, 18 (2011), 287–319 | DOI | MR | Zbl | DOI | MR | Zbl

[20] D. Chevizovich, D. Michieletto, A. Mvogo, F. Zakiryanov, S. Zdravkovic, “A review on nonlinear DNA physics”, Royal Society Open Science, 7 (2020), 200774 | DOI | DOI

[21] S. Zdravkovic, D. Chevizovich, Nonlinear Dynamics of Nanobiophysics, Springer Nature, Singapore, 2022, 384 pp. | DOI | MR | Zbl | DOI | MR | Zbl

[22] L. V. Yakushevich, L. A. Krasnobaeva, “Vliyanie dissipatsii i vneshnego polya na dinamiku lokalnykh konformatsionnykh vozmuschenii v DNK”, Biofizika, 52:2 (2007), 237–243

[23] A. A. Grinevich, A. A. Ryasik, L. V. Yakushevich, “Trajectories of DNA bubbles”, Chaos, Solitons Fractals, 75 (2015), 62–75 | DOI | MR | Zbl | DOI | MR | Zbl

[24] D. W. McLaughlin, A. C. Scott, “Perturbation analysis of fluxon dynamics”, Physical Review A, 18 (1978), 1652–1671 | DOI | DOI

[25] L. V. Yakushevich, L. A. Krasnobaeva, “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, 13 (2021), 315–338 | DOI | DOI

[26] L. A. Krasnobaeva, L. V. Yakushevich, “DNA kinks behavior in the potential pit-trap”, AIMS Biophysics, 9:2 (2022), 130–146 | DOI | DOI

[27] L. V. Yakushevich, L. A. Krasnobaeva, “Plasmid pBR322 and nonlinear conformational distortions (kinks)”, Mathematical Biology and Bioinformatics, 14:1 (2019), 327–339 | DOI | DOI

[28] I. S. Masulis, Z. Sh. Babaeva, S. V. Chernyshov, O. N. Ozoline, “Visualizing the activity of Escherichia coli divergent promoters and probing their dependence on superhelical density using dual-colour fluorescent reporter vector”, Scientific Reports, 5 (2015), 11449 | DOI | DOI

[29] The pET-28b sequence and map, SnapGene (accessed 27.06.2024) https://www.snapgene.com/plasmids/pet_and_duet_vectors_(novagen)/pET-28b(

[30] The mCherry sequence and map, SnapGene (accessed 27.06.2024) https://www.snapgene.com/resources/plasmid-files/?set=fluorescent_protein_genes_and_plasmids&plasmid=mCherry

[31] Grinevich A.A., Masulis I.S., Yakushevich L.V., “Matematicheskoe modelirovanie povedeniya transkriptsionnogo puzyrya v plazmide pPF1 i ee modifikatsiyakh. Svyaz mezhdu energeticheskim profilem plazmidy i napravleniem transkriptsii”, Biofizika, 66 (2021), 248-258 | DOI | DOI

[32] Yakushevich L.V., “On the mechanical analogue of DNA”, Journal of Biological Physics, 43 (2017), 113-125 | DOI | DOI

[33] Yakushevich L.V., Savin A.V., Manevitch L.I., “Nonlinear dynamics of topological solitons in DNA”, Physical Review E, 66 (2002), 016614 | DOI | MR | DOI | MR