Trajectories of solitons movement in the potential field of pPF1 plasmid with non-zero initial velocity

L. V. Yakushevich ; L. A. Krasnobaeva

Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024) no. 1, pp. 232-247.

Résumé

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.