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...

The creation of mechanical analogues of biological systems is known as a useful instrument that helps to understand better the dynamical mechanisms of the functioning of living organisms. Mechanical analogues of biomolecules are usually constructed for imitation of their internal mobility, which is one of the most important properties of the molecules. Among the different types of internal motions, angular oscillations of nitrous bases are of special interest because they make a substantial contribution to the base pairs opening that in turn is an important element of the process of the DNA–protein recognition. In this paper, we investigate the possibility to construct a mechanical analogue for imitation of angular oscillations of nitrous bases in inhomogeneous DNA. It is shown that the analogue has the form of a mechanical chain of non-identical pendulums that oscillate in the gravitational field of the Earth and coupled by identical springs. The masses and lengths of pendulums, as well as the distances between neighboring pendulums and the rigidity of springs are calculated. To illustrate the approach, we present the result of construction of the mechanical analogue of the fragment of the sequence of bacteriophage T7D.

Background: Although the role of dynamic factors in DNA function still remains unclear, research in this direction is a rapidly developing area of molecular biology. In this work, the genetic constructions appY_red and appY_green, based on the plasmid pPF1 and containing a fragment of Escherichia coli (E. coli) DNA with predicted promoter-like regions, are considered complex dynamic systems in which local sites of double helix unwinding, called open states, can arise and propagate. The purpose of the article is to show the existence of a connection between the dynamics of open states and the functioning of predicted promoters. Methods: We experimentally verified the functionality of the predicted promoters using a reporter vector. Using a reverse transcription reaction, transcription start sites were identified indicating the presence of two divergent promoters, one on each strand. In mathematical studies, a dynamic model was used that described open states as one-soliton solutions (kinks) of a system of nonlinear partial differential equations, and the influence of the torque Mτ on the dynamics of kinks was taken into account. Results: Fluorescence analysis of colonies of E. coli cells transformed with plasmid constructions showed that one of the two promoters is stronger than the other and that the strength of the promoters depends on the orientation of the fragment under study in the plasmid. On the other hand, using mathematical modeling, the energy profiles of genetic constructions were calculated and the kink trajectories were constructed. In addition, by studying the effect of torsion moment in model studies, we found threshold torque values at which the behavior of kinks changes dramatically: from oscillatory to translational motion. The minimum values of torsion moment required to initiate the transcription process were also assessed. Conclusions: A comparative analysis of the results of experimental data and model calculations showed a good correlation between the preferred starting points and the direction of transcription, which in turn confirmed the existence of a relationship between the dynamics of open states and the functioning of promoters.

For better understanding the role of dynamic factors in the DNA functioning, it is important to study the internal mobility of DNA and, in particular, the movement of nonlinear conformational distortions -kinks along the DNA chains. In this work, we study the behavior of the kinks in the pPF1 plasmid containing two genes of fluorescent proteins (EGFP and mCherry). To simulate the movement, two coupled nonlinear sine-Gordon equations that describe the angular oscillations of nitrogenous bases in the main and complementary chains and take into account the effects of dissipation and the action of a constant torsion field. To solve the equations, approximate methods such as the quasi-homogeneous approximation, the mean field method, and the block method, were used. The obtained solutions indicate that two types of kinks moving along the double strand can be formed in any part of the plasmid. The profiles of the potential fields in which these kinks are moving are calculated. The results of the calculations show that the lowest energy required for the kink formation, corresponds to the region located between the genes of green and red proteins (EGFP and mCherry). It is shown that it is in this region a pit trap is located for both kinks. Trajectories of the kinks in the pit-trap and nearby are constructed. It is shown that there are threshold values of the torsion field, upon reaching which the kinks behavior changes dramatically: there is a transition from cyclic motion inside the pit-trap to translational motion and exit from the potential pit-trap.