Trajectories of the DNA kinks in the sequences containing CDS regions

Coding regions (CDS) being an integral part of any gene sequence, play an important role in the process of transcription. One of the tasks associated with the CDS regions, consists in the modeling of the passage of transcription bubbles named also open states or DNA kinks through the coding regions. In this paper, we present a simple and convenient approach to the modeling of the passage. It includes the calculation of the energy profile of the sequence and reducing the initial task to the modeling of the movement of a quasi particle in the field with this energy profile. To illustrate the method, we present the results of the calculations of the trajectories of the DNA kinks moving in the sequence of gene coding interferon alpha 17 (IFNA17) that consists of the three regions: the coding region and the two regions with unknown functional properties. To analyze the kink dynamics, we apply approximation where the DNA parameters are being averaged separately over each of the three regions. In the absences of dissipation, the total kink energy is constant. At the same time the kink velocity is constant only inside each of the regions. In the presence of dissipation, the total kink energy decreases. It is shown that the greater the total initial energy of the kink, the faster the energy decrease. It is suggested that the proposed approach could be useful in finding the ways to govern the movement of transcription bubbles at the first stage of the process of transcription

Trajectories of the DNA kinks in the sequences containing CDS regions

Coding regions (CDS) being an integral part of any gene sequence, play an important role in the process of transcription. One of the tasks associated with the CDS regions, consists in the modeling of the passage of transcription bubbles named also open states or DNA kinks through the coding regions. In this paper, we present a simple and convenient approach to the modeling of the passage. It includes the calculation of the energy profile of the sequence and reducing the initial task to the modeling of the movement of a quasi particle in the field with this energy profile. To illustrate the method, we present the results of the calculations of the trajectories of the DNA kinks moving in the sequence of gene coding interferon alpha 17 (IFNA17) that consists of the three regions: the coding region and the two regions with unknown functional properties. To analyze the kink dynamics, we apply approximation where the DNA parameters are being averaged separately over each of the three regions. In the absences of dissipation, the total kink energy is constant. At the same time the kink velocity is constant only inside each of the regions. In the presence of dissipation, the total kink energy decreases. It is shown that the greater the total initial energy of the kink, the faster the energy decrease. It is suggested that the proposed approach could be useful in finding the ways to govern the movement of transcription bubbles at the first stage of the process of transcription

DNA kinks behavior in the potential pit-trap

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

Double energy profile of pBR322 plasmid

A small circular DNA - plasmid pBR322, is considered as a complex dynamic system where nonlinear conformational perturbations which are often named open states or kinks, can arise and propagate. To describe the internal dynamics of the plasmid we use mathematical model consisting of two coupled sine-Gordon equations that in the average field approximation are transformed to two sine-Gordon independent equations with renormalized coefficients. The first equation describes angular oscillations of nitrous bases of the main chain. The second equation describes angular oscillations of nitrous bases in the complementary chain. As a result, two types of kink-like solutions have been obtained. One type kinks were the solutions of the first equation, and the other kinks were the solutions of the second equation. We calculated the main characteristics of the kink motion, including the time dependences of the kink velocity, coordinates, and total energy. These calculations were performed at the initial velocity equal to 1881 m/s which was chosen to avoid reflections from energy barriers corresponding to CDS-1 and CDS-2. The movement of the kinks was investigated by the method of the double energy profile. The maximum complete set of the DNA dynamic parameters was used to calculate the double profile. To calculate the velocity, energy and trajectory of the kinks, the block method was used. The results obtained made it possible to explain in which region of the plasmid the formation of a transcription bubble is most likely, as well to understand in which direction the bubble will move and the transcription process will go

Tautomeric mutation: A quantum spin modelling

A quantum spin model representing tautomeric mutation is proposed for any DNA molecule. Based on this model, the quantum mechanical calculations for mutational rate and complementarity restoring repair rate in the replication processes are carried out. A possible application to a real biological system is discussed.Comment: 7 pages (no figures

Rotational dynamics of bases in the gene coding interferon alpha 17 (IFNA17)

In the present work, rotational oscillations of nitrogenous bases in the DNA with the sequence of the gene coding interferon alpha 17 (IFNA17), are investigated. As a mathematical model simulating oscillations of the bases, we use a system of two coupled nonlinear partial differential equations that takes into account effects of dissipation, action of external fields and dependence of the equation coefficients on the sequence of bases. We apply the methods of the theory of oscillations to solve the equations in the linear approach and to construct the dispersive curves determining the dependence of the frequency of the plane waves (ω) on the wave vector (q). In the nonlinear case, the solutions in the form of kink are considered, and the main characteristics of the kink: the rest energy (E0), the rest mass (m0), the size (d) and sound velocity (C0), are calculated. With the help of the energetic method, the kink velocity (υ), the path (S), and the lifetime (τ) are also obtained

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

The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA

Ensemble of DNA Kinks

The DNA open states, which are locally unwound regions of the double helix within which hydrogen bonds between complementary nitrous bases are broken, are often modeled as quasiparticles – DNA kinks. Most of the works on the DNA kinks are devoted to the studies of their dynamic properties, as well as their role in the functioning of the molecule. However, if not one but N open states are formed in the DNA molecule it is reasonable to consider the problem of the statistics of the ensemble of N DNA kinks. The statistical properties of such an ensemble are still poorly understood. In the present work, we study these properties applying new data on the dynamic characteristics of DNA kinks