Features of the Movement of the Nonlinear Solitary Conformational Waves in Plasmid PTTQ18

Local distortions of the DNA structure that are known as DNA bubbles are modeled by nonlinear solitary conformational waves moving along the polynucleotide chains. The waves are modeled with the help of the sine-Gordon equation modified by adding two terms which more accurately take into account heterogeneous nature of the DNA sequence. The model equation is solved numerically. Topological soliton solutions having the form of kinks are found and the trajectories of the kinks in the plane (z, t) are calculated.

The approach is applied to study the features of the bubbles movement in the sequence of plasmid pTTQ18. For the purpose, we calculate approximately the energetic profile of the sequence, which consists of wells and barriers, and analyze the results in terms of the bubble movement in the potential field defined by the energy profile. We found that 1) the bubbles can overcome or be reflected from the energy barriers, 2) the ability to overcome the barriers depends on the initial velocity of the bubble.

The results on the energy profile are in good correlation with the properties of the main functional regions of the sequence (promoters, terminators and coding regions). Indeed, the promoter region which is known as the most preferable region for bubble activation has the minimal energy barrier according to our calculations. In opposite, the terminator region having the maximal energy barrier, is known as the region, where the bubble movement stops  with large probability.

In general, the obtained results show that there is the dependence of the bubble trajectories on the arrangement of the main functional regions. This can be interpreted as an evidence of the existence of the relation between DNA dynamics and functioning.