Trajectories of DNA bubbles

The DNA molecule is considered as a complex dynamic system where nonlinear conformational waves can be activated and move along the polynucleotide chains. Local nonlinear distortions of the DNA structure named bubbles are studied with the help of the sine-Gordon equation modified by adding two terms that more accurately take into account heterogeneous nature of the DNA sequence. The model equation is solved numerically. Topological soliton solutions ϕ(z,t) having the form of kinks, are found. To obtain the trajectories of the bubbles we project the derivative of the function ϕ(z,t) on the plane (z,t). The approach is applied to artificial sequence consisting of n homogeneous regions separated by (n-1) boundaries, and to the sequence of plasmid pTTQ18. The obtained dependence of the bubble trajectories on the arrangement of the main functional regions (promoters, terminators and coding regions) is interpreted as an evidence of the existence of the relation between DNA dynamics and functioning.