Double energy profile of pBR322 plasmid

Abstract

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.