Plasmid pBR322 and nonlinear conformational distortions (kinks)

Plasmid pBR322 containing two coding regions in the matrix chain is a convenient object to study the DNA nonlinear dynamics that is known to play an important role in the processes of transcription, replication, denaturation and transmission of structural changes and information along the DNA molecule. The aim of the present work is to study by the methods of mathematical modeling the dynamics of local conformational distortions – kinks, in the plasmid pBR322. To calculate the dynamic characteristics of the kinks, we applied the method of McLaughlin–Scott, complemented by the block method. This permitted us to model kinks as quasi-particles moving in the potential field of the plasmid. We calculated the time dependences of the kink energy, velocity and coordinate. Calculations were made for three different values of the initial kink velocity: 150 m/s, 1650 m/s and 1879 m/s. The results obtained presented in the form of 3D trajectories and their projections, showed that the necessary condition for kink passing the entire plasmid is the enough large value of the initial kink velocity: $v\ge$ 1656.66 m/c which is, however, less than the sound velocity (1904.60 m/c).