Mathematical Modeling of Transcription Bubble Behavior in the pPF1 Plasmid and its Modified Versions: The Link between the Plasmid Energy Profile and the Direction of Transcription

In this study we used the kink solutions of the nonlinear sine-Gordon equation to apply methods of mathematical modeling to investigate the dynamics of the transcription bubble in the pPF1 plasmid. Based on the calculated energy profile for the pPF1 plasmid and its modified versions, it was shown that the minimum potential energy of the kink formation or transcription bubble nucleation corresponds to the region between the genes of the Egfp and mCherry proteins. The insertion of homogeneous sequences into the region between Egfp and mCherry showed that the kink is more likely to be activated in polyT or polyC compared to polyA or polyG, which indicates the dependence of nucleation of the transcription bubble on the molecular weight of base pairs. For insertions into the region between Egfp and mCherry of small fragments of the native sequence of Escherichia coli, the model identifies the DNA strands with the highest probability of nucleation of the transcription bubble and, accordingly, determines the direction (towards the Egfp or mCherry gene) of transcription, indicating a link between the direction of transcription and the energy profile of the plasmid.