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.

在这项研究中，我们使用非线性正弦-戈登方程的扭结解来应用数学建模方法来研究 pPF1 质粒中转录气泡的动力学。基于 pPF1 质粒及其修改版本的计算能量分布，表明扭结形成或转录气泡成核的最小势能对应于 Egfp 和 mCherry 蛋白基因之间的区域。将同源序列插入 Egfp 和 mCherry 之间的区域表明，与poly A 或poly C 相比，该扭结更有可能在poly T 或poly C 中被激活。G，表示转录泡的成核对碱基对分子量的依赖性。对于将大肠杆菌天然序列的小片段插入 Egfp 和 mCherry 之间的区域，该模型识别出转录气泡成核概率最高的 DNA 链，并相应地确定方向（朝向 Egfp 或 mCherry 基因) 的转录，表明转录方向和质粒的能量分布之间存在联系。