The stochastic dynamics of zipping/unzipping transition of a DNA hairpin is theoretically investigated within the framework of generalized Langevin equation in a complex cellular environment. Analytical expressions of the distributions of transition path and first passage times are derived. The results reveal that the transition path time of DNA is shorter compared to the Kramers's first passage time. Especially, the transition path time depicts an unexpected behavior as it decreases with an increase in the height of the barrier, while the first passage time reveals an exactly opposite trend. Both mean first passage time and mean transition path time increases with an increase in the complexity/viscoelasticity of the cellular environment due to the caging effect of the hairpin. Our results for the free energy landscape, probability density, transition path time distribution and the mean transition path time of the DNA hairpin are in good agreement with those obtained from experiments and other theoretical studies.

中文翻译：

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DNA 发夹通过过渡路径时间的构象转变

在复杂的细胞环境中，在广义朗之万方程的框架内，理论上研究了 DNA 发夹的压缩/解链转换的随机动力学。推导出过渡路径和首次通过时间分布的解析表达式。结果表明，与 Kramers 的第一次通过时间相比，DNA 的过渡路径时间更短。特别是，过渡路径时间描绘了一种意想不到的行为，因为它随着屏障高度的增加而减少，而第一次通过时间则显示出完全相反的趋势。由于发夹的笼罩效应，平均首次通过时间和平均过渡路径时间都随着细胞环境复杂性/粘弹性的增加而增加。我们对自由能景观、概率密度的结果，