arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1012.0770cond-mat.softcond-mat.stat-mech
收藏

DNA呼吸动力学:相关布朗泛函分布函数的分析结果

DNA breathing dynamics: Analytic results for distribution functions of relevant Brownian functionals

Malay Bandyopadhyay, Shamik Gupta, Dvira Segal

摘要:

我们研究DNA呼吸动力学的建议和检查几个不同的布朗泛函与气泡寿命和反应。气泡动力学被描述为一个过阻尼的随机行走的数目破碎的碱基对。步行发生在波兰-Scheraga自由能源景观。我们提出了几个概率分布函数的呼吸过程的特点,并采用最近研究的向后福克-普朗克方法和路径分解方法作为优雅和灵活的工具来推导这些分布。特别地,对于初始尺寸$x_0$的气泡,我们推导出(i)首次通过时间$t_f$的分布$P(t_f|x_0)$,表征气泡寿命,(ii)直到首次通过时间的区域$A$的分布$P(A|x_0)$,提供关于气泡对DNA内过程的有效反应性的信息,(iii)在首次通过时间之前获得的最大气泡尺寸$M$的分布$P(M)$,和(iv)在首次通过时间之前最大气泡尺寸$M$和其出现的时间$t_m$的联合概率分布$P(M,t_m)$。这些分布进行了分析,在小的和大的气泡尺寸的限制。我们补充我们的分析预测与直接数值模拟相关的朗之万方程,并获得了很好的协议,在适当的限制。原则上,这里分析的各种量的非平凡标度行为可以通过实验来探索。

英文摘要:

We investigate DNA breathing dynamics by suggesting and examining several different Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size $x_0$, we derive analytical expressions for (i) the distribution $P(t_f|x_0)$ of the first-passage time $t_f$, characterizing the bubble lifetime, (ii) the distribution $P(A|x_0)$ of the area $A$ till the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution $P(M)$ of the maximum bubble size $M$ attained before the first-passage time, and (iv) the joint probability distribution $P(M,t_m)$ of the maximum bubble size $M$ and the time $t_m$ of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numerical simulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑