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arXiv 1810.00166cond-mat.stat-mech
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基于位置依赖性偏倚的蛋白质在DNA上的靶向搜索

Target Search of a Protein on DNA in the Presence of Position-dependent Bias

Xi Chen, Xiujun Cheng, Yanmei Kang, Jinqiao Duan

摘要:

我们研究了在非恒定漂移和非高斯$α$稳定Lévy涨落存在的情况下DNA上蛋白质的目标搜索。目标搜索通过易化扩散过程实现。现有的研究工作都是在常值漂移的情况下进行的。从含“汇”项的非定域Fokker-Planck方程出发,得到了蛋白质在时间$t$上发生在位置$x$的可能性密度函数.在此基础上,我们进一步计算生存概率和第一到达密度,以量化的搜索机制。数值结果表明,在线性漂移的情况下,存在一个最佳的$α$指数,使搜索最有可能成功(搜索可靠性达到最大)。该最佳$α$指数取决于初始位置-靶分离。研究还发现,扩散强度对提高搜索成功率起着积极的作用。在初始阶段,非线性双阱漂移比线性漂移能更好地驱动蛋白质到达目标,但从长时间演化来看,线性漂移更有利于目标搜索的成功。与线性漂移情况相比,非线性漂移情况下的搜索可靠性和效率与$α$指数具有单调关系,即,$α$指数越小,蛋白质找到其靶标的可能性越大。

英文摘要:

We study the target searching on the DNA for proteins in the presence of non-constant drift and non-Gaussian $α$-stable Lévy fluctuations. The target searching is realized by the facilitated diffusion process. The existing works are about this problem in the case of constant drift. Starting from a non-local Fokker-Planck equation with a "sink" term, we obtain the possibility density function for the protein occurring at position $x$ on time $t$. Based on this, we further compute the survival probability and the first arrival density in order to quantify the searching mechanisms. The numerical results show that in the linear drift case, there is an optimal $α$ index for the search to be most likely successful (searching reliability reaches its maximum). This optimal $α$ index depends on initial position-target separation. It is also found that the diffusion intensity plays a positive role in improving the searching success. The nonlinear double-well drift could drive the protein to reach the target with a larger possibility than the linear drag at initial time period, but viewing at the long time evolution, the linear drift is more beneficial for target searching success. In contrast to the linear drift case, the search reliability and efficiency with nonlinear drift have a monotonic relationship with the $α$ index, that is, the smaller the $α$ index is, the more possibly a protein finds its target.

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。

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