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Stability and Flipping Dynamics of Delayed Genetic Toggle Switch
Rui-ting Zhang,Han-shuang Chen,Zhong-huai Hou*
Author NameAffiliationE-mail
Rui-ting Zhang Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China  
Han-shuang Chen Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China  
Zhong-huai Hou* Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, ChinaHefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230026, China hzhlj@ustc.edu.cn 
Abstract:
A detailed analysis of the stability and flipping dynamics of a delayed exclusive toggle switch is performed. We use forward flux sampling method combined with delayed stochastic sim-ulation algorithm to get the stationary distribution function, the switching rate, and path-ways, as well as the transition state ensemble. Interestingly, under the influence of time delay, the stationary distribution corresponding to the stable states become narrower and the population in the transition region is significantly enhanced. In addition, the flipping rate increases monotonically with delay. Such findings demonstrate that time delay could reduce the stability of the bistable genetic switch dramatically. Furthermore, the transition pathways, characterized by the difference in the protein numbers and the state of operator, show larger discrepancy between the forward and backward switching process with increas-ing delay, indicating that transcriptional and translational delay can remarkably affect the flipping dynamics. Specifically, for the transition state, the difference in the probability of finding the operator site bound by the two different protein dimers is enlarged by delay, which further illustrates the crucial role of time delay on the stability and switching dynamics of genetic toggle switches.
Key words:  Toggle switch, Delay forward, Flux sampling
FundProject:
延迟基因开关体系的稳定性及转变动力学
张睿挺,陈含爽,侯中怀*
摘要:
对延迟基因开关体系的稳定性及转变动力学进行了系统的研究.通过前向流采样及延迟随机模拟方法,获得了相空间稳态分布、转变路径和速率以及转变态系综的分布等信息.数值结果表明,基因开关体系中的延迟会减小稳态之间的间距,增大体系在转变态的布居.此外,转变速率也会随着延迟时间的增大单调增加,这些现象都说明延迟会削弱双稳基因开关体系的稳定性.转变路径由两种转录因子蛋白质的总的粒子数的差和操纵子位点的状态来描述,对转变路径的数值分析表明转录和翻译过程导致的延迟会显著影响转变动力学.特别是对于转变态系综而言,操纵子结合两种不同二聚体概率的差异随着延迟时间的增加逐渐加大.
关键词:  基因开关,延迟,前向流采样
DOI:10.1088/1674-0068/25/01/53-59
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