bistability, probability transition rate and first-passage time in an autoactivating positive-feedback loop双稳态概率转换速率和首次通过时间autoactivating正反馈循环.pdf

Bistability, Probability Transition Rate and First-Passage Time in an Autoactivating Positive-Feedback Loop 1,3 2 1 Xiu-Deng Zheng , Xiao-Qian Yang , Yi Tao * 1 Key Laboratory of Animal Ecology and Conservational Biology, Centre for Computational and Evolutionary Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, People’s Republic of China, 2 School of Mathematical Sciences, Beijing Normal University, Beijing, People’s Republic of China, 3 Graduate University of the Chinese Academy of Sciences, Beijing, People’s Republic of China Abstract A hallmark of positive-feedback regulation is bistability, which gives rise to distinct cellular states with high and low expression levels, and that stochasticity in gene expression can cause random transitions between two states, yielding bimodal population distribution (Kaern et al., 2005, Nat Rev Genet 6: 451-464). In this paper, the probability transition rate and first-passage time in an autoactivating positive-feedback loop with bistability are investigated, where the gene expression is assumed to be disturbed by both additive and multiplicative external noises, the bimodality in the stochastic gene expression is due to the bistability, and the bistability determines that the potential of the Fokker-Planck equation has two potential wells. Our main goal is to illustrate how the probability transition rate and first-passage time are affected by the maximum transcriptional rate, the intensities of additive and multiplicative noises, and the correlation of additive and multiplicative noises. Our main results show that (i) the increase of the maximum transcription rate will be useful for maintaining a high gene expression level; (ii) the probability transition rate