Stochastic Noise in Auto-regulatory Genetic Network:Model-dependence and Statistical Complication  

作　　者：Ying-zi Shang 

机构地区：[1]School of Management, Xi'an Jiaotong University, Xi'an 710049, China [2]School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第4期563-572,共10页应用数学学报（英文版）

摘　　要：For the single gene network model, there are two basic types. For convenience, we call them Type I and Type II, respectively. The Type I model describes both the dynamics of mRNA and protein. The Type II model is a simplification of the Type I model based on the assumption that the change rate of mRNA is much faster than protein because the half-life of mRNA is short compared with that of protein, the Type II model describes only the dynamics of protein. The analysis of the Type I model is based on the assumption that the ratio of the protein decay rate to the mRNA decay rate is small enough. The main results for Type I model show that the Fano factor of the protein must be bigger than one if there is no negative feedback on the transcription. If there is negative feedback, the relative fluctuation strength in the number of proteins is determined by the size of the feedback regulation strength. For the Type II model, the Fano factor of the protein depends on the effect of the feedback regulation on the translation, i.e., the Fano factor equals one if there is no feedback, and is less than one （or bigger than one） if there is negative feedback （or positive feedback）. These results show clearly that the analysis of the steady-state statistical properties of single gene network is model-dependent.For the single gene network model, there are two basic types. For convenience, we call them Type I and Type II, respectively. The Type I model describes both the dynamics of mRNA and protein. The Type II model is a simplification of the Type I model based on the assumption that the change rate of mRNA is much faster than protein because the half-life of mRNA is short compared with that of protein, the Type II model describes only the dynamics of protein. The analysis of the Type I model is based on the assumption that the ratio of the protein decay rate to the mRNA decay rate is small enough. The main results for Type I model show that the Fano factor of the protein must be bigger than one if there is no negative feedback on the transcription. If there is negative feedback, the relative fluctuation strength in the number of proteins is determined by the size of the feedback regulation strength. For the Type II model, the Fano factor of the protein depends on the effect of the feedback regulation on the translation, i.e., the Fano factor equals one if there is no feedback, and is less than one （or bigger than one） if there is negative feedback （or positive feedback）. These results show clearly that the analysis of the steady-state statistical properties of single gene network is model-dependent.

关 键 词：Genetic network model-dependence fano factor intrinsic noise 

分 类 号：O411.1[理学—理论物理]