Distribution profiles and their dynamic transition in stochastic gene transcription

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• 作者：Feng Jiao^a ; ^b ; Moxun Tang^b ; Jianshe Yu^a ; ^{jsyu@gzhu.edu.cn}
• 关键词：34F05 ; 37H10 ; 60J20 ; 92C37 ; 92C40
• 刊名：Journal of Differential Equations
• 出版年：2013
• 出版时间：15 April, 2013
• 年：2013
• 卷：254
• 期：8
• 页码：3307-3328
• 全文大小：311 K

文摘

Gene transcription is a central process in life. In single cells, it is a random process since many regulatory molecules are present at low copy numbers. The randomness is best characterized by the mass function , the probability that there are m mRNA copies at time t in one cell. However, even for the classical two-state model of stochastic gene transcription, the analytical form of has remained elusive, and its analysis has relied on numerical simulation or empirically defined hypergeometric functions. In this work, we have endeavored to express as simple mathematical functions of the rate constants defined in the two-state model. For this purpose, we have transformed the master equations of into several special types of second order ordinary differential equations, and solved their corresponding initial value problems successfully. This has helped us derive the exact forms of and explore its property in mathematical detail. We have discovered a striking phenomenon that could peak at any prescribed mRNA number m at any prescribed time t over a large set of system parameters. We have also proved that single transcription systems could generate three modes of distributions at different time points, and depicted the dynamic transition among these distributions.