Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA.
Department of Biological Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA.
Phys Rev E. 2017 Oct;96(4-1):040402. doi: 10.1103/PhysRevE.96.040402. Epub 2017 Oct 18.
Single-cell gene expression is inherently stochastic; its emergent behavior can be defined in terms of the chemical master equation describing the evolution of the mRNA and protein copy numbers as the latter tends to infinity. We establish two types of "macroscopic limits": the Kurtz limit is consistent with the classical chemical kinetics, while the Lévy limit provides a theoretical foundation for an empirical equation proposed in N. Friedman et al., Phys. Rev. Lett. 97, 168302 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.168302. Furthermore, we clarify the biochemical implications and ranges of applicability for various macroscopic limits and calculate a comprehensive analytic expression for the protein concentration distribution in autoregulatory gene networks. The relationship between our work and modern population genetics is discussed.
单细胞基因表达本质上是随机的；可以根据描述 mRNA 和蛋白质拷贝数随后者趋于无穷大的化学主方程来定义其涌现行为。我们建立了两种“宏观极限”：Kurtz 极限与经典的化学动力学一致，而 Lévy 极限为 N. Friedman 等人提出的经验方程提供了理论基础。物理评论快报 97, 168302 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.168302。此外，我们澄清了各种宏观极限的生化含义和适用范围，并计算了自调节基因网络中蛋白质浓度分布的综合解析表达式。讨论了我们的工作与现代群体遗传学之间的关系。
