Ge Hao, Qian Hong, Xie X Sunney
Biodynamic Optical Imaging Center (BIOPIC), Peking University, Beijing 100871, People's Republic of China.
Beijing International Center for Mathematical Research (BICMR), Peking University, Beijing 100871, People's Republic of China.
Phys Rev Lett. 2015 Feb 20;114(7):078101. doi: 10.1103/PhysRevLett.114.078101. Epub 2015 Feb 17.
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments show that, at least in E.coli, the gene state switching can be neither extremely slow nor exceedingly rapid as many previous theoretical treatments assumed. Rather, it is in the intermediate region which is difficult to handle mathematically. Under this condition, from a full chemical-master-equation description we derive a model in which the protein copy number, for a given gene state, follows a deterministic mean-field description while the protein-synthesis rates fluctuate due to stochastic gene state switching. The simplified kinetics yields a nonequilibrium landscape function, which, similar to the energy function for equilibrium fluctuation, provides the leading orders of fluctuations around each phenotypic state, as well as the transition rates between the two phenotypic states. This rate formula is analogous to Kramers' theory for chemical reactions. The resulting behaviors are significantly different from the two limiting cases studied previously.
单个细胞中常常会出现多种具有不同基因表达状态的表型状态，这些状态通过正反馈进行转录调控。最近的实验表明，至少在大肠杆菌中，基因状态转换既不像许多先前的理论处理所假设的那样极其缓慢，也不会极其迅速。相反，它处于难以进行数学处理的中间区域。在这种情况下，基于完整的化学主方程描述，我们推导出一个模型，其中对于给定的基因状态，蛋白质拷贝数遵循确定性的平均场描述，而蛋白质合成速率由于随机的基因状态转换而波动。简化后的动力学产生了一个非平衡景观函数，它类似于平衡涨落的能量函数，给出了围绕每个表型状态的涨落的主导阶数，以及两种表型状态之间的转换速率。这个速率公式类似于化学反应的克莱默斯理论。由此产生的行为与先前研究的两种极限情况有显著不同。
