Biodynamic Optical Imaging Center (BIOPIC), Peking University, Beijing, P.R.China.
Beijing International Center for Mathematical Research (BICMR), Peking University, Beijing, P.R.China.
PLoS Comput Biol. 2018 Mar 12;14(3):e1006051. doi: 10.1371/journal.pcbi.1006051. eCollection 2018 Mar.
Within an isogenic population, even in the same extracellular environment, individual cells can exhibit various phenotypic states. The exact role of stochastic gene-state switching regulating the transition among these phenotypic states in a single cell is not fully understood, especially in the presence of positive feedback. Recent high-precision single-cell measurements showed that, at least in bacteria, switching in gene states is slow relative to the typical rates of active transcription and translation. Hence using the lac operon as an archetype, in such a region of operon-state switching, we present a fluctuating-rate model for this classical gene regulation module, incorporating the more realistic operon-state switching mechanism that was recently elucidated. We found that the positive feedback mechanism induces bistability (referred to as deterministic bistability), and that the parameter range for its occurrence is significantly broadened by stochastic operon-state switching. We further show that in the absence of positive feedback, operon-state switching must be extremely slow to trigger bistability by itself. However, in the presence of positive feedback, which stabilizes the induced state, the relatively slow operon-state switching kinetics within the physiological region are sufficient to stabilize the uninduced state, together generating a broadened parameter region of bistability (referred to as stochastic bistability). We illustrate the opposite phenotype-transition rate dependence upon the operon-state switching rates in the two types of bistability, with the aid of a recently proposed rate formula for fluctuating-rate models. The rate formula also predicts a maximal transition rate in the intermediate region of operon-state switching, which is validated by numerical simulations in our model. Overall, our findings suggest a biological function of transcriptional "variations" among genetically identical cells, for the emergence of bistability and transition between phenotypic states.
在同一种系群体中，即使在相同的细胞外环境中，单个细胞也可以表现出各种表型状态。在单个细胞中，随机基因状态转换调节这些表型状态之间的转换的确切作用尚未完全理解，特别是在存在正反馈的情况下。最近的高精度单细胞测量表明，至少在细菌中，相对于活跃转录和翻译的典型速率，基因状态的转换速度较慢。因此，我们以 lac 操纵子为例，在操纵子状态转换的区域，我们提出了一个波动率模型，用于该经典基因调控模块，该模型纳入了最近阐明的更现实的操纵子状态转换机制。我们发现正反馈机制诱导双稳性（称为确定性双稳性），并且其发生的参数范围通过随机操纵子状态转换显著扩大。我们进一步表明，在不存在正反馈的情况下，操纵子状态转换本身必须非常缓慢才能引发双稳性。然而，在正反馈存在的情况下，其稳定诱导状态，生理区域内相对较慢的操纵子状态转换动力学足以稳定未诱导状态，共同产生双稳性的更广泛参数区域（称为随机双稳性）。我们借助最近提出的波动率模型速率公式，说明了两种双稳性中相反的表型转换速率对操纵子状态转换速率的依赖性。该速率公式还预测了操纵子状态转换的中间区域中的最大转换速率，这在我们的模型的数值模拟中得到了验证。总的来说，我们的研究结果表明，在同基因细胞中，转录“变化”为双稳性和表型状态之间的转换的出现提供了生物学功能。
