Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States of America.
PLoS Comput Biol. 2011 Mar;7(3):e1002010. doi: 10.1371/journal.pcbi.1002010. Epub 2011 Mar 10.
Stochastic expression of genes produces heterogeneity in clonal populations of bacteria under identical conditions. We analyze and compare the behavior of the inducible lac genetic switch using well-stirred and spatially resolved simulations for Escherichia coli cells modeled under fast and slow-growth conditions. Our new kinetic model describing the switching of the lac operon from one phenotype to the other incorporates parameters obtained from recently published in vivo single-molecule fluorescence experiments along with in vitro rate constants. For the well-stirred system, investigation of the intrinsic noise in the circuit as a function of the inducer concentration and in the presence/absence of the feedback mechanism reveals that the noise peaks near the switching threshold. Applying maximum likelihood estimation, we show that the analytic two-state model of gene expression can be used to extract stochastic rates from the simulation data. The simulations also provide mRNA-protein probability landscapes, which demonstrate that switching is the result of crossing both mRNA and protein thresholds. Using cryoelectron tomography of an E. coli cell and data from proteomics studies, we construct spatial in vivo models of cells and quantify the noise contributions and effects on repressor rebinding due to cell structure and crowding in the cytoplasm. Compared to systems without spatial heterogeneity, the model for the fast-growth cells predicts a slight decrease in the overall noise and an increase in the repressors rebinding rate due to anomalous subdiffusion. The tomograms for E. coli grown under slow-growth conditions identify the positions of the ribosomes and the condensed nucleoid. The smaller slow-growth cells have increased mRNA localization and a larger internal inducer concentration, leading to a significant decrease in the lifetime of the repressor-operator complex and an increase in the frequency of transcriptional bursts.
在相同条件下，基因的随机表达会导致细菌克隆群体产生异质性。我们使用快速和慢速生长条件下建模的大肠杆菌细胞的充分混合和空间分辨模拟来分析和比较诱导型 lac 遗传开关的行为。我们新的动力学模型描述了 lac 操纵子从一种表型到另一种表型的转换，该模型结合了最近发表的体内单分子荧光实验获得的参数以及体外速率常数。对于充分混合的系统，研究了在诱导剂浓度存在/不存在反馈机制的情况下，电路中的固有噪声作为函数的行为，结果表明噪声在转换阈值附近达到峰值。应用最大似然估计，我们表明基因表达的二态解析模型可用于从模拟数据中提取随机速率。模拟还提供了 mRNA-蛋白质概率景观，这表明转换是跨越 mRNA 和蛋白质阈值的结果。使用大肠杆菌细胞的冷冻电子断层扫描和蛋白质组学研究的数据，我们构建了细胞的空间体内模型，并量化了由于细胞质中的细胞结构和拥挤而导致的噪声贡献和对阻遏物再结合的影响。与没有空间异质性的系统相比，快速生长细胞的模型预测由于异常亚扩散，整体噪声略有降低，阻遏物再结合率增加。在慢速生长条件下生长的大肠杆菌的断层扫描图像确定了核糖体和浓缩核区的位置。较慢生长的较小细胞增加了 mRNA 的定位和更大的内部诱导物浓度，导致阻遏物-操纵子复合物的寿命显著缩短和转录爆发的频率增加。
