Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA.
J Theor Biol. 2010 Sep 7;266(1):41-61. doi: 10.1016/j.jtbi.2010.06.002. Epub 2010 Jun 8.
Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.
过去已经采用了几种方法来模拟细菌细胞群体的异质性，每种方法都侧重于异质性的不同来源。然而，仍然缺乏一种将所有主要来源整合到一个适用于细胞群体的综合框架中的整体方法。在这项工作中，我们提出了一个描述细胞群体动态的细胞群体主方程 (CPME) 的数学公式，该公式考虑了主要的异质源，即反应的随机性、DNA 复制和分裂，以及物种内容随机分配到两个子细胞中。该公式还考虑了细胞生长，并尊重分子含量和细胞数量的离散性质。我们进一步开发了一种用于模拟这里考虑的随机过程的蒙特卡罗算法。为了基准测试我们的新框架，我们首先使用它来量化每个异质源对内在和外在表型可变性的影响，对于 Elowitz 等人实验中使用的著名双启动子系统。(2002)。我们最后将我们的框架应用于一个更复杂的系统，并展示了单个细胞水平上由于蛋白质积累导致的基因表达噪声和生长抑制之间的相互作用如何导致细胞群体水平的复杂行为。我们的框架的通用性使其适合研究各种人工和天然遗传网络。使用我们的蒙特卡罗算法，可以预测感兴趣的遗传结构的细胞群体分布，从而量化细胞内反应的随机性或生长和分裂等生理过程速率的可变性的影响。这种计算机实验可以深入了解细胞群体的行为，并揭示导致细胞群体异质性的主要来源。
