Dorri Faezeh, Pezeshk Hamid, Sadeghi Mehdi
Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran.
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran.
Cell J. 2017 Oct;19(3):343-351. doi: 10.22074/cellj.2017.3919. Epub 2017 Aug 19.
Cellular decision-making is a key process in which cells with similar geneticand environmental background make dissimilar decisions. This stochastic process, which happens in prokaryotic and eukaryotic cells including stem cells, causes cellular diversity and phenotypic variation. In addition, fitness predicts and describes changes in the genetic composition of populations throughout the evolutionary history. Fitness may thus be defined as the ability to adapt and produce surviving offspring. Here, we present a mathematical model to predict the fitness of a cell and to address the fundamental issue of phenotypic variation. We study a basic decision-making scenario where a bacteriophage lambda reproduces in E. coli, using both the lytic and the lysogenic pathways. In the lytic pathway, the bacteriophage replicates itself within the host bacterium. This fast replication overcrowds and in turn destroys the host bacterium. In the lysogenic pathway, however, the bacteriophage inserts its DNA into the host genome, and is replicated simultaneously with the host genome.
In this prospective study, a mathematical predictive model was developed to estimate fitness as an index of survived offspring. We then leverage experimental data to validate the predictive power of our proposed model. A mathematical model based on game theory was also generated to elucidate a rationale behind cell decision.
Our findings indicate that a rational decision that is aimed to maximize life expectancy of offspring is almost identical to bacteriophage behavior reported based on experimental data. The results also showed that stochastic decision on cell fate maximizes the expected number of survived offspring.
We present a mathematical framework for analyzing a basic phenotypic variation problem and explain how bacteriophages maximize offspring longevity based on this model. We also introduce a mathematical benchmark for other investigations of phenotypic variation that exists in eukaryotes including stem cell differentiation.
细胞决策是一个关键过程，在此过程中，具有相似遗传和环境背景的细胞会做出不同的决策。这种随机过程发生在包括干细胞在内的原核和真核细胞中，导致细胞多样性和表型变异。此外，适合度预测并描述了整个进化历史中种群遗传组成的变化。因此，适合度可定义为适应并产生存活后代的能力。在此，我们提出一个数学模型来预测细胞的适合度，并解决表型变异的基本问题。我们研究了一个基本的决策场景，即噬菌体λ在大肠杆菌中通过裂解和溶原途径进行繁殖。在裂解途径中，噬菌体在宿主细菌内自我复制。这种快速复制会使宿主细菌过度拥挤，进而将其破坏。然而，在溶原途径中，噬菌体将其DNA插入宿主基因组，并与宿主基因组同时复制。
在这项前瞻性研究中，开发了一个数学预测模型，以估计适合度作为存活后代的指标。然后，我们利用实验数据来验证我们提出的模型的预测能力。还生成了一个基于博弈论的数学模型，以阐明细胞决策背后的基本原理。
我们的研究结果表明，旨在使后代预期寿命最大化的理性决策与基于实验数据报道的噬菌体行为几乎相同。结果还表明，细胞命运的随机决策使存活后代的预期数量最大化。
我们提出了一个用于分析基本表型变异问题的数学框架，并解释了噬菌体如何基于该模型使后代寿命最大化。我们还为包括干细胞分化在内的真核生物中存在的其他表型变异研究引入了一个数学基准。
