Analytical representation of protein distributions in stochastic models of gene expression

生物学的基本问题之一是阐明引起群体中个体间表型变异的分子机制。已经表明，表型变异可以在基因型或环境因素没有任何潜在差异的情况下出现。这种“非遗传个体性”在从细菌持久性到HIV-1病毒感染的多种细胞过程中观察到，并且由基因表达产物（如mRNA和蛋白质）的细胞水平中的随机性（噪声）驱动。为了量化基因表达中噪声的影响，最近的单细胞实验已经获得了表征细胞群体中蛋白质水平的概率分布。相应地，有必要开发一个通用的分析框架，用于对从这样的单细胞实验中获得的分布进行建模和解释，这将导致对基因表达中的噪声如何被调节的定量见解。该项目的目标是开发新的方法，用于获得基因表达及其调控模型中蛋白质分布的分析结果。该项目将有助于从根本上了解噪声在基因表达中的作用及其在不同细胞过程中的调控。该分析需要物理学和应用数学的工具和方法，并将与教学工作相结合，以有效地培养学生和未来的科学家在这个快速发展的跨学科研究领域。基因表达中的噪声通常使用粗粒度随机模型进行分析。然而，获得相应的蛋白质分布的精确解析表达式一直是一个挑战，但最简单的模型。该项目的研究将涉及整合的工具，从泊松过程的分割为基础的方法，以解决这些挑战的理论。所开发的方法将用于获得基因表达及其调控模型的精确和近似分析结果。由此产生的分析模型与监管机制，如突发，反馈和启动子为基础的监管将导致量化的见解噪声特性的基本积木的遗传电路。该项目的研究还将导致分析结果，表征噪声输入在调节简单的生化开关中的作用，并提出新的方法来估计模型参数的基础上观察噪声。 该项目的分析结果将有多种应用，从合成生物学到了解克隆种群的表型变异。

One of the fundamental problems in biology is elucidating the molecular mechanisms that give rise to phenotypic variations among individuals in a population. It has been shown that phenotypic variations can arise without any underlying differences in the genotype or environmental factors. Such "nongenetic individuality" is observed in diverse cellular processes, ranging from bacterial persistence to HIV-1 viral infections, and is driven by randomness (noise) in the cellular levels of gene expression products such as mRNAs and proteins. To quantify the effects of noise in gene expression, recent single-cell experiments have obtained probability distributions characterizing protein levels across a population of cells. Correspondingly, there is a need to develop a general analytical framework for modeling and interpretation of the distributions obtained from such single-cell experiments that will lead to quantitative insights into how noise in gene expression is regulated. The goal of this project is to develop new approaches for obtaining analytical results for protein distributions in models of gene expression and its regulation. The project will contribute to a fundamental understanding of the role of noise in gene expression and its regulation in diverse cellular processes. The analysis requires tools and approaches from physics and applied mathematics and will be integrated with teaching efforts to effectively train students and future scientists in this fast-developing field of interdisciplinary research.Noise in gene expression is generally analyzed using coarse-grained stochastic models. However, obtaining exact analytical expressions for the corresponding protein distributions has been a challenging for all but the simplest models. The project research will involve integration of tools from queueing theory with approaches based on partitioning of Poisson processes to address such challenges. The approaches developed will be used to obtain both exact and approximate analytical results for models of gene expression and its regulation. The resulting analysis of models with regulatory mechanisms such as bursting, feedback and promoter-based regulation will lead to quantitative insights into noise characteristics of the basic building blocks of genetic circuits. The project research will also lead to analytical results that characterize the role of noisy inputs in regulating simple biochemical switches and suggest new approaches for estimating model parameters based on observations of noise. The analytical results derived in the project will have multiple applications ranging from synthetic biology to understanding phenotypic variation in clonal populations.