Collaborative Research: Mechanistic Models of Cooperative Biopolymerization Processes

合成生物学目前被用于开发利用工程细菌联合体的先进医学治疗。细菌能够根据环境精确地调整生长速度，对突发的环境变化做出有效的反应。细胞中核糖体的丰度与生长速度密切相关，而生长速度受核糖体丰度的控制，核糖体将mRNA转化为蛋白质。这种生物聚合过程受到直接和间接反馈相互关联的网络的影响，这些反馈依赖于基因的转录和核糖体mRNA的翻译。转录和翻译速率在微生物对变化条件的反应时间中起着关键作用。本研究旨在建立一个全面的数学模型来描述细菌中的核糖体组装和丰度控制。该项目强调分子生物学、物理学原理、数学建模和复杂生物系统敏感性分析的广泛知识的整合。本科生和研究生都将接受训练，在广泛的系统生物学领域内使用数学和物理工具，从而为STEM劳动力发展的国家目标贡献具有跨学科技能的数学家。一个新的连续体模型将具有灵活性来描述三个生物聚合过程：核糖体RNA的转录，核糖体蛋白mRNA的转录和核糖体蛋白的翻译。每个流程的模型被称为完整装配模型中的单个隔间。原型室是车辆运动模型的概括，它提供了一种机制，包括流入和流出现象，以及适当时的扭矩辅助转录。完整的核糖体装配模型由一个常微分方程系统描述，其变量与单个室的输出有关。完整的模型还包括一组调节起始和易位率的反馈，这些反馈控制着每个隔室内发生的动力学。核糖体产生速率是细菌生长速率的关键决定因素，它取决于几个基本量，包括营养上移或下移后的反应时间，转录和翻译的联合时间，以及产生核糖体的时间。由于各种酶的可用性的随机性，一些系统参数表现出固有的不确定性。该项目包括敏感性分析工作，以量化最关键的系统参数对每个基本量的影响。检查这些影响及其可变性，可以确定细菌对其环境的平均群落反应。微生物群落对抗生素应用反应的可变性通常是抗生素有效性的重要决定因素。该奖项由MPS数学科学部（DMS）通过数学生物学项目和BIO/MCB通过遗传机制项目共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Synthetic biology is currently used to develop advanced medical treatments using engineered bacterial consortia. Bacteria are able to exquisitely fine-tune their growth rate to their environment, responding efficiently to sudden environmental changes. Abundance of ribosomes in a cell correlates tightly with the growth rate, and growth rate is controlled by the abundance of ribosomes that translate mRNA into protein. This biopolymerization process is influenced by an interconnected web of both direct and indirect feedbacks that depend on both transcription of genes and translation of ribosomal mRNA. Transcription and translation rates play a key role in response time of the microbe to changing conditions. This research seeks to develop a comprehensive mathematical model to describe ribosome assembly and abundance control in bacteria. The project emphasizes the integration of a broad knowledge of molecular biology, principles of physics, mathematical modeling and sensitivity analysis of a complex biological system. Both undergraduate and graduate students will be trained to use tools from mathematics and physics within the broad field of systems biology, thereby contributing mathematicians with interdisciplinary skills towards the national goal of STEM workforce development. A new continuum model will have the flexibility to describe three biopolymerization processes: transcription of ribosomal RNA, transcription of mRNA of ribosomal proteins and the translation of ribosomal proteins. The model for each process is referred to as an individual compartment within the full assembly model. The prototypical compartment is a generalization of vehicular motion models, and it provides a mechanism for including inflow and outflow phenomena as well as torque-assisted transcription when appropriate. The full ribosome assembly model is described by a system of ordinary differential equations whose variables are related to the outputs of the individual compartments. The full model also includes a set of feedbacks that regulate initiation and translocation rates governing the dynamics occurring within each compartment. Ribosome production rate is the key determinant of bacterial growth rate, and it depends on several fundamental quantities including the response time after a nutritional up-shift or down-shift, the combined time of transcription and translation, and the time to produce a ribosome. Several system parameters exhibit inherent uncertainties due to the stochastic nature of availability of various enzymes. The project includes a sensitivity analysis effort to quantify effects of the most crucial system parameters on each fundamental quantity. Examining these effects and their variability allows one to determine the average community response of bacteria to its environment. The variability in microbial community response to antibiotic application is often an important determinant of antibiotic effectiveness.This award is funded jointly by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and BIO/MCB through the Program of Genetic Mechanisms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.