Collaborative Research: Topology and Infection Dynamics of Bacteriophage Viruses

噬菌体是感染细菌的病毒，是噬菌体治疗、药物发现和纳米技术等许多科学领域关注的焦点，因为噬菌体是细菌微生物群的积极调节剂。噬菌体生长过程中的关键步骤包括：将病毒DNA包装在预先形成的二十面体体积内（称为衣壳），在衣壳内对DNA进行三维排列，以及在感染时将DNA分子从衣壳输送到细菌细胞中。这三个步骤都受到空间约束下DNA分子的生物物理性质的高度影响。在这个项目中，研究人员将结合实验和数学模型来全面表征噬菌体衣壳内的DNA组织及其在感染时的传递。该研究将连接几个数学学科，包括液晶的连续介质力学（理论和模拟）、自由边界问题分析、动力学和结理论。理论和实验工作之间的互动是根据材料基因组计划的想法形成的，该计划在数学建模和实验工作之间培养了一种系统的相互关联的方法，旨在提高设计和发现新材料的效率。该项目将培养2名研究生和1名博士后。在这个项目中，研究人员将通过假设和严格证明，根据朗道和德热纳的理论，观察到的DNA结是与液晶构型相关的张量场的线缺陷，来关注由于空间限制而导致的DNA结领域的范式转变。这种范式转变旨在更好地捕捉包装DNA的三维排列和拓扑特性，DNA结的形成及其对环境离子的依赖。在发展数学理论的同时，将进行新的实验工作。特别是，该研究将探索由受限DNA的液晶结构驱动的打结构象的产生。研究人员还将开发模型来研究感染时噬菌体的基因组释放。研究人员将应用先前在聚电解质凝胶研究中开发的方法，结合蛋白质结合工具，开发最先进的基因组释放方法。这个数学问题包括一个离子两相介质的偏微分方程的约束系统：水和DNA，其中包括棘轮力的激活。通过将建模、分析和计算相结合，研究人员旨在描述与基因组传递不同机制相关的时间尺度，并模拟特定病毒的完整感染过程。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。

Bacteriophages (phages), viruses that infect bacteria, have been the focus of attention in many scientific fields such as phage therapy, drug discovery, and nanotechnology, because phages are active regulators of bacterial microbiomes. Key steps in the phage growth process include: the packaging of the viral DNA inside a preformed icosahedral volume (called capsid), the three-dimensional arrangement of DNA inside the capsid and the delivery of the DNA molecule, from the capsid into the bacterial cell, at the time of infection. These three steps are all highly influenced by the biophysical properties of the DNA molecule in spatial confinement. In this project, the investigators will combine experiments and mathematical modeling to provide a thorough characterization of DNA organization inside phage capsids and its delivery at the time of infection. The research will bridge several mathematical disciplines including continuum mechanics (theory and simulations) of liquid crystals, analysis of free boundary problems, dynamics and knot theory. The interaction between the theoretical and experimental work is fashioned following the ideas of the Materials Genome Initiative, that fostered a systematic interconnected approach between mathematical modeling and experimental work, aimed at improving efficiency in the design and discovery of new materials. The project will train two graduate students and one postdoctoral fellow. In this project, the investigators will focus on a paradigm shift in the field of DNA knotting due to spatial confinement by hypothesizing and rigorously proving, according to the theory by Landau and de Gennes, that DNA knots observed are line defects of a tensor field associated to liquid crystal configurations. This paradigm shift is aimed at better capturing the three-dimensional arrangement and topological properties of packaged DNA, the formation of DNA knots, and their dependence on the environmental ions. In parallel with the development of mathematical theory, new experimental work will be pursued. In particular, the research will explore the generation of knotted conformations exclusively driven by the liquid crystalline structure of confined DNA. The investigators will also develop models to study genome release from bacteriophages at the time of infection. The investigators will apply methods previously developed in the study of polyelectrolyte gels combined with tools from protein binding to develop a state-of-the-art approach to genome release. The mathematical problem consists of a constraint system of partial differential equations for an ionic two-phase media: water and DNA, that includes activation by ratchet forces. By combining modeling, analysis, and computation, the investigators aim at characterizing the time scales associated with the different mechanisms of genome delivery and simulate a full infection process for specific viruses.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.