Collaborative Research: Topology and Infection Dynamics of Bacteriophage Viruses

噬菌体是一种感染细菌的病毒，由于噬菌体是细菌微生物群的活性调节器，因此在噬菌体治疗、药物研发和纳米技术等许多科学领域一直是人们关注的焦点。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)，DNA在衣壳内的三维排列，以及在感染时将DNA分子从衣壳运送到细菌细胞。这三个步骤都受到DNA分子在空间限制下的生物物理性质的高度影响。在这个项目中，研究人员将把实验和数学建模结合起来，以提供噬菌体衣壳内的DNA组织及其在感染时的传递的彻底特征。这项研究将跨越几个数学学科，包括液晶的连续介质力学(理论和模拟)、自由边界问题的分析、动力学和纽结理论。理论工作和实验工作之间的互动是按照材料基因组倡议的想法进行的，该倡议在数学建模和实验工作之间培养了一种系统的相互联系的方法，旨在提高设计和发现新材料的效率。该项目将培养两名研究生和一名博士后研究员。在这个项目中，研究人员将通过假设和严格证明，根据Landau和De Gennes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，从而关注由于空间限制而导致的DNA结领域的范式转变。这一范式转变旨在更好地捕捉包装DNA的三维排列和拓扑性质、DNA结的形成以及它们对环境离子的依赖。在发展数学理论的同时，还将开展新的实验工作。特别是，这项研究将探索完全由受限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。研究人员将应用以前在聚电解质凝胶研究中开发的方法，结合蛋白质结合的工具来开发一种最先进的基因组释放方法。数学问题由离子两相介质：水和DNA的偏微分方程组的约束系统组成，其中包括棘轮力的激活。通过结合建模、分析和计算，研究人员旨在描述与不同基因组传递机制相关的时间尺度，并模拟特定病毒的完整感染过程。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.