Multiscale Macromolecular Assembly Pathways via Algebraic Combinatorics

二十面体病毒壳组装是从相同的蛋白质单体开始的，是自然界中发生的对称大分子自组装的一个突出但鲜为人知的例子。我们建议开发和生化验证一种新的多尺度数学和计算模型以及相关的软件工具，以回答有关病毒外壳组装途径的重点问题。提出的方法是基于3种新的成分。(i)关于组装路径结构的仔细聚焦问题的形式化，这些问题仅依赖于静态几何和对称约束。避免动力学有助于计算的可追溯性和直观的路径结构理论。㈡开发一种模块化的双尺度病毒组装模型，使数学变得透明，并在几何复杂性和代数组合学方面开辟新的方向。（iii）使用已知数据和新的实验，对模型的两个独立尺度进行独立的生化验证。在纳米科学和工程、生物传感器和基因治疗方面的一系列应用都是基于对称大分子组装途径的有效模型。这种模型还有助于阻止病毒的自组装，从而阻止许多动植物疾病。开源软件建立在PI的FRONTIER几何约束求解开源软件套件之上，基准病毒数据将用于预测和可视化自组装路径，并进行严格的比较。该基金将培养一个密切互动的跨学科学生群体，并将使他们每个人都接触到数学、结构生物学、理论计算机科学、算法和软件开发方面的研究。计划通过DIMACS或IMA的跨学科讲习班和大学新闻稿进行外联。

Icosahedral viral shell assembly starting from identical protein monomers is an outstanding but poorly understood example of symmetric macromolecularself-assembly occuring in nature. We propose to develop and biochemically validate a novel multiscale mathematical and computational model and associatedsoftware tools to answer focused questions about viral shell assembly pathways. The proposed approach is based on 3 novel ingredients. (i) Formalization of carefully focused questions about the structureof assembly pathways, which depend only on static geometric and symmetry constraints. Avoidance of dynamics facilitates computational tractability and an intuitive theory of pathway structure.(ii) Development of a modular, two-scale virus assembly model that makes the mathematics transparent and leads to new directions in geometric complexity and algebraic combinatorics.(iii)Independent biochemical validation of the 2 separate scales of the model, using known data as well as new experiments.An array of applications in nanoscience and engineering, biosensor and gene therapy follow from effective models of symmetric macromolecular assembly pathways. Such models would additionally help arrest viral self-assembly and hence numerous plant and animal diseases. Opensource software built atop the PI's FRONTIER geometric constraint solving opensource software suite, and benchmark virus data will be developed for prediction and visualization of self-assembly pathways and for rigorous comparisons. The grant will foster a closely interacting, interdisciplinary group of students and will expose each of them to research in mathematics, structural biology, theoretical computer science, algorithms and software development. Outreach is planned via an interdisciplinary workshop at DIMACS or at IMA and in university press releases.