Multiscale Macromolecular Assembly Pathways via Algebraic Combinatorics

从相同的蛋白质单体开始的二十面体病毒壳组装是自然界中发生的对称大分子自组装的一个突出但知之甚少的例子。我们建议开发并生物化学验证一种新颖的多尺度数学和计算模型以及相关的软件工具，以回答有关病毒壳组装途径的重点问题。所提出的方法基于 3 种新颖成分。 (i) 将有关装配路径结构的重点问题形式化，这些问题仅依赖于静态几何和对称约束。避免动力学有利于计算的易处理性和直观的途径结构理论。（ii）开发模块化的两尺度病毒组装模型，使数学透明，并为几何复杂性和代数组合学带来新的方向。（iii）使用已知数据和新实验对模型的两个单独尺度进行独立生化验证。纳米科学和工程、生物传感器和基因治疗中的一系列应用遵循对称大分子组装途径的有效模型。这些模型还有助于阻止病毒自组装，从而阻止许多植物和动物疾病。将开发基于 PI 的 FRONTIER 几何约束求解开源软件套件构建的开源软件和基准病毒数据，用于自组装路径的预测和可视化以及严格的比较。这笔赠款将培养一个密切互动的跨学科学生群体，并使他们每个人都接触数学、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 的跨学科研讨会以及大学新闻稿进行推广。

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.