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杰出但鲜为人知的例子。我们建议开发和生化验证一个新的多尺度数学和计算模型以及相关的软件工具来回答有关病毒外壳组装途径的焦点问题。提出的方法是基于3种新的成分。(1)关于装配路径的结构的仔细集中的问题的正式化，这仅取决于静态的几何和对称约束。避免动力学有利于计算处理和路径结构的直观理论。(Ii)开发模块化的两尺度病毒组装模型，使数学透明，并在几何复杂性和代数组合学方面引入新的方向。(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物化学验证。在纳米科学和工程、生物传感器和基因治疗中的一系列应用源于对称大分子组装路径的有效模型。这样的模型还将有助于阻止病毒的自我组装，从而阻止许多植物和动物疾病。建立在PI的前沿几何约束求解开源软件套件之上的开源软件和基准病毒数据将被开发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、跨学科的学生小组，并将使他们每个人都有机会从事数学、结构生物学、理论计算机科学、算法和软件开发方面的研究。计划通过在DIMACS或IMA举办跨学科讲习班和在大学新闻稿中开展外联活动。

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.