MPS: BIO: Theory, Algorithms, Software, for Predicting Geometric Entropy-driven Virus Assembly, using Multiscale Configuration Space Atlasing and Combinatorial Enumeration

本项目的重点是建模和验证病毒衣壳的大分子组装。对于对称大分子结构自组装过程中发生的许多里程碑过程，缺乏严格的、机械的解释和预测。尽管有许多自组装病毒衣壳的代表性结构是可用的。在这个项目中，我们特别感兴趣的是：a)成核，b)自构，构象开关和c)脚手架移除，所有这些都是由构型和组合熵驱动的过程，这是常用的计算分子模拟范式（包括分子动力学和蒙特卡罗方法）的绊脚石。多尺度几何和对称约束（MGSC）是该PI团队在先前的NSF项目中开发的一种通用且计算效率很高的新建模范式：它补充并集成了以前的范式，同时解决了关键缺点。该项目将使用MGSC范式将由构型和组合熵驱动的生物过程的关键问题转化为阐明几何和对称对这些过程的影响的各种数学和算法问题。这些问题是独立有趣的，并且与组合刚性、构型空间的代数几何、代数组合学和复杂性等长期开放问题有关。此外，使用MGSC，我们将获得一个系统的建模过程，不仅可以提取最小的相关数据（模型输入），还可以回答有关这些过程的重点问题(Occam？S剃刀)，也用于从生物学角度解释答案（模型输出）。最后，该项目将使用现有的实验结果（体外和体内），在co-PI？s实验室)对具有代表性的病毒家族（如小鼠细小病毒（MVM）、玉米条纹病毒（MSV）、腺相关病毒（AAV4））进行了研究，以验证其预测，例如，对关键的分子间相互作用的预测，这些相互作用的去除会破坏组装。病毒衣壳自组装是病毒生命周期的一个阶段，相对独立于宿主细胞的结构和过程。然而，在设计治疗病毒感染的药物或疫苗时，自组装阶段尚未成为目标，也未在基因治疗中设计和使用病毒载体时加以利用。这是因为在纳米尺度上发生的病毒衣壳自组装的快速性、有效性、稳健性、自发性和数学上复杂的编排是非常难以理解的。该项目旨在通过结合两位数学家、一位计算机科学家和一位实验结构生物学家的专业知识，为病毒衣壳自组装过程带来新的见解。该项目将建立在这些结果的基础上，继续开发一个开源软件套件EASAL（高效的装配景观的地图集和搜索）。这有可能被广泛的学科所使用，这些学科对分离驱动大分子自组装的关键原子间相互作用感兴趣。因此，该项目不仅将为研究生和博士后提供出色的跨学科研究经验，也将为pi提供出色的跨学科研究经验。该项目将为当地学校的STEM教师提供研究经验，此外还将涉及Tertl Studos（一家有兴趣在公共领域工作的基于游戏的学习软件公司），创造性地将几何约束求解算法纳入4-12年级的各种数学和科学基准。该提案已提交给DMS数学生物学和计算数学项目，CCF/CISE和MCB/BIO，以回应“亲爱的同事信：生物，数学和物理科学界面的非应邀提案”。它由几个NSF项目共同资助：数学生物学/DMS/MPS，分子和细胞生物学/BIO，算法基础CCF/CISE以及DMS 21世纪网络基础设施（CIF21）基金。

This project is focused on modeling and validating the macromolecular assembly of viral capsids. Rigorous, mechanistic explanations and predictions are lacking for many milestone processes that occur during self-assembly of symmetric macromolecular structures. This is despite the fact that numerous representative structures of self-assembled viral capsids are available. In this project, we are specifically interested in: a) nucleations, b) autostery, conformational switches and c) scaffolding removal, all of which are processes driven by configurational and combinatorial entropy, a stumbling block for commonly used computational molecular simulation paradigms including molecular dynamics and Monte Carlo methods. Multiscale Geometry and Symmetry Constraints (MGSC) is a versatile and computationally highly efficient new modeling paradigm developed by this PI team during a prior NSF project: it complements and integrates with former paradigms while addressing key shortcomings. The project will use the MGSC paradigm to translate key questions about biological processes driven by configurational and combinatorial entropy into diverse mathematical and algorithmic questions that elucidate the influence of geometry and symmetry upon these processes. These questions are independently interesting and are related to longstanding open problems in combinatorial rigidity, algebraic geometry of configuration spaces, algebraic combinatorics, and complexity. Moreover, using MGSC, we will obtain a systematic modeling procedure not only for extracting the minimal, relevant data (model input) for answering focused questions about these processes (Occam?s razor), but also for interpreting the answers (model output) biologically. Finally, the project will use existing experimental results (in vitro and in vivo, performed at a co-PI?s lab) on representative families of viruses (such as the Murine Parvovirus (MVM), Maize Streak Virus (MSV), Adeno associated viruses (AAV4) to validate its predictions, for instance, on crucial inter-molecular interactions whose removal disrupts assembly.Viral capsid self-assembly from its constituent protein molecules is a phase of the viral lifecycle that is relatively independent of the structure and processes of the host cell. Yet, the self-assembly phase has not been targeted in the design of drugs or vaccines for treating viral infections, nor has it been leveraged in the design and use of viral vectors in gene therapy. This is because the rapidity, efficacy, robustness, spontaneity and mathematically complex orchestration of viral capsid self-assembly, occurring at the nano-scale, is extremely difficult to understand. This project aims at bringing new insights into the viral capsid self-assembly process by combining the expertise of two mathematicians, a computer scientist and an experimental structural biologist. The project will build upon these results to continue the development of an open source software suite EASAL (Efficient Atlasing and Search of Assembly Landscapes). This has the potential to be used by a wide variety of disciplines that are interested in isolating the crucial inter-atomic interactions that drive macromolecular self-assembly. Hence the project will provide outstanding interdisciplinary research experience not only to the graduate students and postdocs involved, but to the PIs as well. The project will provide research experience for STEM teachers at local schools and will additionally involve Tertl Studos - a game-based learning software company that is interested in working in the public domain - to creatively incorporate geometric constraint solving algorithms into a wide variety of math and science benchmarks in grades 4-12.This proposal was submitted to the DMS programs in Mathematical Biology and Computational Mathematics, to CCF/CISE and to MCB/BIO in response to the Dear Colleague Letter: Unsolicited Proposals at the Interface of the Biological, Mathematical and Physical Sciences. It is co-funded by sevral NSF programs: Mathematical Biology/DMS/MPS, Molecular and Cellular Biology/BIO, Algorithmic Foundations CCF/CISE as well as by the DMS Cyberinfrastructure for the 21st Century (CIF21) fund.