Collaborative Research: Geometric Elucidation of Supramolecular Assembly and Allostery with Experimental Validation

自然界和工程中的各种超分子结构-从病毒到蛋白质晶体再到纳米材料-在室温下快速自发地组装，具有显着的功效。 许多组装过程包含变构现象，其中分子间相互作用由相互作用分子之一的远程位点处的结合事件控制。 尽管越来越复杂的体内，体外和计算机实验的努力，组装过程知之甚少。 一个更严格的数学，和机械直观的理论是至关重要的，不仅预测和工程组装和变构，而且指导进一步耗时的实验。更深入地了解组装、变构以及后者在前者中的作用将有助于控制传染病、组装用于基因治疗的病毒载体、设计药物和纳米级工程材料。人们自然会期望几何和算法复杂性将在理解组装机制方面发挥关键作用，因为组装过程必须关键地取决于所谓的组装构型空间的复杂形状和体积，其中分子在组装时相对于彼此移动。 相反，人们也很自然地期望，新的数学、算法和软件将来自于对复杂分子构型空间的理解和对它们的计算。 该项目的目标包括新的定理和算法，它们与流行方法的混合，以及开源软件。进展预计长期开放的问题，在刚性，配置空间，距离几何;算法的高效atlasing，搜索，采样和体积计算的高维和拓扑复杂的配置空间;混合方法，联合收割机结合新的算法与现行的基于能量的蒙特卡罗模拟;最重要的是，具体的实验验证的预测。 该项目结合了几何和算法，实验结构生物学和计算化学方面的专业知识，非常适合将三个社区聚集在一起，为研究生提供跨学科培训以及与学校和公众的联系。

A wide variety of supramolecular structures in nature and engineering--from viruses to protein crystals to nanomaterials--assemble rapidly and spontaneously at room temperature with remarkable efficacy. Many assembly processes incorporate the phenomenon of allostery, where intermolecular interaction is controlled by binding events at a remote site of one of the interacting molecules. Despite increasingly sophisticated in vivo, in vitro and in silico experimental efforts, assembly processes are poorly understood. A more mathematically rigorous, and mechanistically intuitive theory is crucial not only to predict and engineer assembly and allostery but also to guide further time-consuming experimentation. Deeper understanding of assembly, allostery, and the role of the latter in the former will help control infectious diseases, assemble viral vectors for gene therapy, design drugs and engineer materials at the nanoscale.It is natural to expect that geometry and algorithmic complexity would play a key role in understanding the mechanisms underlying assembly, since the assembly process must crucially depend on the intricate shape and volume of the so-called assembly configuration space in which the molecules move relative to each other as they assemble. Conversely, it is also natural to expect that new mathematics, algorithms and software will result from the quest to understand intricate molecular configuration spaces and perform computations over them. The project's goals include new theorems and algorithms, their hybridization with prevailing methods, and opensource software. Progress is expected on long open problems in rigidity, configuration spaces, distance geometry; algorithms for efficient atlasing, search, sampling, and volume computation for high dimensional and topologically intricate configuration spaces; hybrid methods that combine the new algorithms with prevailing energy-based Monte Carlo simulation; and most significantly, concrete experimental validation of predictions. The project combines expertise in geometry and algorithms, experimental structural biology, and computational chemistry, and is well-suited for bringing the three communities together, for providing interdisciplinary training for research students as well as for outreach to schools and the public.