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——在室温下迅速自发地组装，效果显著。许多装配过程包含变构现象，其中分子间的相互作用是由相互作用分子的一个远程位点的结合事件控制的。尽管越来越复杂的体内，体外和硅实验的努力，组装过程是知之甚少。一个在数学上更为严谨、机械上更为直观的理论不仅对预测和设计装配和变构至关重要，而且对指导进一步耗时的实验也至关重要。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、在纳米尺度上设计药物和工程材料。很自然地，我们会期望几何和算法复杂性在理解装配机制中发挥关键作用，因为装配过程必须关键地依赖于所谓的装配构型空间的复杂形状和体积，在这个空间中，分子在组装时相对于彼此移动。相反，我们也很自然地期望，新的数学、算法和软件将从理解复杂的分子构型空间的探索中产生，并对它们进行计算。该项目的目标包括新的定理和算法，它们与流行方法的融合，以及开源软件。在刚性、构形空间、距离几何等长开问题上有望取得进展；高维和拓扑复杂构型空间的高效图谱、搜索、采样和体积计算算法；将新算法与流行的基于能量的蒙特卡罗模拟相结合的混合方法；最重要的是，预测得到了具体的实验验证。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，非常适合将这三个社区结合在一起，为研究生提供跨学科培训，并向学校和公众推广。

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.