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

自然界和工程学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。许多组装过程结合了变构现象，其中分子间的相互作用由相互作用分子中的一个远程位置的结合事件控制。尽管在体内、体外和电子实验中的努力越来越复杂，但人们对组装过程知之甚少。一个数学上更严谨、机械上更直观的理论不仅对预测和设计组装和变构至关重要，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、设计药物和设计纳米级的材料。几何和算法复杂性将在理解组装背后的机制方面发挥关键作用，因为组装过程必须关键依赖于所谓组装构型空间的复杂形状和体积，分子在组装时在组装构型空间中相互运动。相反，人们也很自然地期待新的数学、算法和软件将产生于理解复杂的分子构型空间并在其上进行计算的探索。该项目的目标包括新的定理和算法，它们与主流方法的杂交，以及开源软件。预计在刚性、构形空间、距离几何等长期悬而未决的问题上将取得进展；用于高维和拓扑复杂构形空间的有效地图集、搜索、采样和体积计算的算法；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；以及最重要的，对预测的具体实验验证。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，为研究型学生提供跨学科培训，以及向学校和公众进行外联。

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.