INSPIRE: Assessing feasible regions of configuration spaces for macromolecular crystals

INSPIRE项目由CISE/CCF算法基金会、MPS/DMS分析基金会和NSF综合活动办公室共同资助。了解蛋白质分子的三维结构有助于科学地理解蛋白质在细胞内如何发挥其功能。蛋白质数据库中超过100,000种蛋白质的结构已经通过大分子x射线晶体学确定：测量由一个或多个蛋白质分子的许多对称排列的拷贝组成的晶体的x射线光束的衍射，可以提供必须填充的部分信息（傅里叶变换的振幅）（解决“相位问题”，通常通过分子替换-从相关分子中取相）来完成3d结构。分子替代对简单的单域蛋白效果很好，但对多域蛋白和大型复合物则失效；我们需要探索域的可能组合和它们的衍射图案作为替代候选。这个跨学科项目汇集了机器人和纯数学领域的专家，以解决大分子x射线晶体学的“相位问题”。在这个项目中开发的数学和计算框架将使更多的蛋白质结构能够以比现在更省力的方式解决。该项目还通过独特的可视化活动向巴尔的摩市高中生介绍数学和分子生物物理学。组合域的本质是几何的。该团队可以使用机器人领域的铰接多刚体模型来组合结构的刚性部分，这些结构来自具有相似序列的领域。在这些铰接模型中，各区域之间的相对刚体运动成为未知的自由度。晶体填充约束将排除这些域的大多数可能配置，并降低搜索空间的高维性质。该项目将开发新的代数几何和计算方法，快速丢弃配置空间中的大碰撞区域，使搜索集中在这个高维搜索空间中剩余的小体积可行区域。将编写计算机代码，将所得方法集成到现有的分子晶体学软件包中。

This INSPIRE project is jointly funded by Algorithmic Foundations in CISE/CCF, Analysis in MPS/DMS, and the NSF Office of Integrative Activities.Knowledge of the 3-dimensional structure of protein molecules supports scientific understanding of how proteins perform their functions within cells. Structures of over 100,000 proteins in the Protein Data Bank have been determined by macromolecular x-ray crystallography: measuring the diffraction of x-ray beams from crystal composed of many symmetrically arranged copies of one or more protein molecules gives partial information (the amplitudes of the Fourier transform) that must be filled in (solving the "phase problem," often by molecular replacement -- taking phases from related molecules) to complete the 3d structure. Molecular replacement works quite well for simple single-domain proteins, but breaks down for multi-domain proteins and large complexes; one needs to explore the possible combinations of domains and their diffraction patterns as replacement candidates. This cross-disciplinary project brings together experts in robotics and in pure mathematics to address the ''phase problem'' of macromolecular x-ray crystallography. The mathematical and computational framework developed in this project will enable many more protein structures to be solved in a less laborious way than can be done now. The project also introduces Baltimore City high school students to mathematics and molecular biophysics through unique visualization activities.The essence of combining domains is geometric. The team can use articulated multi-rigid-body models from the field of robotics to combine rigid portions of structures, from domains with similar sequences. The relative rigid-body motions between the domains become the unknown degrees of freedom in these articulated models. Crystal packing constraints will rule out the majority of possible configurations for these domains, and reduce the otherwise high-dimensional nature of the search space. The project will develop new algebro-geometric and computational methods for rapidly discarding the large collision regions in configuration space, so that searches will focus on the remaining small-volume feasible regions in this high-dimensional search space. Computer code will be prepared integrating the resulting methods into existing molecular crystallography software packages.