Improved algorithms for macromolecular structure determination by cryo-EM and NMR

描述(申请人提供)：单粒子电子冷冻显微镜(CRYO-EM)和2D核磁共振波谱是观察大小分子三维结构的方法。分别进行了分析。我们建议开发和应用新的算法来解决由这些结构生物学技术提出的困难的数学问题。在低温电子显微镜中，实验数据由噪声的、随机的大分子“粒子”投影图像组成，问题是找到与这些图像一致的3D结构。目前的重建技术依赖于用户输入或自组织模型来启动细化周期。我们提出了一种新的算法--全局一致角度重建算法(GCar)，它为重建问题提供了一种无偏的、直接的解决方案。我们进一步提出了对gCar的扩展，以处理异质粒子种群。我们还将采用一种强大的新方法来确定班级平均数，即“三胞胎班级平均数”。这应该允许gCar与通常获得的信噪比非常低的数据一起使用。来自核磁共振的实验数据包括对原子之间局部距离的估计，目标是找到一个全球一致的坐标系。GCar背后的相同理论，包括稀疏线性算子的性质，可以应用于获得距离几何问题的快速和直接的解决方案。我们将开发和实现所有这些算法，并使用实验低温EM和核磁共振数据对它们进行测试。

DESCRIPTION (provided by applicant): Single-particle electron cryomicroscopy (cryo-EM) and 2D NMR spectroscopy are methods for observing the three-dimensional structures of large and small macromolecules. respectively. We propose to develop and apply novel algorithms for solving the difficult mathematical problems posed by these techniques of structural biology. In cryo-EM the experimental data consist of noisy, random projection images of macromolecular "particles", and the problem is finding the 3D structure which is consistent with these images. Present reconstruction techniques rely on user input or ad hoc models to initiate a refinement cycle. We propose a new algorithm, "globally consistent angular reconstitution" (GCAR) that provides an unbiased and direct solution to the reconstruction problem. We further propose an extension to GCAR to handle heterogeneous particle populations. We also will pursue a powerful new approach to determining class averages, "triplet class averaging". This should allow GCAR to be used with data having very low signal-to-noise ratios, as is commonly obtained. The experimental data from NMR consist of estimates of local distances between atoms, and the goal is to find a globally consistent coordinate system. The same theory behind GCAR, involving the properties of sparse linear operators, can be applied to obtain a fast and direct solution to the distance geometry problem. We will develop and implement all of these algorithms and test them with experimental cryo-EM and NMR data.