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

描述（由申请人提供）：单粒子电子低温显微镜（cryo-EM）和2D NMR光谱法是观察大分子和小分子三维结构的方法。分别我们建议开发和应用新的算法来解决这些结构生物学技术所带来的困难的数学问题。在冷冻EM实验数据包括嘈杂的，随机投影图像的大分子“颗粒”，问题是找到的3D结构，这是符合这些图像。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，“全球一致的角度重建”（GCAR），提供了一个公正的和直接的解决方案的重建问题。我们进一步提出了一个扩展GCAR处理异质粒子群体。我们还将寻求一种强大的新方法来确定类平均值，“三重类平均”。这应该允许GCAR用于具有非常低的信噪比的数据，正如通常获得的那样。核磁共振的实验数据包括原子之间局部距离的估计，目标是找到一个全局一致的坐标系。GCAR背后的相同理论，涉及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cryo-EM和NMR数据对其进行测试。

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.