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

描述（由申请人提供）：单粒子电子冷冻显微镜（cryo-EM）和二维核磁共振波谱是观察大小大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带来的困难的数学问题。在低温电镜中，实验数据是由大分子“粒子”的噪声、随机投影图像组成的，问题是找到与这些图像一致的三维结构。目前的重建技术依赖于用户输入或特别模型来启动一个改进周期。我们提出了一种新的算法“全局一致角度重构”（GCAR），它提供了一种无偏和直接的方法来解决重建问题。我们进一步提出了对GCAR的扩展，以处理异质粒子群。我们还将采用一种强大的新方法来确定类平均，即“三重类平均”。这应该允许GCAR用于通常获得的具有非常低信噪比的数据。来自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直接解。我们将开发和实现所有这些算法，并用实验低温电镜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.