Constrained Maximum Likelihood Cryo-EM Reconstruction in Proteomics

描述（由申请人提供）： 低温电子显微镜（CEM）是一种用于获得蛋白质三维结构的工具， 其他生物大分子。CEM在随机方向上产生结构的噪声二维图像，并且图像处理的挑战是通过对齐和平均图像来产生已知方向上的投影的估计。这些估计值（或平均值）是受约束的，因为它们必须满足所谓的公共线约束。 本申请提出了一种约束最大似然算法，保证产生 满足公共线约束的对齐的平均值。该算法使用修改后的期望- 最大化（EM）技术，以最大化可能性。修改包括确保 在每个EM迭代内满足公共线约束。的约束被证明是线性的，并强制执行使用冯诺依曼交替投影定理。该算法是可证明收敛的，单调提高的可能性，是最佳的。在应用中给出了数学理论和初步模拟。 该应用程序的目标是对算法的有效性进行全面的试点研究。重建的精度和分辨率将通过Monte Carlo模拟与合成和真实的3-D蛋白质和其他大分子结构进行研究。精度将通过重建中的平均均方误差来衡量，分辨率将通过傅立叶壳相关来衡量。此外，将通过重建IP 3 Ca离子通道蛋白来测量算法的性能。这种蛋白质的结构以前已经分析过了，所以与已发表的结构进行比较应该可以很好地表明相对准确度。 这项研究的最终意义在于，它将提供一个有保证的原则性算法， 重建蛋白质三维结构的特性。

DESCRIPTION (provided by applicant): Cryogenic Electron Microscopy (CEM) is a tool for obtaining three dimensional structure of proteins and other biological macromolecules. CEM produces noisy two dimensional images of the structure at random orientations, and the image processing challenge is to produce estimates of projections in known directions by aligning and averaging the images. These estimates (or averages) are constrained because they have to satisfy the so-called common line constraints. This application proposes a constrained maximum-likelihood algorithm that is guaranteed to produce aligned averages that satisfy the common line constraints. The algorithm uses a modified Expectation- Maximization (EM) technique to maximize the likelihood. The modification consists of ensuring that the common lines constraints are satisfied within each EM iteration. The constraints are shown to be linear and are enforced using the von Neuman alternating projections theorem. The algorithm is provably convergent, monotonically improves the likelihood, and is optimal. The mathematical theory and preliminary simulations are presented in the application. The goal of the application is to conduct a through pilot study of the efficacy of the algorithm. The accuracy and resolution of reconstruction will be studied by Monte Carlo simulations with synthetic and real 3-D protein and other macromolecular structures. The accuracy will be measured by the average mean squared error in reconstruction, and resolution will be measured by Fourier shell correlation. Further, the performance of the algorithm will be measured by reconstructing the IP3 Ca ion channel protein. The structure of this protein has been analyzed previously, so a comparison with published structure should provide a good indication of relative accuracy. The ultimate relevance of this research is that it would provide a principled algorithm with guaranteed properties for reconstructing the 3-D structure of proteins.