CLASSIFICATION AND AVERAGING OF SINGLE PARTICLES IN CRYO-ET

这个子项目是许多研究子项目中利用 资源由NIH/NCRR资助的中心拨款提供。子项目和 调查员(PI)可能从NIH的另一个来源获得了主要资金， 并因此可以在其他清晰的条目中表示。列出的机构是 该中心不一定是调查人员的机构。 电子冷冻层析成像在研究具有多形结构的大型物体方面具有优势。然而，由于显微镜柱中样品的倾斜有限，层析成像存在“缺失楔形”的问题。正在开发通过互相关来挑选具有相同对称性、构象或大小的对象，然后分别对子组进行平均的方法，以便提高信噪比，从而提高分辨率。 期望相互关联并平均对应于从断层重建中分离出的颗粒的3D体积。这对于表征单元格的内容很有用，或者在粒子的对称性、大小或构象不确定的情况下开发一个或多个无偏3D模型都很有用。 确定粒子的相对方向对这一操作的成功至关重要。然而，我们在这些比较中遇到了一个困难，必须处理用于断层重建的数据收集的几何形状。由于电子显微镜不能实现90°的倾斜角范围，因此傅里叶空间中倾角大于60-70°的中心截面丢失，导致通常被称为傅里叶空间中丢失楔形的问题。从断层图像提取后，在应用任何旋转之前，对于每个粒子/体积，傅立叶空间中缺失的楔形的方向是相同的。但是，粒子本身的方向相对于彼此是随机的，必须在3D旋转空间中进行搜索。由于来自缺失楔形图案的强信号，互相关图可能仅导致缺失楔形的对准，这肯定是不正确的。在各向同性起始模型可用于3-D对齐的情况下，此问题不会出现相同程度的问题。 我们通过理解互易空间中的相关问题解决了这个问题。当傅立叶空间中的两个3D体积在互相关搜索中彼此相对旋转时，其中一个体积被乘以另一个的复共轭，产生零。当其中一个粒子的缺失数据区域乘以另一个粒子中的数据时，就会发生这种情况，并且在搜索中每增加一个旋转角度，这些零的数量就会发生变化。为了最大限度地减小缺失楔形对三维互相关图整体尺度的影响，我们计算了在傅立叶空间中对搜索两个粒子的空间中每个相对三维方向进行复乘后的非零项的数目，并根据该数目的倒数来缩放该方向搜索角下的三维互相关图。该校正系数大致正确，因为互相关函数的傅里叶变换中的总功率影响随后的互相关图的值。这种归一化很好，足以确定粒子真正正确的相对取向，如我们的模拟数据所示，没有楔形(M.F.施密德，未发表)。 我们还开发了一种方法来解释粒子平均时丢失的楔形。我们的方法可以得到更准确的平均值。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Electron cryo-tomography has advantages for studying large objects having pleomorphic structures. However, tomography suffers from the "missing wedge" problem due to the limited tilts of specimens in the microscope column. Methods are being developed to sort out objects of the same symmetry, conformation or size by cross-correlation and then to average the subgroups separately in order to enhance the signal to noise ratio and thus the resolution. It is desirable to cross-correlate and average 3D volumes corresponding to particles isolated from a tomographic reconstruction. This is useful either to characterize the contents of a cell, or to develop an unbiased 3D model or models if the symmetry, size or conformation of the particles is uncertain. Determining the relative orientations of the particles is crucial to the success of this operation. However, we encountered a difficulty in these comparisons having to do with the geometry of data collection for tomographic reconstructions. Because a tilt angle range of ¿90¿ cannot be achieved in the electron microscope, central sections in Fourier space for tilts higher than 60-70¿ are missing, leading to the problem commonly referred to as the missing wedge in Fourier space. After extraction from the tomogram and before applying any rotations, the orientation of the missing wedge in Fourier space is identical for each particle/volume. However, the orientation of the particles themselves is random with respect to each other and must be searched for in 3D rotation space. Because of the strong signal from the pattern of the missing wedge, the cross-correlation map may merely lead to the alignment of the missing wedges, which is certainly not correct. This problem does not occur to the same extent in cases where an isotropic starting model is available and used for 3-D alignment. We solved this problem by understanding the relevant issues in reciprocal space. As two 3-D volumes in Fourier space, each containing a missing wedge, are rotated against each other in the cross-correlation search, and one volume is multiplied by the complex conjugate of the other, zeros are generated. They occur when the missing-data region for one of the particles is multiplied by data in the other particle, and the number of such zeros changes at each rotation angle increment in the search. To minimize the effect of the missing wedge on the overall scale of the 3-D cross-correlation map, we computed the number of non-zero terms after the complex multiplication in Fourier space for each relative 3-D orientation in the space searched for the two particles, and scaled the 3-D cross-correlation map at that orientation search angle by the reciprocal of this number. This correction factor is approximately right because the total power in the Fourier transform of a cross-correlation function influences the values of the subsequent cross-correlation map. This normalization was good enough to allow the true proper relative orientation of the particles to be determined as demonstrated from our simulated data with missing wedge (M.F. Schmid, unpublished). We also developed methods for accounting for the missing wedge when averaging particles together. Our methods lead to more accurate averages.