CLASSIFICATION AND AVERAGING OF SINGLE PARTICLES IN CRYO-ET

Cryo-ET 中单个颗粒的分类和平均

• 批准号: 7598618
• 负责人: MICHAEL F. SCHMID
• 金额: $ 4.89万
• 依托单位: BAYLOR COLLEGE OF MEDICINE
• 依托单位国家: 美国
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-12-01 至 2007-11-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7598618
• 关键词: 3-Dimensional; Accounting; Cells; Classification; Complex; Computer Retrieval of Information on Scientific Projects Database; Data; Data Collection; Electron Microscope; Electrons; Fourier Transform; Funding; Grant; Institution; Lead; Maps; Methods; Microscope; Modeling; Molecular Conformation; Noise; Numbers; Operative Surgical Procedures; Pattern; Problem Solving; Range; Relative (related person); Research; Research Personnel; Resolution; Resources; Rotation; Signal Transduction; Simulate; Sorting - Cell Movement; Source; Specimen; Structure; Subgroup; Tomogram; United States National Institutes of Health; particle; reconstruction; size; success; three-dimensional modeling; tomography

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.

这个子项目是许多研究子项目中的一个 由NIH/NCRR资助的中心赠款提供的资源。子项目和 研究者（PI）可能从另一个NIH来源获得了主要资金， 因此可以在其他CRISP条目中表示。所列机构为 研究中心，而研究中心不一定是研究者所在的机构。 电子低温断层摄影术对于研究具有多形结构的大型物体具有优势。然而，断层扫描遭受的“丢失的楔形”的问题，由于有限的倾斜的标本在显微镜列。目前正在研究各种方法，通过互相关将对称性、构造或大小相同的物体分类，然后分别对各分组进行平均，以提高信噪比，从而提高分辨率。 期望对与从断层摄影重建中分离的颗粒相对应的3D体积进行互相关和平均。这对于表征细胞的内容物或在颗粒的对称性、大小或构象不确定的情况下开发无偏差的3D模型或模型是有用的。 确定粒子的相对取向对于该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，这与断层重建的数据收集几何形状有关。因为在电子显微镜中不能实现<$90 <$的倾斜角范围，所以傅立叶空间中的中心部分对于高于60-70 <$的倾斜是缺失的，导致通常被称为“倾斜”的问题。 缺楔 在傅立叶空间中。在从断层图像提取之后并且在应用任何旋转之前，对于每个颗粒/体积，傅立叶空间中缺失的楔形的方向是相同的。然而，粒子本身的取向相对于彼此是随机的，并且必须在3D旋转空间中搜索。由于来自缺失楔形图案的强信号，互相关图可能仅仅导致缺失楔形的对准，这当然是不正确的。在各向同性起始模型可用并用于3-D对准的情况下，该问题不会以相同的程度发生。 我们通过理解互惠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3-D体积（每个包含缺失的楔形）在互相关搜索中相对于彼此旋转时，并且一个体积乘以另一个体积的复共轭，生成零。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，并且这种零的数量会在搜索中的每个旋转角度增量处发生变化。为了最小化缺失的楔形物对3-D互相关图的整体尺度的影响，我们计算了在傅立叶空间中对于在空间中搜索两个粒子的每个相对3-D方向的复数乘法之后的非零项的数量，并且通过该数量的倒数在该方向搜索角度处缩放3-D互相关图。该校正因子是近似正确的，因为互相关函数的傅立叶变换中的总功率影响随后的互相关图的值。这种归一化足够好，以允许确定颗粒的真正适当的相对取向，如从我们的具有缺失楔形的模拟数据（M.F. Schmid，unpublished）. 我们还开发了在将粒子平均在一起时考虑缺失楔形的方法。我们的方法导致更准确的平均值。