A statistical approach to computer processing of cryo-electron microscope images: virion classification and 3-D reconstruction

The scattering density of the virus is represented as a truncated weighted sum of orthonormal basis functions in spherical coordinates, where the angular dependence of each basis function has icosahedral symmetry. A statistical model of the image formation process is proposed and the maximum likelihood estimation method computed by an expectation-maximization algorithm is used to estimate the weights in the sum and thereby compute a 3-D reconstruction of the virus particle. If multiple types of virus particle are represented in the boxed images then multiple 3-D reconstructions are computed simultaneously without first requiring that the type of particle shown in each boxed image be determined. Examples of the procedure are described for viruses with known structure: (1). 3-D reconstruction of Flockhouse Virus from experimental images, (2). 3-D reconstruction of the capsid of Nudaurelia Omega Capensis Virus from synthetic images, and (3). 3-D reconstruction of both the capsid and the procapsid of Nudaurelia Omega Capensis Virus from a mixture of unclassified synthetic images.     

An ab initio algorithm for low-resolution 3-D reconstructions from cryoelectron microscopy images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

An ab Initio Algorithm for Low-Resolution 3-D Reconstructions from Cryoelectron Microscopy Images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

Dual-Axis Tomography: An Approach with Alignment Methods That Preserve Resolution

Tomographic reconstructions of biological specimens are now routinely being generated in our high voltage electron microscope by tilting the specimen around two orthogonal axes. Separate tomograms are computed from each tilt series. The two tomograms are aligned to each other with general 3-D linear transformations that can correct for distortions between the two tomograms, thus preserving the inherent resolution of the reconstruction throughout its volume. The 3-D Fourier transforms of the two tomograms are then selectively combined to achieve a single tomogram. Unlike a single-axis tomogram, a dual-axis tomogram shows good resolution for extended features at any orientation in the plane of the specimen; it also has improved resolution in the depth of the specimen. Calculations indicate that the improvements available from double tilting and from tilting to higher angles are largely additive. Actual and model data were used to assess whether varying the increment between tilted views in proportion to the cosine of the tilt angle would allow a reduction in the number of pictures required to achieve a given resolution of reconstruction. Analysis by Fourier sector correlation indicated that the variable tilt increment improved the reconstruction in some respects but degraded it in others. A varying tilt increment thus does not give an unqualified improvement, at least when using back-projection algorithms for the reconstruction.     

Ab initio resolution measurement for single particle structures

A computational method is described that allows the measurement of the signal-to-noise ratio and resolution of a three-dimensional structure obtained by single particle electron microscopy and reconstruction. The method does not rely on the availability of the original image data or the calculation of several structures from different parts of the data that are needed for the commonly used Fourier Shell Correlation criterion. Instead, the correlation between neighboring Fourier pixels is calculated and used to distinguish signal from noise. The new method has been conveniently implemented in a computer program called RMEASURE and is available to the microscopy community.     

Electron microscope analysis of tissue components identified and located by computer-assisted 3-D reconstructions: ultrastructural segmentation of the developing human proximal tubule

A method is described for ultrastructural analysis of renal tubules after precise identification of tubule segments by computerized 3-D reconstruction at the light microscope level. Semithin serial sections were cut of entire nephrons and 3-D coordinate information was obtained by digitization of tubule cross sections in the semithin sections. With the aid of the computer the tubule axis was traced from one section to the other. Precise lengths and positions of the tubules in three dimensions were calculated and stereoscopic images generated. The method was used to analyze the 3-D structure of developing human nephrons, and the ultrastructural development of the proximal tubule. Ultrastructural segmentation of the proximal tubule was demonstrated in the human fetal nephron in developmental stage IV.     

Particle-Based Multidimensional Multispecies Biofilm Model

In this paper we describe a spatially multidimensional (two-dimensional [2-D] and three-dimensional [3-D]) particle-based approach for modeling the dynamics of multispecies biofilms growing on multiple substrates. The model is based on diffusion-reaction mass balances for chemical species coupled with microbial growth and spreading of biomass represented by hard spherical particles. Effectively, this is a scaled-up version of a previously proposed individual-based biofilm model. Predictions of this new particle-based model were quantitatively compared with those obtained with an established one-dimensional (1-D) multispecies model for equivalent problems. A nitrifying biofilm containing aerobic ammonium and nitrite oxidizers, anaerobic ammonium oxidizers, and inert biomass was chosen as an example. The 2-D and 3-D models generally gave the same results. If only the average flux of nutrients needs to be known, 2-D and 1-D models are very similar. However, the behavior of intermediates, which are produced and consumed in different locations within the biofilm, is better described in 2-D and 3-D models because of the multidirectional concentration gradients. The predictions of 2-D or 3-D models are also different from those of 1-D models for slowly growing or minority species in the biofilm. This aspect is related to the mechanism of biomass spreading or advection implemented in the models and should receive more attention in future experimental studies.     

Particle-based multidimensional multispecies biofilm model

In this paper we describe a spatially multidimensional (two-dimensional [2-D] and three-dimensional [3-D]) particle-based approach for modeling the dynamics of multispecies biofilms growing on multiple substrates. The model is based on diffusion-reaction mass balances for chemical species coupled with microbial growth and spreading of biomass represented by hard spherical particles. Effectively, this is a scaled-up version of a previously proposed individual-based biofilm model. Predictions of this new particle-based model were quantitatively compared with those obtained with an established one-dimensional (1-D) multispecies model for equivalent problems. A nitrifying biofilm containing aerobic ammonium and nitrite oxidizers, anaerobic ammonium oxidizers, and inert biomass was chosen as an example. The 2-D and 3-D models generally gave the same results. If only the average flux of nutrients needs to be known, 2-D and 1-D models are very similar. However, the behavior of intermediates, which are produced and consumed in different locations within the biofilm, is better described in 2-D and 3-D models because of the multidirectional concentration gradients. The predictions of 2-D or 3-D models are also different from those of 1-D models for slowly growing or minority species in the biofilm. This aspect is related to the mechanism of biomass spreading or advection implemented in the models and should receive more attention in future experimental studies.     

On the freezing and identification of lipid monolayer 2-D arrays for cryoelectron microscopy

Lipid monolayers provide a convenient vehicle for the crystallization of biological macromolecules for 3-D electron microscopy. Although numerous examples of 3-D images from 2-D protein arrays have been described from negatively stained specimens, only six structures have been done from frozen-hydrated specimens. We describe here a method that makes high quality frozen-hydrated specimens of lipid monolayer arrays for cryoelectron microscopy. The method uses holey carbon films with patterned holes for monolayer recovery, blotting and plunge freezing to produce thin aqueous films which cover >90% of the available grid area. With this method, even specimens with relatively infrequent crystals can be screened using automated data collection techniques. Though developed for microscopic examination of 2-D arrays, the method may have wider application to the preparation of single particle specimens for 3-D image reconstruction.     

Noninvasive measurements of transmural myocardial metabolites using 3-D (31)P NMR spectroscopy

A completely noninvasive three-dimensional (3-D) static magnetic field magnitude spatially localized (31)P spectroscopy technique has been developed and applied to study the in vivo canine myocardium at 9.4 T. The technique incorporates both Fourier series windows and selective Fourier transform methods utilizing all three orthogonal gradients for 3-D phase encoding. The number of data acquisitions for each phase-encoding step was weighted according to the Fourier coefficients to define cylindrical voxels. Spatially localized (31)P spectra can be generated for voxels of desired location within the field of view as a postprocessing step. The quality of localization was first demonstrated by using a three-compartment phantom. The technique was then applied to in vivo canine models and yielded (31)P cardiac spectra with an excellent signal-to-noise ratio. The in vivo validation experiments, using an implanted 2-phosphoenolpyruvate-containing marker, demonstrated that the technique is capable of measuring at least two transmural layers of left ventricular myocardium representing the subepicardium and subendocardium.     

ResLog plots as an empirical metric of the quality of cryo-EM reconstructions

Compared to the field of X-ray crystallography, the field of single particle three-dimensional electron microscopy has few reliable metrics for assessing the quality of 3D reconstructions. New metrics are needed that can determine whether a given 3D reconstruction accurately reflects the structure of the particles from which it was derived or instead depicts a plausible though incorrect structure due to coarse misalignment of particles. Here an empirical procedure is presented for differentiating between a reconstruction with well-aligned particles and a reconstruction with grossly misclassified particles. For a given dataset, 3D reconstructions are computed from subsets of particles with decreasing numbers of particles contributing to the reconstruction. A plot of inverse resolution vs. the logarithm of the number of particles (a “ResLog” plot) provides metrics for the reliability of the reconstruction and the overall quality of the dataset and processing. Specifically, the y-intercept of a regression line provides a measure of the relative accuracy of the particle alignment and classification, and the slope is an indicator of the overall data quality including the imaging conditions and processing steps. ResLog plots can also be used to optimize conditions for data collection and reconstruction parameters. Although resolution estimates can vary by method of calculation, ResLog-derived parameters are consistent whether calculated by Fourier shell correlation or Fourier neighbor correlation, or a new coordinate-based metric that serves as a yardstick for structures where atomic coordinates are available. ResLog plots could become part of a standard set of parameters to be included in 3D reconstruction reports.     

生物组织显微结构三维重建的灰度阴影立体图对显示技术

本文描述了一种新的显示三维重建模型的方法—灰度阴影立体图对方法(shading-stereo-pair method).该方法根据连续切片三维重建的灰度阴影法和立体图对法的显示原理,导出了生成立体图对的视差公式.在灰度阴影法三维重建过程中,根据各切片所处的深度和其本身的厚度,按视差公式计算出它们在图对上的位移量并进行水平方向的移动,经过对各切片的叠加和重组,最后生成一幅具有视差信息的灰度阴影立体图对.在体视仪下观察,即可看到重建模型的三维实体图象.最后还讨论了进一步提高图象质量和改善观察效果所必须采取的措施.     

计算机三维重建华虻复眼性特异小网膜细胞结构

本文在计算机三维重建的基础上讨论了华虻复眼小网膜性特异结构与功能的关系,三维模型展示了中央小网膜细胞和部分外周小网膜细胞的空间构型及相互关系.在生物组织连续切片三维重建的对位技术方面,摸索了一套方法.保证了在Cromemco微机系统上实现对华虻复眼小网膜细胞的三维重建.证实了复眼光感受器性特化区R_7和R_8为并行排列的形式,并与非性特化区的R_7、R_8进行了比较.     

Comparison of the decameric structure of peroxiredoxin-II by transmission electron microscopy and X-ray crystallography.

The decameric human erythrocyte protein torin is identical to the thiol-specific antioxidant protein-II (TSA-II), also termed peroxiredoxin-II (Prx-II). Single particle analysis from electron micrographs of Prx-II molecules homogeneously orientated across holes in the presence of a thin film of ammonium molybdate and trehalose has facilitated the production of a >/=20 A 3-D reconstruction by angular reconstitution that emphasises the D5 symmetry of the ring-like decamer. The X-ray structure for Prx-II was fitted into the transmission electron microscopic reconstruction by molecular replacement. The surface-rendered transmission electron microscopy (TEM) reconstruction correlates well with the solvent-excluded surface of the X-ray structure of the Prx-II molecule. This provides confirmation that transmission electron microscopy of negatively stained specimens, despite limited resolution, has the potential to reveal a valid representation of surface features of protein molecules. 2-D crystallisation of the Prx-II protein on mica as part of a TEM study resulted in the formation of a p2 crystal form with parallel linear arrays of stacked rings. This latter 2-D form correlates well with that observed from the 2.7 A X-ray structure of Prx-II solved from a new orthorhombic 3-D crystal form.     

Compensated Row-Column Ultrasound Imaging System Using Fisher Tippett Multilayered Conditional Random Field Model

3-D ultrasound imaging offers unique opportunities in the field of non destructive testing that cannot be easily found in A-mode and B-mode images. To acquire a 3-D ultrasound image without a mechanically moving transducer, a 2-D array can be used. The row column technique is preferred over a fully addressed 2-D array as it requires a significantly lower number of interconnections. Recent advances in 3-D row-column ultrasound imaging systems were largely focused on sensor design. However, these imaging systems face three intrinsic challenges that cannot be addressed by improving sensor design alone: speckle noise, sparsity of data in the imaged volume, and the spatially dependent point spread function of the imaging system. In this paper, we propose a compensated row-column ultrasound image reconstruction system using Fisher-Tippett multilayered conditional random field model. Tests carried out on both simulated and real row-column ultrasound images show the effectiveness of our proposed system as opposed to other published systems. Visual assessment of the results show our proposed system’s potential at preserving detail and reducing speckle. Quantitative analysis shows that our proposed system outperforms previously published systems when evaluated with metrics such as Peak Signal to Noise Ratio, Coefficient of Correlation, and Effective Number of Looks. These results show the potential of our proposed system as an effective tool for enhancing 3-D row-column imaging.     

Estimation of variance in single-particle reconstruction using the bootstrap technique

Density maps of a molecule obtained by single-particle reconstruction from thousands of molecule projections exhibit strong changes in local definition and reproducibility, as a consequence of conformational variability of the molecule and non-stoichiometry of ligand binding. These changes complicate the interpretation of density maps in terms of molecular structure. A three-dimensional (3-D) variance map provides an effective tool to assess the structural definition in each volume element. In this work, the different contributions to the 3-D variance in a single-particle reconstruction are discussed, and an effective method for the estimation of the 3-D variance map is proposed, using a bootstrap technique of sampling. Computations with test data confirm the viability, computational efficiency, and accuracy of the method under conditions encountered in practical circumstances.     

Three-Dimensional Histology Volume Reconstruction of Axonal Tract Tracing Data: Exploring Topographical Organization in Subcortical Projections from Rat Barrel Cortex

Topographical organization is a hallmark of the mammalian brain, and the spatial organization of axonal connections in different brain regions provides a structural framework accommodating specific patterns of neural activity. The presence, amount, and spatial distribution of axonal connections are typically studied in tract tracing experiments in which axons or neurons are labeled and examined in histological sections. Three-dimensional (3-D) reconstruction techniques are used to achieve more complete visualization and improved understanding of complex topographical relationships. 3-D reconstruction approaches based on manually or semi-automatically recorded spatial points representing axonal labeling have been successfully applied for investigation of smaller brain regions, but are not practically feasible for whole-brain analysis of multiple regions. We here reconstruct serial histological images from four whole brains (originally acquired for conventional microscopic analysis) into volumetric images that are spatially registered to a 3-D atlas template. The aims were firstly to evaluate the quality of the 3-D reconstructions and the usefulness of the approach, and secondly to investigate axonal projection patterns and topographical organization in rat corticostriatal and corticothalamic pathways. We demonstrate that even with the limitations of the original routine histological material, the 3-D reconstructed volumetric images allow efficient visualization of tracer injection sites and axonal labeling, facilitating detection of spatial distributions and across-case comparisons. Our results further show that clusters of S1 corticostriatal and corticothalamic projections are distributed within narrow, elongated or spherical subspaces extending across the entire striatum / thalamus. We conclude that histology volume reconstructions facilitate mapping of spatial distribution patterns and topographical organization. The reconstructed image volumes are shared via the Rodent Brain Workbench (www.rbwb.org).     

3-D image analysis system and megakaryocyte quantitation

A quasi-automatic computer image analysis system has been developed for 3-D reconstruction of stained serial sections and implemented on an IBAS system. Some new automatic image analysis techniques have been designed and incorporated into the system. For image segmentation, a transition region determination based thresholding method is introduced. Neither histogram calculation nor empirical parameters are needed in the automatic threshold selection. A two step 3-D reconstruction procedure--symbolic and pictorial reconstructions--is designed to improve the flexibility and the computational capability of the system. The global level registration and local level registration are separated. The former consists of establishing the relationship among a large numbers of profile pairs dispersed in adjacent sections. A pattern matching method based on pattern recognition principles is devised to exploit the information about the statistical character of mismatch caused by deformation of sections and about the relationship of nearby objects. For the latter, an equivalent elliptical approximation method based on the physical theory of the rotation of rigid bodies is proposed. The system has been used for 3-D reconstruction and quantitation of megakaryocytes in human bone marrow tissue. Features about individual 3-D megakaryocyte cell and the spatial distribution of megakaryocytes are determined. The latter is a new contribution to megakaryocyte quantitation and is not possible by using conventional stereologic techniques. These experimental results have demonstrated the ability of the system to perform quantitative analysis.     

Pristine soils mineralize 3-chlorobenzoate and 2,4-dichlorophenoxyacetate via different microbial populations.

Biodegradation of two chlorinated aromatic compounds was found to be a common capability of the microorganisms found in the soils of undisturbed, pristine ecosystems. We used 2,4-dichlorophenoxyacetate (2,4-D) and 3-chlorobenzoate (3CBA) as enrichment substrates to compare populations of degrading bacteria from six different regions making up two ecosystems. We collected soil samples from four Mediterranean (California, central Chile, the Cape region of South Africa, and southwestern Australia) and two boreal (northern Saskatchewan and northwestern Russia) ecosystems that had no direct exposure to pesticides or to human disturbance. Between 96 and 120 samples from each of the six regions were incubated with 50 ppm of [U-14C]2,4-D or [U-14C]3CBA. Soils from all regions samples mineralized both 2,4-D and 3CBA, but 3CBA was mineralized without a lag period, while 2,4-D was generally not mineralized until the second week. 3CBA degradative capabilities were more evenly distributed spatially than those for 2,4-D. The degradative capabilities of the soils were readily transferred to fresh liquid medium. 3CBA degraders were easily isolated from most soils. We recovered 610 strains that could release carbon dioxide from ring-labeled 3CBA. Of these, 144 strains released chloride and degraded over 80% of 1 mM 3CBA in 3 weeks or less. In contrast, only five 2,4-D degraders could be isolated, although a variety of methods were used in an attempt to culture the degraders. The differences in the distribution and culturability of the bacteria responsible for 3CBA and 2,4-D degradation in these ecosystems suggest that the two substrates are degraded by different populations. We also describe a 14C-based microtiter plate method that allows efficient screening of a large number of samples for biodegradation activity.