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Three-dimensional electron microscopy (3D-EM) is a powerful tool for visualizing complex biological systems. As with any other imaging device, the electron microscope introduces a transfer function (called in this field the contrast transfer function, CTF) into the image acquisition process that modulates the various frequencies of the signal. Thus...
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... Another versatile component is PickerView, implemented in emvis, which is instantiated by the em-viewer program to display the results of particle picking. The underlying PickingModel allows the easy support of different output formats from many programs such as Xmipp (Sorzano et al., 2004;Scheres et al., 2008;de la Rosa-Trevín et al., 2013), RELION (Scheres, 2012;Kimanius et al., 2016;Zivanov et al., 2018), Scipion (de la Rosa-Trevín et al., 2016), EMAN (Tang et al., 2007), crYOLO (Wagner et al., 2019) and Topaz (Bepler et al., 2019). It also facilitates the addition of new programs by providing a minimal amount of code to parse from a specific format. ...
... (Sorzano et al., 2004;Scheres et al., 2008;de la Rosa-Trevín et al., 2013), EMAN2(Tang et al., 2007), Bsoft(Heymann & Belnap, 2007) and RELION(Scheres, 2012;Kimanius et al., 2016;Zivanov et al., ...
Image-processing software has always been an integral part of structure determination by cryogenic electron microscopy (cryo-EM). Recent advances in hardware and software are recognized as one of the key factors in the so-called cryo-EM resolution revolution. Increasing computational power has opened many possibilities to consider more demanding algorithms, which in turn allow more complex biological problems to be tackled. Moreover, data processing has become more accessible to many experimental groups, with computations that used to last for many days at supercomputing facilities now being performed in hours on personal workstations. All of these advances, together with the rapid expansion of the community, continue to pose challenges and new demands on the software-development side. In this article, the development of emcore and emvis , two basic software libraries for image manipulation and data visualization in cryo-EM, is presented. The main goal is to provide basic functionality organized in modular components that other developers can reuse to implement new algorithms or build graphical applications. An additional aim is to showcase the importance of following established practices in software engineering, with the hope that this could be a first step towards a more standardized way of developing and distributing software in the field.
... Matej and Lewitt [11,12] provided a careful investigation of how the blob basis functions should be chosen when they are used in the context of image reconstruction from projections. Since then blobs have been used extensively for image reconstruction in X-ray computerized tomography [13], positron emission tomography [14][15][16][17], single photon emission computerized tomography [18][19][20], optoacoustic tomography [21] and electron microscopy [22][23][24][25][26]. ...
The series expansion approaches to image reconstruction from projections assume that the object to be reconstructed can be represented as a linear combination of fixed basis functions and the task of the reconstruction algorithm is to estimate the coefficients in such a linear combination based on the measured projection data. It is demonstrated that using spherically symmetric basis functions (blobs), instead of ones based on the more traditional pixels, yields superior reconstructions of medically relevant objects. The demonstration uses simulated computerized tomography projection data of head cross-sections and the series expansion method ART for the reconstruction. In addition to showing the results of one anecdotal example, the relative efficacy of using pixel and blob basis functions in image reconstruction from projections is also evaluated using a statistical hypothesis testing based task oriented comparison methodology. The superiority of the efficacy of blob basis functions over that of pixel basis function is found to be statistically significant.
... Matej and Lewitt [5,6] provided a careful investigation of how the blob basis functions should be chosen when they are used in the context of 3D image reconstruction. Since then blobs have been used extensively for 3D image reconstruction in x-ray computed tomography [7], positron emission tomography [8,9], single photon emission computed tomography [10][11][12], and electron microscopy [13][14][15][16]. ...
A technique for optimizing parameters for image representation using blob basis functions is presented and demonstrated. The exact choice of the basis functions significantly influences the quality of the image representation. It has been previously established that using spherically symmetric volume elements (blobs) as basis functions, instead of the more traditional voxels, yields superior representations of real objects, provided that the parameters that occur in the definition of the family of blobs are appropriately tuned. The technique presented in this paper makes use of an extra degree of freedom, which has been previously ignored, in the blob parameter space. The efficacy of the resulting parameters is illustrated.
... The IPR method can be mathematically identified (with appropriate nonessential changes of notations dictated by the problem at hand here) with the Iterative Data Refinement (IDR) method of [5], see also [ [20], and in positron emission tomography (PET) by Crepaldi and De Pierro [8]. Comparing IDR with the IPR outline proposed here the necessary adjustments to the IDR which yield the IPR and the identification of quantities can be observed as follows. ...
We formulate the method of iterative prescription refinement for inverse planning in any fully discretized model of radiation therapy. The method starts out from an ideal dose prescription and repeatedly refines it into a refined dose prescription. This is done computationally without human interaction until a prespecified stopping rule is met, at which point the refined dose vector and the accompanying beamlet intensities vector are evaluated and presented to the planner. The algorithmic regime is general enough to encompass various physical models that may use different particles (photons, protons, etc.) It is formulated for a general inversion operator thus different objective functions or approaches to the optimization problem (such as DVH, gEUD, or TCP and NTCP cost functions) may all be applied. Although not limited to this model, we demonstrate that the approach at all works on two exemplary cases from photon intensity-modulated radiation therapy.
... Due to it being theoretically optimal, the problem of full CTF correction is frequently addressed in the community of 3DEM methods research (e.g. [11,[24][25][26][27][28][29]). ...
... Other ways of doing a full CTF correction have been tried as well, such as the iterative method given by Penczek et al. [32], the iterative data refinement (IDR) technique [25], and the Chahine's method [27]. Differing in important details, these methods all attempt finding an approximation of the original image by iterative refinement or minimization of a residual function. ...
The typical resolution of three-dimensional reconstruction by cryo-EM single particle analysis is now being pushed up to and beyond the nanometer scale. Correction of the contrast transfer function (CTF) of electron microscopic images is essential for achieving such a high resolution. Various correction methods exist and are employed in popular reconstruction software packages. Here, we present a novel approximation method that corrects the amplitude modulation introduced by the contrast transfer function by convoluting the images with a piecewise continuous function. Our new approach can easily be implemented and incorporated into other packages. The implemented method yielded higher resolution reconstructions with data sets from both highly symmetric and asymmetric structures. It is an efficient alternative correction method that allows quick convergence of the 3D reconstruction and has a high tolerance for noisy images, thus easing a bottleneck in practical reconstruction of macromolecules.
... Moreover, we explore the effect of the variability in the estimation of the CTF parameters in subsequent algorithms for CTF correction. In particular, we analyzed its effects on CTF phase correction and CTF amplitude correction using the Iterative Data Refinement (IDR) [16]. We show that in our experiments, the estimation errors of the CTF detection performed in [1] does not significantly deteriorates the CTF correction. ...
The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.
In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.
We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.
... Second, the CTF is corrected using the estimated parameters and one of the existing CTF correction methods , Penczek et al., 1997, Sorzano et al., 2004c. The most difficult part is definitely an accurate CTF estimation, knowing that images may have a very poor SNR, which is the case of low-dose cryo-electron micrographs. ...
Three-dimensional structure of a wide range of biological specimens can be computed from images collected by transmission electron microscopy. This information integrated with structural data obtained with other techniques (e.g., X-ray crystallography) helps structural biologists to understand the function of macromolecular complexes and organelles within cells. In this paper, we compare two three-dimensional transmission electron microscopy techniques that are becoming more and more related (at the image acquisition level as well as the image processing one): electron tomography and single-particle analysis. The first one is currently used to elucidate the three-dimensional structure of cellular components or smaller entire cells, whereas the second one has been traditionally applied to structural studies of macromolecules and macromolecular complexes. Also, we discuss possibilities for their integration with other structural biology techniques for an integrative study of living matter from proteins to whole cells.
... This realignment step follows the spirit of procedures implemented in EMAN 6 and may serve to eliminate bias from an incorrect starting model. The second refinement protocol is based on a combination of multiresolution wavelet refinement 30 and continuous angular assignments 31 and allows correction of CTF amplitudes through iterative data refinement 32 . Both refinement protocols implement 3D reconstruction using the algebraic reconstruction technique (ART) with blobs, which may provide specific advantages over alternative reconstruction methods for small and very noisy data sets or uneven angular distributions 33,34 . ...
We describe a collection of standardized image processing protocols for electron microscopy single-particle analysis using the XMIPP software package. These protocols allow performing the entire processing workflow starting from digitized micrographs up to the final refinement and evaluation of 3D models. A particular emphasis has been placed on the treatment of structurally heterogeneous data through maximum-likelihood refinements and self-organizing maps as well as the generation of initial 3D models for such data sets through random conical tilt reconstruction methods. All protocols presented have been implemented as stand-alone, executable python scripts, for which a dedicated graphical user interface has been developed. Thereby, they may provide novice users with a convenient tool to quickly obtain useful results with minimum efforts in learning about the details of this comprehensive package. Examples of applications are presented for a negative stain random conical tilt data set on the hexameric helicase G40P and for a structurally heterogeneous data set on 70S Escherichia coli ribosomes embedded in vitrified ice.
... This is carried out by shifting phases at 180° for frequencies where contrast is negative (Frank 2006). Both amplitude and phase can be corrected with the following methods: Wiener Wltering of images (Frank and Penczek 1995; GrigorieV 1998 ), Wiener Wltering of volumes computed from focal series (Penczek et al. 1997), Iterative data reWnement (Sorzano et al. 2004d), Maximum entropy (Skoglund et al. 1996), Direct deconvolution in Fourier space (Stark et al. 1997), Chahine's method (Zubelli et al. 2003), etc. ...
Transmission electron microscopy is a powerful technique for studying the three-dimensional (3D) structure of a wide range of biological specimens. Knowledge of this structure is crucial for fully understanding complex relationships among macromolecular complexes and organelles in living cells. In this paper, we present the principles and main application domains of 3D transmission electron microscopy in structural biology. Moreover, we survey current developments needed in this field, and discuss the close relationship of 3D transmission electron microscopy with other experimental techniques aimed at obtaining structural and dynamical information from the scale of whole living cells to atomic structure of macromolecular complexes.
... Once the CTF is estimated it can be corrected with any of the available methods: Wiener filtering (Frank and Penczek, 1995; Grigorieff, 1998), combination of differently defocused volumes (Holmes et al., 2003; Penczek et al., 1997), maximum entropy (Skoglund et al., 1996), iterative data refinement (Sorzano et al., 2004a ), direct deconvolution in Fourier space (Stark et al., 1997), Chahine's method (Zubelli et al., 2003), etc. The CTF estimation method proposed in this work differs from previous methods in many ways, although it takes into account many of their best features. ...
Transmission electron microscopy, as most imaging devices, introduces optical aberrations that in the case of thin specimens are usually modeled in Fourier space by the so-called contrast transfer function (CTF). Accurate determination of the CTF is crucial for its posterior correction. Furthermore, the CTF estimation must be fast and robust if high-throughput three-dimensional electron microscopy (3DEM) studies are to be carried out. In this paper we present a robust algorithm that fits a theoretical CTF model to the power spectrum density (PSD) measured on a specific micrograph or micrograph area. Our algorithm is capable of estimating the envelope of the CTF which is absolutely needed for the correction of the CTF amplitude changes.
