Noise bias in the refinement of structures derived from single particles

Stewart, Alex; Grigorieff, Nikolaus

doi:10.1016/j.ultramic.2004.08.008

Cited by 133 publications

(154 citation statements)

References 34 publications

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“…A more sophisticated way to avoid the inXuence of high-frequency noise is the use of a spatial weighting scheme to assess the similarity of particle and reference images. The weakness of traditional cross-correlation-based alignment procedures to deal with high-frequency noise, and the applicability of weighted correlation coeYcients, have recently been reviewed in detail (Stewart and GrigorieV, 2004). Overall, the results obtained with improper sampling intervals illustrate that the advantages of higher image quality can easily disappear if over-weighting of the high-frequency components of the images occurs during the initial calculations.…”

Section: Discussionmentioning

confidence: 99%

Advantages of CCD detectors for de novo three-dimensional structure determination in single-particle electron microscopy

Sander

Golas

Stark

2005

Journal of Structural Biology

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For three-dimensional (3D) structure determination of large macromolecular complexes, single-particle electron cryomicroscopy is considered the method of choice. Within this Weld, structure determination de novo, as opposed to reWnement of known structures, still presents a major challenge, especially for macromolecules without point-group symmetry. This is primarily because of technical issues: one of these is poor image contrast, and another is the often low particle concentration and sample heterogeneity imposed by the practical limits of biochemical puriWcation. In this work, we tested a state-of-the art 4k £ 4k charge-coupled device (CCD) detector (TVIPS TemCam-F415) to see whether or not it can contribute to improving the image features that are especially important for structure determination de novo. The present study is therefore focused on a comparison of Wlm and CCD detector in the acquisition of images in the low-to-medium (»10-25 Å) resolution range using a 200 kV electron microscope equipped with Weld emission gun. For comparison, biological specimens and radiation-insensitive carbon layers were imaged under various conditions to test the image phase transmission, spatial signal-to-noise ratio, visual image quality and power-spectral signal decay for the complete imageprocessing chain. At all settings of the camera, the phase transmission and spectral signal-to-noise ratio were signiWcantly better on CCD than on Wlm in the low-to-medium resolution range. Thus, the number of particle images needed for initial structure determination is reduced and the overall quality of the initial computed 3D models is improved. However, at high resolution, Wlm is still signiWcantly better than the CCD camera: without binning of the CCD camera and at a magniWcation of 70k£, Wlm is better beyond 21 Å resolution. With 4-fold binning of the CCD camera and at very high magniWcation (>300k£) Wlm is still superior beyond 7 Å resolution. 

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Section: Discussionmentioning

confidence: 99%

Advantages of CCD detectors for de novo three-dimensional structure determination in single-particle electron microscopy

Sander

Golas

Stark

2005

Journal of Structural Biology

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“…4A Upper, first four classes) and particles from additional classes that clearly resembled these averages (SI Fig. 6, marked with a ''ϩ'') were combined and used to calculate a 3D reconstruction by using FREALIGN (37). The 3D structure of the U5.U2/U6 complex in cryo-negative stain is presented in Fig.…”

Section: A Reliable Low-resolution Model Of the U5u2/u6 Complex Obtamentioning

confidence: 99%

“…From cycle six onward, the individual particle images were aligned to the model. The density map was refined and corrected for the contrast transfer function by using FREALIGN (37). The Fourier shell correlation (FSC) curve calculated from our final density map suggests a resolution of either 29 or 23 Å based on the FSC ϭ 0.5 and FSC ϭ 0.143, respectively (38) (SI Fig.…”

Section: A Reliable Low-resolution Model Of the U5u2/u6 Complex Obtamentioning

confidence: 99%

Structural characterization of the fission yeast U5.U2/U6 spliceosome complex

Ohi

Ren

Wall

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

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The spliceosome is a dynamic macromolecular machine that catalyzes the excision of introns from pre-mRNA. The megadalton-sized spliceosome is composed of four small nuclear RNPs and additional pre-mRNA splicing factors. The formation of an active spliceosome involves a series of regulated steps that requires the assembly and disassembly of large multiprotein/RNA complexes. The dynamic nature of the pre-mRNA splicing reaction has hampered progress in analyzing the structure of spliceosomal complexes. We have used cryo-electron microscopy to produce a 29-Å density map of a stable 37S spliceosomal complex from the genetically tractable fission yeast, Schizosaccharomyces pombe. Containing the U2, U5, and U6 snRNAs, pre-mRNA splicing intermediates, U2 and U5 snRNP proteins, the Nineteen Complex (NTC), and second-step splicing factors, this complex closely resembles in vitro purified mammalian C complex. The density map reveals an asymmetric particle, Ϸ30 ؋ 20 ؋ 18 nm in size, which is composed of distinct domains that contact each other at the center of the complex.Cdc5 ͉ cryo-EM ͉ pre-mRNA splicing ͉ Schizosaccharomyces pombe O ne model of pre-mRNA splicing posits that the spliceosome is assembled in a step-wise fashion (1, 2). Spliceosome assembly begins with the recognition of the 5Ј splice site and branch-point sequences of the pre-mRNA by the U1 small nucleotide RNP (snRNP) and the U2 snRNP respectively (Complex A, Fig. 1). After binding of the U4/U6.U5 tri-snRNP, the U4/U6 snRNA duplex is replaced by a U2/U6 snRNA duplex (Complex B, Fig. 1). Furthermore, the U1 snRNA base pairing at the 5Ј splice site is disrupted and exchanged for base pairing between the 5Ј splice site and the U6 snRNA. The subsequent addition of another complex, the Nineteen Complex (NTC), and the release of the U1 and U4 snRNPs marks the transition from an inactive to an active spliceosome composed of the NTC and the U5 and U2/U6 snRNPs (Complex B* and C, Fig. 1). 5Ј-Splice site cleavage and lariat formation, followed by 3Ј-splice site cleavage and exon ligation, occur within the activated spliceosome.Structural information about the organization of spliceosomal complexes is still sparse, mainly because of their large sizes and dynamic natures. Difficulties in isolating sufficient quantities of pure stable spliceosomal complexes have so far limited x-ray crystallographic studies to a few isolated spliceosome components, with much focus centered on the core snRNP Sm and Lsm proteins (3-17). A promising structural approach for obtaining information about spliceosome organization is single-particle cryo-EM, a powerful technique that is ideal for determining the structures of large dynamic complexes at protein concentrations too low for crystallization trials. EM structures of four distinct mammalian spliceosomal complexes have been presented, providing snapshots of the spliceosome at distinct stages of the splicing reaction (18-21). Here we show that the Schizosaccharomyces pombe U5.U2/U6 complex represents a spliceosomal particle involved in ...

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“…Smoothing a function (and thereby, introducing correlations between neighboring function values) by suppressing its high-frequency Fourier components has the same effect. In addition, the alignment of the images during the density reconstruction procedure introduces additional correlations of the noise in these images (25). In cryo-EM, the structure factors are, therefore, too strongly correlated, such that a random choice of the structure factors for the test set, which is usually done in crystallography, is not optimal.…”

Section: Resultsmentioning

confidence: 99%

Cross-validation in cryo-EM–based structural modeling

Falkner

Schröder

2013

Proc. Natl. Acad. Sci. U.S.A.

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Single-particle cryo-EM is a powerful approach to determine the structure of large macromolecules and assemblies thereof in many cases at subnanometer resolution. It has become popular to refine or flexibly fit atomic models into density maps derived from cryo-EM experiments. These density maps are typically significantly lower in resolution than electron density maps obtained from X-ray diffraction experiments, such that the number of parameters that need to be determined is much larger than the number of experimental observables. Overfitting and misinterpretation of the density, thus, become a serious problem. For diffraction data, a cross-validation approach was introduced almost 20 y ago; however, no such approach has been described yet for structure refinement against cryo-EM density maps, although the overfitting problem is, because of the lower resolution, significantly larger. We present a cross-validation approach for realspace refinement against cryo-EM density maps in analogy to cross-validation typically used in crystallography. Our approach is able to detect overfitting and allows for optimizing the choice of restraints used in the refinement. The approach is shown on three protein structures with simulated data and experimental data of the rotavirus double-layer particle. Because cross-validation requires splitting the dataset into at least two independent sets, we further present an approach to quantify correlations between the structure factor sets. This analysis is also helpful for other cross-validation applications, such as refinements against diffraction data or 3D reconstructions of cryo-EM density maps.flexible fitting | real-space structure refinement S ingle-particle cryo-EM has emerged as a powerful tool to determine the structure of large biomolecular systems. The images of single particles in different orientations are recorded, which allows us to reconstruct a 3D density distribution of an average over these individual particles. These reconstructed density maps are typically in the medium-to low-resolution range of about 4-20 Å. These resolutions are usually not sufficient to directly build atomic models of macromolecules. However, in many cases, the cryo-EM density provides enough information to place individual proteins or protein domains that have been determined to higher resolution by X-ray crystallography or NMR spectroscopy or that have been built by homology modeling. Low-resolution density maps (worse than 15 Å) determine mostly the overall shape of a macromolecule, in which case the constituent individual proteins can be docked as rigid bodies into the density map (1-3), which might reveal the organization of complex protein assemblies (4-6). For the medium-resolution range between 4 and 15 Å, where more structural details are visible, a number of tools have been developed to refine or flexibly fit atomic models into density maps (7)(8)(9)(10)(11)(12)(13)(14). Some approaches use additional information during the refinement from either energy functions [e.g., MDFF (10), MDf...

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Noise bias in the refinement of structures derived from single particles

Cited by 133 publications

References 34 publications

Advantages of CCD detectors for de novo three-dimensional structure determination in single-particle electron microscopy

Advantages of CCD detectors for de novo three-dimensional structure determination in single-particle electron microscopy

Structural characterization of the fission yeast U5.U2/U6 spliceosome complex

Cross-validation in cryo-EM–based structural modeling

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