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3D reconstruction

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Protocol (for angular search or reconstruction): e.g. Cross-common lines
Reconstruction software list: e.g. MRC, Spider, EMAN2
CTF correction method: e.g. Each particle
Resolution of the reconstruction (Å): e.g. 12.5 (in angstrom). 'n/a' is only valid for tomograms and subtomogram averages.
Resolution determination method:    
FSC type:    
Euler angles details: e.g. SPIDER: theta 45 degrees, phi 45 degrees
Details: e.g. Final maps were calculated from five averaged datasets

EM protocol

The method used to reconstruct the 3D-map from 2D-projections. In the case of single particles and icosahedral viruses methods relating different projections of a structure to one another make use of 'common lines'. This general method is employed in several approaches including 'angular reconstitution' and 'simultaneous minimisation'. Reconstruction techniques (the mathematical algorithm and its computational realisation). Techniques include :weighted back-projection, Fourier methods, iterative algebraic reconstruction methods. For helical structures computer programs provide facilities for extracting layer line data, averaging data from different particles and computing the 3D map. For 2D crystals, programs for image processing of 2D crystals are used to calculate a transform, mask the diffraction spots and back-transform to calculate a filtered image. Phase information from images of tilted crystals can be generated so that the amplitudes and phases from numbers of micrographs can be merged in any of the 17 2D plane groups. Lattice line fitting is then used to determine the 3D transform. For tomography the number and thickness of sections (2D-projections) obtained from a tilt series are used for the 3D reconstruction.

Example: Common lines
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3D reconstruction software

The software packages used to implement the 3D reconstruction.

Example: MRC, EMAN2
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CTF correction method

The Contrast Transfer Function (CTF) compensation for low contrast specimens is important because for frozen-hydrated specimens phase contrast is the only significant contrast mechanism. Accordingly higher defocus levels must be used to achieve any significant contrast transfer, and several images at different focus levels must be combined to complete the information lost from the contrast transfer gaps from any one image or micrograph. CTF correction can be applied to each extracted particle separately or to the whole micrograph (after digitisation). The simplest level of compensation is to reverse phases at the negative lobes of the CTF.

Example: CTF correction of each particle
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Resolution of 3D reconstruction

Resolution is a quantity in Fourier space and so has dimensions 1/angstrom. Colloquially the real space quantity 1/resolution is also often called the 'resolution' and this is what we shall use here. This Fourier based resolution can be linked to a 'point-to-point' distance in real space by the Rayleigh criterion: two incoherent images, where each image is the transform of the aperture in the diffraction pattern plane can be considered to be resolved when the central maximum of one coincides with the first zero of the second. In crystallography it is common to define resolution by the orders of (object-related) Fourier components available for the Fourier synthesis of the image. In electron crystallography the signal-related Fourier components of the image are distinguished from noise-related components by the fact that the former lie on a regular lattice, while the latter form a continuous background. The resolution can be specified by the radius of the highest orders that stand out from the background. In single particle averaging there is no distinction in the Fourier transform between the appearance of signal and noise and so resolution must be determined by other means.

Range: 1.0 to 100.0 (in angstroms)
Example: 6.5
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Resolution determination method

The method used to determine the effective resolution of the final reconstructed density. This can be achieved by randomly splitting the particles into two sets and calculating the fourier shell correlation obtained from separate reconstructions. Fourier Shell Correlation (FSC) is the calculation of the mean correlation coefficient between the complex structure factors of the two halves of the data as a function of resolution. Q-factor is the mean ratio of the vector sum of the individual structure factors from each image divided by the sum of their moduli, again calculated as a function of resolution. Perfectly accurate measurements would have values of FSC and Q-factor of 1.0 and 1.0, whereas random data containing no information would have values of 0.0 and 0.0. Spectral Signal-to-Noise Ratio (SSNR) effectively measures, as a function of resolution, the overall signal-to-noise ratio squared of the whole of the image data. It is calculated by taking into consideration how well all of the contributing image data agree internally. The FSC method of determining resolution is now widely accepted: The resolution defining threshold can be a value of 0.5 FSC. Alternatively threshold criteria, in terms of standard deviations ( 3*sigma) over the random noise, have been used to avoid a fixed threshold criterion. Additionally, to account for varying numbers of independent voxels in the two Fourier-space 3D shells, a correction factor (the square root) based on the symmetry of the particle and determined by the number of asymmetric units within the given point group symmetry is employed.

Example: Significance threshold for icosahedral structure: 3sigma * square-root(60)
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FSC type

The so-called 'gold standard' FSC is when even/odd maps are refined totally independent, i.e., particles are evenly split in two sets and refined against different models.
The most common approach ('semi-independent'), however, involves to refine all the particles against the same model and then particles are evenly split to compute even/odd maps.

Example: even/odd maps were refined totally independently (gold-standard)

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FSC type

The so-called 'gold standard' FSC is when even/odd maps are refined totally independent, i.e., particles are evenly split in two sets and refined against different models.
The most common approach ('semi-independent'), however, involves to refine all the particles against the same model and then particles are evenly split to compute even/odd maps.

Example: even/odd maps were refined totally independently (gold-standard)

close

FSC type

The so-called 'gold standard' FSC is when even/odd maps are refined totally independent, i.e., particles are evenly split in two sets and refined against different models.
The most common approach ('semi-independent'), however, involves to refine all the particles against the same model and then particles are evenly split to compute even/odd maps.

Example: even/odd maps were refined totally independently (gold-standard)

close

FSC type

The so-called 'gold standard' FSC is when even/odd maps are refined totally independent, i.e., particles are evenly split in two sets and refined against different models.
The most common approach ('semi-independent'), however, involves to refine all the particles against the same model and then particles are evenly split to compute even/odd maps.

Example: even/odd maps were refined totally independently (gold-standard)

close

FSC type

The so-called 'gold standard' FSC is when even/odd maps are refined totally independent, i.e., particles are evenly split in two sets and refined against different models.
The most common approach ('semi-independent'), however, involves to refine all the particles against the same model and then particles are evenly split to compute even/odd maps.

Example: even/odd maps were computed totally independently (gold-standard)

close

Alternative resolution determination method

If the method used to assess resolution is not found in the drop-down list, report it in this text area.

Example: FSC at 0.25 cut-off

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Euler angles details

The interesting information that one can extract from the euler angles is the angular coverage. It is important to give the software package used to derive the angles. In order to know the angular coverage you need two angles,independent of their sign, in SPIDER these are 'theta' and 'phi'. To relate the directions of the coverage with the directions in the volume, the precise angular definitions are important. In SPIDER the euler angles are called phi, theta, and psi:theta around y, psi in plane of the projection, phi around the original volume z-axis. i.e. theta and phi are important for the projecting direction, psi is in the plane. (In SPIDER, going from the volume to the projection phi and psi are negative, theta positive). If r* is a vector in the projection and r a vector in the volume then: r = D(around z,phi pos.). D(around y,theta neg.). D(around z, psi pos.).r* where D is the Drehung or turning matrix given by: | cos angle sin angle | | -sin angle cos angle | An important demand on curves in the graphic data processing is the turning invariance,i.e. that the appearance of the curve does not change on turn of the coordinate system. It is important to note that there are different ways to define the Euler angles.However, the part that is the same for all programs is that the first and last rotations are around a z-axis. The middle angle is sometimes around x, and the signs of the angles may vary. A matrix system turning around x,y,z-axis does not qualify as Euler angles.In SPIDER the Euler angles are stored in a document file. This is a fixed format ascii file with a key number, a number indicating how many numbers follow in the line, and then the numbers. The order of the angles is up to the person who would write the ascii file. For those programs that read them from a document file, there is no standard for the order. It depends on the individual who wrote the program. In the file header the order is fixed.This file would contain one triad for every image, e.g. 30 000 lines for 30 000 images. In IMAGIC the euler angles would be beta and gamma (how the projections turn in their own plane does not matter).

Example: Beta 0 degrees, gamma 90 degrees (IMAGIC)
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3D Reconstruction details

Any additional details used in the 3D reconstruction. Examples: In the case of SINGLE PARTICLES simply back-projecting all available 2D projections through the 3D reconstruction volume will lead to a 'blurred' reconstruction due to the overly strong emphasis of the low frequency components in the overlapping central sections. To avoid this blurring problem, high-pass filtering of the projections ('filtered back-projection'), in which a specific filter is computed for each projection in the reconstruction problem at hand, was developed. For HELICAL assemblies, data from a number helical families of tubes can be combined, and three-dimensional corrections for lattice distortion made. For 2D-CRYSTALS the averaging of images from a number of crystals is used to produce an improvement in the signal-to-noise ratio.

Example: Final maps were calculated from five averaged helical datasets.
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