 |
In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in Fourier space (i.e., as a function of spatial frequency [1] ). The FSC is the three-dimensional extension of the two-dimensional Fourier ring correlation (FRC); [2] also known as: spatial frequency correlation function. [3]
where is the complex structure Factor for volume 1, is the complex conjugate of the structure Factor for volume 2, and is the individual voxel element at radius . [4] [5] [6] In this form, the FSC takes two three-dimensional data sets and converts them into a one-dimensional array.
The FSC originated in cryo-electron microscopy and gradually proliferated to other fields. To measure the FSC, two independently determined 3D volumes are required. In cryo-electron microscopy, the two volumes are the result of two three-dimensional reconstructions, each based on half of the available data set. Typically, random halves are used, although some programs may use the even particle images for one half and the odd particles for the other half of the data set. Some publications quote the FSC 0.5 resolution cutoff, which refers to when the correlation coefficient of the Fourier shells is equal to 0.5. [7] [8] However, determining the resolution threshold remains a controversial issue, with some arguing fixed-value thresholds to be based on incorrect statistical assumptions. [6] [9] Many other criteria using the FSC curve exist, including 3-σ criterion, 5-σ criterion, and the 0.143 cutoff. The half-bit criterion indicates at which resolution we have collected enough information to reliably interpret the 3-dimensional volume, and the (modified) 3-sigma criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise. [6] The FSC 0.143 cutoff was proposed in part to make the resolution measurement comparable to measurements used in X-ray crystallography. [10] Currently, the 0.143 cutoff is the most commonly used criterion for the resolution of cryo-EM reconstructions better than 10 ångström resolution. [11]
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.
An electron microscope is a microscope that uses a beam of electrons as a source of illumination. They use electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing them to produce magnified images or electron diffraction patterns. As the wavelength of an electron can be up to 100,000 times smaller than that of visible light, electron microscopes have a much higher resolution of about 0.1 nm, which compares to about 200 nm for light microscopes. Electron microscope may refer to:
Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope (TEM). It can involve the use of high-resolution transmission electron microscopy images, electron diffraction patterns including convergent-beam electron diffraction or combinations of these. It has been successful in determining some bulk structures, and also surface structures. Two related methods are low-energy electron diffraction which has solved the structure of many surfaces, and reflection high-energy electron diffraction which is used to monitor surfaces often during growth.
A scanning transmission electron microscope (STEM) is a type of transmission electron microscope (TEM). Pronunciation is [stɛm] or [ɛsti:i:ɛm]. As with a conventional transmission electron microscope (CTEM), images are formed by electrons passing through a sufficiently thin specimen. However, unlike CTEM, in STEM the electron beam is focused to a fine spot which is then scanned over the sample in a raster illumination system constructed so that the sample is illuminated at each point with the beam parallel to the optical axis. The rastering of the beam across the sample makes STEM suitable for analytical techniques such as Z-contrast annular dark-field imaging, and spectroscopic mapping by energy dispersive X-ray (EDX) spectroscopy, or electron energy loss spectroscopy (EELS). These signals can be obtained simultaneously, allowing direct correlation of images and spectroscopic data.
Transmission electron cryomicroscopy (CryoTEM), commonly known as cryo-EM, is a form of cryogenic electron microscopy, more specifically a type of transmission electron microscopy (TEM) where the sample is studied at cryogenic temperatures. Cryo-EM, specifically 3-dimensional electron microscopy (3DEM), is gaining popularity in structural biology.
Fluorescence correlation spectroscopy (FCS) is a statistical analysis, via time correlation, of stationary fluctuations of the fluorescence intensity. Its theoretical underpinning originated from L. Onsager's regression hypothesis. The analysis provides kinetic parameters of the physical processes underlying the fluctuations. One of the interesting applications of this is an analysis of the concentration fluctuations of fluorescent particles (molecules) in solution. In this application, the fluorescence emitted from a very tiny space in solution containing a small number of fluorescent particles (molecules) is observed. The fluorescence intensity is fluctuating due to Brownian motion of the particles. In other words, the number of the particles in the sub-space defined by the optical system is randomly changing around the average number. The analysis gives the average number of fluorescent particles and average diffusion time, when the particle is passing through the space. Eventually, both the concentration and size of the particle (molecule) are determined. Both parameters are important in biochemical research, biophysics, and chemistry.
Cryo-electron tomography (cryo-ET) is an imaging technique used to produce high-resolution (~1–4 nm) three-dimensional views of samples, often biological macromolecules and cells. cryo-ET is a specialized application of transmission electron cryomicroscopy (CryoTEM) in which samples are imaged as they are tilted, resulting in a series of 2D images that can be combined to produce a 3D reconstruction, similar to a CT scan of the human body. In contrast to other electron tomography techniques, samples are imaged under cryogenic conditions. For cellular material, the structure is immobilized in non-crystalline, vitreous ice, allowing them to be imaged without dehydration or chemical fixation, which would otherwise disrupt or distort biological structures.
High-resolution transmission electron microscopy is an imaging mode of specialized transmission electron microscopes that allows for direct imaging of the atomic structure of samples. It is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp2-bonded carbon. While this term is often also used to refer to high resolution scanning transmission electron microscopy, mostly in high angle annular dark field mode, this article describes mainly the imaging of an object by recording the two-dimensional spatial wave amplitude distribution in the image plane, similar to a "classic" light microscope. For disambiguation, the technique is also often referred to as phase contrast transmission electron microscopy, although this term is less appropriate. At present, the highest point resolution realised in high resolution transmission electron microscopy is around 0.5 ångströms (0.050 nm). At these small scales, individual atoms of a crystal and defects can be resolved. For 3-dimensional crystals, it is necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron tomography.
Richard Henderson is a British molecular biologist and biophysicist and pioneer in the field of electron microscopy of biological molecules. Henderson shared the Nobel Prize in Chemistry in 2017 with Jacques Dubochet and Joachim Frank.„Thanks to his work, we can look at individual atoms of living nature, thanks to cryo-electron microscopes we can see details without destroying samples, and for this he won the Nobel Prize in Chemistry."
The EM Data Bank or Electron Microscopy Data Bank (EMDB) collects 3D EM maps and associated experimental data determined using electron microscopy of biological specimens. It was established in 2002 at the MSD/PDBe group of the European Bioinformatics Institute (EBI), where the European site of the EMDataBank.org consortium is located. As of 2015, the resource contained over 2,600 entries with a mean resolution of 15Å.
Electron tomography (ET) is a tomography technique for obtaining detailed 3D structures of sub-cellular, macro-molecular, or materials specimens. Electron tomography is an extension of traditional transmission electron microscopy and uses a transmission electron microscope to collect the data. In the process, a beam of electrons is passed through the sample at incremental degrees of rotation around the center of the target sample. This information is collected and used to assemble a three-dimensional image of the target. For biological applications, the typical resolution of ET systems are in the 5–20 nm range, suitable for examining supra-molecular multi-protein structures, although not the secondary and tertiary structure of an individual protein or polypeptide. Recently, atomic resolution in 3D electron tomography reconstructions has been demonstrated.
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images. This method is often used to measure full-field displacement and strains, and it is widely applied in many areas of science and engineering. Compared to strain gauges and extensometers, digital image correlation methods provide finer details about deformation, due to the ability to provide both local and average data.
Resolution in terms of electron density is a measure of the resolvability in the electron density map of a molecule. In X-ray crystallography, resolution is the highest resolvable peak in the diffraction pattern, while resolution in cryo-electron microscopy is a frequency space comparison of two halves of the data, which strives to correlate with the X-ray definition.
In scientific imaging, the two-dimensional spectral signal-to-noise ratio (SSNR) is a signal-to-noise ratio measure which measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings in Fourier space as a function of spatial frequency. It is a multi-particle extension of the Fourier ring correlation (FRC), which is related to the Fourier shell correlation. The SSNR is a popular method for finding the resolution of a class average in cryo-electron microscopy.
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.
Single particle analysis is a group of related computerized image processing techniques used to analyze images from transmission electron microscopy (TEM). These methods were developed to improve and extend the information obtainable from TEM images of particulate samples, typically proteins or other large biological entities such as viruses. Individual images of stained or unstained particles are very noisy, and so hard to interpret. Combining several digitized images of similar particles together gives an image with stronger and more easily interpretable features. An extension of this technique uses single particle methods to build up a three-dimensional reconstruction of the particle. Using cryo-electron microscopy it has become possible to generate reconstructions with sub-nanometer resolution and near-atomic resolution first in the case of highly symmetric viruses, and now in smaller, asymmetric proteins as well. Single particle analysis can also be performed by induced coupled plasma mass spectroscopy (ICP-MS).
Differential dynamic microscopy (DDM) is an optical technique that allows performing light scattering experiments by means of a simple optical microscope. DDM is suitable for typical soft materials such as for instance liquids or gels made of colloids, polymers and liquid crystals but also for biological materials like bacteria and cells.
Fluctuation X-ray scattering (FXS) is an X-ray scattering technique similar to small-angle X-ray scattering (SAXS), but is performed using X-ray exposures below sample rotational diffusion times. This technique, ideally performed with an ultra-bright X-ray light source, such as a free electron laser, results in data containing significantly more information as compared to traditional scattering methods.
Cryogenic electron microscopy (cryo-EM) is a cryomicroscopy technique applied on samples cooled to cryogenic temperatures. For biological specimens, the structure is preserved by embedding in an environment of vitreous ice. An aqueous sample solution is applied to a grid-mesh and plunge-frozen in liquid ethane or a mixture of liquid ethane and propane. While development of the technique began in the 1970s, recent advances in detector technology and software algorithms have allowed for the determination of biomolecular structures at near-atomic resolution. This has attracted wide attention to the approach as an alternative to X-ray crystallography or NMR spectroscopy for macromolecular structure determination without the need for crystallization.
{{cite book}}: |journal= ignored (help)