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Fourier Ring Correlation
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 frequencyHarauz & van Heel, 1986). The FSC is the three-dimensional extension of the two-dimensional Fourier ring correlation (FRC);van Heel, 1982 also known as: spatial frequency correlation function.Saxton & Baumeister, 1982 Calculation : FSC(r) = \frac where F_1 is the complex structure Factor for volume 1, F_2^ is the complex conjugate of the structure Factor for volume 2, and r_i is the individual voxel element at radius r.van Heel & Schatz, 2005 In this form, the FSC takes two three-dimensional data sets and converts them into a one-dimensional array. Applications The FSC originated in cryo-electron microscopy and gradually proliferated to other fields. To measure the FSC, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Biology
Structural biology deals with structural analysis of living material (formed, composed of, and/or maintained and refined by living cells) at every level of organization. Early structural biologists throughout the 19th and early 20th centuries were primarily only able to study structures to the limit of the naked eye's visual acuity and through magnifying glasses and light microscopes. In the 20th century, a variety of experimental techniques were developed to examine the 3D structures of biological molecules. The most prominent techniques are X-ray crystallography, nuclear magnetic resonance, and Electron microscope, electron microscopy. Through the discovery of X-ray, X-rays and its applications to protein crystals, structural biology was revolutionized, as now scientists could obtain the three-dimensional structures of biological molecules in atomic detail. Likewise, Nuclear magnetic resonance spectroscopy, NMR spectroscopy allowed information about protein structure and dynamic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy. In probability and statistics, the term ''cross-correlations'' refers to the correlations between the entries of two random vectors \mathbf and \mathbf, while the ''correlations'' of a random vector \mathbf are the correlations between the entries of \mathbf itself, those forming the correlation mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryo-electron Microscopy
Cryogenic electron microscopy (cryo-EM) is a transmission electron microscopy technique applied to 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 in the structural biology field. In 2017, the Nobel Prize in Chemistry was awarded to Jacques Dubochet, Joachim Frank, and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution." '' Nature Methods'' also named cryo- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigma
Sigma ( ; uppercase Σ, lowercase σ, lowercase in word-final position ς; ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator (mathematics), operator for summation. When used at the end of a Letter case, letter-case word (one that does not use all caps), the final form (ς) is used. In ' (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. The Latin alphabet, Latin letter S derives from sigma while the Cyrillic script, Cyrillic letter Es (Cyrillic), Es derives from a #Lunate sigma, lunate form of this letter. History The shape (Σς) and alphabetic position of sigma is derived from the Phoenician alphabet, Phoenician letter (Shin (letter), ''shin''). Sigma's original name may have been ''san'', but due to the complicated early history of the Greek Archaic Greek alphabets, epich ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-ray Crystallography
X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring the angles and intensities of the X-ray diffraction, a crystallography, crystallographer can produce a three-dimensional picture of the density of electrons within the crystal and the positions of the atoms, as well as their chemical bonds, crystallographic disorder, and other information. X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences between various materials, especially minerals and alloys. The method has also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X-ray crystall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ångström
The angstrom (; ) is a unit of length equal to m; that is, one ten- billionth of a metre, a hundred-millionth of a centimetre, 0.1 nanometre, or 100 picometres. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). It was originally spelled with Swedish letters, as Ångström and later as ångström (). The latter spelling is still listed in some dictionaries, but is now rare in English texts. Some popular US dictionaries list only the spelling ''angstrom''. The unit's symbol is Å, which is a letter of the Swedish alphabet, regardless of how the unit is spelled. However, "A" or "A.U." may be used in less formal contexts or typographically limited media. The angstrom is often used in the natural sciences and technology to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation, and dimensions of integrated circuit p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resolution (electron Density)
Resolution in the context of structural biology is the ability to distinguish the presence or absence of Atom, atoms or groups of atoms in a Biomolecule, biomolecular structure. Usually, the structure originates from methods such as X-ray crystallography, electron crystallography, or Cryogenic electron microscopy, cryo-electron microscopy. The resolution is measured of the "map" of the structure produced from experiment, where an atomic model would then be fit into. Due to their different natures and interactions with matter, in X-ray methods the map produced is of the electron density of the system (usually a Crystal structure, crystal), whereas in electron methods the map is of the electrostatic potential of the system. In both cases, atomic positions are assumed similarly. Qualitative measures In structural biology, Optical resolution, resolution can be broken down into 4 groups: (1) sub-atomic, when information about the electron density is obtained and quantum effects can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books by decree in 1586. It is the second-oldest university press after Cambridge University Press, which was founded in 1534. It is a department of the University of Oxford. It is governed by a group of 15 academics, the Delegates of the Press, appointed by the Vice Chancellor, vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, Walton Street, Oxford, opposite Somerville College, Oxford, Somerville College, in the inner suburb of Jericho, Oxford, Jericho. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
