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Molecular Replacement
Molecular replacement (or MR) is a method of solving the phase problem in X-ray crystallography. MR relies upon the existence of a previously solved protein structure which is similar to our unknown structure from which the diffraction data is derived. This could come from a homologous protein, or from the lower-resolution protein NMR structure of the same protein. The first goal of the crystallographer is to obtain an electron density map, density being related with diffracted wave as follows: \rho(x,y,z)=\frac\sum_h\sum_k\sum_l, F_, \exp(2\pi i(hx+ky+lz)+i\Phi(hkl)). With usual detectors the intensity I=F\cdot F^* is being measured, and all the information about phase (\Phi) is lost. Then, in the absence of phases (Φ), we are unable to complete the shown Fourier transform relating the experimental data from X-ray crystallography (in reciprocal space) to real-space electron density, into which the atomic model is built. MR tries to find the model which fits best experimental i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Drenth
Jan Drenth (born 20 February 1925) is a Dutch chemist. He was a professor of structural chemistry at the University of Groningen from 1969 to 1990. Career Drenth was born in Groningen. He obtained his PhD in mathematics and physics under Eelco Wiebenga at the University of Groningen in 1957, with a dissertation titled: ''Een röntgenografisch onderzoek van excelsine, edestine en tabakszaadglobuline''. Drenth subsequently moved to New York, United States, where he became a post-doc and studied protein crystallography under Barbara Low. Drenth then returned to the Netherlands and in 1967 was appointed as lector. In 1969 he was appointed as professor of structural chemistry, which he remained until his retirement in 1990. He was elected a member of the Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Translation
Translation is the communication of the Meaning (linguistic), meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The English language draws a terminology, terminological distinction (which does not exist in every language) between ''translating'' (a written text) and ''Language interpretation, interpreting'' (oral or Sign language, signed communication between users of different languages); under this distinction, translation can begin only after the appearance of writing within a language community. A translator always risks inadvertently introducing source-language words, grammar, or syntax into the target-language rendering. On the other hand, such "spill-overs" have sometimes imported useful source-language calques and loanwords that have enriched target languages. Translators, including early translators of sacred texts, have helped shape the very l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Protein Structure Prediction
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different from the inverse problem of protein design. Protein structure prediction is one of the most important goals pursued by computational biology; and it is important in medicine (for example, in drug design) and biotechnology (for example, in the design of novel enzymes). Starting in 1994, the performance of current methods is assessed biannually in the CASP experiment (Critical Assessment of Techniques for Protein Structure Prediction). A continuous evaluation of protein structure prediction web servers is performed by the community project CAMEO3D. Protein structure and terminology Proteins are chains of amino acids joined together by peptide bonds. Many conformations of this chain are possible due to the rotation of the main chain abou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinates
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinates
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called '' colatitude'', ''zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Angles
The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478PDF/ref> They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general Basis (linear algebra), basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations. The geometrical definition demonstrates that three composed ''elemental rotations'' (rotations about the axes of a coordinate system) are always sufficient to reach any target frame. The three elemental rotations may be #Conventions by extrinsic rotations, extrinsic (rotations about the axes ''xyz'' of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is Differentiable function, differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Product-moment Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Karl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R-factor (crystallography)
In crystallography, the R-factor (sometimes called residual factor or reliability factor or the R-value or RWork) is a measure of the agreement between the crystallographic model and the experimental X-ray diffraction data. In other words, it is a measure of how well the refined structure predicts the observed data. The value is also sometimes called the discrepancy index, as it mathematically describes the difference between the experimental observations and the ideal calculated values. It is defined by the following equation: :R = \frac, where ''F'' is the so-called structure factor and the sum extends over all the reflections of X-rays measured and their calculated counterparts respectively. The structure factor is closely related to the intensity of the reflection it describes: :I_ \propto , F(hkl), ^2. The minimum possible value is zero, indicating perfect agreement between experimental observations and the structure factors predicted from the model. There is no theoretical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional object has an infinite number of possible central axes and rotational directions. If the rotation axis passes internally through the body's own center of mass, then the body is said to be ''autorotating'' or '' spinning'', and the surface intersection of the axis can be called a ''pole''. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called ''revolving'' or ''orbiting'', typically when it is produced by gravity, and the ends of the rotation axis can be called the ''orbital poles''. Mathematics Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Problem
In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years. Overview Light detectors, such as photographic plates or CCDs, measure only the intensity of the light that hits them. This measurement is incomplete (even when neglecting other degrees of freedom such as polarization and angle of incidence) because a light wave has not only an amplitude (related to the intensity), but also a phase (related to the direction), and polarization which are systematically lost in a measurement. In diffraction or microscopy experiments, the phase part of the wave often contains valuable information on the stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessarily have unit size, or even a particular size at all. Rather, the primitive cell is the closest analogy to a unit vector, since it has a determined size for a given lattice and is the basic building block from which larger cells are constructed. The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its unit cell, which is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations. There are two special cases of the unit cell: the primitive cell and the conventional cell. The primitive cell is a unit cell corresponding to a single lattice point, it is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
