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Molecular Replacement
Molecular replacement (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_\ell, F_, \exp(2\pi i(hx+ky+\ell z)+i\Phi(hk\ell)). 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 exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Drenth
Jan Drenth (20 February 1925 – 11 February 2025) was a Dutch chemist. He was a professor of structural chemistry at the University of Groningen from 1969 to 1990. Life and career Drenth was born in Groningen on 20 February 1925. 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 lector. In 1969 he was appointed professor of structural chemistry, which he remained until his retirement in 1990. Drenth was elected a member of the Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Translation
Translation is the communication of the semantics, 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 terminological distinction (which does not exist in every language) between ''translating'' (a written text) and ''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 languages into which they have translated. Becau ... [...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 Protein secondary structure, secondary and Protein tertiary structure, tertiary structure from Protein primary structure, 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 addresses Levinthal's paradox. Accurate structure prediction has important applications in medicine (for example, in drug design) and biotechnology (for example, in novel enzyme design). Starting in 1994, the performance of current methods is assessed biannually in the ''Critical Assessment of Structure Prediction'' (CASP) experiment. A continuous evaluation of protein structure prediction web servers is performed by the community project ''Continuous Automated Model EvaluatiOn'' (CAMEO3D). Protein structure a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinates
In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular oriented lines, called '' coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the '' origin'' and has as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any dimension . These coordinates are the signed distances from the point to mutually perpendicular fixed h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinates
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are * the radial distance along the line connecting the point to a fixed point called the origin; * the polar angle between this radial line and a given ''polar axis''; and * the azimuthal angle , which is the angle of rotation of the radial line around the polar axis. (See graphic regarding the "physics convention".) Once the radius is fixed, the three coordinates (''r'', ''θ'', ''φ''), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle) is called the ''reference plane'' (sometimes '' fundamental plane''). Terminology The radial distance from the fixed point of origin is also called the ''radius'', or ''radial line'', or ''radial coord ... [...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 three dimensional linear algebra. Classic Euler angles usually take the inclination angle in such a way that zero degrees represent the vertical orientation. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering in which zero degrees represent the horizontal position. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations (i.e. chained rotations). The geometrical definition demonstrates that three consecutive ''elemental rotations'' (rotatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The 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, 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 the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, ML ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Product-moment Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures 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 children from a 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 Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844. The naming ... [...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 disagreement between the crystallographic model and the experimental X-ray diffraction data - lower the R value lower is the disagreement or better is the agreement. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a ''center of rotation''. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientation (geometry), orientations), in contrast to rotation around a fixed axis, rotation around a axis. The special case of a rotation with an internal axis passing through the body's own center of mass is known as a spin (or ''autorotation''). In that case, the surface intersection of the internal ''spin axis'' can be called a ''pole''; for example, Earth's rotation defines the geographical poles. A rotation around an axis completely external to the moving body is called a revolution (or ''orbit''), e.g. Earth's orbit around the Sun. The en ... [...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 stu ... [...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 In mathematics, a unit vector in a normed vector space is a Vector (mathematics and physics), vector (often a vector (geometry), spatial vector) of Norm (mathematics), length 1. A unit vector is often denoted by a lowercase letter with a circumfle ..., 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 parallelogra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
