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Kabsch Algorithm
The Kabsch algorithm, also known as the Kabsch-Umeyama algorithm, named after Wolfgang Kabsch and Shinji Umeyama, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points. It is useful for point-set registration in computer graphics, and in cheminformatics and bioinformatics to compare molecular and protein structures (in particular, see root-mean-square deviation (bioinformatics)). The algorithm only computes the rotation matrix, but it also requires the computation of a translation vector. When both the translation and rotation are actually performed, the algorithm is sometimes called partial Procrustes superimposition (see also orthogonal Procrustes problem). Description Let and be two sets, each containing points in \mathbb^n. We want to find the transformation from to . For simplicity, we will consider the three-dimensional case (n = 3). The sets and can each be represented by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Rotation Matrix
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation (mathematics), rotation in Euclidean space. For example, using the convention below, the matrix :R = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end rotates points in the plane counterclockwise through an angle about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates , it should be written as a column vector, and matrix multiplication, multiplied by the matrix : : R\mathbf = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end = \begin x\cos\theta-y\sin\theta \\ x\sin\theta+y\cos\theta \end. If and are the coordinates of the endpoint of a vector with the length ''r'' and the angle \phi with respect to the -axis, so that x = r \cos \phi and y = r \sin \phi, then the above equations become the List of trigonometric identities#Angle sum and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cross-covariance
In probability and statistics, given two stochastic processes \left\ and \left\, the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation \operatorname E for the expectation operator, if the processes have the mean functions \mu_X(t) = \operatorname \operatorname E _t/math> and \mu_Y(t) = \operatorname E _t/math>, then the cross-covariance is given by :\operatorname_(t_1,t_2) = \operatorname (X_, Y_) = \operatorname X_ - \mu_X(t_1))(Y_ - \mu_Y(t_2))= \operatorname _ Y_- \mu_X(t_1) \mu_Y(t_2).\, Cross-covariance is related to the more commonly used cross-correlation of the processes in question. In the case of two random vectors \mathbf=(X_1, X_2, \ldots , X_p)^ and \mathbf=(Y_1, Y_2, \ldots , Y_q)^, the cross-covariance would be a p \times q matrix \operatorname_ (often denoted \operatorname(X,Y)) with entries \operatorname_(j,k) = \operatorname(X_j, Y_k).\, Thus the term ''cross-covariance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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FoldX
FoldX is a protein design algorithm that uses an empirical force field. It can determine the energetic effect of point mutations as well as the interaction energy of protein complexes (including Protein-DNA). FoldX can mutate protein and DNA side chains using a probability-based rotamer library, while exploring alternative conformations of the surrounding side chains. Applications * Prediction of the effect of point mutations or human SNPs on protein stability or protein complexes * Protein design to improve stability or modify affinity or specificity * Homology modeling The FoldX force field The energy function includes terms that have been found to be important for protein stability, where the energy of unfolding (∆G) of a target protein is calculated using the equation: :∆G = ∆Gvdw + ∆GsolvH + ∆GsolvP + ∆Ghbond + ∆Gwb + ∆Gel + ∆Smc + ∆Ssc Where ∆Gvdw is the sum of the Van der Waals contributions of all atoms with respect to the same intera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Visual Molecular Dynamics
Visual Molecular Dynamics (VMD) is a molecular modelling and Visualization (computer graphics), visualization computer program. VMD is developed mainly as a tool to view and analyze the results of molecular dynamics simulations. It also includes tools for working with volumetric data, sequence data, and arbitrary graphics objects. Molecular scenes can be exported to external rendering tools such as POV-Ray, RenderMan (software), RenderMan, Tachyon (software), Tachyon, Virtual Reality Modeling Language (VRML), and many others. Users can run their own Tcl and Python (programming language), Python scripts within VMD as it includes embedded Tcl and Python interpreters. VMD runs on Unix, Apple Mac macOS, and Microsoft Windows. VMD is available to non-commercial users under a distribution-specific license which permits both use of the program and modification of its source code, at no charge. History VMD has been developed under the aegis of principal investigator Klaus Schulten in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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PyMol
PyMOL is a source-available molecular visualization system created by Warren Lyford DeLano. It was commercialized initially by DeLano Scientific LLC, which was a private software company dedicated to creating useful tools that become universally accessible to scientific and educational communities. It is currently commercialized by Schrödinger, Inc. As the original software license was a permissive licence, they were able to remove it; new versions are no longer released under the Python license, but under a custom license (granting broad use, redistribution, and modification rights, but assigning copyright to any version to Schrödinger, LLC.), and some of the source code is no longer released. PyMOL can produce high-quality 3D images of small molecules and biological macromolecules, such as proteins. PyMOL is widely used. PyMOL is one of the few mostly open-source model visualization tools available for use in structural biology. The ''Py'' part of the software's name refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Eigen (C++ Library)
Eigen may refer to: People with the given name *, Japanese sport shooter *, Japanese professional wrestler * Frauke Eigen (born 1969) German photographer, photojournalist and artist * Manfred Eigen (1927–2019), German biophysicist * Michael Eigen (born 1936) American psychologist and psychoanalyst * Karl Eigen (1927–2016) German farmer and politician * Saint Eigen, female Christian saint * Peter Eigen, (born 1938) German lawyer, development economist and civil society leader Places * Eigen, Schwyz, settlement in the municipality of Alpthal in the canton of Schwyz, Switzerland * Eigen, Thurgau, locality in the municipality of Lengwil in the canton of Thurgau, Switzerland * Eigen-ji, Buddhist temple Others * Eigen (C++ library), computer programming library for matrix and linear algebra operations * Eigen Wereld, is Opgezwolle's third album * Eigen Kweek, was a 2013-2019 Belgian crime comedy television series See also * Eigenvalue, eigenvector and eigenspace in math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Matlab
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the Motion (physics), physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamics (mechanics), dynamic "evolution" of the system. In the most common version, the trajectory, trajectories of atoms and molecules are determined by Numerical integration, numerically solving Newton's laws of motion, Newton's equations of motion for a system of interacting particles, where Force (physics), forces between the particles and their potential energy, potential energies are often calculated using interatomic potentials or molecular mechanics, molecular mechanical Force field (chemistry), force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analyt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by (for ''Hamilton''), or in blackboard bold by \mathbb H. Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b\,\mathbf i + c\,\mathbf j +d\,\mathbf k, where the coefficients , , , are real numbers, and , are the ''basis vectors'' or ''basis elements''. Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, robotics, magnetic resonance i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition#Matrix polar decomposition, polar decomposition. Specifically, the singular value decomposition of an m \times n complex matrix is a factorization of the form \mathbf = \mathbf, where is an complex unitary matrix, \mathbf \Sigma is an m \times n rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \mathbf V^* is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrix, orthogonal matrices; in such contexts, the SVD ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |