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Gaussian Network Model
The Gaussian network model (GNM) is a representation of a biological macromolecule as an elastic mass-and-spring (device), spring network to study, understand, and characterize the mechanical aspects of its long-time large-scale dynamics (mechanics), dynamics. The model has a wide range of applications from small proteins such as enzymes composed of a single protein domain, domain, to large Macromolecular Assembly, macromolecular assemblies such as a ribosome or a viral capsid. Protein domain dynamics plays key roles in a multitude of molecular recognition and cell signalling processes. Protein domains, connected by intrinsically disordered flexible linker domains, induce long-range allostery via Protein dynamics#Global flexibility: multiple domains, protein domain dynamics. The resultant dynamic modes cannot be generally predicted from static structures of either the entire protein or individual domains. The Gaussian network model is a minimalist, coarse-grained approach to stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rouse Model
The Rouse model is one of the simplest coarse-grained descriptions of the dynamics of polymer chains. It treats a single polymer as an Ideal chain of ''N'' point-like beads connected by harmonic springs and neglects both excluded volume and long-range hydrodynamic interactions. Each bead experiences random thermal forces and a Stokes drag, so the chain undergoes overdamped Brownian motion described by Langevin dynamics. Although first proposed for dilute solutions, the model also describes polymer melts whose chain length is below the entanglement threshold. Description A flexible polymer is represented by an ideal freely jointed chain of beads with mean bond length ''l''. Neglecting inertia, the overdamped equation of motion for the position \mathbf_n(t) of bead ''n'' is : \frac=\underbrace_+\underbrace_ where ''k'' is the spring constant, \zeta the one-bead friction coefficient and random force \mathbf f_n(t) a zero-mean Gaussian noise that fulfills the fluctuatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force ''F'' proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive constant. The harmonic oscillator model is important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. If ''F'' is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force ( damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Matrix
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued Function (mathematics), function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Otto Hesse, Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". The Hessian is sometimes denoted by H or \nabla\nabla or \nabla^2 or \nabla\otimes\nabla or D^2. Definitions and properties Suppose f : \R^n \to \R is a function taking as input a vector \mathbf \in \R^n and outputting a scalar f(\mathbf) \in \R. If all second-order partial derivatives of f exist, then the Hessian matrix \mathbf of f is a square n \times n matrix, usually defined and arranged as \mathbf H_f= \begin \dfrac & \dfrac & \cdots & \dfrac \\[2.2ex] \dfrac & \dfrac & \cdots & \dfrac \\[2.2ex] \vdots & \vdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformational Change
In biochemistry, a conformational change is a change in the shape of a macromolecule, often induced by environmental factors. A macromolecule is usually flexible and dynamic. Its shape can change in response to changes in its environment or other factors; each possible shape is called a conformation, and a transition between them is called a ''conformational change''. Factors that may induce such changes include temperature, pH, voltage, light in chromophores, concentration of ions, phosphorylation, or the binding of a ligand. Transitions between these states occur on a variety of length scales (tenths of Å to nm) and time scales (ns to s), and have been linked to functionally relevant phenomena such as allosteric signaling and enzyme catalysis. Laboratory analysis Many biophysical techniques such as crystallography, NMR, electron paramagnetic resonance (EPR) using spin label techniques, circular dichroism (CD), hydrogen exchange, and FRET can be used to study macromo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-ray Structure
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 diffract in specific directions. By measuring the angles and intensities of the X-ray diffraction, a 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 crystallography is still the primary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
Cell Division Cycle
The cell cycle, or cell-division cycle, is the sequential series of events that take place in a cell that causes it to divide into two daughter cells. These events include the growth of the cell, duplication of its DNA (DNA replication) and some of its organelles, and subsequently the partitioning of its cytoplasm, chromosomes and other components into two daughter cells in a process called cell division. In eukaryotic cells (having a cell nucleus) including animal, plant, fungal, and protist cells, the cell cycle is divided into two main stages: interphase, and the M phase that includes mitosis and cytokinesis. During interphase, the cell grows, accumulating nutrients needed for mitosis, and replicates its DNA and some of its organelles. During the M phase, the replicated chromosomes, organelles, and cytoplasm separate into two new daughter cells. To ensure the proper replication of cellular components and division, there are control mechanisms known as cell cycle checkpoin ... [...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] |
