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Conformational Ensemble
In protein chemistry, conformational ensembles, also known as structural ensembles, are models describing the structure of intrinsically unstructured proteins. Such proteins are flexible in nature and cannot be described by a single structural representation. The techniques of ensemble calculation are relatively new on the field of structural biology, and are still facing certain limitations that need to be addressed before it will become comparable to classical structural description methods such as biological macromolecular crystallography. Purpose Ensembles are models consisting of a set of conformations that describe the structure of a flexible protein. Even though the degree of conformational freedom is extremely high, flexible/disordered protein generally differ from fully random coil structures. The main purpose of these models is to gain insights regarding the function of the flexible protein, extending the structure-function paradigm from folded proteins to i ...
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J-coupling
In nuclear chemistry and nuclear physics, ''J''-couplings (also called spin-spin coupling or indirect dipole–dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins that arises from hyperfine interactions between the nuclei and local electrons. In NMR spectroscopy, ''J''-coupling contains information about relative bond distances and angles. Most importantly, ''J''-coupling provides information on the connectivity of chemical bonds. It is responsible for the often complex splitting of resonance lines in the NMR spectra of fairly simple molecules. ''J''-coupling is a frequency ''difference'' that is not affected by the strength of the magnetic field, so is always stated in Hz. Vector model and manifestations for chemical structure assignments The origin of ''J''-coupling can be visualized by a vector model for a simple molecule such as hydrogen fluoride (HF). In HF, the two nuclei have spin . Four st ...
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Intrinsically Disordered Proteins
In molecular biology, an intrinsically disordered protein (IDP) is a protein that lacks a fixed or ordered protein tertiary structure, three-dimensional structure, typically in the absence of its macromolecular interaction partners, such as other proteins or RNA. IDPs range from fully unstructured to partially structured and include random coil, molten globule-like Protein aggregation, aggregates, or flexible linkers in large multi-Protein domain, domain proteins. They are sometimes considered as a separate class of proteins along with globular protein, globular, fibrous protein, fibrous and membrane proteins. IDPs are a very large and functionally important class of proteins. They are most numerous in Eukaryote, eukaryotes, with an estimated 30-40% of residues in the eukaryotic proteome located in disordered regions. Disorder is present in around 70% of proteins, either in the form of disordered tails or flexible linkers. Proteins can also be entirely disordered and lack a define ...
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Error Function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a function \mathrm: \mathbb \to \mathbb defined as: \operatorname z = \frac\int_0^z e^\,\mathrm dt. The integral here is a complex Contour integration, contour integral which is path-independent because \exp(-t^2) is Holomorphic function, holomorphic on the whole complex plane \mathbb. In many applications, the function argument is a real number, in which case the function value is also real. In some old texts, the error function is defined without the factor of \frac. This nonelementary integral is a sigmoid function, sigmoid function that occurs often in probability, statistics, and partial differential equations. In statistics, for non-negative real values of , the error function has the following interpretation: for a real random variable that is normal distribution, normally distributed with mean 0 and standard deviation \frac, is the probability that falls in the range . ...
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Protein Conformation
Protein structure is the three-dimensional arrangement of atoms in an amino acid-chain molecule. Proteins are polymers specifically polypeptides formed from sequences of amino acids, which are the monomers of the polymer. A single amino acid monomer may also be called a ''residue'', which indicates a repeating unit of a polymer. Proteins form by amino acids undergoing condensation reactions, in which the amino acids lose one water molecule per reaction in order to attach to one another with a peptide bond. By convention, a chain under 30 amino acids is often identified as a peptide, rather than a protein. To be able to perform their biological function, proteins fold into one or more specific spatial conformations driven by a number of non-covalent interactions, such as hydrogen bonding, ionic interactions, Van der Waals forces, and hydrophobic packing. To understand the functions of proteins at a molecular level, it is often necessary to determine their three-dimensional st ...
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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 ...
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Nuclear Overhauser Effect
The nuclear Overhauser effect (NOE) is the transfer of spin polarization, nuclear spin polarization from one population of Spin (physics), spin-active nuclei (e.g. 1H, 13C, 15N etc.) to another via Relaxation (NMR), cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic resonance spectroscopy (NMR) is the change in the integrated intensity (positive or negative) of one NMR resonance that occurs when another is saturated by irradiation with an Radio frequency, RF field. The change in resonance intensity of a nucleus is a consequence of the nucleus being close in space to those directly affected by the RF perturbation. The NOE is particularly important in the assignment of NMR resonances, and the elucidation and confirmation of the structures or configurations of organic and biological molecules. The 1H two-dimensional NOE spectroscopy (NOESY) experiment and its extensions are important tools to identify stereochemistry of proteins and other biomolecules in sol ...
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Paramagnetism
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer. Paramagnetism is due to the presence of unpaired electrons in the material, so most atom ...
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Accessible Surface Area
The accessible surface area (ASA) or solvent-accessible surface area (SASA) is the surface area of a biomolecule that is accessible to a solvent. Measurement of ASA is usually described in units of square angstroms (a standard unit of measurement in molecular biology). ASA was first described by Lee & Richards in 1971 and is sometimes called the Lee-Richards molecular surface. ASA is typically calculated using the 'rolling ball' algorithm developed by Shrake & Rupley in 1973. This algorithm uses a sphere (of solvent) of a particular radius to 'probe' the surface of the molecule. Methods of calculating ASA Shrake–Rupley algorithm The Shrake–Rupley algorithm is a numerical method that draws a mesh of points equidistant from each atom of the molecule and uses the number of these points that are solvent accessible to determine the surface area. The points are drawn at a water molecule's estimated radius beyond the van der Waals radius, which is effectively similar to ‘rolli ...
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Residual Dipolar Coupling
The residual dipolar coupling between two spins in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic dipolar couplings. Partial molecular alignment leads to an incomplete averaging of anisotropic magnetic interactions such as the magnetic dipole-dipole interaction (also called dipolar coupling), the chemical shift anisotropy, or the electric quadrupole interaction. The resulting so-called ''residual'' anisotropic magnetic interactions are useful in biomolecular NMR spectroscopy. History and pioneering works NMR spectroscopy in partially oriented media was reported by Alfred Saupe. After this initiation, several NMR spectra in various liquid crystalline phases were reported (see ''e.g.'' ). A second technique for partial alignment that is not limited by a minimum anisotropy is strain-induced alignment in a gel (SAG). The technique was extensively used to study the properties of polymer gels by m ...
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Protein Chemistry
Molecular biophysics is a rapidly evolving interdisciplinary area of research that combines concepts in physics, chemistry, engineering, mathematics and biology. It seeks to understand biomolecular systems and explain biological function in terms of molecular structure, structural organization, and dynamic behaviour at various levels of complexity (from single molecules to supramolecular structures, viruses and small living systems). This discipline covers topics such as the measurement of molecular forces, molecular associations, allosteric interactions, Brownian motion, and cable theory. Additional areas of study can be found on Outline of Biophysics. The discipline has required development of specialized equipment and procedures capable of imaging and manipulating minute living structures, as well as novel experimental approaches. Overview Molecular biophysics typically addresses biological questions similar to those in biochemistry and molecular biology, seeking to find the ...
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