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Loop Entropy
Loop entropy is the entropy lost upon bringing together two residues of a polymer within a prescribed distance. For a single loop, the entropy varies logarithmically with the number of residues N in the loop : \Delta S = \alpha k_ \ln N \, where k_ is the Boltzmann constant and \alpha is a coefficient that depends on the properties of the polymer. This entropy formula corresponds to a power-law distribution P \sim N^ for the probability of the residues contacting. The loop entropy may also vary with the position of the contacting residues. Residues near the ends of the polymer are more likely to contact (quantitatively, have a lower \alpha) than those in the middle (i.e., far from the ends), primarily due to excluded volume effects. Wang-Uhlenbeck entropy The loop entropy formula becomes more complicated with multiples loops, but may be determined for a Gaussian polymer using a matrix method developed by Wang and Uhlenbeck. Let there be M contacts among the residues, whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication. The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names ''thermodynamic function'' and ''heat-potential''. In 1865, German physicist Rudolf Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of hea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residue (chemistry)
In chemistry, residue is whatever remains or acts as a contaminant after a given class of events. Residue may be the material remaining after a process of preparation, separation, or purification, such as distillation, evaporation, or filtration. It may also denote the undesired by-products of a chemical reaction. Food safety Toxic chemical residues, wastes or contamination from other processes, are a concern in food safety. For example, the U.S. Food and Drug Administration (FDA) and the Canadian Food Inspection Agency (CFIA) have guidelines for detecting chemical residues that are possibly dangerous to consume. Characteristic units within a molecule ''Residue'' may refer to an atom or a group of atoms that forms part of a molecule, such as a methyl group. Biochemistry In biochemistry and molecular biology, a residue refers to a specific monomer within the polymeric chain of a polysaccharide, protein or nucleic acid. One might say, "This protein consists of 118 amin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compounds, produces unique physical properties including toughness, high elasticity, viscoelasticity, and a tendency to form amorphous and semicrystalline structures rather than crystals. The term "polymer" derives from the Greek word πολύς (''polus'', meaning "many, much") and μέρος (''meros'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven " defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly . Roles of the Boltzmann constant Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure and volume is proportional to the product of amount of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a Exponentiation, power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excluded Volume Effect
The phenomenon of macromolecular crowding alters the properties of molecules in a solution when high concentrations of macromolecules such as proteins are present. Such conditions occur routinely in living cells; for instance, the cytosol of ''Escherichia coli'' contains about 300– of macromolecules. Crowding occurs since these high concentrations of macromolecules reduce the volume of solvent available for other molecules in the solution, which has the result of increasing their effective concentrations. Crowding can promote formation of a biomolecular condensate by colloidal phase separation. This crowding effect can make molecules in cells behave in radically different ways than in test-tube assays. Consequently, measurements of the properties of enzymes or processes in metabolism that are made in the laboratory (''in vitro'') in dilute solutions may be different by many orders of magnitude from the true values seen in living cells (''in vivo''). The study of biochemical pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ribonuclease A
Pancreatic ribonuclease family (, ''RNase'', ''RNase I'', ''RNase A'', ''pancreatic RNase'', ''ribonuclease I'', ''endoribonuclease I'', ''ribonucleic phosphatase'', ''alkaline ribonuclease'', ''ribonuclease'', ''gene S glycoproteins'', ''Ceratitis capitata alkaline ribonuclease'', ''SLSG glycoproteins'', ''gene S locus-specific glycoproteins'', ''S-genotype-assocd. glycoproteins'', ''ribonucleate 3'-pyrimidino-oligonucleotidohydrolase'') is a superfamily of pyrimidine-specific endonucleases found in high quantity in the pancreas of certain mammals and of some reptiles. Specifically, the enzymes are involved in endonucleolytic cleavage of 3'-phosphomononucleotides and 3'-phosphooligonucleotides ending in C-P or U-P with 2',3'-cyclic phosphate intermediates. Ribonuclease can unwind the RNA helix by complexing with single-stranded RNA; the complex arises by an extended multi-site cation-anion interaction between lysine and arginine residues of the enzyme and phosphate groups of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinant
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix is denoted , , or . The determinant of a matrix is :\begin a & b\\c & d \end=ad-bc, and the determinant of a matrix is : \begin a & b & c \\ d & e & f \\ g & h & i \end= aei + bfg + cdh - ceg - bdi - afh. The determinant of a matrix can be defined in several equivalent ways. Leibniz formula expresses the determinant as a sum of signed products of matrix entries such that each summand is the product of different entries, and the number of these summands is n!, the factorial of (t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Entropy
In classical thermodynamics, entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-nineteenth century from the Greek word τρoπή (''transformation'') to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the system. Ludwig Boltzmann explained the entropy as a measure of the number of possible microscopic configurations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
