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Elasticity Coefficient
The rate of a chemical reaction is influenced by many different factors, such as temperature, pH, reactant, and product concentrations and other effectors. The degree to which these factors change the reaction rate is described by the elasticity coefficient. This coefficient is defined as follows: : \varepsilon_^v=\left(\frac \frac\right)_=\frac \approx \frac where v denotes the reaction rate and s denotes the substrate concentration. Be aware that the notation will use lowercase roman letters, such as s, to indicate concentrations. The partial derivative in the definition indicates that the elasticity is measured with respect to changes in a factor S while keeping all other factors constant. The most common factors include substrates, products, and effectors. The scaling of the coefficient ensures that it is dimensionless and independent of the units used to measure the reaction rate and magnitude of the factor. The elasticity coefficient is an integral part of metabolic con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Restitution
The coefficient of restitution (COR, also denoted by ''e''), is the ratio of the final to initial relative speed between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. It is measured in the Leeb rebound hardness test, expressed as 1000 times the COR, but it is only a valid COR for the test, not as a universal COR for the material being tested. The value is almost always less than 1 due to initial translational kinetic energy being lost to rotational kinetic energy, plastic deformation, and heat. It can be more than 1 if there is an energy gain during the collision from a chemical reaction, a reduction in rotational energy, or another internal energy decrease that contributes to the post-collision velocity. \text (e) = \frac The mathematics were developed by Sir Isaac Newton in 1687. It is also kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Order
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as :v_0\; =\; k mathrmx mathrmy where and express the concentration of the species and usually in moles per liter (molarity, ). The exponents and are the partial ''orders of reaction'' for and and the ''overall'' reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The constant is the reaction rate constant or ''rate coefficient'' of the reaction. Its value may depend on conditions such as temperature, ionic strength, surface area of an adsorbent, or light irradiation. If the reaction goes to completion, the rate equation for the reaction rate v\; =\; k cex cey applies throughou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cellular processes; the conversion of food to building blocks for proteins, lipids, nucleic acids, and some carbohydrates; and the elimination of metabolic wastes. These enzyme-catalyzed reactions allow organisms to grow and reproduce, maintain their structures, and respond to their environments. The word metabolism can also refer to the sum of all chemical reactions that occur in living organisms, including digestion and the transportation of substances into and between different cells, in which case the above described set of reactions within the cells is called intermediary (or intermediate) metabolism. Metabolic reactions may be categorized as '' catabolic'' – the ''breaking down'' of compounds (for example, of glucose to pyruvate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biochemistry Methods
The following outline is provided as an overview of and topical guide to biochemistry: Biochemistry – study of chemical processes in living organisms, including living matter. Biochemistry governs all living organisms and living processes. Applications of biochemistry * Testing ** Ames test – salmonella bacteria is exposed to a chemical under question (a food additive, for example), and changes in the way the bacteria grows are measured. This test is useful for screening chemicals to see if they mutate the structure of DNA and by extension identifying their potential to cause cancer in humans. ** Pregnancy test – one uses a urine sample and the other a blood sample. Both detect the presence of the hormone human chorionic gonadotropin (hCG). This hormone is produced by the placenta shortly after implantation of the embryo into the uterine walls and accumulates. ** Breast cancer screening – identification of risk by testing for mutations in two genes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.C.M. Guldberg and P. Waage,"Studies Concerning Affinity" ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864), 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Derivative
In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined asThomson, p. 1. : \lim_ \frac. The expression under the limit is sometimes called the symmetric difference quotient. A function is said to be symmetrically differentiable at a point ''x'' if its symmetric derivative exists at that point. If a function is differentiable (in the usual sense) at a point, then it is also symmetrically differentiable, but the converse is not true. A well-known counterexample is the absolute value function , which is not differentiable at , but is symmetrically differentiable here with symmetric derivative 0. For differentiable functions, the symmetric difference quotient does provide a better numerical approximation of the derivative than the usual difference quotient. The symmetric derivative at a given point equals the arithmetic mean of the left and right derivatives at that point, if the latter two both exist. Neither Rolle's theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Differentiation
In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function. Finite differences The simplest method is to use finite difference approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (''x'', ''f''(''x'')) and (''x'' + ''h'', ''f''(''x'' + ''h'')). Choosing a small number ''h'', ''h'' represents a small change in ''x'', and it can be either positive or negative. The slope of this line is : \frac. This expression is Newton's difference quotient (also known as a first-order divided difference). The slope of this secant line differs from the slope of the tangent line by an amount that is approximately proportional to ''h''. As ''h'' approaches zero, the slope of the secant line approaches the slope of the tangent line. Therefore, the true derivative of ''f'' at ''x'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill Equation (biochemistry)
In biochemistry and pharmacology, the Hill equation refers to two closely related equations that reflect the binding of ligands to macromolecules, as a function of the ligand concentration. A ligand is "a substance that forms a complex with a biomolecule to serve a biological purpose" ( ligand definition), and a macromolecule is a very large molecule, such as a protein, with a complex structure of components ( macromolecule definition). Protein-ligand binding typically changes the structure of the target protein, thereby changing its function in a cell. The distinction between the two Hill equations is whether they measure ''occupancy'' or ''response''. The Hill–Langmuir equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand.For clarity, this article will use the International Union of Basic and Clinical Pharmacology convention of distinguishing between the Hill-Langmuir equation (for receptor saturation) and Hill equation (for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michaelis–Menten Kinetics
In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate v (rate of formation of product, ce P/math>) to ce S/math>, the concentration of a substrate ''S''. Its formula is given by : v = \frac = V_\max \frac This equation is called the Michaelis–Menten equation. Here, V_\max represents the maximum rate achieved by the system, happening at saturating substrate concentration for a given enzyme concentration. When the value of the Michaelis constant K_\mathrm is numerically equal to the substrate concentration, then the reaction rate is half of V_\max. Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions. Model In 1901, Fre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
