HistidineHistidine (symbol His or H) is an essential amino acid that is used in the biosynthesis of proteins. It contains an α-amino group (which is in the protonated –NH3+ form under biological conditions), a carboxylic acid group (which is in the deprotonated –COO− form under biological conditions), and an imidazole side chain (which is partially protonated), classifying it as a positively charged amino acid at physiological pH. Initially thought essential only for infants, it has now been shown in longer-term studies to be essential for adults also.
PhosphorylationIn biochemistry, phosphorylation is the attachment of a phosphate group to a molecule or an ion. This process and its inverse, dephosphorylation, are common in biology. Protein phosphorylation often activates (or deactivates) many enzymes. Phosphorylation is essential to the processes of both anaerobic and aerobic respiration, which involve the production of adenosine triphosphate (ATP), the "high-energy" exchange medium in the cell.
Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Oxidative phosphorylationOxidative phosphorylation (UK ɒkˈsɪd.ə.tɪv, US ˈɑːk.sɪˌdeɪ.tɪv ) or electron transport-linked phosphorylation or terminal oxidation is the metabolic pathway in which cells use enzymes to oxidize nutrients, thereby releasing chemical energy in order to produce adenosine triphosphate (ATP). In eukaryotes, this takes place inside mitochondria. Almost all aerobic organisms carry out oxidative phosphorylation. This pathway is so pervasive because it releases more energy than alternative fermentation processes such as anaerobic glycolysis.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Substrate-level phosphorylationSubstrate-level phosphorylation is a metabolism reaction that results in the production of ATP or GTP supported by the energy released from another high-energy bond that leads to phosphorylation of ADP or GDP to ATP or GTP (note that the reaction catalyzed by creatine kinase is not considered as "substrate-level phosphorylation"). This process uses some of the released chemical energy, the Gibbs free energy, to transfer a phosphoryl (PO3) group to ADP or GDP. Occurs in glycolysis and in the citric acid cycle.
Theta functionIn mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.
Exchange rateIn finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of the euro. The exchange rate is also regarded as the value of one country's currency in relation to another currency. For example, an interbank exchange rate of 131 Japanese yen to the United States dollar means that ¥131 will be exchanged for or that will be exchanged for ¥131.
Reaction rate constantIn chemical kinetics, a reaction rate constant or reaction rate coefficient (k) is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. For a reaction between reactants A and B to form a product C, where A and B are reactants C is a product a, b, and c are stoichiometric coefficients, the reaction rate is often found to have the form: Here k is the reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
ImidazoleImidazole (ImH) is an organic compound with the formula C3N2H4. It is a white or colourless solid that is soluble in water, producing a mildly alkaline solution. In chemistry, it is an aromatic heterocycle, classified as a diazole, and has non-adjacent nitrogen atoms in meta-substitution. Many natural products, especially alkaloids, contain the imidazole ring. These imidazoles share the 1,3-C3N2 ring but feature varied substituents. This ring system is present in important biological building blocks, such as histidine and the related hormone histamine.
Base (chemistry)In chemistry, there are three definitions in common use of the word "base": Arrhenius bases, Brønsted bases, and Lewis bases. All definitions agree that bases are substances that react with acids, as originally proposed by G.-F. Rouelle in the mid-18th century. In 1884, Svante Arrhenius proposed that a base is a substance which dissociates in aqueous solution to form hydroxide ions OH−. These ions can react with hydrogen ions (H+ according to Arrhenius) from the dissociation of acids to form water in an acid–base reaction.
Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
ChemiosmosisChemiosmosis is the movement of ions across a semipermeable membrane bound structure, down their electrochemical gradient. An important example is the formation of adenosine triphosphate (ATP) by the movement of hydrogen ions (H+) across a membrane during cellular respiration or photosynthesis. Hydrogen ions, or protons, will diffuse from a region of high proton concentration to a region of lower proton concentration, and an electrochemical concentration gradient of protons across a membrane can be harnessed to make ATP.
Glutamic acidGlutamic acid (symbol Glu or E; the ionic form is known as glutamate) is an α-amino acid that is used by almost all living beings in the biosynthesis of proteins. It is a non-essential nutrient for humans, meaning that the human body can synthesize enough for its use. It is also the most abundant excitatory neurotransmitter in the vertebrate nervous system. It serves as the precursor for the synthesis of the inhibitory gamma-aminobutyric acid (GABA) in GABAergic neurons. Its molecular formula is C5H9NO4.
Exchange rate regimeAn exchange rate regime is a way a monetary authority of a country or currency union manages the currency about other currencies and the foreign exchange market. It is closely related to monetary policy and the two are generally dependent on many of the same factors, such as economic scale and openness, inflation rate, the elasticity of the labor market, financial market development, and capital mobility. There are two major regime types: Floating (or flexible) exchange rate regime exist where exchange rates are determined solely by market forces and often manipulated by open-market operations.
Inverse trigonometric functionsIn mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
Fixed exchange rate systemA fixed exchange rate, often called a pegged exchange rate, is a type of exchange rate regime in which a currency's value is fixed or pegged by a monetary authority against the value of another currency, a basket of other currencies, or another measure of value, such as gold. There are benefits and risks to using a fixed exchange rate system. A fixed exchange rate is typically used to stabilize the exchange rate of a currency by directly fixing its value in a predetermined ratio to a different, more stable, or more internationally prevalent currency (or currencies) to which the currency is pegged.
Aqueous solutionAn aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as . The word aqueous (which comes from aqua) means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry.
