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Goldbeter–Koshland Kinetics
The Goldbeter–Koshland kinetics Zoltan Szallasi, Jörg Stelling, Vipul Periwal: ''System Modeling in Cellular Biology''. The MIT Press. p 108. describe a Steady state (chemistry), steady-state solution for a 2-state biological system. In this system, the interconversion between these two states is performed by two enzymes with opposing effect. One example would be a protein Z that exists in a Phosphorylation, phosphorylated form ZP and in an unphosphorylated form ''Z''; the corresponding kinase ''Y'' and phosphatase ''X'' interconvert the two forms. In this case we would be interested in the equilibrium concentration of the protein Z (Goldbeter–Koshland kinetics only describe equilibrium properties, thus no dynamics can be modeled). It has many applications in the description of biological systems. The Goldbeter–Koshland kinetics is described by the Goldbeter–Koshland function: : \begin z = \frac = G(v_1, v_2, J_1, J_2) &= \frac\\ \end with the constants : \begin v_1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steady State (chemistry)
In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, there must be a flow through the system (compare mass balance). A simple example of such a system is the case of a bathtub with the tap running but with the drain unplugged: after a certain time, the water flows in and out at the same rate, so the water level (the state variable Volume) stabilizes and the system is in a steady state. The steady state concept is different from chemical equilibrium. Although both may create a situation where a concentration does not change, in a system at chemical equilibrium, the net reaction rate is zero (products transform into reactants at the same rate as reactants transform into products), while no such limitation exists in the steady state concept. Indeed, there does not have to be a reaction at all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Metabolic pathways depend upon enzymes to catalyze individual steps. The study of enzymes is called ''enzymology'' and the field of pseudoenzyme analysis recognizes that during evolution, some enzymes have lost the ability to carry out biological catalysis, which is often reflected in their amino acid sequences and unusual 'pseudocatalytic' properties. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Other biocatalysts are catalytic RNA molecules, called ribozymes. Enzymes' specificity comes from their unique three-dimensional structures. Like all catalysts, enzymes increase the reaction ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phosphorylation
In chemistry, phosphorylation is the attachment of a phosphate group to a molecule or an ion. This process and its inverse, dephosphorylation, are common in biology and could be driven by natural selection. Text was copied from this source, which is available under a Creative Commons Attribution 4.0 International License. Protein phosphorylation often activates (or deactivates) many enzymes. Glucose Phosphorylation of sugars is often the first stage in their catabolism. Phosphorylation allows cells to accumulate sugars because the phosphate group prevents the molecules from diffusing back across their transporter. Phosphorylation of glucose is a key reaction in sugar metabolism. The chemical equation for the conversion of D-glucose to D-glucose-6-phosphate in the first step of glycolysis is given by :D-glucose + ATP → D-glucose-6-phosphate + ADP : ΔG° = −16.7 kJ/mol (° indicates measurement at standard condition) Hepatic cells are freely permeable to glucose, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinase
In biochemistry, a kinase () is an enzyme that catalyzes the transfer of phosphate groups from high-energy, phosphate-donating molecules to specific substrates. This process is known as phosphorylation, where the high-energy ATP molecule donates a phosphate group to the substrate molecule. This transesterification produces a phosphorylated substrate and ADP. Conversely, it is referred to as dephosphorylation when the phosphorylated substrate donates a phosphate group and ADP gains a phosphate group (producing a dephosphorylated substrate and the high energy molecule of ATP). These two processes, phosphorylation and dephosphorylation, occur four times during glycolysis. Kinases are part of the larger family of phosphotransferases. Kinases should not be confused with phosphorylases, which catalyze the addition of inorganic phosphate groups to an acceptor, nor with phosphatases, which remove phosphate groups (dephosphorylation). The phosphorylation state of a molecule, whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phosphatase
In biochemistry, a phosphatase is an enzyme that uses water to cleave a phosphoric acid Ester, monoester into a phosphate ion and an Alcohol (chemistry), alcohol. Because a phosphatase enzyme catalysis, catalyzes the hydrolysis of its Substrate (chemistry), substrate, it is a subcategory of hydrolases. Phosphatase enzymes are essential to many biological functions, because phosphorylation (e.g. by protein kinases) and dephosphorylation (by phosphatases) serve diverse roles in cell growth, cellular regulation and cell signaling, signaling. Whereas phosphatases remove phosphate groups from molecules, kinases catalyze the transfer of phosphate groups to molecules from Adenosine triphosphate, ATP. Together, kinases and phosphatases direct a form of post-translational modification that is essential to the cell's regulatory network. Phosphatase enzymes are not to be confused with phosphorylase enzymes, which catalyze the transfer of a phosphate group from hydrogen phosphate to an acce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: :S(x) = \frac = \frac=1-S(-x). Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as an alias for the logistic function. Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and hype ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultrasensitivity
In molecular biology, ultrasensitivity describes an output response that is more sensitive to stimulus change than the hyperbolic Michaelis-Menten response. Ultrasensitivity is one of the biochemical switches in the cell cycle and has been implicated in a number of important cellular events, including exiting G2 cell cycle arrests in ''Xenopus laevis'' oocytes, a stage to which the cell or organism would not want to return. Ultrasensitivity is a cellular system which triggers entry into a different cellular state. Ultrasensitivity gives a small response to first input signal, but an increase in the input signal produces higher and higher levels of output. This acts to filter out noise, as small stimuli and threshold concentrations of the stimulus (input signal) is necessary for the trigger which allows the system to get activated quickly. Ultrasensitive responses are represented by sigmoidal graphs, which resemble cooperativity. The quantification of ultrasensitivity is often perfo ... [...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, French ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the Expression (mathematics), expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex number, c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill Coefficient
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] |
Enzyme Kinetics
Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled, and how a drug or a modifier ( inhibitor or activator) might affect the rate. An enzyme (E) is typically a protein molecule that promotes a reaction of another molecule, its substrate (S). This binds to the active site of the enzyme to produce an enzyme-substrate complex ES, and is transformed into an enzyme-product complex EP and from there to product P, via a transition state ES*. The series of steps is known as the mechanism: : E + S ⇄ ES ⇄ ES* ⇄ EP ⇄ E + P This example assumes the simplest case of a reaction with one substrate and one product. Such cases exist: for example, a mutase such as phosphoglucomutase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
