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Michaelis–Menten–Monod Kinetics
For Michaelis–Menten–Monod (MMM) kinetics it is intended the coupling of an enzyme-driven chemical reaction of the Michaelis–Menten type with the Monod growth of an organisms that performs the chemical reaction. The enzyme-driven reaction can be conceptualized as the binding of an enzyme E with the substrate S to form an intermediate complex C, which releases the reaction product P and the unchanged enzyme E. During the metabolic consumption of S, biomass B is produced, which synthesizes the enzyme, thus feeding back to the chemical reaction. The two processes can be expressed as where k_1 and k_ are the forward and backward equilibrium rate constants, k is the reaction rate constant for product release, Y is the biomass yield coefficient, and z is the enzyme yield coefficient. Transient kinetics The kinetic equations describing the reactions above can be derived from the GEBIK equations and are written as where \mu_B is the biomass mortality rate a ... [...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] |
Monod Equation
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910 – 1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient. The Monod equation has the same form as the Michaelis–Menten equation, but differs in that it is empirical while the latter is based on theoretical considerations. The Monod equation is commonly used in environmental engineering. For example, it is used in the activated sludge model for sewage treatment. Equation The empirical Monod equation is: : \mu = \mu_\max where: * ''μ'' is the growth rate of a considered microorganism * ''μ''max is the maximum growth rate of this microorganism * 'S''is the concentration of the limiting substrate ''S'' for growth * ''K''''s'' is the "half-velocity constant"—the value of 'S''when ''μ''/''Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transient Kinetic Isotope Fractionation
Transient kinetic isotope effects (or fractionation) occur when the Chemical reaction, reaction leading to isotope fractionation does not follow pure First order kinetics, first-order kinetics and therefore isotopic effects cannot be described with the classical equilibrium fractionation equations or with steady-state Kinetic isotope effect, kinetic fractionation equations (also known as the Rayleigh equation). In these instances, the general equations for biochemical isotope kinetics (GEBIK) and the general equations for biochemical isotope fractionation (GEBIF) can be used. The GEBIK and GEBIF equations are the most generalized approach to describe isotopic effects in any Chemical reaction, chemical, Chemical reaction#Catalysis, catalytic reaction and Chemical reaction#Biochemical reactions, biochemical reactions because they can describe isotopic effects in equilibrium reactions, kinetic chemical reactions and kinetic biochemical reactions. In the latter two cases, they can de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Function
In 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. Definition Formally, an analytic function ''f''(''z'') of one real or complex variable ''z'' is transcendental if it is algebraically independent of that variable. This can be extended to functions of several variables. History The transcendental functions sine and cosine were tabulated from physical measurements in antiquity, as evidenced in Greece (Hipparchus) and India ( jya and koti-jya). In describing Ptolemy's table of chords, an equivalent to a table of sines, Olaf Pedersen wrote: A revolutionary understanding of these circular functions occurred in the 17th century and was explicated by Leonhard ... [...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] |
