Michaelis–Menten kinetics

In biochemistry, Michaelis–Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions of one substrate and one product. It takes the form of an equation describing the rate reaction rate v (rate of formation of product P, with concentration p) to a, the concentration of the substrate A (using the symbols recommended by the IUBMB). Its formula is given by the Michaelis–Menten equation: : v = \frac{\mathrm{d} p}{\mathrm{d} t} = \frac{V a}{K_\mathrm{m} + a} V, which is often written as V_\max, represents the limiting rate approached by the system at saturating substrate concentration for a given enzyme concentration. When the value of the Michaelis constant K_\mathrm{m} is numerically equal to the substrate concentration, the reaction rate is half of V. Biochemica

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Quantification of biodegradation for o-xylene and naphthalene using first order decay models, Michaelis-Menten kinetics and stable carbon isotopes

At a former wood preservation plant severely contaminated with coal tar oil, in situ bulk attenuation and biodegradation rate constants for several monoaromatic (BTEX) and polyaromatic hydrocarbons (PAH) were determined using (1) classical first order decay models, (2) Michaelis-Menten degradation kinetics (MM), and (3) stable carbon isotopes, for o-xylene and naphthalene. The first order bulk attenuation rate constant for o-xylene was calculated to be 0.0025 d(-1) and a novel stable isotope-based first order model, which also accounted for the respective redox conditions, resulted in a slightly smaller biodegradation rate constant of 0.0019 d(-1). Based on MM-kinetics, the o-xylene concentration decreased with a maximum rate of k(max)=0.1 mu g/L/d. The bulk attenuation rate constant of naphthalene retrieved from the classical first order decay model was 0.0038 d(-1). The stable isotope-based biodegradation rate constant of 0.0027 d(-1) was smaller in the reduced zone, while residual naphthalene in the oxic part of the plume further downgradient was degraded at a higher rate of 0.0038 d(-1). With MM-kinetics a maximum degradation rate of k(max)=12 mu g/L/d was determined. Although best fits were obtained by MM-kinetics, we consider the carbon stable isotope-based approach more appropriate as it is specific for biodegradation (not overall attenuation) and at the same time accounts for the dominant electron-accepting process. For o-xylene a field based isotope enrichment factor epsilon(field) of - 1.4 could be determined using the Rayleigh model, which closely matched values from laboratory studies of o-xylene degradation under sulfate-reducing conditions. (C) 2008 Elsevier B.V. All rights reserved.

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Thermodynamic and kinetic degradation reactions of organic substances in groundwater modelled with PHREEQC

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Aim of this diploma thesis is to approach to kinetic modelling of subsurface hydrochemistry with the program code phreeqc. The reaction considered is the degradation of organic mass and its concomitant reactions. Phreeqc is a program for thermodynamical based equilibrium calculations of geo- and hydrochemistry. Although the degradation of organic matter, and the associated reduction reactions due to the oxidation of organic matter, can be modelled with phreeqc, it does not account for kinetically controlled reactions, whose characteristic feature is the dependency of time. This study focuses on the state of the art of environmental modelling, the thermodynamical based calculation of the degradation of organic matter and on two mathematical approaches to model bacterial degradation of a contaminant, the Monod equation and the Michaelis-Menten approach. Sensitivity analyses of the respective models runs were done. As a result one can see, that the redox chemistry of a natural water depends strongly on the abundance of oxygen and nitrate and, as a matter of course, on the abundance of organic matter. Considering bacterial activity within the degradation process, two basic mathematical formulations have been stated. The Monod equation and the Michaelis-Menten formulation were implemented in a BASIC interpreter in PHREEQC. The sensitivity analyses show, that that a accurate determination of the parameters in laboratory or field is essential. The coupling of kinetically controlled reactions and thermodynamical based equilibrium calculations might lead to auspicious hydrochemical modelling capabilities.

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Real-time monitoring of single-cell secretion with a high-throughput nanoplasmonic microarray

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