Michaelis-Menton constant

The membrane containing the immobilized enzyme is handled by partitioning it into a specified number of volume elements so that Equations 20.23 and 20.24 are valid in this model. While the concentration of each species may vary from element to element, the steady-state assumption (d[ES]/dt = 0) may be invoked independently for each volume element. This results in the definition of the Michaelis-Menton constant, KM ... 

Here k is the rate constant for the irreversible reaction, Ceo is the total enzyme concentration, Cs is the substrate concentration, and is the Michaelis-Menton constant. Both k and KM may be functions of pH, temperature, and other properties of the fermentation medium. From this kinetic expression, we see that at high substrate concentrations the rate of product formation is independent of Cs and is approximately equal to kCm-This is due to the presence of a limited amount of enzyme, which is required for the reaction to proceed, and adding more substrate under these conditions will not cause the reaction rate to increase further. At low substrate concentrations, the rate of product formation becomes first-order with respect to Cs- Under these conditions the substrate concentration becomes the determinant for product formation, and increasing Cs produces a proportional increase in rate. The rate is also proportional to the total enzyme concentration under all conditions of substrate concentration. 

Relates IC50 to Kt under conditions of competitive inhibition Kt equilibrium enzyme inhibitor dissociation constant Km Michaelis-Menton constant, [S] substrate concentration. 

Michaelis-Menton equation/kinetics This equation, which is central to enzymology, describes the relationship between the initial rate of reaction (v) and the substrate concentration (Q. It gives the initial rate of reaction as v = V ax C/(K +C) where V ax is the maximum velocity of reaction, C is the concentration of substrate and is the Michaelis-Menton constant. C is equal to the Michaelis-Menton constant when vis 50% of micro- A prefix meaning small. 

Sudden death is a major factor in cocaine-related fatalities. The mechanism for the cardiotoxicity is not fully understood, but it appears to be poorly predicted from patient to patient. Nevertheless, a rapid immuno-therapeutic response would be essential in treating cocaine-related toxicity, and even catalytic antibodies with low micromolar (M) Michaelis-Menton constant (K ) values may not be fast-acting enough. By comparison, high-affinity anti-drug antibodies typically have dissociation constant (K ) values in the low nanomolar (nM) to high picomolar (pM) range. Therefore, to test the usefulness of catalytic antibodies, it will be important to conduct full dose-response curves with the cocaine catalytic antibodies and to... 

Effective Michaelis-Menton constant, mol/m. Equilibrium constants in the organic and aqueous phases. Apparent equilibrium constant in water. 

The parameter for enzymes that characterizes the sensitivity level for sensors based on the uses of enzymes is the kinetic parameter known as the Michaelis-Menton constant (A m)- Again enzymes can be found... 

Figure 9.32 displays the amperometric response at -200 mV for HRP/MW-CNT200/PS biocomposite sensor to H2O2. A linear response is found in the H2O2 concentration range of 0.02-0.5 luM and Ae detection limit is 25 pM. The apparent Michaelis-Menton constant is calculated from the inserted linear plot to be... 

In this scheme, EOH is the enzyme, IX is the inhibitor (either a carbamate or an organophosphate). EOH(IX) is analogous to the Michaelis Menton comploc seen with the substrate reaction. EOI is the acyl-enzyme intermediate for carbamates or a phosphoro-enzyme intermediate for the organophosphates. The equilibrium constant for this reaction (K ) is defined as k /k and the phosphorylation or carbamylation constant is defined as k2- In this study 42)y ANTX-A(S) was found to be more specific for AChE than BUChE. The double reciprocal and Dixon plot of the inhibition of electric eel AChE indicated that the toxin is a non-competitive inhibitor decreases, k remains unchanged) (Figure 2). 

Non-linear pharmacokinetics are much less common than linear kinetics. They occur when drug concentrations are sufficiently high to saturate the ability of the liver enzymes to metabolise the drug. This occurs with ethanol, therapeutic concentrations of phenytoin and salicylates, or when high doses of barbiturates are used for cerebral protection. The kinetics of conventional doses of thiopentone are linear. With non-linear pharmacokinetics, the amount of drug eliminated per unit time is constant rather than a constant fraction of the amount in the body, as is the case for the linear situation. Non-linear kinetics are also referred to as zero order or saturation kinetics. The rate of drug decline is governed by the Michaelis-Menton equation ... 

The Michaelis-Menton equation is an important biochemical rate law. It relates the rate of the reaction v to a substrate concentration [5] in terms of two constants vmax and KM ... 

Kinetic studies of this reaction have shown that it obeys Michaelis-Menton kinetics as expressed by the Lineweaver-Burk plot, the Michaelis constant (KJ for this reaction at pH 7.0 and 37.5 °C being 2.86 x 10 4 M 24). Free lysine, Leuehs Poly-L-lysine, total hydrolyzates of thermal polylysine, and amino group-modified thermal polylysine are completely inactive. The activity of thermal polylysine depends on the degree of polymerization 24). 

When accurate data can be obtained over a range of both concentrations and temperatures, it is possible from the Michaelis-Menton model to obtain data on the first-order rate constant kz and the constant Km = kz + kz)/ki and their apparent activation energies Ez and Unfortunately, most of the values quoted in the literature for the activation energies of enzyme-catalyzed reactions are derived from the use of overly simple first-order equations to describe the reaction. Consequently these values are a composite of Kmj kzy and the other constants in the Michaelis-Menton equation and cannot be used for interpretive purposes. Where the constants have been separated it is found that the values of Ez are low and of order of magnitude of 5 to 15 Kcal/mole. It is of interest to note that enzyme preparations from different biological sources, which may show different specific activity for a given reaction, have very nearly the same temperature coefficient for their specific rate constants. ... 

The present PK model is a two-compartment model with Michaelis-Menton elimination, vmax and km define the parameters for elimination, k23 and K32 define the intercompartmental transfer rate constants, and vi is the central volume of distribution. As with many biologies, this theoretical agent is being administered intravenously. 

The only difference is that in enzymatic reactions described by the Michaelis-Menton equation substrate is consumed and, therefore, Kk is not a true dissociation constant whereas in equation (2) Kg is a true dissociation constant. 

As an example, the data from Ketchum (37) for the rate of phosphate absorption as a function of both phosphate and nitrate concentration can be satisfactorily fit with a product of two Michaelis-Menton expressions. The resulting fit, obtained by a multiple nonlinear regression analysis, is shown in Figure 5. The Michaelis constants that result are 28.4 p.g NOa-N/liter and 30.3 pg P04-P/liter, with a saturated absorption rate of 15.1 X 10 8 pg P04-P/cell-hr. This approximation to the growth rate behavior as a function of more than one nutrient must be regarded as only a first approximation, however, since the complex interaction reported between the nutrients is neglected. 

In interior wetland areas, the source of nitrate is primarily nitrification, and denitrification rates in these areas are limited by nitrate availability. Several studies have shown that denitrification rates increase with an increase in nitrate concentration. Half-saturation constants (one of the Michaelis-Menton kinetics parameter) reported for denitrification range from 27 to 344 pM for lake and marine sediments (Seitzinger, 1988) and 130 to 1,200 pM for soils (Firestone, 1982). Low half-saturation constants probably reflect carbon limitation in soil or diffusion of nitrate from aerobic sites to anaerobic sites. 

Equation 9 is a hyperbolic relationship, similar to the Michaelis-Menton equation derived for enzyme kinetics (104) the Langmuir equation as applied to adsorption on soils (105), and an adaptation of these models for dechlorination by Fe that we published previously (13). As such, all four models are capable of describing site saturation phenomena commonly found in heterogenous systems however, only the new model (equations 8 and 9) explicitly distinguishes thermodynamically-related parameters from the kinetic constants. 

The potential for such systems to respond radically to small changes in the concentration of effector molecules arises because their kinetic behavior can be described by the Michaelis-Menton equation (see). At steady state, the fraction of protein P in active form (P /P, ,) depends on the rate constants of the ac-... 

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