Michaelis-Menton equation

If a detailed theoretical knowledge of the system is available, it is often possible to construct a mechanistic model which will describe the general behavior of the system. For example, if a biochemist is dealing with an enzyme system and is interested in the rate of the enzyme catalyzed reaction as a function of substrate concentration (see Figure 1.15), the Michaelis-Menton equation might be expected to provide a general description of the system s behavior. 

The Michaelis-Menton equation represents a mechanistic model because it is based on an assumed chemical reaction mechanism of how the system behaves. If the system does indeed behave in the assumed manner, then the mechanistic model is adequate for describing the system. If, however, the system does not behave in the assumed manner, then the mechanistic model is inadequate. The only way to determine the adequacy of a model is to carry out experiments to see if the system does behave as the model predicts it will. (The design of such experiments will be discussed in later chapters.) In the present example, if substrate inhibition occurs, the Michaelis-Menton model would probably be found to be inadequate a different mechanistic model would better describe the behavior of the system. 

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 ... 

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. ... 

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. 

The rate equation deduced for this, as well as for other similar mechanisms (W33), has the form of a modified Michaelis-Menton equation for the example given above, the rate equation is... 

This is the equation for the curve seen in Figure 1. It is in most respects identical to the Michaelis-Menton equation ... 

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. 

The procedure used in deriving the Michaelis-Menton equation is readily generalized. Equation (3-73) supposes that the decomposition of complex X is reversible, but suppose that it is not that is... 

A primary interest is to determine and to model the specific growth rate of a population that consumes a single ( rate-limiting ) substrate. The starting point for most treatments of microbial growth is based on a model suggested by Monod [J. Monod, Ann. Rev. Microbiol., 3, (1949)]. It is essentially a restatement of the Michaelis-Menton equation. 

Assuming that the Michaelis-Menton equation applies, show that a... 

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. 

This result is analogous to the Michaelis-Menton equation that is used to describe enzyme-catalyzed decomposition rates. 

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-... 

This equation is known as the Michaelis-Menton equation. A plot of rate r versus substrate concentration [S] (Figure 2.20) shows that the rate equation follows first-order kinetics fp = (k/kuAS] at low substrate concentrations and zero-order kinetics r = k ed. high substrate concentrations. The tangent to versus [S] plot drawn at [S] = 0 intersects r = k at a point corresponding to [S] = k - This method of tangent can be used to determine the kinetic parameters k and k - Alternatively, we can write the rate equation in linear form as (l/fp) = kM/k) l/[S]) + (1/k) by inverting Equation 2.169. Thus, by making a linear plot of... 

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