Michaelis-Menten relationship

This form of the Michaelis-Menten equation is called the Lineweaver-Burk equation. For enzymes obeying the Michaelis-Menten relationship, a plot of 1/F0 versus 1/[S] (the double reciprocal of the V0 versus [S] plot we have been using to this point) yields a straight line (Fig. 1). This line has a slope of Km/Vmax, an intercept of 1/Fmax on the 1/F0 axis, and an intercept... 

Allosteric enzymes show relationships between V0 and [S] that differ from Michaelis-Menten kinetics. They do exhibit saturation with the substrate when [S] is sufficiently high, but for some allosteric enzymes, plots of V0 versus [S] (Fig. 6-29) produce a sigmoid saturation curve, rather than the hyperbolic curve typical of non-regulatory enzymes. On the sigmoid saturation curve we can find a value of [S] at which V0 is half-maximal, but we cannot refer to it with the designation Km, because the enzyme does not follow the hyperbolic Michaelis-Menten relationship. Instead, the symbol [S]0 e or K0,5 is often used to represent the substrate concentration giving half-maximal velocity of the reaction catalyzed by an allosteric enzyme (Fig. 6-29). 

The graphical significance of the constants in the Monod equation are identical to the corresponding constants in the Michaelis-Menten relationship for enzyme kinetics (see Section 5.4.4). The specific growth rate initially increases with increas-... 

The value of the substrate concentration corresponding to half-maximal velocity is designated as A o.5 and not since the allosteric kinetics do not follow the hyperbolic Michaelis-Menten relationship. 

For enzymes that obey the Michaelis-Menten relationship, a plot of Mr versus 1/[S] the so-called double-reciprocal plot yields a straight line, from which one can obtain more accurate values for the Michaelis constant, Km, and the maximum velocity, Vmax (Figure 6.4). 

The availability of chemically well defined octamers (A and C) as sDNA substitutes provi s a kinetic tool for the determination of the effects of enzyme inhibitors on the DNA binding site of the enzyme. The 6-amino derivative of 1,2-benzoypyrone, (6-aminocoumarin), competitively inhibits at the octamer duplex A or C sites with an apparent Ki of 28 jiM. Without the inhibition at a fixed NAD+ concentration, a Michaelis-Menten relationship exists between Vinit and the concentration of the octamers (lowest curve in Fig. 3) with an apparent binding constant of 1 jiM. The results shown in Fig. 3 identify a novel site of inhibitors, structurally unrelated to NAD" (12), which act at the DNA binding site of the enzyme. 

The Michaelis-Menten rate expression for a monomolecular enzyme-catalyzed reaction is very similar to the Langmuir kinetic expression that we discussed previously for heterogeneous catalyzed systems. The Michaelis-Menten relationship is readily deduced for a simple model where the enzyme molecule (E) equilibrates with substrate molecule (S) to form the enzyme substrate complex (ES). The enzyme-substrate complex then reacts to the product molecule (P) and regenerates the active site of the enzyme (E) in what is considered to be the rate-limiting step of the proposed scheme ... 

Determination of the inhibition kinetic parameter follows the same approach as simple Michaelis-Menten kinetics, discussed earlier, using the linearization approach. Thus, it is better to express Equations 4.33, 4.35, and 4.37 in terms of apparent parameters, as shown in Equation 4.38. This is compatible with a simple Michaelis-Menten relationship. 

The reaction rates for the two sequential reactions are given by the Michaelis-Menten relationship ... 

The biodegradation rate R is characterized by the Monod (or Michaelis-Menten) following relationship ... 

Substituting this relationship into the expression for v gives the Michaelis-Menten equation... 

From the Michaelis-Menten model, there is a relationship between 1/Fo and the initial substrate concentration, expressed as the reciprocal, 1/[Bq]. To develop this relationship we shall repeat Example 9.1 using varying concentrations of B cells. Be sure to subtract the number of Bq cells in each study from the total number of water, D, cells in the setup. 

The Michaelis-Menten equation (29) illustrates in mathematical terms the relationship between initial reaction velocity V and substrate concentration [S], shown graphically in Figure 8-3. 

A plot of the initial reaction rate, v, as a function of the substrate concentration [S], shows a hyperbolic relationship (Figure 4). As the [S] becomes very large and the enzyme is saturated with the substrate, the reaction rate will not increase indefinitely but, for a fixed amount of [E], it reaches a plateau at a limiting value named the maximal velocity (vmax). This behavior can be explained using the equilibrium model of Michaelis-Menten (1913) or the steady-state model of Briggs and Haldane (1926). The first one is based on the assumption that the rate of breakdown of the ES complex to yield the product is much slower that the dissociation of ES. This means that k2 tj. 

If [S] = Km, the Michaelis-Menten equation says that the velocity will be one-half of Vmax. (Try substituting [S] for Km in the Michaelis-Menten equation, and you too can see this directly.) It s really the relationship between Km and [S] that determines where you are along the hyperbola. Like most of the rest of biochemistry, Km is backward. The larger the Km, the weaker the interaction between the enzyme and the substrate. Km is also a collection of rate constants. It may not be equal to the true dissociation constant of the ES complex (i.e., the equilibrium constant for ES E + S). 

This relationship corresponds to the simplest Michaelis-Menten kinetics (Eq. (3)). In addition to the equation derived earlier by Halpern et al. for the simplest model case of a C2-symmetric ligand without intramolecular exchange [21b], every other possibility of reaction sequence corresponding to Scheme 10.3 can be reduced to Eq. (13). Only the physical content of the values of kobs and Km, which must be determined macroscopically, differs depending upon the approach (see [59] for details). Nonetheless, the constants k0bs and KM allow conclusions to be made about the catalyses ... 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

Figure 3. Schematic view of the substrate uptake rate versus concentration relationship as described by the whole-cell Michaelis-Menten kinetics. Q is the substrate uptake rate, <2max the biologically determined maximum uptake rate per biomass, c the substrate concentration, and Kj the whole-cell Michaelis constant, i.e. the concentration resulting in 2max/2 (mass of substrate per volume). At c

Because of its prominent appearance in the whole cell Michaelis-Menten equation, Kt is frequently mistaken as a measure of the substrate affinity. However, from equations (2) and (4), it becomes obvious that the activity versus concentration relationship is characterised by the two independent parameters, 2max, as a descriptor of the zero-order part at high substrate concentration, and a°A, as a descriptor of the slope of the first-order part of the curve. In his much-cited review paper, Button [9] has listed the specific affinities of various organisms for a range of carbon sources and other elements. Reported variations for the same substrates extend over up to four orders of magnitude. Table 1 updates... 

Characteristically, within certain concentration limits, if a chemical is absorbed by passive diffusion, then the concentration of toxicant in the gut and the rate of absorption are linearly related. However, if absorption is mediated by active transport, the relationship between concentration and rate of absorption conforms to Michaelis-Menten kinetics and a Lineweaver-Burk plot (i.e., reciprocal of rate of absorption plotted against reciprocal of concentration), which graphs as a straight line. 

For reversible enzymatic reactions, the Haldane relationship relates the equilibrium constant KeqsNith the kinetic parameters of a reaction. The equilibrium constant Keq for the reversible Michaelis Menten scheme shown above is given as... 

Such a relationship between the polymer yield and the mass of feeded MMA is similar to that in the enzymatic reaction. Therefore, the result was applied to Michaelis-Menten equation and in the case of PVPA, the result shown in Fig. 5 was obtained. 

A Michaelis-Menten type graph for an allosteric enzyme shows not the usual hyperbolic shape as shown in Section 1.4, but a sigmoidal relationship between [S] and activity. 

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