Hyperbolic plot

FIGURE 15.8 Sigmoid versus [S] plot. The dotted line represents the hyperbolic plot characteristic of normal Michaelis-Men ten-type enzyme kinetics. 

The cytochrome P-450-dependent metabolism of trichloroethylene was studied in hepatic microsomal fractions from 23 different humans (Lipscomb et al. 1997). CYP2E1 was the predominant form of P-450 responsible for the metabolism of trichloroethylene in humans. Incubations of trichloroethylene with the microsomal preparations resulted in hyperbolic plots consistent with Michaelis-Menton kinetics. The values ranged from 12 to 55.7 pM, and were not normally distributed, and the values range from 490 to 3,455 pmol/min/mg protein and were normally distributed. The study authors concluded that the human variability in metabolism of trichloroethylene via P-450-dependent pathways was within a 10-fold range. 

A hyperbolic plot illustrating the (approximately) equal incremental increases in v when [S] is increased with respect to /Cm as indicated in O Table 4-2... 

Equation E3.5 in this experiment can be used to determine / values, but hyperbolic plots are obtained. Can you convert Equation E3.5 into an equation that will yield a linear plot without going through all the changes necessary for the Scatchard equation Hint Study the conversion of the Michaelis-Menten equation to the Lineweaver-Burk equation. 

Kinetic constants were determined from concentration/activity curves fit to a hyperbolic plot. Values shown are means S.E.M. from two or three independent experiments. 

Plotting the variation AI of fluorescence decrease as a function of added TNS concentration yields a hyperbolic plot at both pHs (Figure 15.4). However, this hyperbolic plot is more obvious at pH 3 than at pH 7. Hyperbolic plots can be described by the following equation ... 

Figure 3.27 illustrates a rectangular hyperbolic plot [Equation (3.169)], doublereciprocal plot [Equation (3.170)], Scatchard plot [Equation (3.171a)], and Hames plot [Equation (3.171b)] for the binding of NADH to rabbit muscle lactate dehydrogenase. 

FIGURE 4.1 Representative hyperbolic plot indicative of a reaction following Michaelis-Menten kinetics. = substrate concentration necessary to achieve one-half maximum velocity. Vmax = maximum velocity. 

A most satisfactory treatment of kinetic data is the direct linear plot of Eisenthal and Cornish Bowden (1974). Axes are drawn with -S on the abscissa and V on the ordinate, but instead of making the usual hyperbolic plot of S/v (see Enzyme kinetics), corresponding points (each reading of -S and its related v value) are joined by straight lines. The point of intersection of this family of lines gives the values of V and K . Mathematically, this plot corresponds to a rearrangement of the general equation = v + vK ,/... 

The concentration of substrate also influences the initial velocity but not in a simple manner (Figure 6.3b). At a constant [E], the hyperbolic plot obtained with different initial sutetrate concentrations shows that the rate is initially proportional to [S], i.e. first order with respect to substrate. (In the orders of chemical reactions, the reaction is first order when its rate is proportional to the first power of the concentration of just one reactant.) At extremely high substrate concentrations, the reaction rate approaches a constant rate (Section 6.2). This is the maximum velocity (For attainable for this particular [E]. The available active sites of all the enzyme molecules are occupied by the substrate the enzyme is saturated. To increase the rate, additional active sites must be made available by the addition of more enzyme. The reaction rate at V is independent of [S] and is zero order with respect to substrate. Between the extremities, the reaction is a mixture... 

A basic theory of enzyme action was proposed in 1913 when Michaelis and Menten developed a mathematical expression to rationalize the hyperbolic plot of Vj as a function of [S]. The Michaelis-Menten equation aims to describe the interrelationship between the parameters pertaining to an enzymic reaction. This accomplishment was based on two assumptions ... 

Equation (10) is represented graphically by a hyperbolic plot, the van Deemter curve, in Fig. 6. The curve shows the existence of an optimum velocity at which a given column exhibits its highest number of theoretical plates. Shapes of the van Deemter curves are further dependent on a number of variables solute diffusion rates in both phases, column dimensions and various geometrical constants, the phase ratio, and retention times. Highly effective GC separations often depend on thorough understanding and optimization of such variables. 

---