Michaelis-Menten kinetics double-reciprocal plot

Regulatory enzymes are usually identified by the deviation of their kinetics from Michaelis-Menten kinetics plots of velocity versus substrate concentration can be a sigmoidal curve or a modified hyperbola [Fig. 9-7(o)]. If these curves are plotted in the double-reciprocal (Lineweaver-Burk) form, nonlinear graphs are obtained [Fig. 9-7(6)]. 

Figure 3-16. Relationship between the external solute concentration (c°) and the rate of influx (J n) for active uptake according to Michaelis-Menten kinetics, as given by Equation 3.28 (a) linear plot and (b) double-reciprocal plot.

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

FIGURE 4.2 Lineweaver-Burk (double-reciprocal) plot of a reaction that follows Michaelis-Menten kinetics. Kinetic parameters are as defined previously. 

In the first case, if Po > 1 (sq > K), substrate gradient is very high and reaction is limited only by enzyme kinetics, so substrate profile within the stagnant film will be negligible and ss = Sq. In that case the rate equation reduces to a simple Michaelis-Menten equation that can be linearized as already described in Chapter 3. Using the double reciprocal plot ... 

The general property of all above mechanisms is their adherence to the Michaelis-Menten kinetics. In the absence of products, the double reciprocal plots for aU bisubstrate mechanisms represent a family of straight lines with a common intersection point, if one substrate is varied while the other substrate is held at different fixed concentrations. Similarly, the double reciprocal plots for all trisubstrate mechanisms represent a family of straight lines with a common intersection point, if one substrate is varied while the second substrate is held at different fixed concentrations, and the third substrate is held at a fixed concentration. This, however, is tme only if each substrate adds just once if one of them adds twice in sequential fashion, the reciprocal plots will be parabolic. 

Fig. 2. Double reciprocal plot of the Michaelis-Menten equation indicating how the intercepts provide a simplified way of determining the kinetic constants of the equation.

Lineweaver-Burk plot A double-reciprocal plot used to determine the two constants featured in simple enzyme kinetic equations such as Michaelis-Menten kinetics, Monod kinetics, and in similar adsorption isotherm models such as the Langmuir adsorption isotherm. The constants are determined from the intercept with the y-axis and the gradient (see Fig. 26). It was devised and published in 1934 by American chemist Hans Lineweaver (1907-2009) and American biochemist Dean Burk (1904-1988). 

The envelope-bound ATPase activity as a function of ATP concentration followed Michaelis-Menten kinetics with an apparent Kjyj value for ATP of 0.55 mM as determined by the double-reciprocal plot of 1/V versus 1/S (inset of Fig. 1). Compared to the value found by Joyard and Douce (1975), our enzyme had a greater affinity for ATP by a factor of 1.4. A basal ATPase activity, EDTA-insensitive, was associated with chloroplast envelopes. It was stimulated by divalent cations with maximal rates at 0.15 mM CaCl2 and 5 to 10 mM MgCl2 (Fig. 2). In the presence of Ca2+ and Mg2+, calmodulin further stimulated the activity (28-63%, see Table I). The enzyme was sensitive to oligomycin, LaCl3 and NH4VO3. 

Fig. 6.4 Double-reciprocal plot for Michaelis-Menten kinetics.

In the literature, it is sometimes argued that linearisation of nonlinear functions in the era of personal computers is obsolete. Moreover linearisation of Michaelis—Menten kinetics through a double reciprocal plot transforms the region of zero order to a single point, which is not favorable for parameter estimation. 

In ester synthesis and exchange reactions, as well as in hydrolysis re tions induced by PEG-lipase in hydrophobic media, the existence of a trace amount of water in the reaction system was most important in terms of the reactions proceeding. Matsushima et al. [67] carried out a kinetics study of PEG-lipase in transparent benzene solution to estimate the value of water, one of the substrates of lipase in the ester hydrolytic reaction. Indoxyl acetate was hydrolyzed by PEG-lipase to form acetic acid and 3-hydroxyindole, which was photometrically determined. A double-reciprocal plot of the velocity of the indoxyl acetate hydrolysis against water concentration at a given concentration of indoxyl acetate indicated that the hydrolysis took place as a double-displacement reaction (ping-pong reaction). The apparent Michaelis-Menten constant of water and the maximum velocity were calculated to be = 7 X 10 M and Vmax = 4700 xmol/min/mg of protein, respectively. 

The Michaelis-Menten equation is, like Eq. (3-146), a rectangular hyperbola, and it can be cast into three linear plotting forms. The double-reciprocal form, Eq. (3-152), is called the Lineweaver-Burk plot in enzyme kinetics. ... 

FIGURE 13.2 Biochemical plots for the enz5me kinetic characterizations of biotransformation, (a) Direct concentration-rate or Michaelis-Menten plot (b), Eadie-Hofstee plot (c), double-reciprocal or Lineweaver-Burk plot. The Michaelis-Menten plot (a), typically exhibiting hyperbolic saturation, is fundamental to the demonstration of the effects of substrate concentration on the rates of metabolism, or metabolite formation. Here, the rates at 1 mM were excluded for the parameter estimation because of the potential for substrate inhibition. Eadie-Hofstee (b) and Lineweaver-Burk (c) plots are frequently used to analyze kinetic data. Eadie-Hofstee plots are preferred for determining the apparent values of and Umax- The data points in Lineweaver-Burk plots tend to be unevenly distributed and thus potentially lead to unreliable reciprocals of lower metabolic rates (1 /V) these lower rates, however, dictate the linear regression curves. In contrast, the data points in Eadie-Hofstee plot are usually homogeneously distributed, and thus tend to be more accurate. 

Purified cottonseed NAPE synthase enzyme exhibited non-Michaelis-Menten biphasic kinetics with respect to the free fatty acid substrates, palmitic and linoleic acids. Kinetic parameters for the two saturable sites were calculated from various transformations e.g., double-reciprocal and Hill plots Cornish-Bowden, 1995) of initial velocity/ substrate concentration data and are summarized in TABLE 1. Preliminary experiments with several group-specific modifiers indicated that NAPE synthase was progressively inactivated by increasing concentrations of 5,5 -dithiobis(2-nitrobenzoic acid) (DTNB), diisopropyl fluorophosphate (DFP), phenylmethylsulfonylfluoride (PMSF), diethylpyrocarbonate (DEPC) (TABLE 2). These results suggest that NAPE synthase may form a thioester- or ester-intermediate through a cysteine or serine residue, respectively, and a histidine residue may participate in catalysis as well. 

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