Enzyme kinetic plots

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

Eisenthal and Cornish-Bowden (21) and Cornish-Bowden (20) have described a rather different type of enzyme kinetics plot that should be useful in analyzing affinity-labeling kinetics. The equation that forms the basis of the direct linear plot (21) is obtained from Equation 11 by rearrangement of terms to give Equation 12... 

Lineweaver-Burk plot a graphical means for evaluating enzyme kinetics, (p. 638)... 

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

The inhibition analyses were examined differently for free lipase in a batch and immobilised lipase in membrane reactor system. Figure 5.14 shows the kinetics plot for substrate inhibition of the free lipase in the batch system, where [5] is the concentration of (S)-ibuprofen ester in isooctane, and v0 is the initial reaction rate for (S)-ester conversion. The data for immobilised lipase are shown in Figure 5.15 that is, the kinetics plot for substrate inhibition for immobilised lipase in the EMR system. The Hanes-Woolf plots in both systems show similar trends for substrate inhibition. The graphical presentation of rate curves for immobilised lipase shows higher values compared with free enzymes. The value for the... 

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

An analysis of the influence of errors shows clearly that the double-reciprocal plot according to Lineweaver-Burk [32] is the least suitable. Although it is by far the most widely used plot in enzyme kinetics, it cannot be recommended, because it gives a grossly misleading impression of the experimental error for small values of v small errors in v lead to enormous errors in 1/y but for large values of v the same small errors in v lead to barely noticeable errors in 1/17 [23]. Due to the error distribution, that is much more uniform, the plot according to Hanes (Eq. (7)), is the most favored. 

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

Since the propensity to form adducts in chemistry is high and these adducts undergo a variety of reactions, the rate law (1.98) is quite common. This is particularly true in enzyme kinetics. In reality, these reaction schemes give biphasic first-order plots but because the first step is usually more rapid, for example between A and B in (1.101) we do not normally, nor do we need to, examine this step in the first instance. The value of A", in (1.107) obtained kinetically can sometimes be checked directly by examining the rapid preequilibrium before reaction to produce D occurs. In the reactions of Cu(I) proteins with excited Cr and Ru polypyridine complexes, it is considered that (a) and (b) schemes may be operating concurrently. 

Concentration is the most common means for describing the composition of a solution in biochemistry. Enzyme kinetic expressions are typically expressed in these concentration units. Unless otherwise noted, this is the method used throughout this text. Nevertheless, other methods for describing compositions are utilized. For example, mole fractions are often used in Job plots. Gases in solution are commonly measured in terms of partial pressures. Below is a brief description of a few of these other conventions or methods. 

A linear reciprocal transformation of a function of the form [f(a) = a/(l + a)], such that l/f(a) is plotted on the vertical axis and 1/a is plotted on the horizontal axis. In the case of one-substrate enzyme kinetics, the hyperbolic function is ... 

For example, Bachelard used [Mgtotai]/[ATPtotai ] = 1 in his rate studies, and he obtained a slightly sigmoidal plot of initial velocity versus substrate ATP concentration. This culminated in the erroneous proposal that brain hexokinase was allosterically activated by magnesium ions and by magnesium ion-adenosine triphosphate complex. Purich and Fromm demonstrated that failure to achieve adequate experimental control over the free magnesium ion concentration can wreak havoc on the examination of enzyme kinetic behavior. Indeed, these investigators were able to account fully for the effects obtained in the previous hexokinase study. ... 

DOUBLE-RECIPROCAL PLOT ENZYME KINETIC EQUATIONS (1. The... 

This plot is known as a Hill plot in protein-binding chemistry and enzyme kinetics (11). Transformation of Eq. (13) also provides the relation for the mobilities ... 

The main plots used in enzyme kinetics and receptor binding studies are the Scatchard plot, the Lineweaver-Burk plot, and the linearization for estimation of the Hill coefficient. This chapter gives a short survey of these transformations of enzyme kinetics or receptor binding data. 

Figure 8.4 The Lineweaver-Burk plot (A) and the Hanes plot (B) of typical enzyme kinetics in presence of a competitve (a) noncompetive (b), mixed type (c) and uncompetitive (d) inhibitor.

Relatively few detailed studies of enzyme kinetics in organic media have been carried out. Preferably, full kinetics should be studied, allowing the determination of Km and kcat values, but it is much more common to see just reports on the catalytic activity at fixed substrate concentrations as a function of water activity. That such studies can be misleading was shown in an investigation of lipase-catalyzed esterification [26]. When the reaction rate in the esterification reaction was plotted versus the water activity at three different substrate concentrations, maxima were obtained at three different water activities (Figure 1.4). Such maxima should not be used to claim that the optimal water activity of the enzyme was found. Detailed kinetic studies showed that both the kcat and the Km values (for the alcohol substrate) varied with the water activity. The Km value of the alcohol increased with increasing water... 

Determination of the apparent is simple for cDNA-expressed enzymes. Naturally, kinetic plots should indicate the presence of a single Km-Experimental variables will likely introduce a 2- to 3-fold variation in Km values between systems. Variations of more than 3-fold should be investigated further. 

Figure 17.16 Relationships of biodegradation rate, v, to substrate concentration, [/], when Michaelis-Menten enzyme kinetics is appropriate (a) when plotted as hyperbolic relationship (Eq. 17-79 in text), or (b) when plotted as inverse equation, Vv =...

Hyperbolic shape of the enzyme kinetics curve Most enzymes show Michaelis-Menten kinetics (see p. 58), in which the plot of initial reaction velocity, v0, against substrate concentration [S], is hyperbolic (similar in shape to that of the oxygen-dissociation curve of myoglobin, see p. 29). In contrast, allosteric enzymes frequently show a sigmoidal curve (see p. 62) that is similar in shape to the oxygen-dissociation curve of hemoglobin (see p. 29). 

Figure 9-6 Reciprocal plots used to analyze kinetics of two-substrate enzymes. (A) Plot of 1 / against 1 / [A] for a series of different concentrations of the second substrate B. (B) A secondary plot in which the intercepts from graph A are plotted against 1/ [B], (C) Secondary plot in which the slopes from graph A have been plotted against 1 / [B]. The figures have been drawn for the case that Kmp = 10 3 M, Kun, = 2 Km, and K B = KeqAKmB (Eq. 9-46) = KmJ 200 and [A] and [B] are in emits of moles per liter. Eadie-Hofstee plots of v / [A] vs vf at constant [B] can also be used as the primary plots. The student can easily convert Eq. 9-44 to the proper form analogous to Eq. 9-21.

A Lineweaver-Burk plot of enzyme kinetics in the presence and absence of a noncompetitive inhibitor is shown in Figure E5.5. Umax in the presence of a noncompetitive inhibitor is decreased, but KM is unaffected. The effect of a competitive inhibitor on the direct linear plot is shown in Figure E5.6. 

W. Wood et al., Biochemistry, A Problems Approach, 2nd ed. (1981), Benjamin/Cum-mings (San Francisco), pp. 144-172. Enzyme kinetics with an introduction to the direct linear plot. 

D Voet, J Voet, and C Pratt, Fundamentals of Biochemistry, (1999), John Wiley Sons (New York), pp 281-347 Enzymes and kinetics C Whiteley, Biochem. Educ. 25, 144-146 (1997) Enzyme kinetics W Wood et al, Biochemistiy, A Problems Approach, 2nd ed (1981), Benjamin/Cum-mmgs (San Francisco), pp 144-172 Enzyme kinetics with an introduction to the direct linear plot... 

Historically, enzyme kinetics were visualised using the Lineweaver-Burk equation, Equation 11.14, where l/rate is plotted against 1/[S] as seen in Fig. 11.11 A ... 

Included in the following table are some data points from a hypothetical enzyme kinetics study. Using a spreadsheet program with graphing abilities (such as Excel), generate a Line-weaver-Burk plot of the data points in the table. Determine the best-fit line for the data along with Vnax, ATm, and r2 (the square of the correlation coefficient of the line). Does this enzyme follow Michaelis-Menten kinetics Why or why not ... 

Hofstee, B. H. Non-Inverted versus Inverted Plots in Enzyme Kinetics. Nature. 1959, 184, 1296-1298. 

There are several ways of visualizing enzyme kinetic data, and calculating the values of Km and vmax. Each approach has advantages and disadvantages [20,21]. One way to determine the values of Km and vmax is to plot the reciprocal of the reaction velocity, 1/v, against the reciprocal substrate concentration 1/[S], since... 

Lineweaver, H. and Burk, D. (1934) Determination of enzyme dissociation constants./. Am. Chem. Soc., 56, 658. Eadie, G.S. (1942) The inhibition of cholinesterase by physostigmine and prostigmine. /. Biol. Chem., 146, 85. Hofstee, B.H. (1959) Non-inverted versus inverted plots in enzyme kinetics. Nature, 184, 1296. 

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