Linearization Lineweaver—Burk

The same ccmdusians can be reached by means of the linearized Lineweaver-Burk farm of the rate law. From 10.4-8, for the initial rate,... 

These data produce a reasonably linear Lineweaver-Burke plot of slope 2.2 10 -3 min mole liter 1 and intercept 0.62 min. 

Kinetic data obtained from linear Lineweaver-Burk plots. 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

A hypothetical enzyme has activity, with respect to the hydrolysis of a neutral substrate, that is unaffected by pH over a very broad range, pH6 to pH8. However, it shows a much narrower pH-activity range when an alternative substrate, which contains an imidazole group, is used. A total of 50 assays were carried out by using 10 different substrate concentrations with a fixed amount of enzyme, at five different pH values. For each pH, the enzyme gave linear Lineweaver-Burk plots, and the estimates of K, and Vmax were as follows ... 

The rate of hydrolysis of 3H-phenyl-cocaine in the presence and absence of each monoclonal antibody as a function of substrate concentration was determined. Production of radiolabeled benzoic acid at time points corresponding to < 5% reaction extent provided initial rates. A saturation kinetics and a linear Lineweaver-Burk plot for each artificial enzyme were plotted. The first-order rate constants (kcat) and Michaelis constants (Km) of selected antibodies are provided in Table 2. 

Linear Lineweaver-Burk plots178 correspond to enzyme reactions described by the kinetic equation... 

Casting the equation in this form shows us clearly that the expression for e/v is linear in both 1 /[B] and 1 /[A]. It follows that with [B] fixed the enzyme should give a linear Lineweaver-Burk plot for varied [A] and vice versa. If we group the terms according to which variables they contain, Eqn. 15 may be rewritten in a simpler form [47] ... 

Apart from the fact that the rate is expressed here as a specific rate (i.e. divided by enzyme concentration), Eqn. 17 is of the same form as Eqn. 5, the equation for the linear Lineweaver-Burk plot for a 1-substrate reaction. Thus if we plot e/v against 1 /[A] at fixed [B], a straight line should result (Fig. 11). Note however, that the and values it gives will be only apparent and K , because the two composite constants in Eqn. 17 both in fact depend on [B]. Only by saturating with B can one get a plot giving a true e/0Q, and a true for A, a/ o-... 

The inhibition constant of adenine is determined using the Dixon diagram and is Kj = 0.63 X 10 M. The Kj, gpp for thymidine rises according to the formula gpp = Kj (1 +1/ Kj). The Kj value calculated from the formula agrees well with the value determined from the graph. The value for adenine is 0.066 mM (determination from the non-linear Lineweaver-Burk diagram. 

Clearly, if the latter reaction occurred to a significant extent complications would arise in the interpretation of kinetic results. Indeed, Lineweaver-Burk plots were found to be non-linear where DPD was used as substrate (151—154), and initially this was interpreted as evidence for the presence of two active sites for reducing substrate. Walaas et al. (151) provided good evidence that DPD+ could act as an effective electron donor to ceruloplasmin, but they did not recognize that this could lead to non-linear Lineweaver-Burk plots and maintained that there were two different sites. 

Osaki (169) has studied the catal5dic oxidation of ferrous ion by ceruloplasmin, and reported non-linear Lineweaver-Burk plots explicable in terms of two K,a values 0.6, mM and 50 juM. This behavior could arise from the fact that ceruloplasmin may bind Fe(III) as it is known to bind several other metal ions quite strongly (770), and does not provide evidence for more than one type of active site. Ferrous ion is an excellent substrate of ceruloplasmin as evidenced by its very low K i. However, its F ax does not differ greatly from the values of all the substrates tested by Young and Curzon (167). From the data of Osaki (169) Fmax at pH 5.5 is 30e/Cu-min at 30 °C ( cat=3.5sec i). Using the activation energy of 10.9 Kcal/mole reported by Osaki and Walaas (171) for the initial velocity of Fe(II) oxidation the above Fmax can be corrected to 22 e/Cu-min at 25 °C. Thus, it appear that for all substrates of ceruloplasmin Fmax is remarkably independent of the nature of the substrate. 

The necessity of using weighted fits can be seen visually from Fig. 1, which shows envelopes of probable error for data obeying the linear Lineweaver-Burk equation, for the cases where the initial rates have either equal standard errors or the standard errors proportional to initial rates of reaction. When the standard error is proportional to Uoi the variance is proportional to u and the estimation of kinetic parameters by linear regression becomes more reliable (Fig. 1). 

Equation 1-111 is known as the Lineweaver-Burk or reciprocal plot. If the data fit this model, a plot of l/V versus 1/Cg will he linear with a slope K /V x intercept l/V x-... 

Lineweaver-Burk plot Method of analyzing kinetic data (growth rates of enzyme catalyzed reactions) in linear form using a double reciprocal plot of rate versus substrate concentration. 

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. ... 

This is referred to as a double reciprocal or lineweaver Burk plot. From this linear plot, Kd = slope/intercept and the 1 /intercept = Bmax. Finally, a linear plot can be achieved with... 

In each of these cases, the double-reciprocal plots according to the Lineweaver-Burk method are linear. The appearance of these plots, and the parameters obtained from them, are developed in Problem 4-15. 

Linear free energy relations (see LFER) Lineweaver-Burk treatment, 91 Long-chain approximation, 183... 

Lineweaver-Burk plots [11] over the range 0.1 to 1 mM Paraoxon in 100 mM CHES buffer, pH 9.0. Linear regression analysis for Lineweaver-Bulk plot was performed using SigmaPlot software (Systat Software, USA). 

Fig. 39.17. Schematic illustration of Michaelis-Menten kinetics in the absence of an inhibitor (solid line) and in the presence of a competitive inhibitor (dashed line), (a) Plot of initial rate (or velocity) V against amount (or concentration) of substrate X. Note that the two curves tend to the same horizontal asymptote for large values of X. (b) Lineweaver-Burk linearized plot of 1/V against l/X. Note that the two lines intersect at a common intercept on the vertical axis.

Usually, one plots the initial rate V against the initial amount X, which produces a hyperbolic curve, such as shown in Fig. 39.17a. The rate and amount at time 0 are larger than those at any later time. Hence, the effect of experimental error and of possible deviation from the proposed model are minimal when the initial values are used. The Michaelis-Menten equation can be linearized by taking reciprocals on both sides of eq. (39.114) (Section 8.2.13), which leads to the so-called Lineweaver-Burk form ... 

As we have discussed in Chapter 8, this is a typical transformably linear system. Using the well-known Lineweaver-Burk transformation. Equation 17.2 becomes... 

A Scatchard plot of the data is shown in Figure 5.10C. For convenience, the fitted line is the regression of B/F on B (though, as noted earlier, this is statistically unsound) and provides an estimate for Bmax ( -intercept) of 0.654 fmol/mg dry wt. and an estimate for KL (-1/slope) of 132 pM. A Lineweaver-Burk (double-reciprocal) plot is provided for comparison in Figure 5.10D. Linear regression gives another estimate for Bmax (I v-intercept see Eq. (5.29)) of 0.610 fmol/mg dry wt. The estimate of KL from this plot (slope x Bmax) is 114 pM. 

The enzymatic activities of intercalated GOx-AM P layered nanocomposites at various pH values and temperatures were compared with the native enzyme in aqueous solution. In both cases, characteristic linear plots consistent with Michalis-Menton kinetics were obtained. The Lineweaver-Burk plots indicated that the reaction rates (Vmax) for free and intercalated GOx (3.3 and 4.0 pM min 1 respectively), were comparable, suggesting that the turnover rate at substrate saturation was only marginally influenced by entrapment between the re-assembled organoclay sheets. However, the dissociation constant (Km) associated with the activity of the enzyme was higher for intercalated GOx (6.63 mM) compared to native GOx (2.94 mM), suggesting... 

The evaluation of the KM and vmax values for enzymatic reactions is usually carried out using a linear plot of Eq. 14. The Lineweaver-Burke equation is widely used to this aim ... 

This is a linear expression for 1 lr 0 as a function of l/cSo, and was first proposed by Lineweaver and Burk (1934). A plot of 1 lrPo against l/cSo, known as a Lineweaver-Burk plot, produces a straight line with intercept VVmax and slope KmIVmax. 

Repeat Example 10-1 using a linearized form of equation 10.3-1 that is alternative to the linearized form 10.3-2 (the Lineweaver-Burk form). Comment on any advantage(s) of one form over the other. (There is more than one possible alternative form.)... 

Determine the kinetics parameters Km and Vmax, assuming that the standard Michaelis-Menten model applies to this system, (a) by nonlinear regression, and (b) by linear regression of the Lineweaver-Burk form. 

Compare the Lineweaver-Burk linear forms resulting from the four cases in problem 10-8, together with those given by equations 10.3-2 and 10.4-11. Note which cases have the same... 

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. 

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