Lineweaver and Burk

From scheme I, together with the experimentally observed first-order dependence on the total ester concentration, the rate relationship illustrated in Eq. (1) may be derived. In applying this equation, the cycloamylose concentration must be at least tenfold greater than the initial substrate concentration to ensure first-order conditions. Equation (1) may be rearranged in two ways to yield linear forms which permit graphical evaluation of fa, the maximal rate constant for release of phenol from the fully com-plexed ester and Kd, the cycloamylose-substrate dissociation constant (defined in Scheme I as A i/fa). These two methods are illustrated in Eqs. (2) and (3) and may be attributed to Lineweaver and Burk (1934) and to Eadie (1942), respectively. Although in theory both methods should give... 

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. 

Lineweaver and Burk (1934) described a method for the determination of Km which uses the reciprocal form of the Michaeiis equation converting it to a linear relationship (Procedure 8.1) ... 

Vescia and Chance Hi) demonstrated that fluoride and tartrate inhibition vide infra) of acid phosphatase showed completely different kinetics when the hydrolysis of phenyl phosphate was compared with transphosphorylation from this substrate to glucose. Figures 5 and 6 (41) show that fluoride inhibition is competitive when the data are plotted according to Lineweaver and Burk. However, the inhibition is noncompetitive with respect to transphosphorylation of the same substrate to glucose. The authors suggested that there are two distinct sites... 

Graphical transformation of the representation of enzyme kinetics is useful as the value of V max is impossible to obtain directly from practical measurements. A series of graphical transformations/linearisations may be used to overcome this problem. Lineweaver and Burk (see reference(,7)) simply inverted the Michaelis-Menten equation (equation 5.10). Thus ... 

Similarly, the plot of 1/r versus 1 /Cs will result in a straight line according to Eq. (2.33), and the slope will be equal to KM/rmax. The intercept will be 1 / rmax, as shown in Figure 2.6. This plot is known as Lineweaver-Burk plot (Lineweaver and Burk, 1934). 

Before adequate computer hardware and software were widely available, fitting experimental kinetic data to a curve to determine Km and Vmax was a significant challenge. Lineweaver and Burk rearranged the Michaelis-Menten equation to form a new linear relationship, the Lineweaver-Burk equation (Equation 4.13).6... 

The experiments were carried out with partially-purified mouse-liver enzyme and phenolphthalein /3-D-glucosiduronic acid, in acetate buffer, pH 5.2, and dissociation constants were calculated by the method of Lineweaver and Burk.173... 

See Section IV. Results calculated by method of Lineweaver and Burk.173... 

One common transformation of the Michaelis-Menten equation is the double-reciprocal plot of Lineweaver and Burk, which is obtained by taking the reciprocal of both sides of Equation (5.24) to yield... 

Although Km may be determined using data similar to that presented in Figure II-8, it is more accurate and convenient to use one of the linear forms of the Michaelis-Menten equation to determine Km- Lineweaver and Burk first pointed out that equation II-8 can be obtained by inversion of the Michaelis-Menten equation ... 

The Michaelis-Menten equation can be algebraically transformed into more useful way to plot the experimental data. Lineweaver and Burk have taken the reciprocal of both [S] and v of the Michaelis-Menten equation to give Double Reciprocal or Lineweaver-Burke Plot Need in form y = ax + b, so take reciprocals of both sides (Fig. 6.4) and have -... 

Because of the difficulty in determining Vm from a hyperbolic curve, the Michaelis-Menten equation was transformed by Lineweaver and Burk into an equation for a straight line... 

In former days, before electronic caelulations came into existance all calibrations and evaluations had to be carried out manually by graphical methods Linearized solutions had been used instead of nonlinear regression. Lineweaver and Burk 73) derived the linearized equation (19). It was introduced for calibration purposes to TLC by Kufner and Schlegel74). Kaiserf,3), Hulpke and Stegh 64) also used calibration techniques with reciprocal transformations of R and m without reference to the Michaelis-Menten transformation. 

Calculation of Vmax and Km may occur by nonlinear regression or by linearization, such as the Lineweaver and Burk method. Thereafter, reciprocal values of Vand [S] are plotted in a diagram and Eq. (9.2) is transformed to... 

Fig. 24. Graphic estimation of the Michaelis constant. Km, and the maximum rate, vmax, according to Lineweaver and Burk.

Interestingly, when Lineweaver and Burk submitted a paper on the plot, the referees were opposed to its publication in JAMS for a variety of reasons. Some of die reviewers considered the paper "just a mathematical exercise and not really chemistry at all". The method is primarily used nowadays for initial examination of kinetic data and then the data are fitted to an appropriate rate equation using computer programs. 

Methods based on linearization of Eq. 3.11 are the most frequently used for the determination of kinetic parameters. Several of such linear correlations have been proposed, being the reciprocal of the equation, known as Lineweaver-Burk plot (Lineweaver and Burk 1934), the most popular. According to it ... 

The paper by Brunauer, Emmet, and Teller [16], entitled Adsorption of Gases in Multimolecular Layers was published in 1938. In 2003 the American Chemical Society celebrated its 125th anniversary. At this occasion, a ranking list of the 125 most cited papers of the Journal of the American Chemical Society was published. The paper of BrunauerP Emmet and Teller is on rank 4 with 4,808 citations. By the way, the most cited paper from this journal among all is that by Lineweaver and Burk [17] with 10,638 citations. 

The Michaelis constant is obviously inversely proportional to the affinity of the enzyme for the substrate, and is numerically equal to the substrate concentration when the reaction has reached half its maximal velocity. The dimensions of K and are recorded as g mol per litre. However, they are not true equilibrium constants but ratios of velocity constant for the forward and reverse reactions. A suitable determination of is by the graphical method of Lineweaver and Burk (1934), where the initial rate of formation of ES is plotted against substrate concentration, both as reciprocals.This should give a straight line and, if it does, the value of is shown at the intersection of slope and abscissa. 

In further experiments, we measured the initial saturable cell uptake at 1 min as a function of hormone concentration in the mediiun. The data in Fig 6 are plotted according to Lineweaver and Burk. The Km values for T uptake in all four cell lines were similar, ranging from 0.8 to 3.1nM. Maximum velocities, however, were widely disparate, being lowest for the hxunan neuroblastoma cells (Vmax=7.9 fmols/min/10° cells) and highest for the human glioma cells (Vraax=84 fmols/min/10 cells). 

At the time Johnson was writing, the most commonly used transformation of equation (6-8) was that proposed by Lineweaver and Burk ... 

Several methods have been used to evaluate the constants Km and V— The one most often used is that of Lineweaver and Burk, who rearranged equation (1) to obtain the form... 

Inhibition. Graphic analysis of kinetic data according to the method of Lineweaver and Burk has a useful application in the study of inhibitors. Many substances limit the activity of enzymes by reacting with the protein or some other component in such a way as to destroy or decrease the catalytic ability. Other materials inhibit by forming the same sort of complex that a substrate does. In this latter case, the two materials K. B. Augustinsson, Acta Physiol. Scand. 16, Suppl. 52 (1948). 

Km, asmaybe seen from equations (1) and (6), is the dissociation constant of the enzyme-substrate compound (JES) and has a characteristic value for each enzyme. It is known as the Michaelis constant, and the reciprocal /Km = Km, is termed the association constant. Equation (12) has been used extensively for the calculation of enzymic dissociation constants, but the method has been much improved by Lineweaver and Burk (S), who employ the reciprocal of equation (11) for the calculation ... 

There are several ways of visualizing enzyme kinetic data. One approach is to plot the reciprocal rate of conversion of substrate A, I/ca, against the reciprocal substrate concentration, 1/ca, which is known as the Lineweaver-Burk plot (Lineweaver and Burk, 1934) ... 

It is not easy to obtain an accurate value for from a direct plot of V-, against [S] and Lineweaver and Burk (1934) pointed out that both and could be more accurately determined by means of a double reciprocal plot, i.e. by plotting l/V against 1/[S]. This gives a straight line relationship in which l/V ax is given by the intercept on the y-axis and -1/X by the intercept on the jc-axis, as shown in Figure 6.6. 

A more convenient and accurate method for estimating Km is that of Lineweaver and Burk. If the reciprocals of both sides of equation 14 are taken, the following equation is obtained ... 

Fig. 2.25. Evaluation of a two-substrate reaction, proceeding through a ternary enzyme-substrate complex (according to Lineweaver and Burk).

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