Enzymes Lineweaver-Burk equation

This form of the Michaelis-Menten equation is called the Lineweaver-Burk equation. For enzymes obeying the Michaelis-Menten relationship, a plot of 1/F0 versus 1/[S] (the double reciprocal of the V0 versus [S] plot we have been using to this point) yields a straight line (Fig. 1). This line has a slope of Km/Vmax, an intercept of 1/Fmax on the 1/F0 axis, and an intercept... 

Kinetic analysis of tyrosinase and calculation of constants will be described using graphical analysis by the Michaelis-Menten equation, Lineweaver-Burk equation, or the direct linear curve. Procedures for preparing these graphs are described below. Alternatively, students may use available computer software to graph data and calculate kinetic constants. Recommended enzyme kinetic computer software packages include Enzyme... 

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 ... 

In addition to being easier to fit than the hyperbolic Michaelis-Menten equation, Lineweaver-Burk graphs clearly show differences between types of enzyme inhibitors. This will be discussed in Section 4.5. However, Lineweaver-Burk equations have their own distinct issues. Nonlinear data, possibly indicating cooperative multiunit enzymes or allosteric effects, often seem nearly linear when graphed according to a Lineweaver-Burk equation. Said another way, the Lineweaver-Burk equation forces nonlinear data into a linear relationship. Variations of the Lineweaver-Burk equation that are not double reciprocal relationships include the Eadie-Hofstee equation7 (V vs. V7[S]) (Equation 4.14) and the Hanes-Woolf equation8 ([S]/V vs. [S]) (Equation 4.15). Both are... 

For each of the four types of enzyme inhibition given in Table 9.1, derive the Lineweaver-Burk equations and draw archetypal graphs. 

For the Michaelis-Menten equation there are algebraic transformations, in addition to the Lineweaver-Burk equation, that yield straight line plots from enzyme kinetic data. One such plot is due to Eadie and Hofstee their equation takes the following form ... 

This equation is formally similar to the Michaelis-Menten equation of enzyme kinetics, although the analogy is limited because most enzymic reactions are studied with substrate in large excess over enzyme. Equation (1) could be rearranged to give (2) which is formally similar to the Lineweaver-Burk equation, and which permits calculation of and K provided that... 

As explained previously, an enzyme at a given concentration eventually becomes saturated with respect to substrate as the substrate concentration is increased, and the reaction rate becomes maximum, The Lineweaver-Burk equation describes the relationship between the enzyme effectiveness as a catalyst and the maximum rate ... 

D23.4 Refer to eqns 23.26 and 23.27, which are the analogues of the Michaelis-Menten and Lineweaver-Burk equations (23.21 and 23,22), as well as to Figure 23.13, There are three major modes of inhibition that give rise to distinctly different kinetic behavior (Figure 23.13), In competitive inhibition the inhibitor binds only to the active site of the enzyme and thereby inhibits the attachment of the substrate. This condition corresponds to a > 1 and a = 1 (because ESI does not form). The slope of the Lineweaver-Burk plot increases by a factor of a relative to the slope for data on the uninhibited enzyme (a = a = I), The y-intercept does not change as a result of competitive inhibition, In uncompetitive inhibition, the inhibitor binds to a site of the enzyme that is removed from the active site, but only if the substrate is already present. The inhibition occurs because ESI reduces the concentration of ES, the active type of the complex, In this case a = 1 (because El does not form) and or > 1. The y-intercepl of the Lineweaver-Burk plot increases by a factor of a relative to they-intercept for data on the uninhibited enzyme, but the slope does not change. In non-competitive inhibition, the inhibitor binds to a site other than the active site, and its presence reduces the ability of the substrate to bind to the active site. Inhibition occurs at both the E and ES sites. This condition corresponds to a > I and a > I. Both the slope and y-intercept... 

The typical variation in the rate of reaction as a function of the concentration of the reactant is shown in Fig. 34.2. This figure should be compared with Fig. 32.12, which shows the same behavior for a homogeneous catalyst. Note that Eq. (34.5) has the same form as Eq. (32.95), the equation for homogeneous catalysis, which is the same as the Michaelis-Menten law, Eq. (32.100) , for enzymes. Also, Eq. (34.6) has the same form as the Lineweaver-Burk equation for enzymes. 

For each of the four types of inhibition of a Michaelis-Menten enzyme [competitive, Eq. (5.25) noncompetitive and mixed Eq. (5.29) and uncompetitive, Eq. (5.32)], derive the corresponding Lineweaver-Burk equations [Eqs. (5.26), and (5.30), respectively] and draw the characteristic plots that are the basis for the rapid visnal identification of which type of inhibition apphes when analyzing enzyme kinetic data. 

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. ... 

As discussed above, the degree of inhibition is indicated by the ratio of k3/k and defines an inhibitor constant (Kj) [Eq. (3.19)], whose value reports the dissociation of the enzyme-inhibitor complex (El) [Eq. (3.20)]. Deriving the equation for competitive inhibition under steady-state conditions leads to Eq. (3.21). Reciprocal plots of 1/v versus 1/5 (Lineweaver-Burk plots) as a function of various inhibitor concentrations readily reveal competitive inhibition and define their characteristic properties (Fig. 3.5). Notice that Vmax does not change. Irrespective of how much competitive inhibitor is present, its effect can be overcome by adding a sufficient amount of substrate, i.e., substrate can be added until Vmax is reached. Also notice that K i does change with inhibitor concentration therefore the Km that is measured in the presence of inhibitor is an apparent Km- The true KM can only be obtained in the absence of inhibitor. 

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. 

When data in the presence of an enzyme inhibitor are presented in the form of a Lineweaver-Burk plot, a series of straight lines should be obtained. The slopes of these hnes may or may not change, and the hnes may or may not intersect at a common point. The relationships between slopes, intersection points, and inhibitor mechanisms are outlined later. Further information regarding these mechanisms, including velocity equations describing data obtained in the presence of inhibitors with diverse mechanisms, can be found in (Segel, 1993). 

The mixed-type inhibitors combine the effects of the competitive and noncompetitive inhibitors binding at the active center decreases the affinity of the enzyme towards the substrate molecule and also decreases the rate of transformation of the bound substrate. In their presence, the straight line plots intersect in the fourth quarter of the Lineweaver-Burk plot, according to equation ... 

Uncompetitive inhibitors can bind to the enzyme-substrate complex only, but not to the free enzyme molecule. The Lineweaver-Burk plots in such cases give parallel straight lines for activity-substrate concentration profiles, measured at different concentrations of the inhibitor (Figure 8.4), according to equation ... 

There are well-established methods for obtaining the type of inhibition and the value of the inhibition constants from initial-rate kinetics, often from linearized plots such as lineweaver-Burk, Eadie-Hofstee, or Hanes. As these procedures are covered very well by a range of basic textbooks on biochemistry and kinetics (see the list of Suggested Further Reading ) we will not repeat these procedures here. Instead, we will discuss the situation in which an enzyme reaction is followed over more than just the initial range of conversion. Towards this end, the rate equation,... 

In Chapter 4 (Section 4.1.1), we derived the Lineweaver-Burk double-reciprocal relation between the steady state flux of an enzyme reaction and its substrate concentrations. (See Equation (4.5).) Furthermore, we showed in Section 4.4.1 that the same equation can be obtained from a stochastic point of view. Recalling this derivation, consider the basic mechanism... 

Kinetic experiments may be used for revealing the type of inhibition in enzymes. By inserting experimental data to the inverted Michaelis-Menten equation this gives straight-line plots (Lineweaver-Burk), which can be extrapolated to yield the characterizing constants of the enzyme. However, the Michaelis-Menten model cannot account properly for the kinetic properties of allosteric enzymes [34]. 

The Lineweaver-Burk expression is depicted graphically in Fig. 1. This graph correlates the rate as a function of [S], first in the absence of inhibitor (line a), then with added inhibitor concentrations (lines b-e). Note that as more inhibitor is added, the slope of the line increases, but the Fmax does not vary. As 1/[S] approaches zero (infinite [S]), the lines converge on the data in the absence of inhibitor (all of the inhibitor is displaced by substrate), namely, 1/Vmax- At low [S], inhibitor competes effectively with substrate for the enzyme. When a competitive inhibitor binds to the free enzyme, there are fewer enzyme molecules for the substrate to bind to, so the rate decreases. According to Equations 2 and 3, the reciprocal of the rate is proportional to so the slopes of the fines vary with... 

It can be seen from this equation that competitive inhibitors have no effect on the Vmax of the enzyme, but alter the apparent Km. In the presence of inhibitor, Km will be increased by a factor of (1 + /K ). Lineweaver-Burk plots constructed at various inhibitor concentrations provide a useful diagnostic for this type of inhibition. Figure 2.13 shows that identical y intercepts (l/Vmax) are obtained at different inhibitor concentrations, while x intercepts (reciprocal of apparent Km) decrease with increasing [I], and are equal to — / Km + [1]/ ). ... 

The answer is b. (Murray, pp 48-73. Scriver, pp 4571-4636. Sack, pp 3-17. Wilson, pp 287-317.) When an enzyme obeys classic Michaelis-Menten kinetics as seen in the figure presented in question 154, the Michaelis constant (Km) and the maximal rate (V ax) can be readily derived. By plotting a reciprocal of the Michaelis-Menten equation, a straight-line Lineweaver-Burk plot is produced. The y intercept is l/Vmax, while the x intercept is —l/K . Thus, a reciprocal of these absolute values yields Vjnax and Kn. 

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