Double reciprocal plots for reaction

Fig. 7.4. Double reciprocal plot for reactions run using high substrate concentrations.

Fig. 7.6 shows the double reciprocal plots for reactions run in the presence of several concentrations of I. The series of lines intersecting the y-axis at the same point is the diagnostic pattern for the competitive inhibition of a reaction. As in the uninhibited reaction the y-axis intercept is lA max- This is the same for all values of [I] but the x-axis intercepts are the different values of-1/K vi(app) each concentration of I. The slopes of the lines are proportional to K]yi(app) which, as shown in Eqn. 7.27, also contains the term, K, the dissociation constant for the M-I complex. These slopes follow Eqn. 7.28,... 

Fig. 7.6. Double reciprocal plots for reactions run at different fixed concentrations of a competitive inhibitor, 1.

Double-reciprocal plots for an ordered pathway. Measurements made at different fixed values of [S2] give a set of lines that intersect to the left of the ordinate. The two values of Km, Vm.ix and ATsl can be obtained by replotting the slopes and intercepts of these lines as functions of 1/[S2]. A random pathway gives similar results, but can be distinguished by making such measurements for the reverse reaction (Pi + P2 — Si + S2) in addition to the forward reaction. 

In contrast to what is observed with a random bisubstrate reaction, with an ordered bisubstrate process the rate data obtained on varying the concentration of A at constant concentrations of B do not give reciprocal plots which are symmetrical to Fig. 7.12. Comparing Eqn. 7.54 with Eqn. 7.58, the double reciprocal equation for reactions in which [A] is varied at constant [B], shows the differences between the two systems. 

Fig. 7.14. Double reciprocal plots for ping-pong reactions run at several fixed concentrations of B.

Figure 5.4 Patterns of double reciprocal plots for two substrate reactions, (a) Ping-pong. The double reciprocal plots for one substrate in the presence of fixed concentrations of the other are parallel, no matter which substrate reacts first, (b) Rapid equilibrium random, (c) Rapid equilibrium ordered, first binding substrate only.

Fig. 11. Schematic double reciprocal plot for a 2-substrate reaction obeying Eqn. 16. The primary plot here is analogous to the Lineweaver-Burk plot for a 1-substrate reaction, but the and obtained from such a plot as the solid line here are apparent true only for the fixed value of [B] at...

Aromatic nitriles are strong oxidants in their excited states (see Table I). Since they fluoresce strongly, the involvement of the singlet states can be easily proved by application of fluorescence quenching techniques. In all of the tested cases, it has been found that the Stern Volmer constant obtained from fluorescence analysis and that obtained from the double reciprocal plots of reaction quantum yield vs. quencher concentration are nearly equal, thus proving that the singlet stale is actually involved In the photochemical reaction. Actually it has been observed that a AG < 0 and polar solvents are necessary (although not sufficient, see Section 3) conditions for the photochemical proc-... 

The nomenclature of Cleland is very versatile and can be applied to even more complex inhibition patterns that occur in double reciprocal plots. In addition, the nomenclature of Cleland is also applicable to double reciprocal plots for bisubstrate and tiisubstrate reactions, in the absence and in the presence of the products of reaction, which makes this nomenclamre even more versatile. 

Figure 2.12 shows the sjv and double-reciprocal plots for an enzyme incubated with various concentrations of a competitive inhibitor. If the concentration of substrate is increased, it will compete more effectively with the inhibitor for the active site of the enzyme. This means that at high concentrations of substrate the enzyme will achieve the same maximum rate of reaction (V ) in the presence or absence of inhibitor. It is simply that in the presence of inhibitor the enzyme requires a higher concentration of substrate to achieve saturation — in other words, the of the enzyme is higher in the presence of a competitive inhibitor. 

Show that the reaction follows first-order kinetics when [A]0 s> [S]o, and show that lAi > varies linearly with l/[A]. The same pattern is seen when maleic anhydride (B) is used instead of A, except that the line in the double reciprocal plot is parallel to the abscissa. It intersects the ordinate at the same point as the y-intercept for A. Why are the slopes for A and B different, and their intercepts the same ... 

Rate law and reaction scheme. Interpret quantitatively the data21 presented in the accompanying two graphs in terms of either or both of the sequences that might be considered for experiments in which [Ph2C2] and [CO] [Co2(CO)8]o- The reciprocal of k varies linearly with the reciprocal of the diphenyl acetylene concentration at constant [CO]. The slopes of these double reciprocal plots are directly proportional to [CO]. 

For either of the ternary complex mechanisms described above, titration of one substrate at several fixed concentrations of the second substrate yields a pattern of intersecting lines when presented as a double reciprocal plot. Hence, without knowing the mechanism from prior studies, one can not distinguish between the two ternary complex mechanisms presented here on the basis of substrate titrations alone. In contrast, the data for a double-displacement reaction yields a series of parallel lines in the double reciprocal plot (Figure 2.15). Hence it is often easy to distinguish a double-displacement mechanism from a ternary complex mechanism in this way. Also it is often possible to run the first half of the reaction in the absence of the second substrate. Formation of the first product is then evidence in favor of a doubledisplacement mechanism (however, some caution must be exercised here, because other mechanistic explanations for such data can be invoked see Segel, 1975, for more information). For some double-displacement mechanisms the intermediate E-X complex is sufficiently stable to be isolated and identified by chemical and/or mass spectroscopic methods. In these favorable cases the identification of such a covalent E-X intermediate is verification of the reaction mechanism. 

At very low substrate concentration ([S] approaches zero), the enzyme is mostly present as E. Since an uncompetitive inhibitor does not combine with E, the inhibitor has no effect on the velocity and no effect on Vmsa/Km (the slope of the double-reciprocal plot). In this case, termed uncompetitive, the slopes of the double-reciprocal plots are independent of inhibitor concentration and only the intercepts are affected. A series of parallel lines results when different inhibitor concentrations are used. This type of inhibition is often observed for enzymes that catalyze the reaction between two substrates. Often an inhibitor that is competitive against one of the substrates is found to give uncompetitive inhibition when the other substrate is varied. The inhibitor does combine at the active site but does not prevent the binding of one of the substrates (and vice versa). 

A procedure used to assist in identifying sequential mechanisms when the double-reciprocal plots exhibit parallel lines ". In some cases, bireactant mechanism can have various collections of rate constants that result in so-called parallel line kinetics, even though the mechanism is not ping pong. However, if the concentrations of A and B are kept in constant ratio with respect to each other, a sequential mechanism in a 1/v v. 1/[A] plot would be nonlinear (since in the denominator the last term of the double-reciprocal form of the rate expression contains [A] for example, for the steady-state ordered Bi Bi reaction scheme in which [B] = a[A], the double-reciprocal rate expression becomes 1/v =... 

Initial rate patterns for bovine brain tubulin tyrosine ligase (Reaction detyrosinated tubulin (Tb) + i-tyrosine + ATP = tyrosinated tubulin + ADP + orthophosphate). The results of each set of experiments are shown as a single frame containing the same data points plotted as a function of one or the other varied substrate. The nonvar-ied substrate concentration is shown in the lower right-hand corner of every double-reciprocal plot. (From ref. 2.)... 

Initial rate patterns for Escherichia coli NAD+-dependent coenzyme A-linked aldehyde dehydrogenase (Reaction NAD+ + CoA-SFI + acetaldehyde = NADFI + acetyl-S-CoA + FI+). The results of each of three experiments are shown as a single double-reciprocal plot, and the nonvaried substrate concentrations for each curve are indicated above the data points. 

A double-reciprocal plot of 1/v vx. 1/[A] at varying levels of [B] will yield a series of parallel lines for this reaction scheme (having no abortives or isomerization steps), the slope equal to KJV a, the vertical intercepts equal to (l/l max)(l + b/[B]), and the horizontal intercepts equal to 1/[A] = -(1/Xa)(l + Xb/[B]). Thus, a replot of the vertical intercepts vs. 1/[B] will produce a straight line having a slope of Xt/Umax, a vertical intercept of 1/Umax, and a horizontal intercept of 1/[B] = 1/Xb. Similarly,... 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

In these double-reciprocal plots (see Box 6-1), the concentration of substrate 1 is varied while the concentration of substrate 2 is held constant. This is repeated for several values of [S2], generating several separate lines, (a) Intersecting lines indicate that a ternary complex is formed in the reaction (b) parallel lines indicate a Ping-Pong (double-displacement) pathway. 

Bimolecular reactions of two molecules, A and B, to give two products, P and Q, are catalyzed by many enzymes. For some enzymes the substrates A and B bind into the active site in an ordered sequence while for others, bindingmay be iii a random order. The scheme shown here is described as random Bi Bi in a classification introduced by Cleland. Eighteen rate constants, some second order and some first order, describe the reversible system. Determination of these kinetic parameters is often accomplished using a series of double reciprocal plots (Lineweaver-Burk plots), such as those at the right. 

A mathematical model has also been proposed for evaluating cellulase preparations. Sattler et al.209 describe a relationship between hydrolysis extent, reaction time, and enzyme concentration. This procedure permits the effectiveness of different enzymes and of different pretreatment methods to be ranked. This method examines cellulose hydrolysis data collected from hyperbolic functions of substrate concentration versus cellulase enzyme concentration at various timed incubations. The model is based on a double reciprocal plot of the relationship... 

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