Kinetic Ping-pong

The above poem [89] reflects the notion that transporters operating according to the Singer model should exhibit ping-pong kinetics. Ping-pong kinetics are observed in... 

If the enzyme-catalyzed reaction is to be faster than the uncatalyzed case, the acceptor group on the enzyme must be a better attacking group than Y and a better leaving group than X. Note that most enzymes that carry out covalent catalysis have ping-pong kinetic mechanisms. 

FIGURE 19.34 The galactose-l-phosphate uridylyltransferase reaction involves a ping-pong kinetic mechanism. 

Acetyl-CoA Carboxylase Is Biotin-Dependent and Displays Ping-Pong Kinetics... 

If the kinetic theory is applicable to gases, we should expect pressure to be affected by other factors than the number of moles per unit volume. For example, the mass of the molecules and their velocities should be important, as well. After all, a baseball exerts more push on a catcher s mitt than would a ping-pong ball thrown with the same velocity. Also, a baseball exerts more push on the mitt if a fast ball is thrown rather than a slow ball. To see how the mass of the molecules and their velocities are dealt with in the kinetic theory, we must consider temperature. 

In nature, aminotransferases participate in a number of metabolic pathways [4[. They catalyze the transfer of an amino group originating from an amino acid donor to a 2-ketoacid acceptor by a simple mechanism. First, an amino group from the donor is transferred to the cofactor pyridoxal phosphate with formation of a 2-keto add and an enzyme-bound pyridoxamine phosphate intermediate. Second, this intermediate transfers the amino group to the 2-keto add acceptor. The readion is reversible, shows ping-pong kinetics, and has been used industrially in the production ofamino acids [69]. It can be driven in one direction by the appropriate choice of conditions (e.g. substrate concentration). Some of the aminotransferases accept simple amines instead of amino acids as amine donors, and highly enantioselective cases have been reported [70]. 

The emphasis in kinetic studies of E-IIs has been on the analysis of the rates of phosphorylation of the sugar by the phosphoryl group donor. In the early studies the question was addressed whether phosphorylated E-II would be a catalytic intermediate in the reaction or whether the phosphoryl group would be transferred directly from the donor to the sugar on a ternary complex between the enzyme and its substrates [66,75,95-100]. This matter has been satisfactorily resolved by a number of other techniques in favor of the first option and possible reasons why some systems did not behave according to a ping-pong type of mechanism have been discussed [1]. 

The two substrate kinetics of the overall reaction catalyzed by the complex in permeabilized membranes showed classical ping-pong kinetics in accordance with a phosphorylated enzyme intermediate. The affinity constants for fructose and P-enolpyruvate were 8 and 25 /iM, respectively. 

Many studies have demonstrated that enzymes in organic media keep their conventional Michaelis-Menten or ping-pong behavior [10,132,133,137]. Nevertheless, enzyme activity usually decreases and kinetic parameters are dramatically changed when compared to biocatalysis in aqueous media [136]. 

Several mechanisms have been proposed for lipase-catalyzed reactions. Kinetic studies of hydrolysis [14,15] and esterification [50] catalyzed by Pseudomonas cepecia lipase, demonstrate that the enzyme has a ping-pong mechanism. 

The Ping-Pong Mechanism. Kinetic Control by Substrate and/or Cosubstrate... 

FIGURE5.3. Ping-pong mechanism. Variation of the peak or plateau current with the kinetic parameter from no catalysis and the pure kinetic conditions leading to plateau-shaped responses for several values of the competition parameter s from top to hottom 0, 0.31, 0.725, 1.25, 2.5, 5, 10, 20, oo. Adapted from Figure 2 in reference 10, with permission from the American Chemical Society. 

Figure 4.13 Effect of reaction mechanism on the concentrations of Sj and B in the basic system when operated as a fed-batch reactor. The kinetic mechanism and the values of the parameters Ka and Ki, are indicated on top of each section —indicates that the parameter is not applicable for the ping-pong mechanism. The values used for all other parameters are given in Table 4.1, set I.

From Figure 4.54 it can he seen that the family of reciprocal plots obtained at different fixed concentrations of NADP are essentially parallel to one another. This is also indicated in Figure 4.55, where the value of the slopes of the tines seem to be approximately constant. These results imply that the velocity equation for the ping-pong mechanism [146] can be used to describe the rate of the reaction catalyzed by G6PDH. Although initial velocity studies alone cannot define the exact kinetic mechanism [146,147], we are more interested in the appropriate rate equation that describes the reaction progress. 

The formation of a ternary complex is entropically disfavoured relative to binary ones. However, kinetic and spectroscopic investigations [39] gave no indication of, e.g., a ping-pong mechanism, and/or the involvement of covalent intermediates... 

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 =... 

With this protocol, ping pong reactions will yield at least one plot containing parallel lines. However, it is difficult with this procedure to obtain values for a number of the kinetic parameters (eg., Michaelis constants) for the reaction. An example of a system studied with this procedure is provided by E. coli CoA-linked aldehyde dehydrogenase. See Frieden Protocol... 

A mathematical equation indicating how the equilibrium constant of an enzyme-catalyzed reaction (or half-reaction in the case of so-called ping pong reaction mechanisms) is related to the various kinetic parameters for the reaction mechanism. In the Briggs-Haldane steady-state treatment of a Uni Uni reaction mechanism, the Haldane relation can be written as follows ... 

RANDOM SCISSION KINETICS RANDOM TER TER MECHANISM RANDOM UNI Bl MECHANISM RANDOM UNI UNI Bl Bl PING PONG MECHANISM RANDOM VARIABLE STATISTICS (A Primer)... 

Toluene, hexane, diisopropylether, trichloroethane Evaluation of the ping-pong kinetics [135]... 

Figure 2.11 Transesterification of a racemic mixture of a secondary alcohol (1 -phenoxy-2-propanol, 1 in Table 2.1) with a butanoic acyl donor follows a ping-pong bi-bi mechanism in which Substrate 1 (acyl donor) enters the enzyme, forms an acyl enzyme expelling Product 1 (the leaving alcohol from the acyl donor). Then another Substrate 2 (the enantiomers of the alcohol to be resolved) reacts with the acyl enzyme to liberate Product 2 (the enantiomers of the produced esters), leaving the enzyme in its original form. In a kinetic resolution one of the enantiomeric alcohols reacts faster than the other to form an excess of one enantiomer of the esters (ideally enantiopure, for 1 the (R)-ester was formed with very high ee). The success of the resolution is expressed by the enantiomeric ratio E, which depends on the difference in free energy of activation of the two diastereomeric transition states. These are in turn related to the two tetrahedral intermediates.

Computer programs for ping-pong bi-bi kinetics which use ee-values measured at several degrees of conversion are available (Anthonsen, Hoff and Anthonsen, 1996 Rakels, Straathof and Heijnen, 1993). If both enantiomers are available in pure forms, it is also possible to determine E and K, from initial rate measurements. 

Many enzymes, which transform two different substrates to one or two product(s), could be characterized using equation (8.1), if the concentration of one substrate is high enough to saturate the enzyme. If the two substrate molecules bind to the enzyme independently from each other, the calculated KM values will reflect the affinity of the substrate to the complex of the other substrate molecule and the enzyme. Further, the Vj ax " ill characterize the rate of the reaction at the excess concentrations of both substrates (the enzyme is saturated by both substrates). However, this could be just a coarse approximation, and there are kinetic analytical methods for a more exact characterization of such two-substrate enzymic reactions, which could run on different ways e.g. random Bi-Bi, ping-pong Bi Bi mechanisms (Keleti, 1986 Fersht, 1985 Segel, 1975 Comish-Bowden, 1995). 

Studies of product inhibition357,358 and initial velocity359 of the dehydrogenase reaction are consistent with a hexa uni ping-pong mechanism,359 which requires that an irreversible step of the process should occur in the reaction sequence prior to addition of the second molecule of NAD to the enzyme. The irreversible step is, most probably, formation of the uronic acid (90a) from the aldehyde 93, and several mechanisms may be written to explain the kinetics ob-... 

Although Equation 4, Equation 5, Equation 6, and Equation 7 may be used to establish the E-value of a catalyst in many cases of interest, they certainly do not cover the full range of possible situations. This holds in particular for the commonly employed hydrolases that show bi bi ping pong kinetics. For enzymes that follow this kinetic scheme, the ratio of reaction rates in the case of a so-called A-P resolution, Ars + <=> PR-S + Q (see [31]) takes the following form (Equation 7) ... 

By what appears to be a convenient coincidence, it turns out that the barriers that contribute to ksp for a more realistic kinetic scheme, notably the bi bi ping pong scheme adopted by the majority of hydrolases that are currently employed in biocatalytic resolutions reactions, are equally simple to identify. Figure 2.4 shows the barriers that contribute. By straightforward manipulation of the kinetic equations one obtains Equation 16 ... 

Figure 2.4 Schematic profile for the acylation stage involving the R-enantiomer of an enantioselective reaction catalyzed by an enzyme that follows bi bi ping pong kinetics. The reaction is an example of the so-called A-...

One less kinetic parameter can be obtained from an analysis of the data for a ping-pong mechanism than can be obtained for ordered reactions. Nevertheless, in Eq. 9-47, twelve rate constants are indicated. At least this many steps must be considered to describe the behavior of the enzyme. Not all of these constants can be determined from a study of steady-state kinetics, but they may be obtained in other ways. 

Product inhibition (Section A,12) can also provide information about mechanisms. For example, if 1 / v is plotted against 1 / [A] in the presence and absence of the product Q, the product will be found to compete with A and to give a typical family of lines for competitive inhibition. On the other hand, a plot of 1 / v vs 1 / [B] in the presence and absence of Q will indicate noncompetitive inhibition if the binding of substrates is ordered (Eq. 9-43). In other words, only the A-Q pair of substrates are competitive. Product inhibition is also observed with enzymes having ping-pong kinetics (Eq. 9-47) as a result of formation of nonproductive complexes. 

Kinetics. In a double-displacement mechanism the enzyme shuttles between free enzyme and the intermediate carrying the substrate fragment (here, the glycosyl enzyme). With sucrose phosphorylase the maximum velocity varies with the concentrations of sucrose and HP042 in the characteristic fashion expected for this "ping-pong" mechanism (Eq. 9-47)43... 

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