Product inhibition Ping Pong

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. 

The kinetics of the yeast lipoamide dehydrogenase in the direction of NAD+ reduction indicate a bi-bi ping-pong mechanism is operative in this species also (117). If the enzyme from yeast indeed proves to have a tighter EHa-NADH complex than does the mammalian enzyme, product inhibitions studies should show impressive dependence on the fixed substrate (9S). 

Hexokinase does not yield parallel reciprocal plots, so the Ping Pong mechanism can be discarded. However, initial velocity studies alone will noi discriminate between the rapid equilibrium random and steady-state ordered mechanisms. Both yield ihe same velocity equation and families of intersecting reciprocal plots. Other diagnostic procedures must be used (e.g., product inhibition, dead-end inhibition, equilibrium substrate binding, and isotope exchange studies). These procedures are described in detail in the author s Enzyme Kinetics behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems, Wiley-Interscience (1975),... 

The interactions of CM and OP anticholinesterase compounds with AChE and BuChE have also been viewed as a Ping Pong Bi Bi kinetic mechanism that simplifie.s to an Ordered Uni Bi kinetic mechanism. since water is always present in excess. The primary difference between hydroly.sis of ACh and inhibition by OP and CM compounds is the rate at which the acylatcd intermediates arc reactivated by water to form the second product and free, uninhibited enzyme (reaction 3 in Fig. 2 and in Fig. 5). In the ca.se of ACh, the acetylated enzyme exists for only... 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

Figure 9. Product inhibition by P in the Ping Pong Bi Bi system. Graphical presentation of Eq. (9.64) with B as a constant and A as a variable substrate.

Some hyperbolic bisubstrate mechanisms can be easily distinguished by their primary double reciprocal plots in the absence of products, such as ordered from the Ping Pong mechanism. However, in many cases, the bisubstrate mechanisms cannot be distinguished in this way. Fortunately, in most cases, they can be clearly separated on the basis of their product inhibition patterns (Plowman, 1972) (Table 3). 

Initial velocity studies can place all the mechanisms listed in Table 3 into only three groups (Ping Pong, sequential, and equilibrium ordered), while aU of these can be told apart by product inhibition analysis. This clearly illustrates the immense power of the product inhibition analysis. 

In the absence of products, aU initial velocity patterns are parallel, in the same way as in the Ping Pong Bi Bi mechanism. However, the product inhibition patterns are different, and may serve to distinguish between the different systems (Table 6). 

Table 6. Product inhibition in hybrid Theorell-Chance Ping Pong systems...

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