Isotopic Exchange in Ping Pong Mechanisms

Equations for the initial rate of isotope exchange in Ping Pong mechanisms may be derived by one of the methods described in Chapter 4 the usual procedure will be to apply the King-Altman method or the net rate constant method (Cleland, 1975) (Table 4). 

Bi Bi Uni Uni Ping Pong Ter Ter mechanism (Rate equation in the absence of C and R) 

The last equation in Table 4 for the Bi Bi Uni Uni Ping Pong mechanism (in the absence of C and R) is relatively long and complex. The right-hand portion of the denominator in this equation represents the reciprocal concentration of free enzyme in chemical equilibrium multiplied by [EJ. If the products C and R are present, the distribution equation for [E]/[Eo] would be more complex (Eq. (12.73)) consequently, the resulting full rate equation for the A - Q isotope exchange becomes rather cumbersome. 

Isotope exchange is a powerful method for probing Ping Pong systems, because isolated portions or the partial reactions of the overall reaction sequence can be studied. For example, in a Ping Pong Bi Bi system, the A - P and P A exchange can be measured in the absence of B and Q  

Almost immediately after mixing E, A, and P, the system wiU come to equilibrium at essentially the established [P]/[A] ratio. If no exchange takes place between the suspected A and P pair unless aU reactants are present, then the system is sequential. 

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