Steady-State Random product inhibition

Fromm and Rudolph have discussed the practical limitations on interpreting product inhibition experiments. The table below illustrates the distinctive kinetic patterns observed with bisubstrate enzymes in the absence or presence of abortive complex formation. It should also be noted that the random mechanisms in this table (and in similar tables in other texts) are usually for rapid equilibrium random mechanism schemes. Steady-state random mechanisms will contain squared terms in the product concentrations in the overall rate expression. The presence of these terms would predict nonhnearity in product inhibition studies. This nonlin-earity might not be obvious under standard initial rate protocols, but products that would be competitive in rapid equilibrium systems might appear to be noncompetitive in steady-state random schemes , depending on the relative magnitude of those squared terms. See Abortive Complex... 

EB][A]/[EAB], and = [EA][B]/[EAB]. The steady-state random Bi Bi rate expression is a more complex equation containing additional terms of [A] [B] and [A][B] in the numerator and [A], [B], [A] [B], and [A][B] in the denominator. Rudolph and Fromm" have looked at the effect of the magnitude of these other terms on initial rate and product inhibition studies. See Multisubstrate Mechanisms... 

As pointed out previously in this review the steady-state kinetics of mitochondrial transhydrogenase, earlier interpreted to indicate a ternary Theorell-Chance mechanism on the basis of competitive relationships between NAD and NADH and between NADP and NADPH, and noncompetitive relationships between NAD" and NADP" and between NADH and NADPH, has been reinterpreted in the light of more recent developments in the interpretation of steady-state kinetic data. Thus, although the product inhibition patterns obtained in the earlier reports [75-77] using submitochondrial particles were close to identical to those obtained in a more recent report [90] using purified and reconstituted transhydrogenase, the reinterpretation favors a random mechanism with the two dead-end complexes NAD E NADP and NADH E NADPH. A random mechanism is also supported by the observation that the transhydrogenase binds to immobilized NAD as well as NADP [105] in the absence of the second substrate. 

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),... 

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)... 

A distinction between mechanisms I and III can be made by measuring the effect of product inhibition on the initial rate. (Note that for the random, rapid equilibration mechanism, 4 = 203/0i unfortunately the experimental precision is generally not sufficient to utilize this relationship as a reliable mechanistic indicator.) Thus experiments can be carried out with varying concentrations of A, B, and C in the absence of D and with varying concentrations of A, B, and D in the absence of C. The steady-state initial velocities for mechanism I for these two cases are... 

Label from P can appear in the corresponding substrate even in the absence of Q. All that is needed is the presence of a sufficient level of EQ in the steady state. The exchange of label from Q into a substrate will not occur unless a significant concentration of P is present. Thus, one can test both products separately at levels at or above their inhibition constants, and establish the order of product release. Thus, the order of product release can be established the first product released is that which exchanges with a substrate in the absence of the another product, and the second product released is that which does not. If both products show exchange, than their release must be random. 

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