Single-step, binding mechanism

Figure 6.2 Effect of preincubation time with inhibitor on the steady state velocity of an enzymatic reaction for a very slow binding inhibitor. (A) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the single-step binding mechanism of scheme B of Figure 6.3. (B) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the two-step binding mechanism of scheme C of Figure 6.3. Note that in panel B both the initial velocity (y-intercept values) and steady state velocity are affected by the presence of inhibitor in a concentration-dependent fashion.

Until 1984, all of the stopped-flow and temperature-jump kinetic studies of alpha cyclodextrin inclusion-complex formation were explainable in terms of a single-step, binding mechanism. According to this mechanism, the observed rate constant, kobs, (for stopped-flow) and the reciprocal relaxation time, 1/t, (for temperature-jump) should show a linear dependence on the edpha cyclodextrin concentration. Sano and coworkers, however, in the case of the iodide-alpha cyclodextrin interaction, and Hersey and Robinson,in the case of various azo dye-alpha cyclodextrin interactions (see Fig. 7), found that certain guest species exhibit a limiting value of kobs and 1/t at high concentrations of alpha cyclodextrin. This behavior can most simply be explained in terms of a mechanism of the type,... 

Hersey and Robinson also foundthat many guest species that show kinetic behavior apparently explicable in terms of a single-step binding, give a discrepancy between the values of the equilibrium constant determined kinetically and those determined from equilibrium studies. It was found that the equilibrium constant, deterrmned spectrophotometrically, was usually greater than the ratio of the forward and backward rate-constants, determined kinetically. They therefore suggested that this discrepancy could be adequately explained if the two-step mechanism just described was used to interpret the results. A similar proposal has also been made by Hall and coworkers, who observed a large discrepancy between AV° values for the inclusion of 1-butanol and 1-pentanol by alpha cyclodextrin, calculated from equilibrium-density measurements and kinetic, ultrasonic-absorption data. 

Fortunately, a usual assumption for applying the steady-state condition to mechanism (34) is that k2 k-1. This resolves the problem, because then the Michaelis constant can be interpreted as an ordinary single-step equilibrium constant and the binding volume as a simple association volume. 

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