Inhibitors have proved to be useful probes of chemical and kinetic mechanisms of enzyme-catalyzed reactions. The action of inhibitors has also provided background information for the development of specific bioactive compounds to act as chemotherapeutic agents or as herbicides. Most studies have been performed with classical inhibitors. These are substrate analogues that give rise to linear competitive inhibition with respect to the substrate through the reversible formation of dead-end complexes that can only dissociate back to the components from which they were formed. Usually, the kinetic investigations have been performed under conditions in which the concentrations of substrate and inhibitor are much greater than the concentration of the enzyme, and all the equilibria are set up rapidly, conforming to Michaelis-Menten kinetics. The rapid interaction of an inhibitor (I) at the active site of an enzyme (E) to form an EI complex is described by equation 1.
The dissociation constant (Ki) for the reaction, a thermodynamic quantity, is defined by the relationships given in equation (2).
Rapid establishment of the equilibrium, on the time scale of a steady-state kinetic experiment of seconds to minutes, requires that the magnitudes of the apparent first-order rate constants for the formation of EI, k^I, and for the dissociation of EI, k^ be relatively high, with values greater than about 1s-1. If the binding is very tight, however, dissociation will be intrinsically slow; for example, if Ki is in the micromolar range, k4 can be no greater than 10-6 k3 in units of s-1. Consequently, a tight-binding inhibitor will tend to dissociate slowly and might not fulfill the requirements for rapid equilibration.
It has now been established that the equilibrium between enzyme, inhibitor, and the enzyme-inhibitor complex is not always set up rapidly, so that the inhibition becomes time-dependent. Compounds that behave in this manner have been referred to as slow-binding inhibitors (1). This term conveys the idea that binding, which is the establishment of all equilibria involving the inhibitor, occurs slowly on the steady-state time scale of seconds to minutes. Slow-binding inhibition resembles transient-state kinetics on a different time scale. The definition is an operational one, as it is always possible that the time to reach equilibrium could vary with the experimental conditions. The simplest scheme to illustrate slow-binding inhibition of an enzyme-catalyzed reaction is shown as mechanism A in Figure 1.
Figure 1. Kinetic mechanisms for the slow-binding inhibition of enzyme-catalyzed reactions by substrate analogues.
A second mechanism to account for slow-binding inhibition is mechanism B in Figure 1, which involves the rapid formation of a collision complex (EI), with the inhibitor behaving initially as a classical competitive inhibitor (cf eqs. 1 and 2). The EI complex then undergoes a slow conformational change, or isomerization reaction, to form a more stable complex, EI*. The overall dissociation constant for the reaction, K*, would be defined as
where
The degree to which the initial binding is enhanced through the isomerization reaction will depend on the ratio k5 / k^. The absolute values of these rate constants must be such as to allow observation, on a steady-state time scale, of the isomerization as manifested by the slow increase in inhibition.
Under conditions in which the total concentration of a slow-binding inhibitor is at least 10 times greater than the total enzyme concentration and the reaction is started by the addition of enzyme, the progress curve in the presence of a single inhibitor concentration is described for either mechanism A or mechanism B by an integrated rate equation (eq. 4).
For this equation, which contains both a linear term and an exponential term, P represents the concentration of product, vs and vo denote steady-state and initial velocities, respectively, k represents an apparent first-order rate constant whose meaning varies with the mechanism. Equation 4 predicts, and curve b of Figure 2 illustrates, that when the reaction is started by adding enzyme, there is an initial burst or transient phase. The velocity then settles down to a slower steady-state rate, as represented by the asymptote of the curve, because of the slow establishment of the equilibrium between enzyme, inhibitor, and the enzyme-inhibitor complex(es). If the enzyme is preincubated with the inhibitor and the reaction is started by the addition of substrate, equation 4 still applies. But there is now a slow decrease in the degree of inhibition, an apparent activation, because of the establishment of new equilibria that involve interactions of both substrate and inhibitor with the enzyme (Fig. 2, curve c), consequently, the initial velocity is less than the steady-state velocity. Whichever procedure is used to study the inhibition, the same steady-state velocity will be obtained. All this discussion assumes that the enzyme is not inactivated or activated by other phenomena.
Figure 2. Progress curves for an enzyme-catalyzed reaction in (a) the absence, and (b, c) the presence, of a slow-binding inhibitor. The reactions were started (b) by adding enzyme or (c) by adding substrate after preincubation of enzyme and inhibitor. The dashed lines represent steady-state rates in the presence of inhibitor.
Figure 3 shows the basic types of plots obtained when reactions conforming to either mechanism A or mechanism B are run in the presence of different concentrations of a slow-binding inhibitor, and started by the addition of enzyme. The two families of curves are similar except that, for mechanism A, the initial velocity of the reaction is independent of the inhibitor concentration. By contrast, the initial velocity of a reaction that conforms to mechanism B is described by the equation for linear competitive inhibition (Table 1). This same general equation describes the variation with inhibitor concentration of the asymptotes for each family of curves (Table 1). As the concentration of the inhibitor increases, so also does the rate at which the curves for the two mechanisms turn over. This is a function of the value for the apparent first-order rate constant (k), which increases with inhibitor concentration (Table 1). It will be noted that, in the presence of a fixed concentration of substrate (A), the variation of k as a function of inhibitor concentration is linear for mechanism A and hyperbolic for mechanism B. The linear plot has an intercept with the vertical ordinate equal to k4.
The hyperbolic plot has limiting values of (k5 + k^) and k6 at infinite and zero inhibitor concentrations, respectively.
Figure 3. Progress curves for the slow-binding inhibition of enzyme-catalyzed reactions conforming to mechanisms ( a) and (b). In each case, the reaction was starting by adding enzyme to a mixture of substrate and varying amounts of the inhibitor.
Slow-binding Inhibition Mechanisms a
|
Parameter in equation (4) |
Mechanism A |
Mechanism B |
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Initial velocity Steady-state velocity k |
 |
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Although values for the kinetic parameters associated with slow-binding inhibition can be determined by graphic procedures, it is greatly preferable to make an overall least-squares fit of the data to equations that describe mechanisms A and B, namely, equation 4, plus those listed in Table 1. This approach allows discrimination between the two mechanisms, as well as determination of values for each kinetic parameter, together with their standard errors. The nonlinear regression analysis involves using about 20 points from each curve and the utilization of a graphic procedure to obtain estimates of the k value for each curve (2, 3). The same basic approach is used for the study and analysis of slow-binding inhibition when an enzyme has multiple substrates. Analysis of inhibition data is simplified, however, if all substrates other than the one for which the inhibitor is an analogue are present at saturating concentrations.
There are several points to note about the detection and study of slow-binding inhibition (2). It will not be observed, on starting the reaction by adding the enzyme, if the rate of interaction of enzyme and inhibitor (mechanism A) or the rate of isomerization of the enzyme-inhibitor complex (mechanism B) are very slow relative to the rate of the reaction catalyzed. Therefore, the enzyme should also be preincubated with the inhibitor, and inhibition should be studied as a function of enzyme concentration. The ratio of the concentration of substrate to its Km (Michaelis constant) should not be high; if it is, the concentration of free enzyme is reduced considerably and there is a concomitant reduction in the collision rate for enzyme and inhibitor. Thus, it could appear that the inhibition conforms to mechanism A rather than to mechanism B. With any progress curve investigation, it is important that there is no other inactivation of the enzyme. This can be confirmed by the observation of an extended linear asymptote or by the application of Selwyn’s test (4). Reactions in the presence of the inhibitor should be run for a sufficiently long period, but not beyond the point at which the reaction in the absence of inhibitor ceases to be linear.
In the original formulation of mechanism B, consideration was not given to the possibility that the step for the formation of an initial collision complex between E and I was at steady state rather than at thermodynamic equilibrium (Fig. 1). Subsequent theoretical investigations have demonstrated the difficulties associated with the use of steady-state kinetic techniques to distinguish mechanism B from the more general but more complex mechanism B, with both steps involving the formation of enzyme-inhibitor complexes being at steady state equilibrium (5).
When a slow-binding inhibitor causes inhibition at concentrations comparable to that of the enzyme, the inhibitor is described as being of the slow, tight-binding type (1). The inhibition can still be described in terms of mechanisms A and B (Fig. 1), but the equations to describe the inhibition are more complex because of the change in the concentration of free inhibitor as the inhibition proceeds. The availability of a computer program that allows straightforward analysis of slow, tight-binding inhibition data has facilitated the study of this type of inhibition (3). Consideration has been given recently to kinetic schemes for slow- and tight-binding inhibition where the inhibitor can also combine with an enzyme-substrate complex and influence the binding or the rate of product formation, or both (6) (see Competitive Inhibition and Noncompetitive Inhibition ).
From a list of enzymes subject to slow-binding and slow, tight-binding inhibition (1), it appears that the predominant mechanism of inhibition is that described by mechanism B.
