Enzyme-inhibitor dissociation constant

No discussion of this subject would be complete without emphasizing the point that the relative rates of hydrolysis of two substrates, which may be quite different from their relative affinities for an enzyme, may be at least as important as regards the physiological action of the enzyme. Dissociation constants measure affinity only (affinity = 1/dissociation constant). Thus, despite its 10-fold smaller affinity, phenyl /3-glucuronide is hydrolyzed nearly as rapidly as phenolphthalein /3-glucuronide by the purified enzyme from female-rat preputial gland at saturation with both substrates, in terms of moles of aglycon liberated.40 In the presence of a combined inhibitor (see Section IX, 3), there is a fall in the rate of hydrolysis, despite the increased affinity of the enzyme for the substrate. 

The active site structure of trypsin-like enzymes is considered to be very similar to that of bovine trypsin, yet little is known about them. Refinement of these structures is important also for the purpose of designing physiologically active substances. With a view to comparing the spatial requirements of active sites of these enzymes, dissociation constants of the acyl enzyme-ligand complex, K-, which were defined before, were successfully analyzed By taking advantage of inverse substrates which have an unlimited choice of the acyl component, development of stable acyl enzymes could be possible. These transient inhibitors for trypsin-like enzymes could be candidates for drugs. In this respect, the determination of the deacylation rate constants for the plasmin- and thrombin-catalyzed hydrolyses of various esters were undertaken 77). 

Competitive inhibitors are so named because they compete for the active site with the native substrate, meaning that only enzyme-inhibitor or enzyme-substrate complex formation is possible (Fig. 7-3a). In this case, the inhibition constant, or enzyme-inhibitor complex dissociation constant, can be defined ... 

The binding of two iminoalditol inhibitors showed bell-shaped profiles, with the acid limb corresponding to the acid dissociation of the enzyme (constant K-s) and the basic limb to the deprotonation the inhibitor, acid dissociation constant Ki [eqn. (5.27)]. 

Fig. 2 Therrnolysin phosphonamide and analog inhibitors with dissociation constants of enzyme-inhibitor complexes...

In many circumstances, inhibitors affect enzyme activity in an irreversible fashion. It is sometimes difficult to distinguish between the effects of a reversible and irreversible inhibitors since irreversible inhibition could be interpreted as noncompetitive reversible inhibition. However, the apparent enzyme-inhibitor equilibrium dissociation constant (Ki) derived for an irreversible inhibitor is dependent on enzyme concentration, preincubation time, and substrate concentration. A true equilibrium Ki would be independent of all these factors. Not a conclusive proof, time dependence of the inhibitory effects may be indicative of irreversibiUty. 

In such inhibition, the inhibitor and die substrate can simultaneously bind to the enzyme. The nature of the enzyme-inhibitor-substrate binding has resulted in a ternary complex defined as EIS. The Ks and Kt are identical to the corresponding dissociation constants. It is also assumed that the EIS does not react further and is unable to deliver any product P. The rate equation for non-competitive inhibition, unvAX, is influenced ... 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

The Ki value is the dissociation constant of an enzyme-inhibitor complex. If [E] and [I] are the concentrations of enzyme and its inhibitor and [El] is the concentration of the enzyme-inhibitor complex, there is an equilibrium of complex formation and detachment as follows ... 

Certain substances known as competitive inhibitors, symbolized I, may lower the catalytic efficiency of the enzyme (or other catalyst) by binding to it. Consider that the E I complex has a dissociation constant K. ... 

Inhibition of Glycosidases by AIdono-l,S-lactones and Aldohexoses Expressed by the Dissociation Constant K of the Enzyme-Inhibitor Complex... 

A case similar to the slow, practically irreversible inhibition of jack bean a-D-mannosidase by swainsonine is represented by the interaction of castanospermine with isomaltase and rat-intestinal sucrase. Whereas the association constants for the formation of the enzyme-inhibitor complex were similar to those of other slow-binding glycosidase inhibitors (6.5 10 and 0.3 10 M s for sucrase and isomaltase, respectively), the dissociation constant of the enzyme-inhibitor complex was extremely low (3.6 10 s for sucrase) or could not be measured at all (isomaltase), resulting in a virtually irreversible inhibition. Danzin and Ehrhard discussed the strong binding of castanospermine in terms of the similarity of the protonated inhibitor to a D-glucosyl oxocarbenium ion transition-state, but were unable to give an explanation for the extremely slow dissociation of the enzyme-inhibitor complex. 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

Comparisons of affinity among different inhibitors for a common enzyme, or among different enzymes for a common inhibitor, are best done in terms of the relative dissociation constants or the related Gibbs free energy of binding. 

As we have seen before, the enzymatic reaction begins with the reversible binding of substrate (S) to the free enzyme ( ) to form the ES complex, as quantified by the dissociation constant Ks. The ES complex thus formed goes on to generate the reaction product(s) through a series of chemical steps that are collectively defined by the first-order rate constant kCM. The first mode of inhibitor interaction that can be con-... 

A noncompetitive inhibitor is one that displays binding affinity for both the free enzyme and the enzyme-substrate complex or subsequent species. In this situation the binding affinity cannot be defined by a single equilibrium dissociation constant ... 

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

As we described in Chapter 3, the binding of reversible inhibitors to enzymes is an equilibrium process that can be defined in terms of the common thermodynamic parameters of dissociation constant and free energy of binding. As with any binding reaction, the dissociation constant can only be measured accurately after equilibrium has been established fully measurements made prior to the full establishment of equilibrium will not reflect the true affinity of the complex. In Appendix 1 we review the basic principles and equations of biochemical kinetics. For reversible binding equilibrium the amount of complex formed over time is given by the equation... 

Characterization of inhibition modality, and from this quantitative determination of enzyme-inhibitor dissociation constants, constitutes the only rational, quantitative means of assessing relative compound affinity for a target enzyme. 

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