Enzyme-inhibitor dissociation constant reactions

An inhibitor is a compound that decreases the rate of an enzyme-catalyzed reaction. Moreover, this inhibition can be reversible or irreversible. Reversible enzyme inhibition can be competitive, uncompetitive, or linear mixed type, each affecting Ks and Vmax in a specific fashion. In this chapter, each type of reversible inhibition is discussed in turn. This is followed by two examples of strategies used to determine the nature of the inhibition as well as to obtain estimates of the enzyme-inhibitor dissociation constant (Ki). 

The hydrolysis of maltose by glucoamylase from Rhizopus niveus was carried out in the presence an d absence of dextran sulphate, which are the components of supports of immobilized enzymes.The interaction between dextran and the enzyme was observed by fluorescence spectrophotometry. The kinetic and fluorescence experiments indicated that dextran became bound to glucoamylase and was apparently a non-competitive inhibitor of the enzyme. The dissociation constant of the enzyme-dextran complex was estimated to be 34%. The reaction rate was hardly affected at pH 4.0 and 4.5 by addition of dextran sulphate, whereas the kinetic parameters depended considerably on the concentration of dextran sulphate at pH 3.5. These findings indicated that there might exist some interactions between the enzyme and dextran sulphate. 

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 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. ... 

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-... 

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... 

A dimensionless quantity used to assess the extent of inhibition by a particular compound at a specific concentration on the initial rate of an enzyme-catalyzed reaction. The degree of inhibition, symbolized by ei, is equal to (vo Vi)/Vo where Vo in the reaction rate in the absence of the inhibitor and Vi is the rate in the presence of the inhibitor. Whenever ej values are reported, the inhibitor concentration and initial rate conditions have to be provided as well. The degree of inhibition is a useful parameter in the early stages of an investigation. However, it does not address the type of inhibition nor provide much information on the dissociation constant for the inhibitor. See Inhibition (as well as specific type of inhibition)... 

This linearization of the tight-binding scheme allows the investigator the opportunity to calculate values for [Etotai] and Ki, the dissociation constant for the inhibitor. In the Henderson plot, [Itotai]/(l v/Vo) is plotted as a function of vjv where Vq is the steady-state velocity of the reaction in the absence of the inhibitor. The slope of the line is the apparent dissociation constant for the inhibitor. Secondary plots (from repeating the inhibition experiment at different substrate concentrations) will yield the Ki value. The vertical intercept is equal to [Etotai]- Hence, repeating the experiment at a different concentration of enzyme will produce a parallel line. 

Transition state inhibitors. Suppose that a chemical reaction of a compound S takes place with rate constant /cx through transition state T. Let the equilibrium constant for formation of T be Kj-. Assume that an enzyme E can combine either with S with dissociation constant Kds or with the compound in its transition state structure T with dissociation constant Kdj (Eq. 9-83). 

Many inhibitors with very low dissociation constants appear to have a slow onset of inhibition when they are added to a reaction mixture of enzyme and substrate. This was once interpreted as the inhibitors having to induce a slow conformational change in the enzyme from a weak binding to a tight binding state. But in most cases, the slow binding is an inevitable consequence of the low concentrations of inhibitor used to determine its Ki. For example, consider the inhibition of trypsin by the basic pancreatic trypsin inhibitor. Kx is 6 X 10-14 M and the association rate constant is 1.1 X 106 s-1 M-1 (Table 4.1). To determine the value of Ki, inhibitor concentrations should be in the range of K1, where the observed first-order rate constant for association is (6 X Q U M) X (1.1 X 106 s-1 M-1) that is, 6.6 X 10-8 s 1. The half-life is (0.6931/6.6) X 108 s, which is more than 17 weeks. 

Since substrate and inhibitor do not compete for a same site for the formation of enzyme-substrate or enzyme-inhibitor complex, we can assume that the dissociation constant for the first equilibrium reaction is the same as that of the third equilibrium reaction, as... 

It should be recalled here that the alcoholic hydroxyl of serine does not possess a dissociation constant within the pH range, accessible to enzymic reactions. Therefore, this amino acid cannot influence the pH-activity curve. On the other hand, it is well known that DFP inhibition is initially reversible and becomes only slowly irreversible. This has been demonstrated for true ChE from electric eel by Nachmansohn and associates (46) and for plasma ChE by Mackworth and Webb (47). Similarly, a stepwise reaction with inhibitors, containing the diethyl phosphoryl moiety, has been made probable by Hobbiger (34)- Therefore, it appears possible that phosphates are first attacked by the imidazol moiety of the esteratic site, in conformity with the catalytic influence of free imidazol on phosphate hydrolysis (48). This step is followed by transfer to serine. The final product is a trialkyl phosphate XV, which is not split by imidazol (scheme F). 

Affinity labeling agents are intrinsically reactive compounds that initially bind reversibly to the active site of the enzyme then undergo chemical reaction (generally an acylation or alkylation reaction) with a nucleophile on the enzyme (Scheme 8). To differentiate a reversible inhibitor from an irreversible one, often the dissociation constant is written with a capital i, K (65), instead of a small i, K, which is used for reversible inhibitors. The K denotes the concentration of an inactivator that produces half-maximal inactivation. Note that this kinetic Scheme is similar to that for substrate turnover except instead of the catalytic rate constant, kcat for product formation, kmact is used to denote the maximal rate constant for inactivation. 

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