Enzyme complex, dissociation constant

Symbol for the dissociation constant of an inhibitor with respect to a particular form of the enzyme. This dissociation constant is associated with the intercept term in the double-reciprocal form of the initial-rate equation. For example, consider an inhibitor that can bind to either the free enzyme, E, or the binary central complex, EX, of a Uni Uni mechanism. Ka would be the dissociation constant for the EX -t 1 EXl step and is equal to [EX][1]/[EX1]. The binding of 1 to the free enzyme (i.e., E -t 1 El) is governed by Kis (equal to [E][1]/[E1]). 

As we discussed in Chapter 3, the KM for an enzymatic reaction is not always equal to the dissociation constant of the enzyme-substrate complex, but may be lower or higher depending on whether or not intermediates accumulate or Briggs-Haldane kinetics hold. Enzyme-substrate dissociation constants cannot be derived from steady state kinetics unless mechanistic assumptions are made or there is corroborative evidence. Pre-steady state kinetics are more powerful, since the chemical steps may often be separated from those for binding. 

Kinetic studies of NMP kinases, as well as many other enzymes having ATP or other nucleoside triphosphates as a substrate, reveal that these enzymes are essentially inactive in the absence of divalent metal ions such as magnesium (Mg2+) or manganese (Mn2+), but acquire activity on the addition of these ions. In contrast with the enzymes discussed so far, the metal is not a component of the active site. Rather, nucleotides such as ATP bind these ions, and it is the metal ion-nucleotide complex that is the true substrate for the enzymes. The dissociation constant for the ATP-Mg2+ complex is approximately 0.1 mM, and thus, given that intracellular Mg + concentrations are typically in the millimolar range, essentially all nucleoside triphosphates are present as NTP-Mg + complexes. 

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 phosphorolysis reaction is started by activated phosphorylase b. In method A, the ES complex is first formed and then phosphorolysis is triggered by the addition of AMP. The kcat value (21 s ) of the inactivate phosphorylase was similar to kcat = 18s of the AMP-activated enzyme, hi addition, the kcat value of AMP-activated enzyme also gave a similar fccat value (18 s ). This result indicates that the inactivated enzyme could be activated by the addition of AMP and shows the same activity as the AMP-activated enzyme. The dissociation constant for AMP (JCamp) was found to be 1.0 X 10 M, and this is a reasonable value as the dissociation constant for small substrates. The Kamp obtained from the QCM method was consistent with a previous determination using a radio-isotope method in the bulk solution (Kamp = 1-2 x 10 M) [73]. 

Abbreviations V, velocity at a given substrate concentration V nax, maximum velocity the binding affinity between substrate and enzyme Kg, dissociation constant of substrate-enzyme complex Ki, dissociation constant of inhibitor-enzyme complex fobs> rate of inactivation at a given inhibitor concentration krmot maximal rate of inactivation Ki, half maximal rate of inactivation (exact physical meaning is not defined) MI, metabolite-intermediate Ki, dissociation constant of inhibitor-enzyme complex in the presence of substrate S, substrate concentration IC50, concentration of inhibitor that gives rise to a 50% decrease in activity. 

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. 

Many foodstuffs contain a metabolic intermediate of biotin, biocytin s-N-biotinyUysine), which is cleaved in the intestinal tract by the enzyme biotinidase. Only free biotin can be resorbed in the proximal small intestine, a process, which can be blocked by avidin, a glycoprotein with a molar mass of ca. 70,000. Avidin occurs in greater amounts in egg-white, and forms with biotin an extraordinarily stable molecular complex (dissociation constant at 25 °C K = 10 M), which can be cleaved neither by acids nor by peptidases. Only irradiation or longer exposure to heat leads to denaturation of avidin and thereby the release of biotin. This is another reason why a breakfast egg ought to be cooked for at least AVi minutes. In this way avidin is denatured and loses its harmful effect. Similarly stable complexes are formed by biotin with neutravidin (de-glycosyl-ated avidin), streptavidin and stravidin from certain Streptomyces and Saccharo-myces species respectively. 

Their inhibition potency of peptides and peptidomimetics is usually characterized by two inhibition constants (Eq. 10.2, minimal two-step mechanism for irreversible enzyme inhibition where E=enzyme, 1=inhibitor, El=noncovalent enzyme-inhibitor complex, E-I=inactivated enzyme) the dissociation constant Ki, characterizing the preliminaiy reversible complexation step, and the first-order rate constant of inhibition ki, ascribing the rate of irreversible enzyme alkylation (Fig. 10.7) [46]. 

An advantage of the CT model, however, is the fact that it is possible to estimate the magnitude of the enzyme-substrate dissociation constant of the enzyme. This is not possible with the Hill equation. As described before, the Hill constant is a complex term that is related but is not equivalent to, the enzyme-substrate dissociation constant. By using the CT model, it is also possible to obtain estimates of the allosteric constant, L. This may prove useful in the study of allosteric modulators of enzyme activity. 

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

The substrate concentration when the half maximal rate, (Vmax/2), is achieved is called the Km. For many simple reactions it can easily be shown that the Km is equal to the dissociation constant, Kd, of the ES complex. The Km, therefore, describes the affinity of the enzyme for the substrate. For more complex reactions, Km may be regarded as the overall dissociation constant of all enzyme-bound species. 

The Michaelis constant has the units of a dissociation constant however, the dissociation constant of the enzyme—substrate complex is k dk, which is not equal to Km unless k 2-... 

There are important consequences for this statement. The enzyme must stabilize the transition-state complex, EX, more than it stabilizes the substrate complex, ES. Put another way, enzymes are designed by nature to bind the transition-state structure more tightly than the substrate (or the product). The dissociation constant for the enzyme-substrate complex is... 

Thus, the enzymatic rate acceleration is approximately equal to the ratio of the dissociation constants of the enzyme-substrate and enzyme-transition-state complexes, at least when E is saturated with S. 

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. ... 

The affinity of an enzyme for its substrate is the inverse of the dissociation constant for dissociation of the enzyme substrate complex ES. 

Maximal speed (Vmax) and supposed Michaelis constant (K ) of pectin hydrolysis reaction (catalyzed by the studied pectinesterase) were determined in Zinewedwer — Berk coordinated, They were determined in the range of substrate concentration values that was below optimum one V = 14.7 10 M min K = 5.56 10 M. The value of dissociated constant (KJ of the triple enzyme—substrate complex was determined from the experimental data at high substrate concentration. It was the following Kj= 0.22 M. Bunting and Murphy method was used for determination. 

KDHRF A homologous restriction factor binds to C8 65KDHRF A homologous restriction factor, also known as C8 binding protein interferes with cell membrane pore-formation by C5b-C8 complex Kcat Catalytic constant a measure of the catalytic potential of an enzyme Ka Equilibrium dissociation constant kD Kilodalton Kd Dissociation constant KD Kallidin... 

The binary complex ES is commonly referred to as the ES complex, the initial encounter complex, or the Michaelis complex. As described above, formation of the ES complex represents a thermodynamic equilibrium, and is hence quantifiable in terms of an equilibrium dissociation constant, Kd, or in the specific case of an enzyme-substrate complex, Ks, which is defined as the ratio of reactant and product concentrations, and also by the ratio of the rate constants kM and km (see Appendix 2) ... 

Thus, as described by Equation (2.1), the equilibrium dissociation constant depends on the rate of encounter between the enzyme and substrate and on the rate of dissociation of the binary ES complex. Table 2.1 illustrates how the combination of these two rate constants can influence the overall value of Kd (in general) for any equilibrium binding process. One may think that association between the enzyme and substrate (or other ligands) is exclusively rate-limited by diffusion. However, as described further in Chapter 6, this is not always the case. Sometimes conformational adjustments of the enzyme s active site must occur prior to productive ligand binding, and these conformational adjustments may occur on a time scale slower that diffusion. Likewise the rate of dissociation of the ES complex back to the free... 

Consider the enzyme-catalyzed and noncatalyzed transformation of the ground state substrate to its transition state structure. We can view this in terms of a thermodynamic cycle, as depicted in Figure 2.4. In the absence of enzyme, the substrate is transformed to its transition state with rate constant /cM..M and equilibrium dissociation constant Ks. Alternatively, the substrate can combine with enzyme to form the ES complex with dissociation constant Ks. The ES complex is then transformed into ESt with rate constant kt , and dissociation constant The thermodynamic cycle is completed by the branch in which the free transition state molecule, 5 binds to the enzyme to form ESX, with dissociation constant KTX. Because the overall free energy associated with transition from S to ES" is independent of the path used to reach the final state, it can be shown that KTX/KS is equal to k, Jkail (Wolfenden,... 

Miller and Wolfenden, 2002). This latter ratio is the inverse of the rate enhancement achieved by the enzyme. In other words, the enzyme active site will have greater affinity for the transition state structure than for the ground state substrate structure, by an amount equivalent to the fold rate enhancement of the enzyme (rearranging, we can calculate KJX = Ksik Jk, )). Table 2.2 provides some examples of enzymatic rate enhancements and the calculated values of the dissociation constant for the /A binary complex (Wolfenden, 1999). 

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. 

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