Enzyme-substrate dissociation constant

This association/dissociation is assumed to be a rapid equilibrium, and is the enzyme substrate dissociation constant. At equilibrium,... 

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. 

Two points should be noted (1) Because the rate constants are pseudo-unimolecular, there is a concentration dependence, so ka and koff may be resolved without the amplitude factor. (2) There is a lower limit to 1/r that is, 1/t cannot be less than koS. This sets a limit on the measurement of these rate constants. A good stopped-flow spectrophotometer can cope only with rate constants of 1000 s 1 or less, and many enzyme-substrate dissociation constants are faster than this. 

Subsequent studies led to the suggestion that the modified conformative response is strongly reflected in the binding properties of the enzyme 120). Although lacking direct support, this suggestion provides a single explanation for two sets of discrepancies observed when a comparison is made of enzyme-substrate dissociation constants based on the catalytic activity with those based on the conformative response (74). 

Michaelis constant, Km is named after the German biochemist, Leonor Michaelis. Km =(k i +kcat) / k+iy When k at k+j, the Km approximates Ks, the enzyme-substrate dissociation constant. 

When a nominal initial level of 100 /tAf of (II) was added to the pyruvate kinase in three increments, about 50% inactivation occurred (see the table). The relationship between the degree of inactivation and the initial concentration of (II) was not examined further. Inactivation was prevented by 15-sec hydrolysis of (II) in the buffer prior to addition of enzyme. Pyruvate kinase inactivated by (II) did not regain activity when stored in the assay medium for 16 hr at 22°. Protection of the enzyme from a 100 / A/ nominal level of (II) was afforded by 100 /tAf ATP, 2.5 mAf ADP, or 1.5 mAf phosphoenolpyruvate, the levels of the last two compounds being selected so as to be in excess of their enzyme-substrate dissociation constants (0.8 mAf and 0.08 mAf, respectively). Protection by these three substrates was concluded to imply that the action of (II) is probably ATP-site-directed. ... 

This results in an apparent increase in the enzyme-substrate dissociation constant (Ks) (i.e., an apparent decrease in the affinity of enzyme for... 

The Hill constant is an index of the affinity of the enzyme for the substrate, but it is not the enzyme-substrate dissociation constant. It has units of (concentration)", which makes comparison between reactions with different n values difficult. 

A useful parameter sometimes reported in kinetic studies is the nonexclusive binding coefficient (c). This coefficient is defined as the ratio of the intrinsic enzyme-substrate dissociation constants for the enzyme in the R... 

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. 

Dissociation rate constants are much lower than the diffusion-controlled limit, since the forces responsible for the binding must be overcome in the dissociation step. In some cases, enzyme-substrate dissociation is slower than the subsequent chemical steps, and this gives rise to Briggs-Haldane kinetics. 

Using the symmetry model, the fraction of the binding sites occupied at any given substrate concentration can be described with an expression that includes the substrate dissociation constants for the two conformations (KR and Kr) and the equilibrium constant between the T and R conformations in the absence of substrate, L = [T]/[R], Thus, the symmetry model attempts to explain the difference between Kx and K2 in equation (3) by introducing a third independent parameter. Considering that equation (3) can fit the experimental data for a dimeric enzyme with only two pa-... 

Relates IC50 to Kt under conditions of competitive inhibition Kt equilibrium enzyme inhibitor dissociation constant Km Michaelis-Menton constant, [S] substrate concentration. 

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. 

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]. 

The interaction of antibodies with their antigens is comparable, in its specificity, to the binding of substrates with enzymes. The dissociation constants are most commonly within the range of 10 -10" M. From the examples described in Table... 

The kinetic parameters and Umax are estimated from the Michaelis-Menten equation and provide quantitative information regarding enzyme function. or the Michaelis constant is operationally defined as the concentration of substrate at which half-maximal velocity of the reaction is achieved (Fig. 4.1). With respect to the single substrate reaction scheme (Scheme 4.1), it should be realized that is equal to k + k2)lkx and thus is the amalgamation of several rate constants. With respect to affinity, unfortunately, is frequently (and incorrectly) used interchangeably with which is the substrate dissociation constant. Though may sometimes approximate the two do not have to be equal and numerous examples exist where these parameter values vary dramatically. 

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. 

We wish to propose that Km does in fact represent a substrate dissociation constant, and that the observed K.. values represent actual inhibitor dissociation constants. This leads to the proposition that the dissociation of substrate is in actual fact independent of the state of ionization of the enzyme, and that the sigmoidal variation in k is a reflection of the changes in concentration of the appropriate state of ionization of the enzyme-substrate complex. 

Phosphorus-31 NMR was used to observe the substrates and products interconverting on the surface of the enzyme at equilibrium for the five phosphoryl transfer enzymes and one nucleotidyl-transfer enzyme discussed in Section III,A. In these experiments the concentrations of the enzyme (3-5 mAf) and all the different substrates, whether they contain P or not (2-4 mAf), are such that 80-90% of the reactants and products will be bound to the enzyme (for dissociation constants less than —200 iiM). The results obtained for the difiTerent enzymes are now summarized. 

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-... 

The interpretations of Michaelis and Menten were refined and extended in 1925 by Briggs and Haldane, by assuming the concentration of the enzyme-substrate complex ES quickly reaches a constant value in such a dynamic system. That is, ES is formed as rapidly from E + S as it disappears by its two possible fates dissociation to regenerate E + S, and reaction to form E + P. This assumption is termed the steady-state assumption and is expressed as... 

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. 

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