Enzyme apparent Michaelis constant

Most natural substrates of enzyme systems are charged molecules. Their local concentradon within any polyelectrolydc environment is given by Eq. (43). Therefore, as a second consequence of the presence of the electrostatic potential, the apparent Michaelis constant of the reac-... 

While this model explained the action of the brain enzyme on a number of hexose substrates and nonsubstrate inhibitory analogs, the mode had its weaknesses. It assumed that the other conformations of a hexose that are in equilibrium with the active conformer act as competitive inhibitors relative to this conformer. One cannot evaluate the effect of a competitive inhibitor which is present in a constant proportion relative to the active substrate by initial velocity measurements. Moreover, the use of apparent Michaelis constants may not provide accurate estimates of affinity, which is more directly related to a dissociation constant. The chief limitation of the model, however, is that an equally great number of experimental facts can be satisfactorily explained in terms of a simpler scheme involving the binding and phosphorylation of the Cl conformer. Furthermore, one can understand more directly how the enzyme can phosphorylate glucopyranose and fructofuranose equally well. 

Using the steady state assumption for the mechanism shown in Eq. 9-14, and writing a mass balance equation that includes not only free enzyme and ES but also El we obtain an equation relating rate to substrate concentration. It is entirely analogous to Eq. 9-15 but Km is replaced by an apparent Michaelis constant, K m ... 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

Enzyme kinetics were evaluated in a PDMS-glass chip using a continuous-flow system. A biotinylated enzyme (HRP or (5-galactosidase) was coupled to streptavidin-coated beads via the amide coupling of an aminocaproyl spacer. These beads (15.5 pm) were retained by a weir in the chip. The channel wall was passivated by 1 mg/mL BSA. The apparent enzyme kinetic parameters were evaluated using the Lilly-Homby model, as developed for the packed-bed enzymatic reactor systems. It was found that the apparent Michaelis constant (Km) approached the tme Km value of the free enzyme at zero-flow rate of a homogeneous reaction [845]. 

Acetylcholineesterase, urease, glucose oxidase and butyryl chloinesterase. Immobilized enzyme on to the sensor chip by corsslinking with glutaraldehyde and BSA. Conductivity changes, produced by the enzyme-catalyzed hydrolysis of ACh were measured for the analysis. Detection limits for ACh was 0.07 mM with corresponding sensitivity of 5.6 0.2 pS/mM. The device could be also used for apparent Michaelis constant determination. [85]... 

Let us assume that substrate inlet concentration is much higher than the enzyme s apparent Michaelis constant, K m, so that enzyme kinetics is expressed according to zero order kinetics, i.e., R = KE = Vmax-... 

In contrast to the fractions M-la and M-Ib isolated from the extracellular acid phosphatase of tobacco XD-6 cells, which had maximum activity at pH 6.8, the fraction M-//exhibited a pH optimum at 5.8, indicating an acid phosphatase. When a temperature of 55°C (instead of 30°C) was used for the para-nitrophenyl phosphatase activity of the three enzyme fractions from phosphate-supplied culture, the activity of M-la was rather stable, whereas fractions M-lb and M-11 were inactivated by about 35% and 90%, respectively, in 30 min. The Lineweaver-Burk plot of the rate of para-nitrophenyl phosphate hydrolysis by enzyme fractions from a phosphate-supplied culture showed that the apparent Michaelis constant of fractions M-la and M-lb was 0.9 mM, whereas that of M-11 was 0.3 mM (Ninomiya et al., 1977). 

Studies of this enzyme from Ehrlich ascites tumor cells, eiythrocytes, and Salmonella typhimurium have indicated a number of features which are at least potential mechanisms for the control of its activity. Thus, although Mg + is needed to form the actual substrate, MgATP, free Mg + also stimulates enzyme activity (36, 37). One of the most interesting effectors is inorganic phosphate, for which there is an absolute requirement. With the tumor cell enzyme, 50 mM phosphate is required for maximal activity with an apparent Michaelis constant of 3.3 mM (36, 40). A biphasic response of the bacterial enzyme to phosphate was observed with apparent Michaelis constants of 2.3 and 40 mM (37). In both cases, arsenate was a weak substitute. Wong and Murray (40) found that the Michaelis constant for ATP did not vary with phosphate concentration, whereas that for ribose-5-P did vary. Hershko et al. (4I) and others have also shown stimulation of enzyme activity by phosphate in intact erythrocytes and Ehrlich ascites tumor cells incubated in media containing varying concentrations of phosphate. 

The apparent Michaelis constants differ with enzyme source and pH, but... 

Adenosine kinase has a low activity toward deoxyadenosine the apparent Michaelis constant of the partly purified enzyme from rabbit liver for deoxyadenosine (2 X 10 M) is about 1000 times that for adenosine 37). 

Whether there are other kinase activities, perhaps specific for the purine deoxyribonucleosides, remains an open question. The phosphorylation of deoxyguanosine has been demonstrated [for example, in fish milt extracts (Sdeoxycytidine kinase to catalyze this reaction. The apparent Michaelis constant for the phosphorylation of deoxyguanosine by the calf liver kinase is 3.1 X 10 M, about two orders of magnitude higher than that for deoxycytidine 36),... 

The E. coli enzyme is subject to allosteric regulation it is activated by by dCDP and dCTP, and inhibited by dTTP, but not by dTDP or thy-midylate. In the presence of dCDP, the apparent Michaelis constant for thymidine decreases and the Fm increases the sigmoidal nature of the rate-... 

Benzylpenicillin isocyanate has a /S-Iactam ring that could be hydrolyzed by the enzyme. When benzylpenicillin isocyanate binds to the catalytic site and hydrolysis and inactivation proceed simultaneously, these reactions should take place through the same reversible complex (E-BPI) as represented above. Although the rate was over 100 times less than that with benzylpenicillin, the hydrolysis of benzylpenicillin isocyanate did occur with concomitant inactivation of the enzyme. The apparent Michaelis constant, k-iks)/ki, was coincident with K (400 fJiM) obtained in the inactivation reaction described. Other penicillin isocyanates may be hydrolyzed in a similar manner by yS-lactamase. 

It has been found experimentally that in most cases v is directly proportional to the concentration of enzyme [.E0] and that v generally follows saturation kinetics with respect to the concentration of substrate [limiting value called Vmax. This is expressed quantitatively in the Michaelis-Menten equation originally proposed by Michaelis and Menten. Km can be seen as an apparent dissociation constant for the enzyme-substrate complex ES. The maximal velocity Vmax = kcat E0. ... 

Although it is only for the simple Michaelis-Menten mechanism or in similar cases that Ku = Ks, the true dissociation constant of the enzyme-substrate complex, Km may be treated for some purposes as an apparent dissociation constant. For example, the concentration of free enzyme in solution may be calculated from the relationship... 

The linear response range of the glucose sensors can be estimated from a Michaelis-Menten analysis of the glucose calibration curves. The apparent Michaelis-Menten constant KMapp can be determined from the electrochemical Eadie-Hofstee form of the Michaelis-Menten equation, i = i - KMapp(i/C), where i is the steady-state current, i is the maximum current, and C is the glucose concentration. A plot of i versus i/C (an electrochemical Eadie-Hofstee plot) produces a straight line, and provides both KMapp (-slope) and i (y-intercept). The apparent Michaelis-Menten constant characterizes the enzyme electrode, not the enzyme itself. It provides a measure of the substrate concentration range over which the electrode response is approximately linear. A summary of the KMapp values obtained from this analysis is shown in Table I. 

The catalytic efficiency of an enzyme is indicated by its kcatIKM value, the value combining the effectiveness of both the productive substrate binding and the subsequent conversion of substrate molecules into product (Copeland, 2000). This value is the apparent second-order rate constant for enzyme action under conditions in which the binding site of the enzyme is largely unoccupied by substrate. The kcatIKM value is the index for comparing the relative rates of cleavage of alternative, competing substrates. The KM is the Michaelis constant, an apparent dissociation constant and hence a measure of substrate affinity. This value equals the concentration of substrate needed to reach half maximum velocity of the enzyme reaction. 

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