Michaelis constant , definition

The turnover number of an enzyme is defined as the maximum number of moles of substrate reacted per mole of enzyme (or molecules per molecule) per minute under optimum conditions (i.e., saturating substrate concentration, optimum pH, etc). If 2 mg/cm3 of a pure enzyme (50,000 molecular weight, Michaelis constant Km = 0.03 mole/m3) catalyzes a reaction at a rate of 2.5 jumoles/nUksec when the substrate concentration is 5 x 10 3 moles/m3, determine the turnover number corresponding to this definition and the actual number of moles of substrate reacting per minute per mole of enzyme. 

This is a more general definition of the Michaelis constant than that given in Section 10.2.1. If kr, it simplifies to the form developed in 10.2.1. 

The Michaelis constant, KM, for an enzyme-substrate interaction has two meanings (1) Ku is the substrate concentration that leads to an initial reaction velocity of V" /2 or, in other words, the substrate concentration that results in the filling of one-half of the enzyme active sites, and (2) KM = (k2 + ki)/kv The second definition of Ku has special significance in certain... 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

The Michaelis constant was determined to be = 0.60 mM. Turnover numbers are relatively low (kcai 0.4 x lO /min) but are definitely present. Furthermore, we found that the template molecule itself is a powerful competitive inhibitor with = 0.025 mM, i.e. it is bound more strongly than the substrate by a factor of 20. It is remarkable that such a strong binding of substrate or template occurs in water-acetonitrile 1 1. Binding in aqueous solution by the usual electrostatic interactions or hydrogen bonding is much weaker. 

The alkaline phosphatase of both human intestine and placenta are L-phenyl-alanine-sensitive and undergo uncompetitive inhibition to the same extent (nearly 80%) by 0.005 M L-phenylalanine. However, we have been able to find several distinguishing biochemical characteristics of the two enzymes (1) the anodic mobility of intestinal alkaline phosphatase remains unchanged after neuraminidase treatment, whereas the placental enzyme is sialidase-seusitive and hence the electrophoretic mobility on starch gel is considerably reduced by such treatment, (2) the Michaelis constant of placental alkaline phosphatase at a definite pH is appreciably higher than that of the intestinal enzyme (at pH 9.3 the Km values of placenta and intestine are 316 and 160 ixM, respectively), and (3) the pH optima (with 0.018 Af phenyl phosphate as substrate) of the two enzymes are different the values for intestinal and placental enzymes with 0.006 Af n-phenylalanine are 9.9 and 10.6, respectively, and the respective values in the presence of 0.005 Af L-phenylalanine are 10.2 and 11.1. Finally, contrary to the behavior of intestinal alkaline phosphatase, placental enzyme is completely heat stable (P19). 

Serine and cysteine peptidases are not perfect acyltransferases. Therefore, it is useful to have a method for the prediction of the outcome of the kinetically controlled peptide synthesis. In order to get a simple efficiency parameter we decided to introduce the partition value p11061 analogous with the definition of the Michaelis constant according to Eq. (3), where P2 = Ac-OH, P3 = Ac-N, and N = HN. 

In the 1-substrate case one can at least say that the dissociation constant may not exceed K -, there is therefore a formal mathematical relationship between the two constants. For some mechanisms involving more than one reactant, not even this limited degree of linkage exists. Michaelis constants are empirical kinetic parameters. They have an entirely adequate definition in kinetic terms and should not be equated with thermodynamic constants without sound theoretical or experimental justification. 

The definition of Michaelis constants, Vi, and V is the same as above. In addition, coefC coefP... 

The reaction rates, 91, 91 and 913, are in terms of the mole concentration of glucose, maltose and maltotriose, 5, S2 and. The maximum reaction velocities, Michaelis constants and inhibition constants in the reaction rates follow the Arrhenius dependency. The definitions of the symbols and their corresponding data can be obtained from the literature (Gee and Ramirez, 1988 Wang and Jing, 2(XX)). 

Thus, the Michaelis constant. Km, is equal to the substrate concentration at which the reaction rate is half of its maximal value. Km is independent of enzyme concentration. The lower the value of Km, the higher the affinity of the enzyme for the substrate, i. e. the substrate will be bound more tightly by the enzyme and most probably will be more efficiently converted to product. Usually, the values of Km, are within the range of 10 to 10 mol 1. Erom the definition of Km ... 

The membrane containing the immobilized enzyme is handled by partitioning it into a specified number of volume elements so that Equations 20.23 and 20.24 are valid in this model. While the concentration of each species may vary from element to element, the steady-state assumption (d[ES]/dt = 0) may be invoked independently for each volume element. This results in the definition of the Michaelis-Menton constant, KM ... 

In a study of the highly purified alanine racemase of E. coli, Lambert and Neuhaus determined significant differences in the maximal velocities and the Michaelis-Menten constants of the substrates in the forward (L - dl) and reverse directions (d - dl) [37]. From these data the value calculated for Keq is 1.11 0.15. The time course of the reaction showed that in 10 min with L-alanine as substrate ca. 0.09 jumol of D-alanine were formed. With the same amount of enzyme (750 ng) and in the same time period, ca. 0.05 jamol of L-alanine were formed from D-alanine. Similar results have been reported for the same enzyme from S. faecalis and for proline racemases [37]. Thus, in these cases, there are definite kinetic differences, as expected for the existence of two diastereoisomers formed between enzyme and two substrate enantiomers. 

Conditions where [S] are often known as the fccat conditions of catalysis. When [S] Km there is no free biocatalyst E at all, hence the first equilibrium effectively disappears and the measured rate constant of reaction, kp in Equation (8.107), becomes identified directly with the first order Michaelis-Menten term kcat according to Equations (8.1) and (8.9). In a similar way, AGo+in Equation (8.108) becomes identified directly with AG+p by definition. If both ES and ES+are bound equally more effectively by a uniform value AGp (Figure 8.55), then Ks and by implication K are reduced, but there is no change in fccat- If ES is bound to... 

The reciprocal form of the equation produced a straight line with intercept values on the Y axis of 1/Vmax and on the X axis of -1/Km (Figure 2). This advancement in analysis of the Michaelis-Menten equation allowed for a simplified way of analyzing the effect of compounds that altered the catalytic activity of enzyme systems. Changes in enzymatic activity were observed to result from changes in the substrate affinity or maximum velocity (Lineweaver Burk 1934) resulting in the definition of inhibitory equations based on their effects on the kinetic constants of the Michaelis-Menten equation. 

---