Enzyme reactions Michaelis-Menten kinetics

Hyperbolic shape of the enzyme kinetics curve Most enzymes show Michaelis-Menten kinetics (see p. 58), in which the plot of initial reaction velocity, v0, against substrate concentration [S], is hyperbolic (similar in shape to that of the oxygen-dissociation curve of myoglobin, see p. 29). In contrast, allosteric enzymes frequently show a sigmoidal curve (see p. 62) that is similar in shape to the oxygen-dissociation curve of hemoglobin (see p. 29). 

Shapes of the kinetics curves for simple and allosteric enzymes Enzymes following Michaelis-Menten kinetics show hyperbolic curves when the initial reaction velocity (v0) of the reaction is plotted against substrate concentration. In contrast, allosteric enzymes generally show sigmoidal curves. 

Another type of kinetic behavior that is very common for enzyme-catalyzed reactions (Michaelis-Menten kinetics) has also been observed in a number of homogeneous catalytic systems. The rate expression in such cases is given by... 

If an enzyme obeys Michaelis-Menten kinetics, a plot of the reciprocal of the reaction velocity 1/v as a function of the reciprocal of the substrate concentration 1/[S] will fit a straight line. The slope of the line is KJV m. The intercept on the vertical axis is The intercept on the horizontal... 

With respect to acetyl-L-alanine, the substrate of the hydrolysis reaction, the enzyme exhibits Michaelis-Menten kinetics (Fig. 7-19 A). The hydrolysis activity is inhibited by acetate (Fig. 7-19 B) and L-alanine (Fig. 7-19 C). These are the substrates of the synthesis reaction (see below) acting as inhibitory products. 

The products of the reaction they catalyze may inhibit many enzymes through Michaelis-Menten kinetic retroaction. Protons, which are involved as products or reactants in a number of cases, may also influence the enzymatic kinetics. The course of the reaction may therefore be altered by the attending production or depletion of protons. It is thus interesting to examine whether these phenomena may be revealed by the effect they might have on the electrochemical responses of immobilized enzyme films under appropriate conditions [92]. A first clue of the existence of such inhibition effects is the observation of hysteresis behaviors of the type shown in Fig. 18(a) where data obtained with 10 glucose oxidase monolayers with ferrocene methanol as cosubstrate have been taken as example. In the absence of inhibition, the forward and reverse traces should be exactly superimposed. Hysteresis increases to the point of making a peak appear on the forward trace as the scan rate decreases and as the concentration of the buffer decreases, as illustrated in Fig. 18c, c , c , c by comparison with Fig. 18(a). 

The simplest model for any catalytic reaction is the one most commonly used for enzymes—the Michaelis-Menten kinetic model. As previously shown in Figure 9.3, the sub-... 

Fig. 2.28. The effect of substrate concentration on the catalytic reaction rate, a Enzyme obeying Michaelis-Menten kinetics b allosterically regulated enzyme with positive cooperativity c allosterically regulated enzyme with negative cooperativity...

Not all enzymes obey Michaelis-Menten kinetics. The experimental dependence of the reaction rate on the substrate concentration is different from Michaehs-Menten type of concentration-substrate curves and follows a sigmoidal, or S-shaped, curve. 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The initial reaction rate (v0) obtained from each substrate concentration was fitted to Michaelis-Menten kinetics using enzyme kinetics. Pro (EKP) Software (ChemSW product,... 

Runge-Kutta. Consider the disappearance of substrate in an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics ... 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

The initial condition for [SE] assumes that the enzyme was charged to the reactor in pristine condition. It makes no difference whether the enzyme is free or immobilized provided the reaction follows Michaelis-Menten kinetics. 

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. ... 

Let us consider the determination of two parameters, the maximum reaction rate (rITOIX) and the saturation constant (Km) in an enzyme-catalyzed reaction following Michaelis-Menten kinetics. The Michaelis-Menten kinetic rate equation relates the reaction rate (r) to the substrate concentrations (S) by... 

Quite often the asymptotic behavior of the model can aid us in determining sufficiently good initial guesses. For example, let us consider the Michaelis-Menten kinetics for enzyme catalyzed reactions,... 

Pyruvate kinase (PK) is one of the three postulated rate-controlling enzymes of glycolysis. The high-energy phosphate of phosphoenolpyruvate is transferred to ADP by this enzyme, which requires for its activity both monovalent and divalent cations. Enolpyruvate formed in this reaction is converted spontaneously to the keto form of pyruvate with the synthesis of one ATP molecule. PK has four isozymes in mammals M, M2, L, and R. The M2 type, which is considered to be the prototype, is the only form detected in early fetal tissues and is expressed in many adult tissues. This form is progressively replaced by the M( type in the skeletal muscle, heart, and brain by the L type in the liver and by the R type in red blood cells during development or differentiation (M26). The M, and M2 isozymes display Michaelis-Menten kinetics with respect to phosphoenolpyruvate. The Mj isozyme is not affected by fructose-1,6-diphosphate (F-1,6-DP) and the M2 is al-losterically activated by this compound. Type L and R exhibit cooperatively in... 

In the presence of sucrose alone as the single substrate, initial reaction rates follow Michaelis-Menten kinetics up to 200 mM sucrose concentration, but the enzyme is inhibited by higher concentrations of substrate.30 The inhibitor constant for sucrose is 730 mM. This inhibition can be overcome by the addition of acceptors.31,32 The enzyme activity is significantly enhanced, and stabilized, by the presence of dextran, and by calcium ions. 

Most catalytic cycles are characterized by the fact that, prior to the rate-determining step [18], intermediates are coupled by equilibria in the catalytic cycle. For that reason Michaelis-Menten kinetics, which originally were published in the field of enzyme catalysis at the start of the last century, are of fundamental importance for homogeneous catalysis. As shown in the reaction sequence of Scheme 10.1, the active catalyst first reacts with the substrate in a pre-equilibrium to give the catalyst-substrate complex [20]. In the rate-determining step, this complex finally reacts to form the product, releasing the catalyst... 

Because of the complexity of biological systems, Eq. (1) as the differential form of Michaelis-Menten kinetics is often analyzed using the initial rate method. Due to the restriction of the initial range of conversion, unwanted influences such as reversible product formation, effects due to enzyme inhibition, or side reactions are reduced to a minimum. The major disadvantage of this procedure is that a relatively large number of experiments must be conducted in order to determine the desired rate constants. 

Enzyme mimics catalyze reactions by mechanisms which are demonstrably enzyme-like. The minimum requirement is that the reactions concerned should involve an initial binding interaction between the substrate and the catalyst. This gives rise to Michaelis-Menten kinetics reactivity is measured in terms of the familiar parameters kCat and Km and we use E to denote enzyme mimic as well as enzyme. ... 

MS is lower than that of M the system is in the regime of substrate saturation addition of more S does not lead to a rate increase. The behaviour of the reaction rate in case B is typical of enzymes and in biochemistry this is referred to as Michaelis-Menten kinetics. The success of the application of the Michaelis-Menten kinetics in biochemistry is based on the fact that indeed only two reactions are involved the complexation of the substrate in the pocket of the enzyme and the actual conversion of the substrate. Usually the exchange of the substrate in the binding pocket is very fast and thus we can ignore the term k2[H2] in the denominator. Complications arise if the product binds to the binding site of the enzyme, product inhibition, and more complex kinetics result. 

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