Maximum enzyme velocity

Equation (3-150) is the Michaelis-Menten equation, Vm is the maximum velocity (for the enzyme concentration ,), and is the Michaelis constant. 

The immobilization procedure may alter the behavior of the enzyme (compared to its behavior in homogeneous solution). For example, the apparent parameters of an enzyme-catalyzed reaction (optimum temperature or pH, maximum velocity, etc.) may all be changed when an enzyme is immobilized. Improved stability may also accrue from the minimization of enzyme unfolding associated with the immobilization step. Overall, careful engineering of the enzyme microenvironment (on the surface) can be used to greatly enhance the sensor performance. More information on enzyme immobilization schemes can be found in several reviews (7,8). 

The term Vmax refers to the maximum velocity obtained at infinite substrate concentration. VW is mathematically equivalent to the product of kC3) and the enzyme concentration ... 

Thus from Equation (2.13) we see that a working definition of KM is the substrate concentration that yields a velocity equal to half of the maximum velocity. Stated another way, the Ku is that concentration of substrate leading to half saturation of the enzyme active sites under steady state conditions. 

This equation is fundamental to all aspects of the kinetics of enzyme action. The Michaelis-Menten constant, KM, is defined as the concentration of the substrate at which a given enzyme yields one-half of its maximum velocity. is the maximum velocity, which is the rate approached at infinitely high substrate concentration. The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It provides the quantitative calculation of enzyme characteristics and the analysis for a specific substrate under defined conditions of pH and temperature. KM is a direct measure of the strength of the binding between the enzyme and the substrate. For example, chymotrypsin has a Ku value of 108 mM when glycyltyrosinylglycine is used as its substrate, while the Km value is 2.5 mM when N-20 benzoyltyrosineamide is used as a substrate... 

Monophenolase activity shows a characteristic lag period before the maximum velocity of the hydroxylation step is reached. The time required to reach the steady-state rate depends on several factors enzyme source concentration of monophenol ... 

In none of the cases mentioned were substrates that were polymerized to different degrees used at equimolar concentrations, so that, in some cases, it is not clear to what extent the differences in the rate of cleavage reflect the effective concentration of the terminal bonds (as assumed by Mill154) and to what extent they reflect the differences in the enzyme reaction-mechanism. More satisfactory information would be obtainable by comparing the values of the maximum velocities. 

The true concentration of enzyme is difficult to measure especially in terms of molar concentration but if the substrate concentration is large compared with that of the enzyme, all of the enzyme will be present as the ES complex and the reaction will proceed at maximum velocity. Under these conditions of excess substrate and maximum velocity (Vmax) ... 

The value for the maximum velocity is related to the amount of enzyme used but the Michaelis constant is peculiar to the enzyme and is a measure of the activity of the enzyme. Enzymes with large values for Km show a reluctance to dissociate from the substrate and hence are often less active than enzymes with low Km values. The substrate concentration required for a particular enzyme assay is related to and when developing an assay, the value for Km should be determined. 

Not all inhibitors fall into either of these two classes but some show much more complex effects. An uncompetitive inhibitor is defined as one that results in a parallel decrease in the maximum velocity and the Km value (Figure 8.8). The basic mode of action of such an inhibitor is to bind only to the enzyme-substrate complex and not to the free enzyme and so it reduces the rate of formation of products. Alkaline phosphatase (EC 3.1.3.1) extracted from rat intestine is inhibited by L-phenylalanine in such a manner. 

Figure 8.7 The kinetic effects of a non-competitive inhibitor. The effect of a noncompetitive inhibitor is not reversed by high concentrations of substrate and the enzyme reaction shows a reduced value for the maximum velocity. The enzyme remaining is unaltered and gives the same value for the Michaelis constant as originally shown by the uninhibited enzyme.

To achieve maximum velocity, a substrate concentration which is at least ten times greater than the Km value for the enzyme should be used. Although maximum velocity is only theoretically achieved at an infinite substrate concentration, it is possible using the Michaelis-Menten equation to calculate the percentage of maximum velocity given by any concentration of substrate. For a substrate concentration of ten times greater than the Km value the velocity (v) achieved will be ... 

Lineweaver-Burk plot (Figure 8.11). In such cases the chosen substrate concentration must give the highest reaction velocity possible. It is important, when describing any enzyme assay, to report the percentage maximum velocity which the method will give. 

The relative rates of formation and dissociation of [ES] is denoted as Km, the Michaelis constant. Each enzyme/substrate combination has a Km value under defined conditions. Numerically, the Km is the substrate concentration required to achieve 50% of the maximum velocity of the enzyme the unit for Km is therefore the same as the unit for substrate concentration, typically )Xmol/l or mmol/1. The maximum velocity the enzyme-catalysed reaction can achieve is expressed by the Vmax typical unit Llmol/min. The significance of Km and Vmax will be discussed in greater detail in Chapter 2. 

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

An obvious consequence of signal binding to a defined region of the receptor is that the number of engagements is limited by the number of receptors. Once a signal concentration is reached that exceeds that number of receptors, the cell will be maximally stimulated. Here then we have another analogy with enzymes the maximum velocity of the reaction (Vmax) occurs when the enzyme is saturated with substrate (Figure 4.12). 

Other 4-nitrophenyl esters have also been reported to be substrates of various hydrolases. For example, 4-nitrophenyl hexanoate (7.19) was hydrolyzed by bovine serum albumin [39], The affinity of the substrate for the macromolecule was found to be high (Km/n = 0.040 mM, where n is the number of sites), but the reaction itself was slow ( = 5 10-3 s-1, where k2 is the first-order rate constant of the formation of the phenol product from the enzyme-substrate complex). Another ester, 4-nitrophenyl pivalate (7.20), was hydrolyzed by cytoplasmic aldehyde dehydrogenase at a maximum velocity ca. 1/3 and an affinity ca. 1/20 those of the acetate [40], However, the rate-limiting steps were different for the two substrates, namely acylation of the enzyme for the pivalate, and acyl-enzyme hydrolysis for the acetate (see Chapt. 3). 

The other constant in the equation, is often used to compare enzymes. is the substrate concentration required to produce half the maximum velocity. Under certain conditions, is a measure of the affinity of the enzyme for its substrate. When comparing two eu2ymes, the one with the higher has a lower affinity for its substrate. The value is an intrinsic property of the enzyme-substrate system and cannot be altered by changing [S] or [E]. 

Vmax = maximum velocity with a specified amount of enzyme... 

The quotient of rate constants obtained in steady-state treatments of enzyme behavior to define a substrate s interaction with an enzyme. While the Michaelis constant (with overall units of molarity) is a rate parameter, it is not itself a rate constant. Likewise, the Michaelis constant often is only a rough gauge of an enzyme s affinity for a substrate. 2. Historically, the term Michaelis constant referred to the true dissociation constant for the enzyme-substrate binary complex, and this parameter was obtained in the Michaelis-Menten rapid-equilibrium treatment of a one-substrate enzyme-catalyzed reaction. In this case, the Michaelis constant is usually symbolized by Ks. 3. The value equal to the concentration of substrate at which the initial rate, v, is one-half the maximum velocity (Lmax) of the enzyme-catalyzed reaction under steady state conditions. 

An enzyme is said to obey Michaelis-Menten kinetics, if a plot of the initial reaction rate (in which the substrate concentration is in great excess over the total enzyme concentration) versus substrate concentration(s) produces a hyperbolic curve. There should be no cooperativity apparent in the rate-saturation process, and the initial rate behavior should comply with the Michaelis-Menten equation, v = Emax[A]/(7 a + [A]), where v is the initial velocity, [A] is the initial substrate concentration, Umax is the maximum velocity, and is the dissociation constant for the substrate. A, binding to the free enzyme. The original formulation of the Michaelis-Menten treatment assumed a rapid pre-equilibrium of E and S with the central complex EX. However, the steady-state or Briggs-Haldane derivation yields an equation that is iso-... 

A plot of the rate constant, the initial velocity, the maximum velocity of a catalyzed reaction, or the ratio of an enzyme-catalyzed reaction (or the decadic logarithm of any of these quantities) as a function of the pH value of the solution, all other variables being held constant. See also pH Effects... 

The ratio of maximum velocity, F ax, or kcat value to the true value for a particular substrate, with units of a bimolecular rate constant M sIn comparing substances that act as substrates for a single enzyme, a higher Fmax/ m or kgat/ m fafio rcflects a higher apparent rate of enzyme-substrate complexation. 

The substitution of a 2-deoxy-/3-D-en/t/iro-pentofuranosyl group for the /3-D-ribofuranosyl group in the nucleoside residue is permissible thus, the 5 -(a-D-glucopyranosyl pyrophosphates) of 2 -deoxyuri-dine239,364 and thymidine357,364 are substrates for the enzyme, although their apparent KM values are about 15-fold higher than those for the uridine and 5-methyluridine derivatives, and the maximum velocities are diminished. 

If such enzymes occur at the same levels in relevant microbial populations, Vmax may be directly related to other metrics of biomass presence such as cell numbers, biomass dry weight, or protein concentrations. In an attempt to enable extending results from one system to another (e.g., from laboratory observations to field situations), one often normalizes Fmax by such biomass parameters. For example, in Table 17.7, the observed Vmax values are normalized to the protein contents of the tested microbial populations or isolated enzymes, and the result is given as values Vmax (the prime is added to emphasize the normalization). To apply such information to new situations, one must multiply the normalized maximum velocities by a measure of the relevant enzyme concentration or biomass protein in the new system of interest (e.g., Vmax x microbial protein content in new case involving intact microorganisms). Of course, one is assuming that the ratio of enzyme to total protein is the same in the old and new situation. 

This equation can be further simplified. Because the maximum velocity occurs when the enzyme is saturated (that is, with [ES] = [Et]) Vmax can be defined as k2[Et]. Substituting this in Equation 6-20 gives Equation 6-9 ... 

This is the Michaelis-Menten equation, the rate equation for a one-substrate enzyme-catalyzed reaction. It is a statement of the quantitative relationship between the initial velocity V0, the maximum velocity Vnmx, and the initial substrate concentration [S], all related through the Michaelis constant Km. Note that Km has units of concentration. Does the equation fit experimental observations Yes we can confirm this by considering the limiting situations where [S] is very high or very low, as shown in Figure 6-12. 

Equation 9-15 provides a relationship between the velocity observed at a particular substrate concentration and the maximum velocity that would be achieved at infinite substrate concentration. The quantities Vmax and Km are often referred to as the kinetic parameters of an enzyme and their determination is an important part of the characterization of an enzyme. Equation 9-15 can be derived by setting the rate of formation of the ES complex (/cl[E][S]) in the steady state equal to its rate of breakdown, ([/c2 + /c3][ES]). Rearranging and substituting Km, as defined in Eq. 9-15, we obtain Eq. 9-17. 

The maximum velocity, Vmax = /c3[E]t, is attained only when all of the enzyme is converted into ES. Under other conditions v = /c3[ES] and Eq. 9-19 holds. 

For some enzyme-catalyzed reactions the equilibrium lies far to one side. However, many other reactions are freely reversible. Since a catalyst promotes reactions in both directions, we must consider the action of an enzyme on the reverse reaction. Let us designate the maximum velocity in the forward direction as Vf and that in the reverse direction as Vr There will be a Michaelis constant for reaction of enzyme with product Kmp, while Kms will refer to the reaction with substrate. 

Tlie kinetic parameters of Eq. 9-44 are Vf, the maximum velocity in the forward direction, the two Michaelis constants, KmB and KmA, and the equilibrium constant Ke, for reversible dissociation of the complex EA and which is equal to k2/k1. The relationship between the parameters of Eq. 9-44 (Km s, V s, and KeqA s) and the rate constants /q- kw is not obvious. However, remember that the parameters are experimental quantities determined by measurements on the enzyme. Sometimes, but not always, it is possible to deduce some of the values of individual rate constants from the experimental parameters. 

A commonly used test for competitive inhibition is to plot 1 / v vs 1 / [S] (Eq. 9-61), both in the absence of inhibitor and in the presence of one or more fixed concentrations of I. The result, in each case, is a family of lines of varying slope (Fig. 9-10) that converge on one of the axes at the value 1/Vmax. We see that the maximum velocity is unchanged by the presence of inhibitor. If sufficient substrate is added, the enzyme will be saturated with substrate and the inhibitor cannot bind. The value of Kt can be calculated using Eq. 9-61 from the change in slope caused by addition of inhibitor. 

Figure 9-11 shows inhibition data for both the noncompetitive and the competitive cases plotted vs log [S]. The shift of the midpoint to the right in each case reflects the tendency of the inhibitor to exclude the substrate from binding, while the lowered value of the maximum velocity in the case of noncompetitive inhibition results from the failure of the substrate to completely displace the inhibitor from the enzyme... 

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