Substrate saturation

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

FIGURE 15.11 Heterotropic allosteric effects A and I binding to R and T, respectively. The linked equilibria lead to changes in the relative amounts of R and T and, therefore, shifts in the substrate saturation curve. This behavior, depicted by the graph, defines an allosteric K system. The parameters of such a system are (1) S and A (or I) have different affinities for R and T and (2) A (or I) modifies the apparent for S by shifting the relative R versus T population. 

The converse situation applies in the presence of I, which binds only to T. T binding will lead to an increase in the population of T conformers, at the expense of Rq (Figure 15.11). The decline in [Rq] means that it is less likely for S (or A) to bind. Consequently, the presence of I increases the cooperativity (that is, the sigmoidicity) of the substrate saturation curve, as evidenced by the shift of this curve to the right (Figure 15.11). The presence of I raises the apparent value of L. 

In this form, Alhas the units of torr.) The relationship defined by Equation (A15.4) plots as a hyperbola. That is, the MbOg saturation curve resembles an enzyme substrate saturation curve. For myoglobin, a partial pressure of 1 torr for jbOg is sufficient for half-saturation (Figure A15.1). We can define as the partial pressure of Og at which 50% of the myoglobin molecules have a molecule of Og bound (that is, F= 0.5), then... 

Figure 8-6. Representation of sigmoid substrate saturation kinetics.

To refer to the kinetics of allosteric inhibition as competitive or noncompetitive with substrate carries misleading mechanistic implications. We refer instead to two classes of regulated enzymes K-series and V-se-ries enzymes. For K-series allosteric enzymes, the substrate saturation kinetics are competitive in the sense that is raised without an effect on V. For V-series allosteric enzymes, the allosteric inhibitor lowers... 

The question arises as to whether comparisons with protein enzymes are justified. In other words, what can ribozymes really do An important parameter for measuring the efficiency of enzymes is the value of kc-JK. This quotient is derived from the values of two important kinetic parameters kc-Al is a rate constant, also called turnover number, and measures the number of substrate molecules which are converted by one enzyme molecule per unit time (at substrate saturation of the enzyme). Km is the Michaelis-Menten constant it corresponds to the substrate concentration at which the rate of reaction is half its maximum. 

The enzymatic activities of intercalated GOx-AM P layered nanocomposites at various pH values and temperatures were compared with the native enzyme in aqueous solution. In both cases, characteristic linear plots consistent with Michalis-Menton kinetics were obtained. The Lineweaver-Burk plots indicated that the reaction rates (Vmax) for free and intercalated GOx (3.3 and 4.0 pM min 1 respectively), were comparable, suggesting that the turnover rate at substrate saturation was only marginally influenced by entrapment between the re-assembled organoclay sheets. However, the dissociation constant (Km) associated with the activity of the enzyme was higher for intercalated GOx (6.63 mM) compared to native GOx (2.94 mM), suggesting... 

Figure 38, Chapter 3. A bifurcation diagram for the model of the Calvin cycle with product and substrate saturation as global parameters. Left panel Upon variation of substrate and product saturation (as global parameter, set equalfor all irreversible reactions), the stable steady state is confined to a limited region in parameter space. All other parameters fixed to specific values (chosen randomly). Right panel Same as left panel, but with all other parameters sampled from their respective intervals. Shown is the percentage r of unstable models, with darker colors corresponding to a higher percentage of unstable models (see colorbar for numeric values).

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. 

Several catalases, including the type B catalase-peroxidases, seem to show true substrate saturation at much lower levels of peroxide than originally observed for the mammalian enzyme (in the range of a few millimolar). This means that the limiting maximal turnover is less and the lifetime of the putative Michaelis-Menten intermediate (with the redox equivalent of two molecules of peroxide bound) is much longer. The extended scheme for catalase in Fig. 2B shows that relationships between free enzyme and compound I, and the presumed rate-limiting ternary complex with least stability or fastest decay in eukaryotic enzymes of type A and greatest stability or slowest decay in prokaryotic type B enzymes. 

In contrast to the kinetics of isosteric (normal) enzymes, allosteric enzymes such as ACTase have sigmoidal (S-shaped) substrate saturation curves (see p. 92). In allosteric systems, the enzyme s af nity to the substrate is not constant, but depends on the substrate concentration [A]. Instead of the Michaelis constant Km (see p. 92), the substrate concentration at half-maximal rate ([AJo.s) is given. The sigmoidal character of the curve is described by the Hill coef cient h. In isosteric systems, h = 1, and h increases with increasing sigmoid icity. 

Figure 3. Computed three-dimensional free energy diagram for proline racemase x-axis, the reaction coordinate y-axis, free energy and z-axis, substrate saturation. At the front of the diagram, [S] = [P] = 1 /aM, where the enzyme is unsaturated at the back of the diagram, [S] = [P] = 1 M, where the enzyme is oversaturated. Reproduced from reference 9 with permission of the authors and the American Chemical Society.

R . The extent of substrate saturation of two Michaelis-Menten enzymes with different values will be identical if their R values are the same. For example, if R = 1, then v/ymax = 0.5 for both enzymes. Likewise, R values of 5 and 10 yield respective velocities of... 

Correction for endogenous substrate present in enzyme preparations is difficult. Measuring the endogenous rate (obtained by omitting the substrate involved) and subtracting this from the overall rate is generally incorrect (R5). Due to the nonlinearity of the substrate saturation curve, the endogenous rate will be more important in the control mixture than... 

Obviously, extrapolation procedures are impractical for routine determination of enzyme activities. When substrate saturation-curves conform to rectangular hyperbolas, reasonable concentrations of substrates should equal 10 to 20 times the respective Km values. As outlined above, application of this rule to assays of bilirubin UDP-glycosyltransferase activities is hampered by substrate inhibition and by occasional deviation from Michaelis-Menten kinetics. The best alternative in such cases may be to choose the concentrations at optimal enzyme activity. However, great care should be exercised in interpreting the results. When a bio-... 

The first product of nitrosyl transfer to nitrite in Eq. (2), E N203, contains N-N bonded N2O3 which is itself a well-known and powerful nitrosyl donor. It is reasonable to suppose therefore that nitrosyl transfer reactions with N- and O-nucleophiles could involve both E NO (or E HONO) and E N205. In addition, the involvement of a second molecule of nitrite for denitrification would require that the substrate saturation curve should be sigmoidal to reflect a term second-order in nitrite concentration. No such effect has been reported to our knowledge. The use of bimolecular substrate kinetics in dilute solutions to generate an intermediate subject to solvolysis seems metabolically unwise hut not impossible. 

We conclude that the neutral substrate enters 1 to form a host-guest complex, leading to the observed substrate saturation. The encapsulated substrate then undergoes encapsulation-driven protonation, presumably by deprotonation of water, followed by acid-catalyzed hydrolysis inside 1, during which two equivalents of the corresponding alcohol are released. Finally, the protonated formate ester is ejected from 1 and further hydrolyzed by base in solution. The reaction mechanism (Scheme 7.7) shows direct parallels to enzymes that obey Michaelis-Menten kinetics due to the initial pre-equilibrium followed by a first-order rate-limiting step. 

Lineweaver-Burk analysis using the substrate saturation curves afforded the corresponding Michaelis-Menten kinetic parameters of the reaction V max=l-79 xIO- Ms , KM=21.5mM, kcat = 8.06x 10 s for 69, and Knax = 9.22x 10... 

For heterotropic allosteric enzymes, those whose modulators are metabolites other than the normal substrate, it is difficult to generalize about the shape of the substrate-saturation curve. An activator may cause the curve to become more nearly hyperbolic, with a decrease in Z0.5 but no change in Fmax, resulting in an increased reaction velocity at a fixed substrate concentration (V0 is higher for any value of [S] Fig. 6-29b, upper curve). 

Other heterotropic allosteric enzymes respond to an activator by an increase in Fmax with little change in if0i5 (Fig. 6-29c). A negative modulator (an inhibitor) may produce a more sigmoid substrate-saturation curve,... 

Here Et is the total enzyme, namely, the free enzyme E plus enzyme-substrate complex ES. The equation holds only at substrate saturation, that is, when the substrate concentration is high enough that essentially all of the enzyme has been converted into the intermediate ES. The process is first order in enzyme but is zero order in substrate. The rate constant k is a measure of the speed at which the enzyme operates. When the concentration [E]t is given in moles per liter of active sites (actual molar concentration multiplied by the number of active sites per mole) the constant k is known as the turnover number, the molecular activity, or kcat. The symbol fccat is also used in place of k in Eq. 9-6 for complex rate expressions in which fccat cannot represent a single rate constant but is an algebraic expression that contains a number of different constants. 

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