Hyperbolic inhibition reactions

Let us, now, depart from monosubstrate reactions and turn our attention to a much more realistic case of a hyperbolic inhibition in bisubstrate reactions (Segel, 1975 Dixon Webb, 1979 f rich Allison, 2000). In the rapid equilibrium reaction (6.14), A and B are the substrates while I is a nonexclusive inhibitor ... 

For a monosubstrate reaction, the kinetic model is analogous to a general model for a nonlinear hyperbolic inhibition, described in Chapter 6 (Section 6.1) ... 

Flo. 16. Hyperbolic and sigmoidal inhibition curves. The velocity of the inhibited reaction (v is expressed in percent of the velocity of the uninhibited reaction (v) and is plotted against inhibitor concentration. 

Full and partial competitive inhibitory mechanisms, (a) Reaction scheme for full competitive inhibition indicates binding of substrate and inhibitor to a common site, (b) Lineweaver-Burk plot for full competitive inhibition reveals a common intercept with the 1/v axis and an increase in slope to infinity at infinitely high inhibitor concentrations. In this example, Ki = 3 pM. (c) Replot of Lineweaver-Burk slopes from (b) is linear, confirming a full inhibitory mechanism, (d) Reaction scheme for partial competitive inhibition indicates binding of substrate and inhibitor to two mutually exclusive sites. The presence of inhibitor affects the affinity of enzyme for substrate and the presence of substrate affects the affinity of enzyme for inhibitor, both by a factor a. (e) Lineweaver-Burk plot for partial competitive inhibition reveals a common intercept with the 1/v axis and an increase in slope to a finite value at infinitely high inhibitor concentrations. In this example, Ki = 3 pM and = 4. (f) Replot of Lineweaver-Burk slopes from (e) is hyperbolic, confirming a partial inhibitory mechanism... 

Figure Cl. 1.2 shows a typical time course resulting from a continuous assay of product formation in an enzyme-catalyzed reaction. The hyperbolic nature of the curve illustrates that the reaction rate decreases as the reaction nears completion. The reaction rate, at any given time, is the slope of the line tangent to the curve at the point corresponding to the time of interest. Reaction rates decrease as reactions progress for several reasons, including substrate depletion, reactant concentrations approaching equilibrium values (i.e., the reverse reaction becomes relevant), product inhibition, enzyme inactivation, and/or a change in reaction conditions (e.g., pH as the reaction proceeds). With respect to each of these reasons, their effects will be at a minimum in the initial phase of the reaction—i.e., under conditions corresponding to initial velocity measurements. Hence, the interpretation of initial velocity data is relatively simple and thus widely used in enzyme-related assays.

Another example of reactions that can be described by Figure 7 is the effect of dapsone on naproxen metabolism by CYP2C9. In this case, dapsone makes the biphasic naproxen curve more hyperbolic. Finally, one can expect similar influences on reactions that show substrate inhibition. If ESB has a metabolic rate similar to ES, one would expect activation at high substrate concentrations. Conversely, if the rate is similar to ESS, inhibition would be expected at intermediate substrate concentrations, with little effect at Vm. 

MichaeUs-Menten kinetics predict that as the concentration of the substrate increases, the rate increases hyperbolically. However, some enzymes exist in which a maximum velocity is obtained at low substrate concentration, but further increases in the substrate concentration lead to a decrease in velocity. This effect is known as substrate inhibition and can eventually lead to complete enzyme inhibition or partial enzyme inhibition. It is thought that substrate inhibition occurs if two substrate molecules bind to the enzyme simultaneously in an incorrect orientation and produce an inactive E S S complex, analogous to that discussed for uncompetitive inhibition. The rate of the enzyme reaction that undergoes substrate inhibition is given by Equation 17, where K represents the... 

In the presence of activator, pyruvate, the substrate saturation curves of the R. ruhrum ADP-Glc PPase are hyperbolic at low temperatures. Using kinetic studies its reaction mechanism was studied. The product inhibition patterns eliminated all known sequential mechanisms except the ordered BiBi or Theorell—Chance mechanisms. Small intercept effects suggested the existence of significant concentrations of central transis-tory complexes. Kinetic constants obtained in the study also favored the ordered BiBi mechanism. In addition studies using ATP-[ P]-pyrophosphate isotope exchange at equilibrium supported a sequential-ordered mechanism, which indicated that ATP is the first substrate to bind and that ADP-Glc is the last product to... 

Substrate Inhibition Substrate inhibition represents another example of cooperativity in enzyme kinetic reactions, but of a different profile than described to this point. With substrate inhibition kinetics, the velocity of a reaction increases (as expected for hyperbolic profiles) to an apex, however, beyond this point the velocity of the reaction decreases with increasing substrate concentrations (Fig. 4.7). 

FIGURE 4.9 Eadie-Hofstee plots useful to diagnose the type of kinetics occurring in a reaction for (a) hyperbolic (Michaelis-Menen) kinetics, (b) Sigmoidal kinetics, (c) Biphasic kinetics with no saturation of second phase, and (d) Substrate inhibition kinetics. 

Thymidine kinase serves as a salvage reaction in the phosphorylation of thymidine to yield dTMP. Its activity is under allosteric control as revealed by Okazaki and Kornberg with a highly purified preparation from E. coli [186]. Sigmoidal kinetics are obtained with ATP as substrate, and this is converted to a hyperbolic form by dCDP which functions as an activator. The affinity for thymidine is also increased by dCDP. Feedback inhibition is obtained with dTTP, the end product of the pathway. Inhibition by dTTP is competitive with the phosphate acceptor, thymidine, and noncompetitive with the donor, ATP. The kinetics of inhibition in the presence of the activator are difficult to interpret in terms of a simple competition between dTTP and dCDP for an allosteric site. This type of control apparently serves the same function as that described for dCMP deaminase above where the activity of the enzyme is decreased by the end product, dTTP, and increased when other deoxyribonucleotides accumulate. 

If the human enzyme is not saturated with glutamine, variations in glutamine concentrations would be expected to affect the rate of purine biosynthesis, although less exquisitely than variations in concentrations of PP-ribose-P. The kinetics of the amidotransferase reaction are hyperbolic with respect to glutamine at all levels of PP-ribose-P, in the presence or absence of nucleotide inhibitors [47,63]. Purine ribonucleotide inhibition is non-competitive with respect to glutamine [47,63] and glutamine does not reverse the association of amidotransferase subunits caused by ribonucleotides [48]. 

To make an appropriate assessment of the pattern of inhibition, one need only compare the pattern of reaction velocity versus [S] observed relative to the pattern predicted from an application of the hyperbolic kinetics model. This requires making an estimate of V ax and from the data available. Transforming the original data to a Lineweaver-Burke plot (despite the aforementioned limitations) indicates that only four data points (at low [S]) can be used to estimate Vmax and Km (as 3.58 units and 0.48 mM, respectively. Fig. 14.10). The predicted (uninhibited) behavior of the enzyme activity can now be calculated by applying the rectangular hyperbola [Eq. (14.5)] (yielding the upper curve in Fig. 14.11), and it becomes clear that inhibition was obvious at [S] <1 mM. The degree of inhibition is expressed appropriately as the difference between observed and predicted activity at any [S] value, if one makes interpretations within the context of the Michaelis-Menten model. 

A useful explanation for the function of HS chains is that they catalyze molecular interactions between proteins, as seen most commonly in the inhibition of thrombin by the serpin antithrombin III [23, 24]. The idea is that the HS chain provides a surface to which both proteins bind and thus will encounter each other at a much more rapid rate than they would in solution. This effect of reduced dimensionality can explain both the acceleration of molecular interactions and the hyperbolic effect of the HS chain on the reaction [24]. 

DPG. In order to elucidate whether the hyperbolic response of the mutant PRPP synthetase to increasing phosphate concentration in hemolysate reflects an abnormal response to inhibitors, a system devoid of inhibitors was employed. Using stroma-free charcoal-adsorbed hemolysate treated with DEAE-cellulose, the difference in reaction to increasing inorganic phosphate concentration between the mutant enzyme and the normal enzyme disappeared both exhibiting a hyperbolic response (Fig. 2). It was furthermore found that the mutant enzyme had a decreased sensitivity to inhibition by GDP, ADP,... 

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