Saturation curve hyperbolic

Referring to an enzyme whose kinetic properties do not yield hyperbolic saturation curves in plots of the initial rate as a function of the substrate concentration. 

Allosteric enzymes show relationships between V0 and [S] that differ from Michaelis-Menten kinetics. They do exhibit saturation with the substrate when [S] is sufficiently high, but for some allosteric enzymes, plots of V0 versus [S] (Fig. 6-29) produce a sigmoid saturation curve, rather than the hyperbolic curve typical of non-regulatory enzymes. On the sigmoid saturation curve we can find a value of [S] at which V0 is half-maximal, but we cannot refer to it with the designation Km, because the enzyme does not follow the hyperbolic Michaelis-Menten relationship. Instead, the symbol [S]0 e or K0,5 is often used to represent the substrate concentration giving half-maximal velocity of the reaction catalyzed by an allosteric enzyme (Fig. 6-29). 

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). 

In the absence of activators AMP aminohydrolase from brain (149), erythrocytes (143, 150), muscle (145), and liver (128) gave sigmoid curves for velocity vs. AMP concentration which were hyperbolic after the addition of monovalent cations, adenine nucleotides, or a combination of monovalent cations and adenine nucleotides. For the rabbit muscle enzyme (145), addition of K+, ADP, or ATP produced normal hyperbolic saturation curves for AMP as represented by a change in the Hill slope nH from 2.2 to 1.1 Fmax remained the same. The soluble erythrocyte enzyme and the calf brain enzyme required the presence of both monovalent cations and ATP before saturation curves became hyperbolic. In contrast, the bound human erythrocyte membrane enzyme did not exhibit sigmoid saturation curves and K+ activation was not affected by ATP (142). 

The hyperbolic saturation curve that is commonly seen with enzymatic reactions led Leonor Michaelis and Maude Men-ten in 1913 to develop a general treatment for kinetic analysis of these reactions. Following earlier work by Victor Henri, Michaelis and Menten assumed that an enzyme-substrate complex (ES) is in equilibrium with free enzyme... 

In this equation, a hyperbolic saturation curve is described by two constants, Vm and Km. In the simple example in Figure IB, v is velocity, Vm is simply [EJ and Km is (k2 + 23) 12- Umax (or Vm) is the reaction velocity at saturating concentrations of substrate, and Km is the concentration of the substrate that achieves half the maximum velocity. Although the constant Km is the most useful descriptor of the affinity of the substrate for the enzyme, it is important to note the difference between Km and Kh. Even for the simplest reaction scheme (Fig. IB), the Km term contains the rate constant for conversion of substrate to product ( 23) If the rate of equilibrium is fast relative to k23, then Km approaches Kh. 

Substrate A has a hyperbolic saturation curve Enzymes that bind to only one substrate molecule will show hyperbolic saturation kinetics. However, the observation of hyperbolic saturation kinetics does not necessarily mean that only one substrate molecule is interacting with the enzyme (see discussion of non-Michaelis-Menten kinetics in sec. IV). 

Figure 4 Effect of quinine on the carbamazepine saturation curve. Quinine makes the sigmoidal saturation curve more hyperbolic. Source Courtesy of K. Nandigama and K. Korzekwa (unpublished results).

Two other examples of sigmoidal reactions that are made linear by an activator include a report by Johnson et al. (31), who showed that pregnenolone has a nonlinear double-reciprocal plot that was made linear by the presence of 5 pM 7,8-benzoflavone, and Ueng et al. (23), who showed that aflatoxin B1 has sigmoidal saturation curve that is made more hyperbolic by 7,8-benzoflavone. As with the effect of quinine on carbamazepine metabolism, 7,8-benzoflavone is an activator at low aflatoxin B1 concentrations and an inhibitor at high aflatoxin B1 concentrations. 

The shape of the saturation curve defined by Eq. (9.59) depends on the values of L and c. If L = 0, then the T form of the protein does not exist and Y = XR[X]/(1 + XR[X]). This defines a hyperbolic binding function. Similarly if L = Y = XT[X]/(1 + XT[X]). Thus, deviations from hyperbolic binding occur only if both R and T forms exist otherwise the situation described for the Adair equation in Example 9.13 applies since binding is independent and identical at each site. 

Figure 2-13. Oxygen saturation curves for myoglobin and adult hemoglobin (HbA). Myoglobin has a hyperbolic saturation curve. HbA has a sigmoidal curve. The HbA curve shifts to the right at lower pH, with higher concentrations of 2,3-bisphosphoglycerate (BPG), or as C02 binds in the tissues. Thus, 02 is released more readily. P50 ( ) is the partial pressure of 02 at which HbA is half-saturated with 02.

Figure 5. Saturation kinetics the dependence of enzyme catalysis on the concentration of substrate. Reaction velocity represents the rate at which product is formed. (A) shows a hyperbolic saturation curve for two hypothetical enzymes. One binds its substrate more tightly than the other and reaches saturation at lower substrate concentration. This enzyme has a lower value, the substrate concentration where the reaction is half of maximum. The other binds the substrate more loosely and reaches the same velocity but requires higher substrate concentrations. (B) shows hypothetical velocities for cooperative enzymes. Although more complex, these enzymes also show the phenomenon of saturation.

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... 

Irrespective of the interpretative approach, it is now widely recognised that many enzymes do show marked deviations from Michaelis-Menten behaviour, and the deviation is often interpretable in terms of regulatory function in vivo. Thus, for example, a number of enzymes, including threonine deaminase [30] and aspartate transcarbamylase [31] as textbook cases, show a sigmoid, rather than hyperbolic dependence of rate upon substrate concentration. This, like the oxygen saturation curve of haemoglobin, permits a response to changes in substrate concentration... 

FIGURE 16.1 Hyperbolic saturation curve of CYP2C19-catalyzed (5)-mephenytoin 4 -hydroxylation in human liver microsomes. Am and Vmax values were calculated with Equation 16.1 (Am = 23.7 2.15 jlM and Fmax = 0.36 0.01 nmol/min/mg). Data were fitted by nonlinear regression (Eq. 16.1, SigmaPlot 9.0). 

ATP saturation curve changes to hyperbolic in the presence of activator. Both inhibitory and activating nucleotides appear to induce dimerization of the enzyme, a step thought to be necessary for the enzyme to assume active or inactive conformations in response to the nucleotide effectors (49). 

Consequently, substrate saturation curves are sigmoid instead of hyperbolic. CTP exerts its inhibitory effect by increasing the interaction between the four catalytic binding sites, which decreases the affinity of the enzyme for the substrate. 

The rate of PP-ribose P synthesis in the dialyzed supernatant increases almost linearly with ribose-5-P concentration in the absence of ATP and of an ATP regenerating system (Fig. lA). There is nearly no PP-ribose-P synthesized from ribose-l-P under these conditions (Fig. IB). In the presence of phosphoenolpyruvate and pyruvate kinase, but without any addition of ATP, both substrate saturation curves are hyperbolic. The apparent Km of PP-ribose-P synthetase for ribose-5-P is 224 57 yM, and the apparent V ax is 48.7 5.6 nmoles per h per mg protein. Similar values are measured in the presence of ribose-l-P. However, it is not a substrate for the PP-ribose-P S3mthetase purified from rat liver (1). Ribose-l-P is probably converted first to ribose-5-P by a phosphoribomutase which is present in rat liver (4). 

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