Enzymes hyperbolic saturation curve

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. 

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 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.

A parameter used to assess the degree of cooperativity exhibited by an enzyme ". Rs equals the ratio of [S]o.9/ [S]o.o9 that is, the ratio of the substrate concentration needed for 90% saturation divided by the substrate concentration needed for 10% saturation. For a normal, hyperbolic, noncooperative curve, Rs equals 81. Thus, positively cooperative systems will have an Rs ratio less than 81, whereas negatively cooperative systems will have values larger than 81. The ratio is insensitive to the shape of the curve and does not address any questions concerning the substrate concentration range between the 10% and 90% points. 

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). 

At low substrate concentrations ([S]) a doubling of [S] leads to a doubling of VQ, whereas at higher [S] the enzyme becomes saturated and there is no further increase in V0. A graph of V(l against [S] will give a hyperbolic curve. 

For a given amount of enzyme, the reaction rate increases as substrate is added up to the point where the enzyme is saturated with substrate, the Em ax. For most enzymes, the shape of the curve of reaction rate as a function of substrate concentration is hyperbolic, as described by the Michaelis-Menten equation. 

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... 

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. 

In the semilogarithmic plot (Figure 112.1a), the curves have the same sigmoidal shape and differ only by lateral displacement. The symmetrical sigmoidal shape is a property of the hyperbolic saturation function, which is frequently used to fit fluence-response curves and other types of stimulus-response relationships in sensory physiology, - in photochemical kinetics, and in other areas of biophysics and biology, including the well-known MichaeHs-Menten enzyme kinetics (see below). 

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-... 

Calibration is necessary for in-situ spectrometry in TLC. Either the peak height or the peak area data are measured, and used for calculation. Although the nonlinear calibration curve with an external standard method is used, however, it shows only a small deviation from linearity at small concentrations [94.95 and fulfils the requirement of routine pharmaceutical analysis 96,97J. One problem may be the saturation function of the calibration curve. Several linearisation equations have been constructed, which serve to calculate the point of determination on the basis of the calibration line and these linearisation equations are used in the software of some scanners. A more general problem is the saturation function of the calibration curve. It is a characteristic of a wide variety of adsorption-type phenomena, such as the Langmuir and the Michaelis-Menten law for enzyme kinetics as detailed in the literature [98. Saturation is also evident for the hyperbolic shape of the Kubelka-Munk equation that has to be taken into consideration when a large load is applied and has to be determined. 

Figure 7.3 shows the binding behavior of a typical antibody as a function of ligand concentration. The form of this hyperbolic curve is similar to figure 7.1, the pattern for enzyme kinetics. Antibodies also show saturation behavior at... 

---