Michaelis-Menten kinetics curve

Figure 7-18. Michaelis-Menten kinetics curve analysis.

Ritchie, R. J., Prvan, T. (1996). A simulation study on designing experiments to measure the km of michaelis-menten kinetics curves. J. Theor. Biol. 178,239-254. 

Fig. 39.17. Schematic illustration of Michaelis-Menten kinetics in the absence of an inhibitor (solid line) and in the presence of a competitive inhibitor (dashed line), (a) Plot of initial rate (or velocity) V against amount (or concentration) of substrate X. Note that the two curves tend to the same horizontal asymptote for large values of X. (b) Lineweaver-Burk linearized plot of 1/V against l/X. Note that the two lines intersect at a common intercept on the vertical axis.

The effect of non-participating ligands on the copper catalyzed autoxidation of cysteine was studied in the presence of glycylglycine-phosphate and catecholamines, (2-R-)H2C, (epinephrine, R = CH(OH)-CH2-NHCH3 norepinephrine, R = CH(OH)-CH2-NH2 dopamine, R = CH2-CH2-NH2 dopa, R = CH2-CH(COOH)-NH2) by Hanaki and co-workers (68,69). Typically, these reactions followed Michaelis-Menten kinetics and the autoxidation rate displayed a bell-shaped curve as a function of pH. The catecholamines had no kinetic effects under anaerobic conditions, but catalyzed the autoxidation of cysteine in the following order of efficiency epinephrine = norepinephrine > dopamine > dopa. The concentration and pH dependencies of the reaction rate were interpreted by assuming that the redox active species is the [L Cun(RS-)] ternary complex which is formed in a very fast reaction between CunL and cysteine. Thus, the autoxidation occurs at maximum rate when the conditions are optimal for the formation of this species. At relatively low pH, the ternary complex does not form in sufficient concentration. 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

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-... 

MICHAELIS CONSTANT (APPARENT) MICHAELIS-MENTEN EQUATION L HOPITAL S RULE MICHAELIS CONSTANT MICHAELIS-MENTEN KINETICS PROGRESS CURVE ANALYSIS UNI UNI MECHANISM ZERO-ORDER REACTIONS MICHAELIS-MENTEN KINETICS MICHAELIS-MENTEN EQUATION UNI UNI MECHANISM... 

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-... 

Rate-concentration curve for Michaelis-Menten kinetics... 

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... 

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). 

FIGURE 15-35 Elasticity coefficient, e, of an enzyme with typical Michaelis-Menten kinetics. At substrate concentrations far below the Km, each increase in [S] produces a correspondingly large increase in the reaction velocity, v. For this region of the curve, the enzyme has an elasticity, e, of about 1.0. At [S] Km, increasing [S] has little effect on v s here is close to 0.0. 

Hyperbolic shape of the enzyme kinetics curve Most enzymes show Michaelis-Menten kinetics (see p. 58), in which the plot of initial reaction velocity, v0, against substrate concentration [S], is hyperbolic (similar in shape to that of the oxygen-dissociation curve of myoglobin, see p. 29). In contrast, allosteric enzymes frequently show a sigmoidal curve (see p. 62) that is similar in shape to the oxygen-dissociation curve of hemoglobin (see p. 29). 

Shapes of the kinetics curves for simple and allosteric enzymes Enzymes following Michaelis-Menten kinetics show hyperbolic curves when the initial reaction velocity (v0) of the reaction is plotted against substrate concentration. In contrast, allosteric enzymes generally show sigmoidal curves. 

Allosteric enzymes do not follow the Michaelis-Menten kinetic relationships between substrate concentration Fmax and Km because their kinetic behaviour is greatly altered by variations in the concentration of the allosteric modulator. Generally, homotrophic enzymes show sigmoidal behaviour with reference to the substrate concentration, rather than the rectangular hyperbolae shown in classical Michaelis-Menten kinetics. Thus, to increase the rate of reaction from 10 per cent to 90 per cent of maximum requires an 81-fold increase in substrate concentration, as shown in Fig. 5.34a. Positive cooperativity is the term used to describe the substrate concentration-activity curve which is sigmoidal an increase in the rate from 10 to 90 per cent requires only a nine-fold increase in substrate concentration (Fig. 5.346). Negative cooperativity is used to describe the flattening of the plot (Fig. 5.34c) and requires requires over 6000-fold increase to increase the rate from 10 to 90 per cent of maximum rate. 

Figure 3.28 shows the consumption functions C(S) for both nonmonotonic and Michaelis-Menten kinetics together with the removal function R(S) = —D S in a line. The intersection ) of C(S) and S(S) are the steady states. It is clear that for Michaelis-Menten3 kinetics, i.e., for nonlinearity with saturation, see Figure 2.2, there is only one steady state for the whole range of D. This is the simplest case of a CSTR without bifurcation. However, for substrate-inhibited nonmonotonic kinetics as depicted by the nonmonotonic curve in Figure 3.28, more than one steady state may occur over a certain range of D values. 

Multiple substrate mechanisms follow Michaelis-Menten kinetics. Experiments are performed with constant concentrations of the enzyme and one substrate with variation of the second substrate concentration ([S2]). (Note that the second substrate concentration [S2] is not the same as a deceptively similar term, the square of the substrate concentration [S]2.) Plotting V against [S2] gives a hyperbolic curve and allows determination of Km for the second substrate. The Km values for all substrates may be found in a similar fashion. 

The catalytic, synthetic, hormonal, and inhibitory activities that have been found in proteinoids or proteinoid microspheres are listed in Table 2. The possibility that metabolic activities found were due to contamination by micro-organisms is denied by experiments under aseptic condition or by the several experimental observations. The activities of proteinoids are generally weak. In some cases, proteinoids act several orders of magnitude more slowly than do modern enzymes or organisms, but free amino acids or Leuchs polypeptides usually have no activity or less than the proteinoid composed of the same amino acids. In general, activities of proteinoids increase approximately in proportion to its molecular weight. One or more of the proteinoids has been found to meet the salient requirements of enzymes such as Michaelis-Menten kinetics, pH-activity curves, etc. 

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). 

Kmi would be the standard Michaelis constant for the binding of the first substrate, if [ESS] = 0. Km2 would be the standard Michaelis constant for the binding of the second substrate, if [E] = 0 (i.e., the first binding site is saturated). In the complete equation, these constants are not true Km values, but their form (i.e., Km] = (k2 + k25)/k 2) and significance are analogous. Likewise, k25 and k35 are Vmi/Et and Vm2/Et terms when the enzyme is saturated with one and two substrate molecules, respectively. Equation (10) describes several non-Michaelis-Menten kinetic profiles. Autoactivation (sigmoidal saturation curve) occurs when k35 > k24 or Km2 < Km 1, substrate inhibition occurs when k24 > 35, and a biphasic saturation... 

The feedback mechanisms are mediated via mineralocorticoid and glucocorticoid receptors (MR, GR), which means overlapping of nonlinear positive and negative feedback loops with nonlinear dependencies on cortisol (Michaelis-Menten kinetics, sigmoidal activation curves of corticoid receptors). 

Regulatory enzymes are usually identified by the deviation of their kinetics from Michaelis-Menten kinetics plots of velocity versus substrate concentration can be a sigmoidal curve or a modified hyperbola [Fig. 9-7(o)]. If these curves are plotted in the double-reciprocal (Lineweaver-Burk) form, nonlinear graphs are obtained [Fig. 9-7(6)]. 

In the first approach, we examine the rate progress curves at various substrate concentrations, and use linear regression to evaluate initial rates. These initial rates are then fitted to the Michaelis-Menten equation (Eqn. 9.14) (Exercise 3 Michaelis-Menten kinetics I). This method has the advantage of being simple and robust. It has the disadvantage that the choice of data points used to obtain initial rates is often arbitrary, and also that the progress curves at low substrate concentrations show marked curvature because of substrate depletion. 

The importance of the changes in quaternary structure in determining the sigmoidal curve is illustrated nicely by studies of the isolated catalytic trimer, freed by p-hydroxymercuribenzoate treatment. The catalytic subunit shows Michaelis-Menten kinetics with kinetic parameters that are indistinguishable from those deduced for the R state. Thus, the term tense is apt in the T state, the regulatory dimers hold the two catalytic trimers sufficiently close to one another that key loops on their surfaces collide and interfere with conformational adjustments necessary for high-affinity substrate binding and catalysis. 

The Henri-Michaelis-Menten equation describes the curve obtained when initial velocity is plotted versus substrate concentration. The curve shown in Figure 4-7 is a right rectangular hyperbola with limits of and - K . The curvature is fixed regardless of the values of and V mxx- Consequently, the ratio of substrate concentrations for any two fractions of Vj m is constant for all enzymes that obey Henri-Michaelis-Menten kinetics. For example, the ratio of substrate required for 90% of Vmat to the substrate required for... 

D. Without ADP, the curve is sigmoidal, so Michaelis-Menten kinetics are not exhibited. Vm is the same at all ADP concentrations shown. The substrate concentration at V2 Vm decreases as the ADP concentration increases therefore, ADP decreases the Km, activating the enzyme. (The velocity is higher at lower substrate concentrations in the presence of ADP.)... 

Figure 7.10. Concentration-dependent kinetics of arsenate uptake in rice (Oryza sativa) roots with (closed symbols) and without iron plaque (open symbols). The curves are fitted to Michaelis-Menten kinetics, with a poor fit with iron plaque. (Adapted from Chen et al., 2005.)...

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