Michaelis- Menten enzyme kinetics competitive inhibition

If two different substrates bind simultaneously to the active site, then the standard Michaelis-Menten equations and competitive inhibition kinetics do not apply. Instead it is necessary to base the kinetic analyses on a more complex kinetic scheme. The scheme in Figure 6 is a simplified representation of a substrate and an effector binding to an enzyme, with the assumption that product release is fast. In Figure 6, S is the substrate and B is the effector molecule. Product can be formed from both the ES and ESB complexes. If the rates of product formation are slow relative to the binding equilibrium, we can consider each substrate independently (i.e., we do not include the formation of the effector metabolites from EB and ESB in the kinetic derivations). This results in the following relatively simple equation for the velocity ... 

Cyclodextrins as catalysts and enzyme models It has long been known that cyclodextrins may act as elementary models for the catalytic behaviour of enzymes (Breslow, 1971). These hosts, with the assistance of their hydroxyl functions, may exhibit guest specificity, competitive inhibition, and Michaelis-Menten-type kinetics. All these are characteristics of enzyme-catalyzed reactions. 

Corey also pointed out that 16 reflects the transition-state of an enzyme-substrate complex. Its formation was later supported by the observation of Michaelis-Menten-type kinetics in dihydroxylation reactions and in competitive inhibition studies [37], This kinetic behavior was held responsible for the non-linearity in the Eyring diagrams, which would otherwise be inconsistent with a concerted mechanism. Contrary, Sharpless stated that the observed Michaelis-Menten behavior in the catalytic AD would result from a step other than osmylation. Kinetic studies on the stoichiometric AD of styrene under conditions that replicate the organic phase of the catalytic AD had revealed that the rate expression was clearly first-order in substrate over a wide range of concentrations [38],... 

The term should be used for enzymes that display Michaelis-Menten kinetics. Thus, it is not used with allosteric enzymes. Technically, competitive and noncompetitive inhibition are also terms that are restricted to Michaelis-Menten enzymes, although the concepts are applicable to any enzyme. An inhibitor that binds to an allosteric enzyme at the same site as the substrate is similar to a classical competitive inhibitor. One that binds at a different site is similar to a noncompetitive inhibitor, but the equations and the graphs characteristic of competitive and noncompetitive inhibition don t work the same way with an allosteric enzyme. 

For each of the four types of inhibition of a Michaelis-Menten enzyme [competitive, Eq. (5.25) noncompetitive and mixed Eq. (5.29) and uncompetitive, Eq. (5.32)], derive the corresponding Lineweaver-Burk equations [Eqs. (5.26), and (5.30), respectively] and draw the characteristic plots that are the basis for the rapid visnal identification of which type of inhibition apphes when analyzing enzyme kinetic data. 

Kinetic Model Reversible CYP inhibition is dependent on the mode of interaction between CYP enzymes and inhibitors and is further characterized as competitive, noncompetitive, uncompetitive, and mixed. Evaluation of reversible inhibition of CYP reactions is often conducted under conditions where Michaelis-Menten (MM) kinetics is obeyed. Based on Scheme 1 below, various types of reversible inhibition are described from the scheme during catalysis which can lead to enzyme inhibition ... 

Aiming at a computer-based description of cellular metabolism, we briefly summarize some characteristic rate equations associated with competitive and allosteric regulation. Starting with irreversible Michaelis Menten kinetics, the most common types of feedback inhibition are depicted in Fig. 9. Allowing all possible associations between the enzyme and the inhibitor shown in Fig. 9, the total enzyme concentration Er can be expressed as... 

Carrier-mediated passage of a molecular entity across a membrane (or other barrier). Facilitated transport follows saturation kinetics ie, the rate of transport at elevated concentrations of the transportable substrate reaches a maximum that reflects the concentration of carriers/transporters. In this respect, the kinetics resemble the Michaelis-Menten behavior of enzyme-catalyzed reactions. Facilitated diffusion systems are often stereo-specific, and they are subject to competitive inhibition. Facilitated transport systems are also distinguished from active transport systems which work against a concentration barrier and require a source of free energy. Simple diffusion often occurs in parallel to facilitated diffusion, and one must correct facilitated transport for the basal rate. This is usually evident when a plot of transport rate versus substrate concentration reaches a limiting nonzero rate at saturating substrate While the term passive transport has been used synonymously with facilitated transport, others have suggested that this term may be confused with or mistaken for simple diffusion. See Membrane Transport Kinetics... 

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.

Also characteristic of enzymes that obey Michaelis-Menten kinetics is that suitable inhibitors can compete with the substrate for the enzyme active site, thus impeding the reaction. If the inhibitor binds reversibly to the enzyme active site, then the substrate can compete for the active site leading to competitive inhibition. To test for... 

Reversible Inhibition One common type of reversible inhibition is called competitive (Fig. 6-15a). A competitive inhibitor competes with the substrate for the active site of an enzyme. While the inhibitor (I) occupies the active site it prevents binding of the substrate to the enzyme. Many competitive inhibitors are compounds that resemble the substrate and combine with the enzyme to form an El complex, but without leading to catalysis. Even fleeting combinations of this type will reduce the efficiency of the enzyme. By taking into account the molecular geometry of inhibitors that resemble the substrate, we can reach conclusions about which parts of the normal substrate bind to the enzyme. Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the Michaelis-Menten equation (Eqn 6-9) becomes... 

The enzymatic activity of the L-19 IVS ribozyme results from a cycle of transesterification reactions mechanistically similar to self-splicing. Each ribozyme molecule can process about 100 substrate molecules per hour and is not altered in the reaction therefore the intron acts as a catalyst. It follows Michaelis-Menten kinetics, is specific for RNA oligonucleotide substrates, and can be competitively inhibited. The kcat/Km (specificity constant) is 10s m- 1 s lower than that of many enzymes, but the ribozyme accelerates hydrolysis by a factor of 1010 relative to the uncatalyzed reaction. It makes use of substrate orientation, covalent catalysis, and metalion catalysis—strategies used by protein enzymes. 

Reversible inhibition occurs rapidly in a system which is near its equilibrium point and its extent is dependent on the concentration of enzyme, inhibitor and substrate. It remains constant over the period when the initial reaction velocity studies are performed. In contrast, irreversible inhibition may increase with time. In simple single-substrate enzyme-catalysed reactions there are three main types of inhibition patterns involving reactions following the Michaelis-Menten equation competitive, uncompetitive and non-competitive inhibition. Competitive inhibition occurs when the inhibitor directly competes with the substrate in forming the enzyme complex. Uncompetitive inhibition involves the interaction of the inhibitor with only the enzyme-substrate complex, while non-competitive inhibition occurs when the inhibitor binds to either the enzyme or the enzyme-substrate complex without affecting the binding of the substrate. The kinetic modifications of the Michaelis-Menten equation associated with the various types of inhibition are shown below. The derivation of these equations is shown in Appendix S.S. 

In relation to enzymic cytochrome P-450 oxidations, catalysis by iron porphyrins has inspired many recent studies.659 663 The use of C6F5IO as oxidant and Fe(TDCPP)Cl as catalyst has resulted in a major improvement in both the yields and the turnover numbers of the epoxidation of alkenes. 59 The Michaelis-Menten kinetic rate, the higher reactivity of alkyl-substituted alkenes compared to that of aryl-substituted alkenes, and the strong inhibition by norbornene in competitive epoxidations suggested that the mechanism shown in Scheme 13 is heterolytic and presumably involves the reversible formation of a four-mernbered Fev-oxametallacyclobutane intermediate.660 Picket-fence porphyrin (TPiVPP)FeCl-imidazole, 02 and [H2+colloidal Pt supported on polyvinylpyrrolidone)] act as an artificial P-450 system in the epoxidation of alkenes.663... 

Substances that cause enzyme-catalyzed reactions to proceed more slowly are termed inhibitors, and the phenomenon is termed inhibition. When an enzyme is subject to inhibition, the reaction still may obey Michaelis-Menten kinetics but with apparent Km and Vmax values that vary with the inhibitor concentration. If the inhibitor acts only on the apparent Km, it is a competitive inhibitor if it affects only the apparent Vmax, it is a noncompetitive inhibitor and if it affects both constants, it is an uncompetitive inhibitor. 

Competitive inhibition occurs, when substrate and inhibitor compete for binding at the same active site at the enzyme. Based on the Michaelis-Menten kinetics, Vmax is unchanged whereas Km increases. In case of noncompetive inhibition, the inhibitor and the substrate bind to different sites at the enzyme. Vmax decrease whereas the Km value is unaffected. Binding of the inhibitor only to the enzyme-substrate complex is described as uncompetitive inhibition. Both, Vmax and Km decrease. Finally, mixed (competitive-noncompetitive) inhibition occurs, either the inhibitor binds to the active or to another site on the enzyme, or the inhibitor binds to the active site but does not block the binding of the substrate. 

Many substances interact with enzymes to lower their activity that is, to inhibit them. Valuable information about the mechanism of action of the inhibitor can frequently be obtained through a kinetic analysis of its effects. To illustrate, let us consider a case of competitive inhibition, in which an inhibitor molecule, I, combines only with the free enzyme, E, but cannot combine with the enzyme to which the substrate is attached, ES. Such a competitive inhibitor often has a chemical structure similar to the substrate, but is not acted on by the enzyme. For example, malonate (-OOCCH2COO-) is a competitive inhibitor of succinate (-OOCCH2CH2COO-) dehydrogenase. If we use the same approach that was used in deriving the Michaelis-Menten equation together with the additional equilibrium that defines a new constant, an inhibitor constant, A),... 

The effects of macromolecules other than surfactants on the rates of organic reactions have been investigated extensively (Morawetz, 1965). In many cases, substrate specificity, bifunctional catalysis, competitive inhibition, and saturation (Michaelis-Menten) kinetics have been observed, and therefore these systems also serve as models for enzyme-catalyzed reactions and, in these and other respects, resemble micellar systems. Indeed, in some macromolecular systems micelle formation is very probable or is known to occur, and in others mixed micellar systems are likely. Recent books and reviews should be consulted for a more detailed description of macromolecular systems and for their applicability as models for enzymatic catalysis and other complex interactions (Morawetz, 1965 Bruice and Benkovic, 1966 Davydova et al., 1968 Winsor, 1968 Jencks, 1969 Overberger and Salamone, 1969). 

The formation of a reversible Michaelis-Menten-type complex of the enzyme and ferrocytochrome c [ES1S2 in Eq. (3) ] can be postulated from initial steady-state kinetics of the cytochrome c peroxidase reaction (17). Since cytochrome c peroxidase and cytochrome c are acidic and basic proteins, respectively, their interaction may be governed principally by electrostatic attraction. This assumption is further supported by the fact that several polycations which reversibly and irreversibly bind cytochrome c peroxidase inhibit its enzymic activity in competition with ferrocytochrome c 17,62). 

Steady-state kinetic studies showed that the kinetics of the enzyme resemble those of the vanadium bromoperoxidases. The chloroperoxidase exhibits a pH profile similar to vanadium bromoperoxidases although the optimal pH of 4.5-5.0 is at a lower value. At low pH the enzyme is inhibited by chloride in a competitive way whereas at higher pH values the activity displays normal Michaelis-Menten type of behavior (see Michaelis Constant). The log Km for chloride increases linearly with pH whereas that for hydrogen peroxide decreases with pH demonstrating that in the catalytic mechanism protons are involved. These observations have led to a simplified ping-pong type of mechanism for the chloroperoxidase similar to that shown in (Figure 1). 

Michaelis-Menten kinetics and, depending on their preference of binding to the free enzyme and/or the enzyme-substrate complex, competitive, uncompetitive, and noncompetitive inhibition patterns can be distinguished. For the purposes of this discussion it will be assumed that the initial equilibrium of free and bound substrate is established significantly faster than the rate of the chemical transformation of substrate to product, that is,... 

How can we determine whether a reversible inhibitor acts by competitive or noncompetitive inhibition Let us consider only enzymes that exhibit Michaelis- Menten kinetics. Measurements of the rates of catalysis at different concentrations of substrate and inhibitor serve to distinguish the three types of inhibition. In competitive inhibition, the inhibitor competes with the substrate for the active site. The dissociation constant for the inhibitor is given by... 

In textbooks dealing with enzyme kinetics, it is customary to distinguish four types of reversible inhibitions (i) competitive (ii) noncompetitive (iii) uncompetitive and, (iv) mixed inhibition. Competitive inhibition, e.g., given by the product which retains an affinity for the active site, is very common. Non-competitive inhibition, however, is very rarely encountered, if at all. Uncompetitive inhibition, i.e. where the inhibitor binds to the enzyme-substrate complex but not to the free enzyme, occurs also quite often, as does the mixed inhibition, which is a combination of competitive and uncompetitive inhibitions. The simple Michaelis-Menten equation can still be used, but with a modified Ema, or i.e. ... 

The answer is c. (Murray, pp 48-73. Scriver, pp 4571-4636. Sack, pp 3-17. Wilson, pp 287-317.) Allosteric enzymes, unlike simpler enzymes, do not obey Michaelis-Menten kinetics. Often, one active site of an allosteric enzyme molecule can positively affect another active site in the same molecule. This leads to cooperativity and sigmoidal enzyme kinetics in a plot of [S] versus V The terms competitive inhibition and noncompetitive inhibition apply to Michaelis-Menten kinetics and not to allosteric enzymes. 

The inhibition of certain enzymes by specific metabolites is an important element in the regulation of intermediary metabolism and most often occurs with cooperative enzymes that are regulated allosterically. Inhibition of enzymes that obey the Michaelis-Menten equation, noncooperative enzymes, is more commonly used by pharmacists to alter a patient s metabolism. Reversible inhibition of noncooperative enzymes is classified into three groups which can be distinguished kinetically and which have different mechanisms and effects when administered. The classes are called competitive, uncompetitive, and noncompetitive inhibition. Mixed inhibition also occurs. In all these types of inhibition, the inhibitor (usually a small molecule) binds reversibly and rapidly with the enzyme. 

D23.4 Refer to eqns 23.26 and 23.27, which are the analogues of the Michaelis-Menten and Lineweaver-Burk equations (23.21 and 23,22), as well as to Figure 23.13, There are three major modes of inhibition that give rise to distinctly different kinetic behavior (Figure 23.13), In competitive inhibition the inhibitor binds only to the active site of the enzyme and thereby inhibits the attachment of the substrate. This condition corresponds to a > 1 and a = 1 (because ESI does not form). The slope of the Lineweaver-Burk plot increases by a factor of a relative to the slope for data on the uninhibited enzyme (a = a = I), The y-intercept does not change as a result of competitive inhibition, In uncompetitive inhibition, the inhibitor binds to a site of the enzyme that is removed from the active site, but only if the substrate is already present. The inhibition occurs because ESI reduces the concentration of ES, the active type of the complex, In this case a = 1 (because El does not form) and or > 1. The y-intercepl of the Lineweaver-Burk plot increases by a factor of a relative to they-intercept for data on the uninhibited enzyme, but the slope does not change. In non-competitive inhibition, the inhibitor binds to a site other than the active site, and its presence reduces the ability of the substrate to bind to the active site. Inhibition occurs at both the E and ES sites. This condition corresponds to a > I and a > I. Both the slope and y-intercept... 

The reaction rate for the hydrolysis of starch (Eq. 2.1 in Table 3) is a Michaelis-Menten type model, which considers competitive product inhibition of glucose and substrate inhibition of starch. The hydrolysis of maltose (Eq. 2.2 in Table 3) is represented by a Michaelis-Menten type model with competitive product inhibition. These equations were tested by Lopez et al. [3] for hydrolysis of chestnut puree by an alpha and glucoamylase mixture. As the enzyme STARGEN also contains amormts of alpha and glucoamylase, it was not surprising that they (Eqs. 2.1-2.2 in Table 3) fit the hydrolysis data better than non-inhibitory Michaelis-Menten kinetics. 

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