Enzymes saturation kinetics

The rate of a-chymotrypsin-catalyzed hydrolysis as a function of overall GPANA concentration in CTAB reversed micelles and in aqueous solution are shown in Figure 5. It is apparent that the reaction rate in the reversed micellar solution is on the order of 50 times more rapid than in the aqueous system. Furthermore, in the reversed micellar system there is no indication of enzyme saturation as the reaction is first order in substrate concentration. As enzyme saturation kinetics are not observed, it is impossible to differentiate between the parameters kcat and Kg. Instead a second order bimolecular rate constant for both the micelle interior ( micelle) and for what is experimentally observed ( observed) is defined. 

Reversibly fonned micelles have long been of interest as models for enzymes, since tliey provide an amphipatliic environment attractive to many substrates. Substrate binding (non-covalent), saturation kinetics and competitive inliibition are kinetic factors common to botli enzyme reaction mechanism analysis and micellar binding kinetics. 

Interestingly, at very low concentrations of micellised Qi(DS)2, the rate of the reaction of 5.1a with 5.2 was observed to be zero-order in 5.1 a and only depending on the concentration of Cu(DS)2 and 5.2. This is akin to the turn-over and saturation kinetics exhibited by enzymes. The acceleration relative to the reaction in organic media in the absence of catalyst, also approaches enzyme-like magnitudes compared to the process in acetonitrile (Chapter 2), Cu(DS)2 micelles accelerate the Diels-Alder reaction between 5.1a and 5.2 by a factor of 1.8710 . This extremely high catalytic efficiency shows how a combination of a beneficial aqueous solvent effect, Lewis-acid catalysis and micellar catalysis can lead to tremendous accelerations. 

The often fast binding step of the inhibitor I to the enzyme E, forming the enzyme inhibitor complex E-I, is followed by a rate-determining inactivation step to form a covalent bond. The evaluation of affinity labels is based on the fulfillment of the following criteria (/) irreversible, active site-directed inactivation of the enzyme upon the formation of a stable covalent linkage with the activated form of the inhibitor, (2) time- and concentration-dependent inactivation showing saturation kinetics, and (3) a binding stoichiometry of 1 1 of inhibitor to the enzyme s active site (34). 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

To refer to the kinetics of allosteric inhibition as competitive or noncompetitive with substrate carries misleading mechanistic implications. We refer instead to two classes of regulated enzymes K-series and V-se-ries enzymes. For K-series allosteric enzymes, the substrate saturation kinetics are competitive in the sense that is raised without an effect on V. For V-series allosteric enzymes, the allosteric inhibitor lowers... 

As a simple model for the enzyme penicillinase, Tutt and Schwartz (1970, 1971) investigated the effect of cycloheptaamylose on the hydrolysis of a series of penicillins. As illustrated in Scheme III, the alkaline hydrolysis of penicillins is first-order in both substrate and hydroxide ion and proceeds with cleavage of the /3-lactam ring to produce penicilloic acid. In the presence of an excess of cycloheptaamylose, the rate of disappearance of penicillin follows saturation kinetics as the cycloheptaamylose concentration is varied. By analogy to the hydrolysis of the phenyl acetates, this saturation behavior may be explained by inclusion of the penicillin side chain (the R group) within the cycloheptaamylose cavity prior to nucleophilic attack by a cycloheptaamylose alkoxide ion at the /3-lactam carbonyl. The presence of a covalent intermediate on the reaction pathway, although not isolated, was implicated by the observation that the rate of disappearance of penicillin is always greater than the rate of appearance of free penicilloic acid. 

Most of enzyme kinetics (and mechanism) revolves around the active site. As we ll see later, saturation kinetics is one of the direct consequences of an active site. 

Mathematically, the Michaelis-Menten equation is the equation of a rectangular hyperbola. Sometimes you ll here reference to hyperbolic kinetics, this means it follows the Michaelis-Menten equation. A number of other names also imply that a particular enzyme obeys the Michaelis-Menten equation Michaelis-Menten behavior, saturation kinetics, and hyperbolic kinetics. 

Abstract This chapter updates but mostly supplements the author s Ange-wandte Review,111 setting in context recent advances based on protein and nucleic acid engineering. Systems qualify as a true enzyme mimics if there is experimental evidence for both the initial binding interaction and catalysis with turnover, generally in the shape of saturation kinetics. They are discussed under five broad headings mimics based on natural enzymes, on other proteins, on other biopolymers, on synthetic macromolecules and on small-molecule host-guest interactions. 

Silverman has pointed out that several criteria must be met to demonstrate that a compound is a true suicide substrate 1101 (1) Loss of enzyme activity must be time-dependent, and it must be first-order in [inactivator] at low concentrations and zero-order at higher concentrations (saturation kinetics), (2) substrate must protect the enzyme from inactivation (by blocking the active site), (3) the enzyme must be irreversibly inactivated and be shown to have a 11 stoichiometry of suicide substrate active site (dialysis of enzyme previously treated with radiolabeled suicide substrate must not release radiolabel into the buffer), (4) the enzyme must unmask the suicide substrate s potent electrophile via a catalytic step,1121 and (5) the enzyme must not be covalently labeled with the activated form of the suicide substrate following its escape from the active site (the presence of bulky scavenging thiol nucleophiles in the buffer must not decrease the observed rate of inactivation). 

It has been found experimentally that in most cases v is directly proportional to the concentration of enzyme [.E0] and that v generally follows saturation kinetics with respect to the concentration of substrate [limiting value called Vmax. This is expressed quantitatively in the Michaelis-Menten equation originally proposed by Michaelis and Menten. Km can be seen as an apparent dissociation constant for the enzyme-substrate complex ES. The maximal velocity Vmax = kcat E0. ... 

Figure 11.1 illustrates the behavior of Equation 11.6. By the assumption of rapid equilibrium the rate determining step is the unimolecular decomposition. At high substrate composition [S] KM and the rate becomes zero-order in substrate, v = Vmax = k3 [E0], the rate depends only on the initial enzyme concentration, and is at its maximum. We are dealing with saturation kinetics. The most convenient way to test mechanism is to invert Equation 11.6... 

The enzyme termed flavopapain, reacts with dihydronicotinamides. The catalyst exhibits saturation kinetics and modest rate enhancements over appropriate model compounds. 

In general, this first generation of abzymes obtained from TSAs behave like enzymes, present saturation kinetics, substrate specificity, a stereoselectivity and competitive inhibition phenomena. However the acceleration factors obtained, cat/ ncat> remain weak and are limited in theory by the ratio of the constant of... 

Follow-up experiments with the similar Klebsiella pneumoniae enzyme (66, 67) also showed that the pH profiles for CatPx are quite different from those for classical catalases. The latter s catalatic activities are essentially pH-independent from pH 5 to 10 (6S) CatPx of Klebsiella showed a sharp pH optimum between pH 6 and 7 (66). A similar eukaryotic fungal CatPx (69) was also characterized by a sharp pH sensitivity and saturation kinetics K 3.4 mM) and, like the bac-... 

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... 

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. 

Non-linear pharmacokinetics are much less common than linear kinetics. They occur when drug concentrations are sufficiently high to saturate the ability of the liver enzymes to metabolise the drug. This occurs with ethanol, therapeutic concentrations of phenytoin and salicylates, or when high doses of barbiturates are used for cerebral protection. The kinetics of conventional doses of thiopentone are linear. With non-linear pharmacokinetics, the amount of drug eliminated per unit time is constant rather than a constant fraction of the amount in the body, as is the case for the linear situation. Non-linear kinetics are also referred to as zero order or saturation kinetics. The rate of drug decline is governed by the Michaelis-Menton equation ... 

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