Enzyme kinetics saturation behavior

Rates for this reaction may easily be measured by disappearance of azide UV absorption. Most importantly, kinetic saturation behavior is noted with sufficient amounts of the reactants cycloaddition velocity becomes independent of substrate concentration. As is familiar from enzyme catalysis, this indicates complete occupancy of all available cucurbituril by reacting species. In actuality, the rate of the catalyzed reaction under conditions of saturation was found to be the same as that for release of the product from cucurbituril. Such a stoichiometric triazole complex was independently prepared and its kinetics of dissociation were examined by the displacement technique previously outlined, giving the identical rate constant of 1.7xl0 s under the standard conditions. (It is not uncommon for product release to be rate-limiting in enzymic reactions). 

In summary, for an enzyme model to be operative, a certain number of criteria, characteristic of enzyme catalysis, must be fulfilled, among which is substrate specificity—that is, selective differential binding. The enzymelike catalyst must also obey Michaelis-Menten kinetics (saturation behavior), lead to a rate enhancement, and show bi- and/or multifunctional catalysis (348). 

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. 

This behavior can be explained by the following kinetic considerations. The reaction leading to new RNA templates is catalyzed by a complex of enzyme and template. The affinity between these partners is so high that at the concentrations used every RNA molecule binds to an enzyme. The number of catalytically active complexes then rises exponentially until the RNA concentration becomes equal to the concentration of enzyme. At this point the enzyme is saturated with RNA. From now on the number of catalytically active RNA-enzyme complexes remains constant and the synthesis enters the linear phase, that is, the rate of appearance of new RNA molecules becomes constant. The new RNA molecules, now in excess over the enzyme, bind not only as templates but also, less strongly, at the site of synthesis. This leads to inhibition of synthesis by... 

Michaelis-Menten kinetics — is the dependence of an initial -> reaction rate upon the concentration of a substrate S that is present in large excess over the concentration of an enzyme or another catalyst (or reagent) E with the appearance of saturation behavior following the Michaelis-Menten equation,... 

Can a phosphorylation-dephosphorylation switch be more sensitive to the level of kinase concentration than n = 1 as given in Equation 5.12 We note that the kinetic scheme in Equation (4.7) is obtained under the assumption of no Michaelis-Menten saturation. Since this assumption may not be realistic, let us move on to study the enzyme kinetics in Figure (5.2) in terms of saturable Michaelis-Menten kinetics. The mechanism by which saturating kinetics of the kinase and phosphatase leads to sensitive switch-like behavior is illustrated in Figure 5.4. The reaction fluxes as a function of / (the ratio [S ]/Sc) for two cases are plotted. The first case (switch off)... 

Hydrolysis by the enzyme for dsDNA (1) and 3 -free ssDNA (5) was also investigated. When ATP concentrations injected in step 2 were changed in the range of 2.5-200 jiM, the initial rates of step 2 showed the saturation behavior of Michaelis-Menten kinetics. The catalytic hydrolysis rate constant (fccat)> fCm for ATP, and apparent second-order rate (fccat/ffm) are also summarized in Table 2. The kcat/ffm value for (1) was fourfold larger than that for (4) due to the large kcat and the constant Km values for (1). Thus, the binding ability of ATP to the enzyme-DNA complex was independent of the DNA structure, and the DNase can efficiently hydrolyze the dsDNA compared with the ssDNA. 

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... 

Fig. 3 Michael s-Menten enzyme kinetics. Rate versus concentration profile for two competing substrates A and B, both showing simple saturation behavior. The kinetic domains are defined relative to the respective Michaelis constants that represent the substrate concentrations at which just one half of the maximal rate is reached.

Michaelis constant, which leads to Eq. 9.52, which is called the Michaelis-Menten equation. This equation predicts a kinetic scenario that will show saturation behavior when [S] Km-Under this condition, the rate of the reaction is equal to /Ccai[E]o/ which is called the maximum velocity (Vmax)- If is the fastest that the catalytic reaction can occur, because all the catalyst has been converted to the catalyst-substrate complex (E S). The catalyst/enzyme is considered to be saturated with the substrate. 

Enzymes have a kinetic characteristics that show saturation behavior ... 

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. 

Similar to Eq. (67), the first reaction (incorporating the enzyme phosphofructo-kinase) exhibits a Hill-type inhibition by its substrate ATP [126]. The overall ATP utilization v3 (ATP) is modeled by a saturable Michaelis Menten function. The system is specified by five kinetic parameters (with Gx lumped into Vm ), the Hill coefficient n, and the total concentration, 4 / = [ATP] + [ADP]. Note that the model is not intended to capture biological realism, rather it serves as a paradigmatic example to identify dynamic behavior in metabolic pathways. 

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... 

In most kinetic investigations, one assumes the enzyme remains stable over the course of the measurement. When this is the case, corrective measures must be taken to obtain valid kinetic data. A useful test for any enzyme system is to plot enzyme activity versus time. This is readily accomplished by using a standardized assay (usually at optimal or saturating substrate concentrations) to measure the enzyme s specific activity periodically during the course of some experiment. This approach may fail to detect a reduction in activity characterized by lower affinity for substrate however, use of a subsaturating substrate concentration in a time-course study will reveal this behavior. 

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... 

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-... 

There are quite a few situations in which rates of transformation reactions of organic compounds are accelerated by reactive species that do not appear in the overall reaction equation. Such species, generally referred to as catalysts, are continuously regenerated that is, they are not consumed during the reaction. Examples of catalysts that we will discuss in the following chapters include reactive surface sites (Chapter 13), electron transfer mediators (Chapter 14), and, particularly enzymes, in the case of microbial transformations (Chapter 17). Consequently, in these cases the reaction cannot be characterized by a simple reaction order, that is, by a simple power law as used for the reactions discussed so far. Often in such situations, reaction kinetics are found to exhibit a gradual transition from first-order behavior at low compound concentration (the compound sees a constant steady-state concentration of the catalyst) to zero-order (i.e., constant term) behavior at high compound concentration (all reactive species are saturated ) ... 

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