Enzyme kinetics second-order

That is, k t/K,n is an apparent second-order rate constant ior the reaction of E and S to form product. Because A , is inversely proportional to the affinity of the enzyme for its substrate and is directly proportional to the kinetic efficiency of the enzyme, A , provides an index of the catalytic efficiency of an enzyme operating at substrate concentrations substantially below saturation amounts. 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

C15-0037. Write one-sentence explanations for the following kinetic terms (a) first order (b) second order (c) isolation method (d) elementaiy step (e) catalyst (f) intermediate and (g) enzyme. 

CO3 species was formed and the X-ray structure solved. It is thought that the carbonate species forms on reaction with water, which was problematic in the selected strategy, as water was produced in the formation of the dialkyl carbonates. Other problems included compound solubility and the stability of the monoalkyl carbonate complex. Van Eldik and co-workers also carried out a detailed kinetic study of the hydration of carbon dioxide and the dehydration of bicarbonate both in the presence and absence of the zinc complex of 1,5,9-triazacyclododecane (12[ane]N3). The zinc hydroxo form is shown to catalyze the hydration reaction and only the aquo complex catalyzes the dehydration of bicarbonate. Kinetic data including second order rate constants were discussed in reference to other model systems and the enzyme carbonic anhy-drase.459 The zinc complex of the tetraamine 1,4,7,10-tetraazacyclododecane (cyclen) was also studied as a catalyst for these reactions in aqueous solution and comparison of activity suggests formation of a bidentate bicarbonate intermediate inhibits the catalytic activity. Van Eldik concludes that a unidentate bicarbonate intermediate is most likely to the active species in the enzyme carbonic anhydrase.460... 

In chymotrypsin and other serine proteases the imidazole moiety of histidine acts as a general base not as a nucleophile as is probably the case in the catalysis of activated phenyl ester hydrolysis by (26). With this idea in mind, Kiefer et al. 40) studied the hydrolysis of 4-nitrocatechol sulfate in the presence of (26) since aryl sulfatase, the corresponding enzyme, has imidazole at the active center. Dramatic results were obtained. The substrate, nitrocatechol sulfate, is very stable in water at room temperature. Even the presence of 2M imidazole does not produce detectable hydrolysis. In contrast (26) cleaves the substrate at 20°C. Michaelis-Menten kinetics were obtained the second-order rate constant for catalysis by (26) is 10 times... 

The reduction in concentration of reactants, enzymes, and solute molecules can provide important information about kinetic systems. For example, one can readily differentiate a first-order process from a second-order process by testing whether the period required to reduce a reactant concentration to 50% of its initial value depends on dilution. First-order processes and intramolecular processes should not exhibit any effect on rate by diluting a reactant. In terms of enzyme-catalyzed processes, the Michaelis-Menten equation requires that the initial reaction velocity depends strictly on the concentration of active catalyst. Dilution can also be used to induce dissociation of molecular complexes or to promote depolymerization of certain polymers (such as F-actin and microtubules). 

In Chapter 8, we addressed proton transfer reactions, which we have assumed to occur at much higher rates as compared to all other processes. So in this case we always considered equilibrium to be established instantaneously. For the reactions discussed in the following chapters, however, this assumption does not generally hold, since we are dealing with reactions that occur at much slower rates. Hence, our major focus will not be on thermodynamic, but rather on kinetic aspects of transformation reactions of organic chemicals. In Section 12.3 we will therefore discuss the mathematical framework that we need to describe zero-, first- and second-order reactions. We will also show how to solve somewhat more complicated problems such as enzyme kinetics. 

Hence, sometimes phenomena associated with enzyme kinetics control the rate of biotransformations. If suitable enzymes are present in the microbial community, for example due to consumption of structurally related growth substrates, then we may see immediate degradation of compounds of interest like BQ when they are added to these metabolically competent microbial communities (Fig. 17.17). For such cases, if the abundance of the bacteria is varied, the rate of removal changes accordingly. Consequently, the removal of BQ could be described by a second-order rate law (Smith et al., 1978) ... 

Bimolecular reactions of two molecules, A and B, to give two products, P and Q, are catalyzed by many enzymes. For some enzymes the substrates A and B bind into the active site in an ordered sequence while for others, bindingmay be iii a random order. The scheme shown here is described as random Bi Bi in a classification introduced by Cleland. Eighteen rate constants, some second order and some first order, describe the reversible system. Determination of these kinetic parameters is often accomplished using a series of double reciprocal plots (Lineweaver-Burk plots), such as those at the right. 

Second order reactions 458 Secondary kinetic isotope effect 592, 600 on fumarate hydratase 684 Secondary plots for kinetics of multisubstrate enzymes 465 Secondary structure 63... 

Table 4.5 shows that for some efficient enzymes, kcJKM may be as high as 3 X 108 s-1 M l. In these cases, the rate-determining step for this parameter, which is the apparent second-order rate constant for the reaction of free enzyme with free substrate, is close to the diffusion-controlled encounter of the enzyme and the substrate. Briggs-Haldane kinetics holds for these enzymes (Chapter 3, section B3). 

It is possible to devise kinetic curiosities that give Michaelis-Menten kinetics without the enzyme being saturated with the substrate. For example, in the following scheme—where the active form of the enzyme reacts with the substrate in a second-order reaction to give the products and an inactive form of the enzyme, E, which slowly reverts to the active form—apparent saturation kinetics are followed with cat = k2 and Ku = k2/k1. Equation 3.24 applies to this example if E is treated as a bound form of the enzyme ... 

This ratio is of fundamental importance in the relationship between enzyme kinetics and catalysis. In the analysis of the Michaelis-Menten rate law (equation 5.8), the ratio cat/Km is an apparent second-order rate constant and, at low substrate concentrations, only a small fraction of the total enzyme is bound to the substrate and the rate of reaction is proportional to the free enzyme concentration ... 

Polymer catalysts showing interactions with the substrate, similar to enzymes, were prepared and their catalytic activities on hydrolysis of polysaccharides were investigated. Kinetical analyses showed that hydrogen bonding and electrostatic interactions played important roles for enhancement of the reactions and that the hydrolysis rates of polysaccharides followed the Michaelis-Menten type kinetics, whereas the hydrolysis of low-molecular-weight analogs proceeded according to second-order kinetics. From thermodynamic analyses, the process of the complex formation in the reaction was characterized by remarkable decreases in enthalpy and entropy. The maximum rate enhancement obtained in the present experiment was fivefold on the basis of the reaction in the presence of sulfuric acid. 

Copper has a direct role in the catalytic mechanism. Complete removal of both copper and zinc destroys the activity of the enzyme which can be restored by addition of cupric ion but not by other metals (12). Pulse radiolytic methods have been used to generate superoxide ion and to follow the enzyme kinetics (24, 25). The reaction is second order with a rate constant of 2.37 X 109 M"1 sec-1 at 25°, independent of pH over the range 4.8-9.5. The following two-step mechanism has been proposed to account for the enzyme activity ... 

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