Enzyme rate constant

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

A combination of several rate constants affecting the rate of an enzyme-substrate reaction. 

Chemical kinetic methods also find use in determining rate constants and elucidating reaction mechanisms. These applications are illustrated by two examples from the chemical kinetic analysis of enzymes. 

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

Enzyme and substrate first reversibly combine to give an enzyme-substrate (ES) complex. Chemical processes then occur in a second step with a rate constant called kcat, or the turnover number, which is the maximum number of substrate molecules converted to product per active site of the enzyme per unit time. The kcat is, therefore, a rate constant that refers to the properties and reactions of the ES complex. For simple reactions kcat is the rate constant for the chemical conversion of the ES complex to free enzyme and products. 

The quantity kcat/Km is a rate constant that refers to the overall conversion of substrate into product. The ultimate limit to the value of k at/Km is therefore set by the rate constant for the initial formation of the ES complex. This rate cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate, which is between 10 to 10 per mole per second. The quantity kcat/Km is sometimes called the specificity constant because it describes the specificity of an enzyme for competing substrates. As we shall see, it is a useful quantity for kinetic comparison of mutant proteins. 

In zero-orrler kinetics, a constant amount of a chemical compound is excreted per unit of rime. In most cases, this phenomenon is caused by the saturation of a rate-limiting enzyme, and the enzyme commonly functions at its maximal rate, i.e., a constant amount of a chemical compound is metabolized per unit time. A good example is ethyl alcohol alcohol dehydrogenase becomes saturated at relatively low concentrations. Because of this saturation, ethyl alcohol is eliminated at a constant rate about 7 g/h. However, rhe reason is not always an enzyme anv... 

At 20 C, the rate constant for this uncatalyzed reaction, uncat is 0.03/sec. In the presence of the enzyme carbonic anhydrase, the rate constant for this reaction, is 10 /sec. 

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. 

But k must always be greater than or equal to k h / (A i + kf). That is, the reaction can go no faster than the rate at which E and S come together. Thus, k sets the upper limit for A ,. In other words, the catalytic effieiency of an enzyme cannot exceed the diffusion-eontroUed rate of combination of E and S to form ES. In HgO, the rate constant for such diffusion is approximately (P/M - sec. Those enzymes that are most efficient in their catalysis have A , ratios approaching this value. Their catalytic velocity is limited only by the rate at which they encounter S enzymes this efficient have achieved so-called catalytic perfection. All E and S encounters lead to reaction because such catalytically perfect enzymes can channel S to the active site, regardless of where S hits E. Table 14.5 lists the kinetic parameters of several enzymes in this category. Note that and A , both show a substantial range of variation in this table, even though their ratio falls around 10 /M sec. 

Enigmas abound in the world of enzyme catalysis. One of these surrounds the discussion of how the rate enhancement by an enzyme can be best expressed. Notice that the nncatalyzed conversion of a substrate S to a product P is usually a simple first-order process, described by a first-order rate constant... 

Enzyme catalysis requires that Kj- < Kg. According to transition-state theory (see references at end of chapter), the rate constants for the enzyme-catalyzed k ) and uncatalyzed k reactions can be related to Kg and K by ... 

D-Methylmalonyl-CoA, the product of this reaction, is converted to the L-isomer by methylmalonyl-CoA epunerase (Figure 24.19). (This enzyme has often and incorrectly been called methylmalonyl-CoA racemase. It is not a racemase because the CoA moiety contains five other asymmetric centers.) The epimerase reaction also appears to involve a carbanion at the a-position (Figure 24.20). The reaction is readily reversible and involves a reversible dissociation of the acidic a-proton. The L-isomer is the substrate for methylmalonyl-CoA mutase. Methylmalonyl-CoA epimerase is an impressive catalyst. The for the proton that must dissociate to initiate this reaction is approximately 21 If binding of a proton to the a-anion is diffusion-limited, with = 10 M sec then the initial proton dissociation must be rate-limiting, and the rate constant must be... 

The overall rate constant for conversion of the E S complex to products E + P is called the turnover number because it represents the number of substrate molecules the enzyme turns over into product per unit time. A value of about 103 per second is typical. 

Enzymes, like all other catalysts, lower the activation energy for reaction. They can be enormously effective it is not uncommon for the rate constant to increase by a factor of... 

In general, enzymes are proteins and cany charges the perfect assumption for enzyme reactions would be multiple active sites for binding substrates with a strong affinity to hold on to substrate. In an enzyme mechanism, the second substrate molecule can bind to the enzyme as well, which is based on the free sites available in the dimensional structure of the enzyme. Sometimes large amounts of substrate cause the enzyme-catalysed reaction to diminish such a phenomenon is known as inhibition. It is good to concentrate on reaction mechanisms and define how the enzyme reaction may proceed in the presence of two different substrates. The reaction mechanisms with rate constants are defined as ... 

In non-competitive inhibition, the substrate (S) and inhibitor (I) have equal potential to bind to the free enzyme (E). The inhibitor forms a ternary complex with enzyme-substrate (ES) whereas the substrate will form another ternary complex with enzyme-inhibitor (El). Since the non-competitive inhibitor had no effect on the binding of substrate to the enzyme, the Km value remained consistent (or unchanged). There are two different ways for the formation of ESI ternary complex this complex would not form the product and therefore was decreased. Non-competitive inhibitor had no effect on substrate binding or the enzyme-substrate affinity, therefore the apparent rate constant (K ) was unchanged.5 A possible reason for product inhibition was because of the nature of 2-ethoxyethanol,... 

In order to change the rate constant of a given reaction, it is crucial that the enzyme will recognize some change in the reacting system. Such a change... 

The overall catalytic rate constant of SNase is (see, for example, Ref. 3) kcat — 95s 1 at T = 297K, corresponding to a total free energy barrier of Ag at = 14.9 kcal/mol. This should be compared to the pseudo-first-order rate constant for nonenzymatic hydrolysis of a phosphodiester bond (with a water molecule as the attacking nucleophile) which is 2 x 10 14 s corresponding to Ag = 36 kcal/mol. The rate increase accomplished by the enzyme is thus 101S-1016, which is quite impressive. 

It has been frequently suggested that dynamical factors are important in enzyme catalysis (Ref. 9), implying that enzymes might accelerate reactions by utilizing special fluctuations which are not available for the corresponding reaction in solutions. This hypothesis, however, looks less appealing when one examines its feasibility by molecular simulations. That is, as demonstrated in Chapter 2, it is possible to express the rate constant as... 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

The equilibrium constant for the second-order attachment of a substrate to the active site of an enzyme was found to be 326 at 310 K. At the same temperature, the rate constant for the second-order attachment is 7.4 X 107 L-mol-s. What is the rare constant for the loss of unreacted substrate from the active site (the reverse of the attachment reaction) ... 

Hypothermia slows down enzyme catalysis of enzymes in plasma membranes or organelle membranes, as well as enzymes floating around in the cytosol. The primary reason enzyme activity is decreased is related to the decrease in molecular motion by lowering the temperature as expressed in the Arrhenius relationship (k = where k is the rate constant of the reaction, Ea the activation energy,... 

Table 16-7 The surface or enzyme-catalyzed reaction rate constant, Mn/ for oxidation of Mn normalized for oxygen concentration [O2], pH and particulate concentration [X]. d[Mn ]/dt = Mn [Mn][02][0H] [X]...

Rate Constants and Activation Parameters for the Non-enzymic Hydrolysis of D-Glucopyranoside at pH 5... 

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