Rate expressions enzyme catalysis

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... 

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... 

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,... 

Hence the dimension ("the order") of the reaction is different, even in the simplest case, and hence a comparison of the two rate constants has little meaning. Comparisons of rates are meaningful only if the catalysts follow the same mechanism and if the product formation can be expressed by the same rate equation. In this instance we can talk about rate enhancements of catalysts relative to another. If an uncatalysed reaction and a catalysed one occur simultaneously in a system we may determine what part of the product is made via the catalytic route and what part isn t. In enzyme catalysis and enzyme mimics one often compares the k, of the uncatalysed reaction with k2 of the catalysed reaction if the mechanisms of the two reactions are the same this may be a useful comparison. A practical yardstick of catalyst performance in industry is the space-time-yield mentioned above, that is to say the yield of kg of product per reactor volume per unit of time (e.g. kg product/m3.h), assuming that other factors such as catalyst costs, including recycling, and work-up costs remain the same. 

A more realistic but still relatively simple model of enzyme catalysis includes binding of both substrate and product as described by Equation 11.9. This reaction is characterized by five individual rate constants k and k2, and k4 and k5, correspond to the forward and reverse binding steps of the substrate S and product P to the enzyme E, respectively, while k3 expresses the irreversible chemical conversion at the enzyme active site ... 

It was Henri who first proposed that enzyme catalysis depended on the formation of a transient complex of enzyme and substrate, followed by the breakdown i.e., chemical conversion) of bound substrate into product. Nonetheless, credit for derivation of the rate expression for the initial rate phase of one-substrate enzyme-catalyzed reactions is given to Michaelis and Menten. Both treatments gave the same general result ... 

Thus the invocation of the steady-state assumption results in a rate law involving two independent dimensionless parameters C/KM, which compares the bulk substrate concentration with the Michaelis constant for the enzyme, and k3CEd2/DKM, which in effect compares the rate of catalysis with the rate of diffusion. These two parameters may be varied to show their effect on the detected current, and the reader is directed to the cited papers to view the results of this simulation. What is intended here, however, is a specific example of the use of the steady-state assumption in the development of an atypical rate expression (Eq. 20.102). 

The turnover frequency, N, (commonly called the turnover number) defined, as in enzyme catalysis, as molecules reacting per active site in unit time, can be a useful concept if employed with care. In view of the problems in measuring the number of active sites discussed in 1.2.4, it is important to specify exactly the means used to express Q in terms of active sites. A realistic measure of such sites may be the number of surface metal atoms on a supported catalyst but in other cases estimation on the basis of a BET surface area may be the only readily available method. Of course, turnover numbers (like rates) must be reported at specified conditions of temperature, initial concentration or initial partial pressures, and extent of reaction. 

Adsorption on a solid catalyst surface, complex formation in homogeneous catalysis with metallo-organic complexes and in biocatalysis with enzymes share the same principle, i.e. the total number of sites is constant. Therefore, the rate expressions for reactions on heterogeneous, homogeneous and biocatalysts have a similar form. The constant number of active sites results in rate expressions that differ from homogeneous gas phase kinetics. Partial pressures are usually used in rate expressions for gas-phase reactions, while concentrations are used when the reactions take place in the liquid phase. It appears that definitions and nomenclature of particular kinetics constants in the different sub-communities differ sometimes. In the following sections the expressions used by the different subdisciplines will be compared and their conceptual basis outlined. 

As the concentration of the substrate increases, eventually a saturation point is reached beyond this point, the reaction cannot be further accelerated. The plot above is based on the model of enzyme catalysis expressed in the following chemical equation, where the enzyme (E) reacts with the substrate (S) to form some product or products (P). The rates of forward and reverse enzyme-substrate bonding are expressed as ki and k.i, and the rate of product molecule production is expressed as k2. 

The turnover rate becomes proportional to the surface coverage 0, Equation (1.6) is the Langmuir - Hinshelwood expression and is very similar to the Michaelis - Menten expression used in enzyme catalysis. Consider the following mechanism describing... 

Specific detail on Michaelis-Menten kinetics, quasi steady-state approximations, competitive and non-competitive inhibitions, substrate inhibition, rate expressions for enzyme catalysis and deactivations, Monod growth kinetics, etc. are not presented in an extensive manner although additional information is available in the work of Vasudevan for the interested leader. " Also note that the notation adopted by Vasudevan is employed throughout this chapter. 

Reaction quotient (Q) An expression with the same form as Kbut involving arbitrary rather than equilibrium partial pressures, 333-334 Reaction rate The ratio of the change in concentration of a species divided by the time interval over which the change occurs, 285 catalysis for, 305-307 collision model, 298-300 concentration and, 287-292,314q constant, 288 enzymes, 306-307 egression, 288... 

Selectivity is an intrinsic properly of enzymatic catalysis. [3] Following the nomenclature proposed by Cleland [24, 25], the pseudo second-order rate constant for the reaction of a substrate with an enzyme, kml/KM, is known as the specificity constant, ksp. [26] To express the relative rates of competing enzymatic reactions, involving any type of substrates, the ratio of the specificity constants appears to be the parameter of choice [3]. Since the authoritative proposition by Sih and coworkers [27], the ratio of specificity constants for the catalytic conversion of enantiomeric substrates, R and S, is commonly known as the enantiomeric ratio or E -value (Equation 1) ... 

Mutarotation of 0.3% solutions of the freshly dissolved sugars in 12 ml of 5 mM EDTA, pH 7.4 was followed. Significant differences in mutarotation rates (AK) in the presence and absence of 100 units of bovine kidney enzyme were expressed as the ratio AK/Ksp. Differences of less than 5% in these rate constants were not considered significant. Of the 18 sugars listed, nine have been tested previously as substrates for other mammalian mutarotases with essentially the same pattern as described here. The pattern of specificity indicates that a 3-point attachment of enzyme and substrate is necessary for catalysis of mutarotation. b Data from 72). 

As has already been pointed out, any rate equation containing the concentration of the free catalyst is of little practical use if that concentration is unknown, is difficult or impossible to measure, and may vary with conversion, as is the case if a significant fraction of the total catalyst material is present in the form of intermediates of the reaction. This is often true in catalysis by enzymes or other trace-level catalysts. To be sure, the equations in terms of free-catalyst concentration remain correct. However, unless practically all the catalyst material is present as free catalyst, they no longer reflect the actual reaction orders. This is because the concentrations of the participants affect the rate not only directly as expressed explicitly in those equations, but also indirectly and implicitly through their effect on the free-catalyst concentration As the reactant concentration decreases, so do those of the intermediates in turn, this produces an increase in the free-catalyst concentration that boost the rate and, thereby, decreases the apparent reaction order. To reflect this facet correctly, what is needed are rate equations in terms of the total amount of catalyst material, a quantity that is constant and known. 

We want an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps. Our starting point is that the catalytic rate is equal to the product of the concentration of the ES complex and A 2. 

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