Reaction velocity, enzymatic

One of the most important assumptions in MM kinetics is that the reaction in question wiU proceed in a three-dimensional vessel filled with a well-stirred fluid that obeys Pick s law for diffusion. This is rarely the case in a living cell, where many reactions are localized to membranes (two dimensions) or to small regions somewhere within the cell, creating an effectively one-dimensional environment with little or no diffusion. To circumvent this limitation, fractal kinetics have been developed which allow for the approximation of enzymatic reaction velocities in vivo [7]. Fractal kinetics can utilize MM-type kinetic constants to create a model of events in a spatially restricted environment. Briefly, as the dimensionality of a reaction is reduced from three dimensions to one, the kinetic order of a bimolec-ular reaction, for example, increases from 2 in a three-dimensional case, to 2.46 in a two-dimensional environment (e.g., membrane), to 3 in a one-dimensional channel, up to 50 for the case where fractal dimensions are less than 1. In simple terms, the kinetic order is the sum of all stoichiometric coefficients of the reactants in a balanced chemical reaction equation. Rearranging the familiar equation for MM kinetics... 

The three most common types of inhibitors in enzymatic reactions are competitive, non-competitive, and uncompetitive. Competitive inliibition occurs when tlie substrate and inhibitor have similar molecules that compete for the identical site on the enzyme. Non-competitive inhibition results in enzymes containing at least two different types of sites. The inhibitor attaches to only one type of site and the substrate only to the other. Uncompetitive inhibition occurs when the inhibitor deactivates the enzyme substrate complex. The effect of an inhibitor is determined by measuring the enzyme velocity at various... 

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]. 

Kinetics is the branch of science concerned with the rates of chemical reactions. The study of enzyme kinetics addresses the biological roles of enzymatic catalysts and how they accomplish their remarkable feats. In enzyme kinetics, we seek to determine the maximum reaction velocity that the enzyme can attain and its binding affinities for substrates and inhibitors. Coupled with studies on the structure and chemistry of the enzyme, analysis of the enzymatic rate under different reaction conditions yields insights regarding the enzyme s mechanism of catalytic action. Such information is essential to an overall understanding of metabolism. 

If the velocity of an enzymatic reaction is decreased or inhibited, the kinetics of the reaction obviously have been perturbed. Systematic perturbations are a basic tool of experimental scientists much can be learned about the normal workings of any system by inducing changes in it and then observing the effects of the change. The study of enzyme inhibition has contributed significantly to our understanding of enzymes. 

We consider the initial velocities V, observed with different substrate concentrations X in a rate-limited enzymatic reaction [15] ... 

The initial velocity of reaction is defined by the slope of a linear plot of product (or substrate) concentration as a function of time (Chapter 2), and we have just discussed the importance of measuring enzymatic activity during this initial velocity phase of the reaction. The best measure of initial velocity is thus obtained by continuous measurement of product formation or substrate disappearance with time over a convenient portion of the intial velocity phase. However, continuous monitoring of assay signal is not always practical. Copeland (2000) has described three types of assay readouts for measuring reaction velocity continuous assays, discontinuous... 

Figure 4.6 Reaction velocity as a function of enzyme concentration for a non-ideal enzymatic activity assay. Note the deviations from the expected linear relationship at low and at high enzyme concentration.

Enzymatic reactions are influenced by a variety of solution conditions that must be well controlled in HTS assays. Buffer components, pH, ionic strength, solvent polarity, viscosity, and temperature can all influence the initial velocity and the interactions of enzymes with substrate and inhibitor molecules. Space does not permit a comprehensive discussion of these factors, but a more detailed presentation can be found in the text by Copeland (2000). Here we simply make the recommendation that all of these solution conditions be optimized in the course of assay development. It is worth noting that there can be differences in optimal conditions for enzyme stability and enzyme activity. For example, the initial velocity may be greatest at 37°C and pH 5.0, but one may find that the enzyme denatures during the course of the assay time under these conditions. In situations like this one must experimentally determine the best compromise between reaction rate and protein stability. Again, a more detailed discussion of this issue, and methods for diagnosing enzyme denaturation during reaction can be found in Copeland (2000). 

Figure 6.2 Effect of preincubation time with inhibitor on the steady state velocity of an enzymatic reaction for a very slow binding inhibitor. (A) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the single-step binding mechanism of scheme B of Figure 6.3. (B) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the two-step binding mechanism of scheme C of Figure 6.3. Note that in panel B both the initial velocity (y-intercept values) and steady state velocity are affected by the presence of inhibitor in a concentration-dependent fashion.

Figure 6.19 Fractional velocity for the enzymatic reaction of COX2 as a function of preincubation time with varying concentrations of the slow binding inhibitor DuP697. The lines drawn through the data represent the best fits to Equation (6.4).

The net rate of an enzymatic reaction is usually referred to as its velocity and is assigned the symbol V. In this case... 

At equilibrium the net reaction velocity must be zero. In terms of the enzymatic kinetic constants, equation 7.3.40 then indicates that... 

V velocity of an enzymatic reaction Pi order of the reaction with respect to... 

The velocity v of an enzymatic reaction is defined as the rate at which a substrate disappears or at which a product is formed, the two being identical ... 

According to transition state theory, if the transmission coefficient k = 1, T and ET will be transformed to products at the same rate. Thus, if the mechanisms of the nonenzymatic and enzymatic reactions are assumed the same, the ratio of maximum velocities for first-order transformation of ES and S will be given by Eq. 9-85. For some enzymes the ratio... 

How is the instantaneous initial velocity of an enzymatic reaction measured What precautions must be taken to ensure that a true instantaneous velocity is being obtained ... 

We see that the rate of the enzyme-catalyzed reaction depends linearly on the enzyme concentration, and in a more complicated way on the substrate concentration. Thus, when [S] Km, (Eq. (2.41)) reduces to v = k2[E]0, and the reaction is zero order in [S], This means that there is so much substrate that all of the enzyme s active sites are occupied. It also means that [S] remains effectively unchanged, even though products are formed. This situation is known as saturation kinetics. The value k2[E]0 is also called the maximum velocity of the enzymatic reaction, and written as vmax. 

When the velocity of an enzymatic reaction is equal to its Vmax, then the rate of substrate conversion to the product may be increased by... 

Other scientists, among them Hearon (36), have simply taken up the fundamental ideas, especially the expressions for the reciprocal velocity of linear (open or closed) sequences and used them as they stand for their special purposes or have developed them in several directions. In this connection it may be mentioned that Hammett (37) recommends the use of such expressions. As a more recent example it may also be mentioned that Sch0nheyder (38) with the same method arrived at a rather unexpected mechanism for an enzymatic reaction, the saponification of racemic i-caprylyl glycerol, by means of a certain lipase. 

For an enzymatic reaction (in contrast to a binding reaction), the initial velocity v0 is determined by the concentration of the enzyme substrate complex therefore, what form does equation (9.48) take ... 

The increase of velocity in methanolysis of the waste edible oil can be explained as follows. Water in the oil is attracted to the glycerol layer generated by methanolysis. Because the water goes out of the field of enzymatic methanolysis (oil layer), the reaction velocity gradually increased. Actually, the content of water in the acylglycerols/FAMEs layer (oil layer) decreased from 0.2 to 0.05 wt% and that of the glycerol layer was 4.1 wt% after five cycles (Watanabe et al, 2001). 

A large group of scientists, including the author, believe that a chemical catalytic process, as well as an enzymatic reaction contains a certain sequence of elementary chemical steps. Each of these steps proceeds by ordinary laws of chemical kinetics. The accelerating action of a catalyst is accounted for by the fact that its active centers become involved in such chemical reactions with substrate molecules, which lead to an increase in the velocity of the process as a whole. Within the framework of this concept, enzymes are characterized by a set of certain specific properties, which have been polished off in the course ofbiological evolution. 

We have demonstrated for the first time that we could apply the theory of generalized Thiele modulus to an enzymatic reaction both in n-hexane and SC CO2. The comparison between the two reaction media is not so clear in n-hexane the real reaction velocity is higher than that obtained in SC C02. Nevertheless, the Thiele modulus values indicates a limitation due to the internal mass transfer rate g 1. Thus we observed, in the hexane case, a diffusional control, while in SC C02 an intermediate rate between the reactional and diffusional rates was apparent. It therefore, seems that SC CO2 should be the solvent of choice in reactions catalyzed by immobilized enzymes, since it reduces problems with internal mass transfer. An other advantage is that the value of the inhibition constant is 43 mM in n-hexane and 120 mM in SC CO2 [14], so SC CO2 should be more convenient if we have to work with higher ethanol concentration. The economic feasibility of an industrial scale lipase catalyzed reaction on C02 may depend upon possible costs for high-pressure equipment. 

Figure 5 Initial reaction velocity V[ of the enzymatically catalyzed transesterification of ( )-menthol and isopropenyl acetate in SC-CO2 as a function of water activity aw...

Figure II-8 The relationship of substrate concentration and initial velocity in enzymatic reactions.

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