Enzyme kinetics reaction rates

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

Some enzymes are so fast and so selective that their k2/Km ratio approaches the molecular diffusion rates (108-109m s-1). Such enzymes are called kinetically perfect [21]. With these enzymes, the reaction rate is diffusion controlled, and every collision is an effective one. However, since the active site is very small compared to the entire enzyme, there must be some extra forces which draw the substrate to the active sites (otherwise, there would be many fruitless collisions). The work of these forces was dubbed by William Jencks in 1975 as the Circe effect [22], after the mythological sorceress of the island of Aeaea, who lured Odysseus men to a feast and then turned them into pigs [23,24]. 

The kinetic behaviour of electrochemical biosensors is most commonly characterized using the dependence of the steady-state amperometric current on the substrate concentration. This type of analysis has some limitations because it does not allow for a decoupling of the enzyme-mediator and enzyme-substrate reaction rates. The additional information required to complete the kinetic analysis can be extracted either from the potential dependence of the steady-state catalytic current or from the shift of the halfwave potential with substrate concentration [154]. Saveant and co-workers [155] have presented the theoretical analysis of an electrocatalytic system... 

In enzyme kinetics the rate of reaction (fe) is related to the energy of activation (E) by the Arrhenius equation ... 

Bedner, E., Melamed, M.R., and Darzynkiewicz, Z. (1998) Enzyme kinetic reactions and fluorochrome uptake rates measured in individual cells by laser scanning cytometry (LSC). Cytometry, 33, 1-9. 

In a metabolic pathway, the initial enzyme is regulated by allosteric or other mechanisms as discussed below. The subsequent enzymes in the pathway obey Michaelis-Menten kinetics. If the initial enzyme is down-regulated (its reaction rate falls), the concentration of its product falls. Since this product is the substrate for the second enzyme, its reaction rate will fall according to the Michaelis-Menten equation. Hence, its production concentration will fall, and so on down the whole pathway. 

The use of enzymes to lyse cells, hydrolyze fat emulsions, solubilize proteinaceous colloids, liquify or saccharify starch gels and granules, and degrade various components of celluloslc substrates indicates that many substrates are present in a particulate form. Kinetic forms for such enzyme catalyzed reaction rates are here noted, and will be revisited in the subsequent discussion of immobilized enzyme kinetics. 

Fig. 2. Specifying the reactions, (a) Molecular species are divided into three adjacent regions, EC (extracellular), CM (cell membrane), and /C (intracellular). Reactions can be specified in any of these three compartments, (b) In the Reaction Kinetic Editor, we specify the reaction rate expression, as well as the kinetic reaction rates associated with the expression. (c) In this model, the reactions are defined in CM. Solid lines going from molecular species to reaction sites connect reactants solid lines going from reaction sites to molecular species connect products and dotted lines connect enzymes to reaction sites.

The response of an enzyme sensor in the steady state depends largely on the ratio of the substrate concentration [5] to the enzyme Michaelis constant K. When [S K is large, the reaction rate reaches a maximal value V,, which is proportional to the number of active sites of the immobilized enzyme. The reaction rate is independent of the substrate concentration, and the product concentration at the contact with the electrode is the same for all high substrate concentration. The quantify of enzyme in the layer determines the linear zone in the response to the substrate concentration. This zone corresponds to first-order kinetics with respect to substrate concentration, whereas the region with a plateau has zeroth-order kinetic. When the substrate concentration is very high([5] K ), the biosensor is no longer capable of determining the substrate but may determine inhibitors which affect the minimal rate of the enzymatic reaction... 

FIGURE 16.2 Michaelis-Menten kinetics of an enzyme-catalyzed reaction rate dependence on substrate concentration. The example is plot for Vniax=4 mol 1 s and K = 1 mol 1 . ... 

By protodetritiation of the thiazolium salt (152) and of 2 tritiothiamine (153) Kemp and O Brien (432) measured a kinetic isotope effect, of 2.7 for (152). They evaluated the rate of protonation of the corresponding yiides and found that the enzyme-mediated reaction of thiamine with pyruvate is at least 10 times faster than the maximum rate possible with 152. The scale of this rate ratio establishes the presence within the enzyme of a higher concentration of thiamine ylide than can be realized in water. Thus a major role of the enzyme might be to change the relative thermodynamic stabilities of thiamine and its ylide (432). 

The earliest examples of analytical methods based on chemical kinetics, which date from the late nineteenth century, took advantage of the catalytic activity of enzymes. Typically, the enzyme was added to a solution containing a suitable substrate, and the reaction between the two was monitored for a fixed time. The enzyme s activity was determined by measuring the amount of substrate that had reacted. Enzymes also were used in procedures for the quantitative analysis of hydrogen peroxide and carbohydrates. The application of catalytic reactions continued in the first half of the twentieth century, and developments included the use of nonenzymatic catalysts, noncatalytic reactions, and differences in reaction rates when analyzing samples with several analytes. 

Selectivity The analysis of closely related compounds, as we have seen in earlier chapters, is often complicated by their tendency to interfere with one another. To overcome this problem, the analyte and interferent must first be separated. An advantage of chemical kinetic methods is that conditions can often be adjusted so that the analyte and interferent have different reaction rates. If the difference in rates is large enough, one species may react completely before the other species has a chance to react. For example, many enzymes selectively cat-... 

Assay of Enzymes In body fluids, enzyme levels aie measured to help in diagnosis and for monitoiing treatment of disease. Some enzymes or isoenzymes are predominant only in a particular tissue. When such tissues are damaged because of a disease, these enzymes or isoenzymes are Hberated and there is an increase in the level of the enzyme in the semm. Enzyme levels are deterrnined by the kinetic methods described, ie, the assays are set up so that the enzyme concentration is rate-limiting. The continuous flow analyzers, introduced in the early 1960s, solved the problem of the high workload of clinical laboratories. In this method, reaction velocity is measured rapidly the change in absorbance may be very small, but within the capabiUty of advanced kinetic analyzers. 

Enzymatic Catalysis. Enzymes are biological catalysts. They increase the rate of a chemical reaction without undergoing permanent change and without affecting the reaction equiUbrium. The thermodynamic approach to the study of a chemical reaction calculates the equiUbrium concentrations using the thermodynamic properties of the substrates and products. This approach gives no information about the rate at which the equiUbrium is reached. The kinetic approach is concerned with the reaction rates and the factors that determine these, eg, pH, temperature, and presence of a catalyst. Therefore, the kinetic approach is essentially an experimental investigation. 

Enzyme-Catalyzed Asymmetric Synthesis. The extent of kinetic resolution of racemates is determined by differences in the reaction rates for the two enantiomers. At the end of the reaction the faster reacting enantiomer is transformed, leaving the slower reacting enantiomer unchanged. It is apparent that the maximum product yield of any kinetic resolution caimot exceed 50%. 

Lineweaver-Burk plot Method of analyzing kinetic data (growth rates of enzyme catalyzed reactions) in linear form using a double reciprocal plot of rate versus substrate concentration. 

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. 

Before beginning a quantitative treatment of enzyme kinetics, it will be fruitful to review briefly some basic principles of chemical kinetics. Chemical kinetics is the study of the rates of chemical reactions. Consider a reaction of overall stoichiometry... 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The initial reaction rate (v0) obtained from each substrate concentration was fitted to Michaelis-Menten kinetics using enzyme kinetics. Pro (EKP) Software (ChemSW product,... 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

Table 5.1 presents the intrinsic kinetic parameters (Km and Vln lx) for the free lipase system and apparent kinetic parameters (K and V ) for the immobilised lipase in the EMR using fixed 2g-l 1 lipase concentration. The immobilised lipase showed higher maximum apparent reaction rate and greater enzyme-substrate (ES) affinity compared with free lipase. 

The inhibition analyses were examined differently for free lipase in a batch and immobilised lipase in membrane reactor system. Figure 5.14 shows the kinetics plot for substrate inhibition of the free lipase in the batch system, where [5] is the concentration of (S)-ibuprofen ester in isooctane, and v0 is the initial reaction rate for (S)-ester conversion. The data for immobilised lipase are shown in Figure 5.15 that is, the kinetics plot for substrate inhibition for immobilised lipase in the EMR system. The Hanes-Woolf plots in both systems show similar trends for substrate inhibition. The graphical presentation of rate curves for immobilised lipase shows higher values compared with free enzymes. The value for the... 

The kinetics of enzyme reactions were first studied by the German chemists Leonor Michaelis and Maud Menten in the early part of the twentieth century. They found that, when the concentration of substrate is low, the rate of an enzyme-catalyzed reaction increases with the concentration of the substrate, as shown in the plot in Fig. 13.41. However, when the concentration of substrate is high, the reaction rate depends only on the concentration of the enzyme. In the Michaelis-Menten mechanism of enzyme reaction, the enzyme, E, and substrate, S, reach a rapid preequilibrium with the bound enzyme-substrate complex, ES ... 

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