Enzyme reaction kinetics kinetic parameters, evaluation

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

M. Stoytcheva, Electrochemical evaluation of the kinetic parameters of a heterogeneous enzyme reaction in presence of metal ions. Electroanalysis 14, 923-927 (2002). 

Prior to being able to study the function and mechanism of an enzyme, it is essential that suitable assays be available to monitor enzyme activity toward different substrates and to determine the kinetic parameters kcat and Km for the reactions. A brief overview of the known assays for the evaluation of PLCB(. activity is thus appropriate. The ideal assay for a phospholipase C would utilize a phospholipid substrate, not an analogue with a modified headgroup or side chains. Such an assay should be sensitive to minimize the quantities of enzyme and substrates that would be required, and it should be convenient to implement so that analyses may be readily performed. 

The direction of a reaction can be assessed straightforwardly by comparing the equilibrium constant (Keq) and the ratio of the product solubility to the substrate solubility (Zsat) [39]. In the case of the zwitterionic product amoxicillin, the ratio of the equilibrium constant and the saturated mass action ratio for the formation of the antibiotic was evaluated [40]. It was found that, at every pH, Zsat (the ratio of solubilities, called Rs in that paper) was about one order of magnitude greater in value than the experimental equilibrium constant (Zsat > Keq), and hence product precipitation was not expected and also not observed experimentally in a reaction with suspended substrates. The pH profile of all the compounds involved in the reaction (the activated acyl substrate, the free acid by-product, the antibiotic nucleus, and the product) could be predicted with reasonable accuracy, based only on charge and mass balance equations in combination with enzyme kinetic parameters [40]. 

All of the above treatments are apphcable only to unimolecular irreversible enzyme reactions. In case of more comphcated reactions, additional kinetic parameters must be evaluated, but plots similar to that for Equation 3.32, giving straight lines, are often used to evaluate kinetic parameters. 

Commercial yeast invertase (Bioinvert ) was immobilized by adsorption on anion-exchange resins, collectively named Dowex (1x8 50-400,1x4 50-400, and 1x2 100-400). Optimal binding was obtained at pH 5.5 and 32°C. Among different polystyrene beads, the complex Dowex-1x4-200/invertase showed a yield coupling and an immobilization coefficient equal to 100%. The thermodynamic and kinetic parameters for sucrose hydrolysis for both soluble and insoluble enzyme were evaluated. The complex Dowex/inver-tase was stable without any desorption of enzyme from the support during the reaction, and it had thermodynamic parameters equal to the soluble form. The stability against pH presented by the soluble invertase was between 4.0 and 5.0, whereas for insoluble enzyme it was between 5.0 and 6.0. In both cases, the optimal pH values were found in the range of the stability interval. The Km and Vmax for the immobilized invertase were 38.2 mM and 0.0489 U/mL, and for the soluble enzyme were 40.3 mM and 0.0320 U/mL. 

Enzyme kinetics were evaluated in a PDMS-glass chip using a continuous-flow system. A biotinylated enzyme (HRP or (5-galactosidase) was coupled to streptavidin-coated beads via the amide coupling of an aminocaproyl spacer. These beads (15.5 pm) were retained by a weir in the chip. The channel wall was passivated by 1 mg/mL BSA. The apparent enzyme kinetic parameters were evaluated using the Lilly-Homby model, as developed for the packed-bed enzymatic reactor systems. It was found that the apparent Michaelis constant (Km) approached the tme Km value of the free enzyme at zero-flow rate of a homogeneous reaction [845]. 

Initial rates of a hydrolase (10.0 nM)-catalyzed reaction are measured and tabulated overleaf. Evaluate the kinetic parameters of this Uni-substrate reaction. Calculate the turnover number of the enzyme. 

A plot of l/rp against 1/CA would give a straight line with an intercept of 1/ Vmax. The line crosses the %-axis at 1 /Km, as shown in Figure 3.6a. Although the Lineweaver-Burk plot is widely used to evaluate the kinetic parameters of enzyme reactions, its accuracy is affected greatly by the accuracy of data at low substrate concentrations. 

The biocatalysts obtained were evaluated with respect to the composition, morphology, activity and stability of the immobilised enzyme in the starch hydrolysis reaction. In general, two alternative methods can be used, considering the bioartificial matrix as a substrate for the enzyme (this method is used for example to drive drug release into erosion control devices), or alternatively, as in the case of this work, after blending the enzyme with a polymer, and investigating its activity against an external substrate. The apparent kinetic parameters of the reaction catalyzed by the immobilised and native enzymes were determined and compared. 

For simple kinetic mechanisms, like irreversible one-substrate reactions, both rapid equilibrium and steady-state hypothesis lead to rate equations that are formally equal in parametric terms, so when those parameters are experimentally determined, results are the same no matter what hypothesis is considered. Kinetic parameters are to be experimentally determined to obtain validated rate expressions to be used for the design or performance evaluation of enzyme reactors. 

Ishikawa H, Tanaka T, Kuro K et al. (1987) Evaluation of tme kinetic parameters for reversible immobihzed enzyme reactions. Biotechnol Bioeng 29 924-933 Jeison D, Ruiz G, Acevedo F et al. (2003) Simulation of the effect of intrinsic reaction kinetics and particle size on the behavior of immobihzed enzymes under internal diffusional restrictions and steady state operation. Proc Biochem 39(3) 393-399 Katchalski-Katzir E, Kraemer DM (2000) Eupergit C, a carrier for immobDization of enzymes of industrial potential. J Mol Catal B Enzym 10 157-176 Kheirolomoom A, Khorasheh F, Fazehnia H (2002) Influence of external mass transfer limitation on apparent kinetic parameters of peniciUin G acylase immobihzed on nonporous ultrafine silica particles. J Biosci Bioeng 93 125-129... 

The term enzyme activity includes not only such kinetic parameters as Michaelis constants and maximum velocities, but also a consideration of the fraction of the potential activity which is available under the actual intracellular conditions of pH, temperature, ionic strength, etc. These factors cannot be evaluated for the reactions in question at the present time. 

For a multienzyme process, this evaluation is critically important to achieve a better theoretical understanding of the process and to achieve useful modeling and process design. The reaction considerations describe the key characteristics to understand how the interaction between enzymes and components can be interpreted for modehng. Furthermore, such information forms the basis for the formulation of reaction rates for the different enzymes that are involved in multienzyme process. In this manner, a preliminary idea of enzyme mechanisms and kinetic parameters, that can be expected when developing a model, may be obtained. Key information (Figure 10.3) may be described as... 

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". ... 

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