Kinetic analysis enzyme reactions

Describe the effects of competitive and noncompetitive inhibitors on the kinetics of enzyme reactions. Apply kinetic measurements and analysis to determine the nature of an inhibitor. 

Kinetic analysis of reactions catalyzed by enzymes is a difficult subject. Flowever, many systems can be represented by rather simple kinetic models that have been successfully appUed by many workers. While we will not treat some of the more esoteric and advanced topics associated with enzyme kinetics, a knowledge of the basic concepts is necessary for students in chemical kinetics and biochemistry. We will now describe these concepts in sufficient detail to provide a basis for further study of this important field. 

An enzyme reaction curve is a function of dependent variables, which are ptropwrtional to concentrations of a substrate or product, with respect to reaction time as the predictor variable. In general, there are two types of enzyme reaction curves. The first type involves the action of just one enzyme, and employs either a selective substrate to detect the activity of one enzyme of interest or a specific enzyme to act on a unique substrate of interest. The second type involves the actions of at least two enzymes, and requires at least one auxiliary enzyme as a tool to continuously monitor a reaction curve. The second type is an enzyme-coupled reaction system. For kinetic analysis of reaction curve, there are many reports on... 

In theory, enzyme reactions may tolerate reversibility, the activation/ inhibition by substrates/products, and even thermo-inactivation of enzyme. From a mathematic view, it is still feasible to estimate parameters of an enzyme reaction system by kinetic analysis of reaction curve if the roles of all those factors mentioned above are included in a kinetic model (Baywenton, 1986 Duggleby, 1983, 1994 Moruno-Davila, et al., 2001 Varon, et al, 1998). However, enzyme kinetics is usually so complex due to the effects of those mentioned factors that there are always some technical challenges for kinetic analysis of reaction curve. Hence, most methods for kinetic analysis of reaction curve are reported for enzymes whose actions suffer alterations by those mentioned factors as few as possible. 

In the past ten years, our group studied chemometrics for kinetic analysis of reaction curve to estimate parameters of enzyme reaction systems the following results were foimd. (a) In terms of reliability and performance for estimating parameters, the use of the integrated rate equations with the predictor variable of reaction time is superior to the use of the integrated rate equations with predictor variables other than reaction time (Liao, et al., 2005a) (b) the integration of kinetic analysis of reaction curve with other methods to quantify initial rates... 

To estimate parameters by kinetic analysis of reaction curve, the desired parameters are included in a set of parameters for the best fitting. Regardless of the number of enzymes involved in a reaction curve, there are the following two approaches for kinetic analysis of reaction curve based on different ways to realize NLSF and their data transformation. 

With any enzyme, iterative numerical integration of the differential rate equation(s) from a starting point with sets of preset parameters can be universally applicable regardless of the complexity of the kinetics. Thus, the second approach exhibits better imiversality and there are few technical challenges to kinetic analysis of reaction curve via NLSF. In fact, however, the second approach is occasionally utilized while the first approach is widely practiced. 

The second prerequisite is that enzyme reaction should be irreversible. In theory, the estimation of prarameters by kinetic analysis of reaction curve is still feasible when reaction reversibility is considered, but the estimated prarameters possess too low rehabihty to have practical roles (data impnbhshed). Generally, a prepraration of a substance with contaminants less than 1% in mass content can be taken as a pure substance. Namely, a reagent leftover in a reaction accoimting for less than 1% of that before reaction can be negligible. For convenience, therefore, an enzyme reaction is considered irreversible when the leftover level of a substrate of interest in equilibrium is much less than l%of its initial one. To promote the consumption of the substrate of interest, the concentrations of other substrates should be preset at levels much over 10 times the initial level of the substrate of interest. In this case, the enzyme reaction is ap>p)arently irreversible and follows kinetics on single substrate. Or else, the use of scavenging reactions to remove products can drive the reaction forward. The concurrent uses of both approaches are usually better. 

The forth prerequisite is that the enzyme should be stable to validate Equ.(2), or else the inactivation kinetics of the enzyme should be included in the kinetic model. Enzyme stability should be checked before kinetic analysis of reaction curve. When the inactivation kinetics of an enzyme is included in a kinetic model for kinetic analysis of reaction curve, the integrated rate equation is usually quite complex or even inaccessible if the inactivation kinetics is too complex. For kinetic analysis of reaction curve of complicated kinetics, numerical integration to produce calculated reaction curves for NLSF to a reaction curve of interest, instead of NLSF with Equ. (4), can be used to estimate parameters (Duggleby, 1983, 1994 Moruno-Davila, et al., 2001 Varon, et al., 1998 Yang, et al., 2010). 

Kinetic analysis of reaction curve requires more considerations when activities of enzymes are altered by their substrates/products. In this case, more parameters can be included in kinetic models similar to Equ.(2) for kinetic analysis of reaction curve, but there must be complicated process to optimize reaction conditions and preset parameters. Based on the principle for kinetic analysis of reaction curve described above, we developed some new integration strategies to successfully quantify enzyme initial rates and substrate with absorbing performance even when the activities of enzymes of interest are altered significantly by substrates/products (Li, et al., 2011 Liao, 2007a Zhao, L.N., et al., 2006). 

By simulation with such a new approach for kinetic analysis of enzyme-coupled reaction curve recorded at 1-s intervals, the upper limit of linear response for measuring ALT initial rates is increased to about five times that by the classical initial rate method. This new approach is resistant to reasonable variations in data range for analysis. By experimentation using the sampling intervals of 10 s, the upper limit is about three times that by the classical initial rate method. Therefore, this new approach for kinetic analysis of enzyme-coupled reaction curve is advantageous, and can potentially be a universal approach for kinetic analysis of reaction curve of any system of much complicated kinetics. 

Any analytical method should have favourable analysis efficiency, wide linear range, low cost and strong robustness. Kinetic analysis of reaction curve for Vm and So assay can have much better upper limit of linear response, but inevitably tolerates low analysis efficiency when wide linear range is required. Based on kinetic analysis of reaction curve, however, our group developed two integration strategies for enzyme initial rate and substrate assay, respectively, with both favourable analysis efficiency and ideal linear ranges. 

The integration of kinetic analysis of reaction curve using proper integrated rate equations with the classical initial rate method gives an integration strategy to measure enzyme initial... 

After the integration strategy for enzyme initial rate assay is validated, a switch point should be determined for changing from the classical initial rate method to kinetic analysis of reaction curve. The estimation of Vm by kinetic analysis of reaction curve usually prefers substrate consumption percentages reasonably high. Therefore, the substrate consumption percentage that gives an enzyme activity from 90% to 100% of the upper limit of linear response by the classical initial rate method can be used as the switch point. 

As for enzyme-coupled reaction system, initial rate itself is estimated by kinetic analysis of reaction curve based on numerical integration and NLSF of calculated reaction curves to a reaction curve of interest. Consequently, neither the conversion of indexes nor the optimization of parameters for such conversion is required and the integration strategy can be realized easily. By kinetic analysis of enzyme-coupled reaction curve, there still should be a minimum number of the effective data and a minimum substrate consumption percentage in the effective data for analysis these prerequisites lead to unsatisfactory lower limits of linear response for favourable analysis efficiency (the use of reaction duration within 5.0 min). The classical initial rate method is effective to enzyme-coupled reaction systems when activities of the enzyme of interest are not too high. Therefore, this new approach for kinetic analysis of enzyme-coupled reaction curve can be integrated with the classical initial rate method to quantify enzyme initial rates potentially for wider linear ranges. 

For simplicity in programming, we used Visual Basic 6.0 to write the source code and working windows (Liu, et al., 2011). The executable program has the main window to perform kinetic analysis of reaction curve (Fig. 11). Original data for each reaction curve is stored as a text file, and keywords are used to indicate specific information related to the reaction curve including sample numbering, the enzyme used, the quantification method, some necessary kinetic parameters, and usually initial signal before enzyme action. Such information is read into memory by the software for kinetic analysis of reaction curve. 

On the main window to perform kinetic analysis of reaction curve, original data are listed and plotted for eyesight-checking of data for steady-state reaction. Text boxes are used to input some common parameters like fC, and most parameters are read from the text file for the reaction curve. Subprogram for an enzyme reaction system is called for running results are displayed on the main window and may be saved in text file for further analysis. 

Reversibly fonned micelles have long been of interest as models for enzymes, since tliey provide an amphipatliic environment attractive to many substrates. Substrate binding (non-covalent), saturation kinetics and competitive inliibition are kinetic factors common to botli enzyme reaction mechanism analysis and micellar binding kinetics. 

In contrast to SDS, CTAB and C12E7, CufDSjz micelles catalyse the Diels-Alder reaction between 1 and 2 with enzyme-like efficiency, leading to rate enhancements up to 1.8-10 compared to the reaction in acetonitrile. This results primarily from the essentially complete complexation off to the copper ions at the micellar surface. Comparison of the partition coefficients of 2 over the water phase and the micellar pseudophase, as derived from kinetic analysis using the pseudophase model, reveals a higher affinity of 2 for Cu(DS)2 than for SDS and CTAB. The inhibitory effect resulting from spatial separation of la-g and 2 is likely to be at least less pronoimced for Cu(DS)2 than for the other surfactants. 

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. 

While many enzymes have a single substrate, many others have two—and sometimes more than two—substrates and products. The fundamental principles discussed above, while illustrated for single-substrate enzymes, apply also to multisubstrate enzymes. The mathematical expressions used to evaluate multisubstrate reactions are, however, complex. While detailed kinetic analysis of multisubstrate reactions exceeds the scope of this chapter, two-substrate, two-product reactions (termed Bi-Bi reactions) are considered below. 

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