Data analysis, enzyme kinetics methods

Selected entries from Methods in Enzymology [vol, page(s)] Dilution of enzyme samples, 63, 10 lipolysis substrate effect, 64, 361, 362 dilution jump kinetic assay, 74, 14-19, 28 dilution method [for dissociation equilibria, 61, 65-96 continuous dilution cuvette, 61, 78-96 data analysis, 61, 74, 75 equations, 61, 70-74 errors, 61, 76-78 experimental procedures, 61, 69, 70 merits, 61, 75, 76 theory, 61, 68, 69... 

Selected entries from Methods in Enzymology [vol, page(s)] Enzyme-substrate complex formation, 64, 53 data analysis, 64, 56, 57 extensions of technique, 64, 57-59 as evidence for occurrence of intermediate, 64, 47-59 kinetic equation, 64, 49-52 limitations, 64, 57-59 mixing procedure, 64, 53-56 reaction condition, 64, 56, 57 termination, 64, 56, 57. 

Cleland WW. Statistical analysis of enzyme kinetic data. Methods Enzymol 1979 63 103-138. 

The fundamental concept of the transition state stabilization was introduced to Linus Pauling in 1948 who said I think that enzymes are molecules that are complementary in structure to the activated complex of the reactions that they catalyze, that is, the molecular configuration that is intermediate between the reacting substances and the product of the reaction . This concept was widely accepted and used for the interpretation of experimental structural and kinetics data on enzyme catalysis, for the design of new substrates and inhibitors and for chemical mimicking of enzyme reactions. Decisive contributions in this area have been made by structural physical methods, X-ray analysis, in particular, and site-directed mutagenesis. 

Cleland WW (1979) Statistical analysis of enzyme kinetic data. In Methods in Enzymol-ogy, Vol. 63A, DL Punch, Ed. Academic Press, Orlando, FL. 

This chapter presents a brief summary of the essentials of statistics that are particularly appropriate for handling biochemical data. This is followed by a section on the quantitative analysis of experimental results which deals chiefly with binding processes and enzyme kinetics. The chapter concludes with a brief discussion of methods of sequence analysis and databases, including a description of the FASTA and Needleman and Wunsch algorithms which form the basis of most of the sequence alignment methods currently in use. 

The results of biochemical investigations can only rarely be interpreted without some form of quantitative analysis of the experimental data. In this chapter, we describe methods that can be used for such analysis taking typical biochemical topics such as enzyme kinetics and the thermodynamics and kinetics of molecular interactions as our examples. The aim of the computer-based exercises in this chapter is to provide the reader with direct experience of methods of data analysis that, we hope, will enable them to apply these approaches to their own data. We also indude a short revision of the essentials of thermodynamics and kinetics relevant to the applications discussed. 

Figure 2 Intermediate in the EPSP synthase pathway, (a) The mechanism of the reaction catalyzed by EPSP synthase is shown. The reaction proceeds by an addition-elimination mechanism via a stable tetrahedral intermediate, (b) A single turnover reaction is shown in which 10- xM enzyme was mixed with 1 OO-m-M S3P and 3.5-riM radiolabeled PEP. Analysis by rapid-quench kinetic methods showed the reaction of PEP to form the intermediate, which then decayed to form EPSP in a single turnover. The smooth lines were computed from a complete model by numerical integration of the equations based on a global fit to all available data. Reproduced with permission from Reference 7.

Calibration is necessary for in-situ spectrometry in TLC. Either the peak height or the peak area data are measured, and used for calculation. Although the nonlinear calibration curve with an external standard method is used, however, it shows only a small deviation from linearity at small concentrations [94.95 and fulfils the requirement of routine pharmaceutical analysis 96,97J. One problem may be the saturation function of the calibration curve. Several linearisation equations have been constructed, which serve to calculate the point of determination on the basis of the calibration line and these linearisation equations are used in the software of some scanners. A more general problem is the saturation function of the calibration curve. It is a characteristic of a wide variety of adsorption-type phenomena, such as the Langmuir and the Michaelis-Menten law for enzyme kinetics as detailed in the literature [98. Saturation is also evident for the hyperbolic shape of the Kubelka-Munk equation that has to be taken into consideration when a large load is applied and has to be determined. 

In the context of the analysis of enzyme kinetics it is sometimes stated that one should always use a non-linear least-squares method for such data, because the usual, unweighted least-squares fits depend on the particular analysis method (Lineweaver-Burk, Hanes, etc.) used. We have seen in section 3.5 that the latter part of this statement is correct. But how about the former ... 

The kinetic analysis of an enzyme mechanism often begins by analysis in the steady state therefore, we first consider the conclusions that can be derived by steady-state analysis and examine how this information is used to design experiments to explore the enzyme reaction kinetics in the transient phase. It has often been stated that steady-state kinetic analysis cannot prove a reaction pathway, it can only eliminate alternate models from consideration (5). This is true because the data obtained in the steady state provide only indirect information to define the pathway. Because the steady-state parameters, kcat and K, are complex functions of all of the reactions occurring at the enzyme surface, individual reaction steps are buried within these terms and cannot be resolved. These limitations are overcome by examination of the reaction pathway by transient-state kinetic methods, wherein the enzyme is examined as a stoichiometric reactant, allowing individual steps in a pathway to be established by direct measurement. This is not to say that steady-state kinetic analysis is without merit rather, steady-state and transient-state kinetic studies complement one another and analysis in the steady state should be a prelude to the proper design and interpretation of experiments using transient-state kinetic methods. Two excellent chapters on steady-state methods have appeared in this series (6, 7) and they are highly recommended. 

In the almost 20 years since this volume s predecessor appeared enzyme kinetics has come of age. Extended theory and the availability of much more sensitive measuring equipment have made possible incisive kinetic analysis of multi-substrate enzymes. One must also add, however, that the full potential of the method has been achieved in rather few cases. Much of the published information has been collected by investigators primarily interested in function rather than mechanism, and is therefore of descriptive value only. Even when a more thorough-going analysis is attempted, it is often difficult and tedious to obtain enough data to remove all ambiguity. Hence doubt and controversy regarding the mechanisms of many important enzymes remain. In the space available here it is not possible to go into much detail about individual cases. The intention, therefore, is to sketch out current approaches and problems. 

Before the advent of computer technology and the computerized statistical methods for data analysis, a procedure that was employed extensively in the analysis of enzyme kinetic data was linear regression. It is important to point out that linear regression performed by the least squares method should not be used unless the values are weighted. If it is used without proper weighting one can get bad results. 

Although graphical analysis is a quick and useful way to visualize enzyme kinetic data, for any definitive work, the data must be subjected to statistical analysis so that the precision of the kinetic constants can be evaluated. However, there are good reasons why plotting methods are essential. The human eye is much less easily deceived than any computer program and is capable of detecting unexpected behavior even if nothing currently available is found in the literature. 

Graphical analysis must always precede the statistical analysis. It is imperative to keep short the time elapsed between data acquisition and data analysis, and in most cases, it is advisable to perform the graphical analysis even while the experiment is still in progress. Wien the data clearly define the nature ofthe rate or binding equation, statistical analysis is not needed to do this. Nevertheless, for a definitive work, statistical methods are necessary for parameter estimation as well as for model discrimination (Senear Bolen, 1992). Computer programs are now available for even the most sophisticated problems in enzyme kinetics (see Section 18.2.4). 

Carnahan, B., Luther, H.A., Wilkes, J.O. Applied numerical methods, WUey, New York. Cornish-Bowden, A. (1995) Analysis of enzyme kinetic data, Oxford Science Publications, Oxford. Daniel, W.W. (1995) Biostatistics, 6th ed., Wiley, New York. 

Inhibition. Graphic analysis of kinetic data according to the method of Lineweaver and Burk has a useful application in the study of inhibitors. Many substances limit the activity of enzymes by reacting with the protein or some other component in such a way as to destroy or decrease the catalytic ability. Other materials inhibit by forming the same sort of complex that a substrate does. In this latter case, the two materials K. B. Augustinsson, Acta Physiol. Scand. 16, Suppl. 52 (1948). 

Cleland, W.W. (1979). Statistical analysis of Enzyme Kinetic Data. Methods in EnzymoL, Vol. 63, pp. 103-138... 

In steady-state kinetic studies, the total concentration of the enzyme should be much less than the concentration of the substrate(s), product(s), and effector(s) typically, by at least a thousandfold. When this condition is not true, the steady-state condition will not be valid and other methods, such as global analysis, have to be utilized to analyze the kinetic data. 

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