Initial rate data statistical analysis

The graphical analysis of initial rate data, which is described extensively in this chapter, is useful, especially while the experiment is still in progress. However, it is important to emphasize that, for definitive results, one should always fit the data with appropriate rate equations for statistical analysis (Cleland, 1979). 

The first task in enzyme kinetics is a proper measurement and collection of initial rate data, binding data, or other kinetic data. Thus, the most important part of enz5mie kinetics is a correct choice of kinetic data to be measured and the technically correct estimation of the same. The second important part of enzyme kinetics is an appropriate statistical analysis of experimental data. 

The analysis of initial rate data is performed graphically and statistically. 

The problems of parameter estimation and model discrimination by statistical analysis are most easily understood in relation to a specific example. Let us consider a bisubstrale reaction that obeys the rate Eq. (18.50). The initial rate data from Table 1 are presented graphically in Figs. 3 and 4. The reciprocal plot of l/Uo versus 1/A is a family of straight lines which, in this case, may look either parallel or intersecting due to the fact that the crossover point is distant from the vertical axis, because If is much smaller than K, it would be... 

We should note in passing that we do not really need a statistical analysis of the data presented in Table 3 to convince us that the six rate coefficients constitute an homogeneous set. The sub-set of runs 1, 2 and 3, which were carried out, as far as was possible, under identical conditions, shows a scatter of values overlapping those obtained under different initial concentrations (runs 4, 5 and 6). 

Statistical Analysis of Initial Rate and Binding Data... 

After a kinetic experiment has been carried out, the initial velocities should be plotted for preliminary examination, so that one can tell which rate equation or equations to use in fitting the data. With the rapid advent of computer technology and personal computers, computer programs for the statistical analysis of kinetic data are now the main instmment for statistical analysis. 

Chapter 6 deals with the analysis of kinetic data, another subject that receives scant attention in most existing texts. First, various techniques to test the suitability of a given rate equation are developed. This is followed by a discussion of how to estimate values of the unknown parameters in the rate equation. Initially, graphical techniques are used in order to provide a visual basis for the process of data analysis, and to demystify the subject for visual learners . Then, the results of the graphical process are used as a starting point for statistical analysis. The use of non-linear regression to fit kinetic data and to obtain the best values of the unknown kinetic parameters is illustrated. The text explains how non-linear regression can he carried out with a spreadsheet. 

The demonstration that yield-time data for a particular rate process are satisfactorily represented by a rate equation from the set in Table 3.3. is a usefiil initial result (as in all kinetic analyses), but formulation of a reaction model requires more support than a statistical comparison with the fit of the same data to other rate equations. Some important aspects of kinetic analysis are summarized below. 

Data should be collected by the plant operators throughout the lifetime of the plant to check or update the analysis. These should include statistical data on initiating event frequencies, component failure rates and plant unavailability during periods of testing, maintenance or repair. The analysis should be assessed in the light of the new data. 

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