Graphical procedures, kinetic analysis

A General Integral Method for the Analysis of Kinetic Data—Graphical Procedure. 

Integral Methods for the Analysis of Kinetic Data—Numerical Procedures. While the graphical procedures discussed in the previous section are perhaps the most practical and useful of the simple methods for determining rate constants, a number of simple numerical procedures exist for accomplishing this task. 

Kinetic analysis of tyrosinase and calculation of constants will be described using graphical analysis by the Michaelis-Menten equation, Lineweaver-Burk equation, or the direct linear curve. Procedures for preparing these graphs are described below. Alternatively, students may use available computer software to graph data and calculate kinetic constants. Recommended enzyme kinetic computer software packages include Enzyme... 

This simple step-by-step procedure reveals how the use of extensive and accurate in situ data combined with simple graphical manipulations can provide a wealth of information of use in both scale-up and in furthering both practical and fundamental mechanistic understanding of complex catalytic reactions in a fraction of the time and number of experiments required by classical kinetic analysis. 

A more detailed exploration of the reactivity of biphenyl resolves the problem. The ra-phenyl substituent reduces the rate of substitution in the benzene nucleus (Table 7). Qualitatively, this effect is in agreement with the predictions based on the rate of solvolysis of ra-phenylphenyl-dimethylcarbinyl chloride (Brown and Okamoto, 1958) and with the expected electron-withdrawing properties of the phenyl group. The data conform to the Selectivity Relationship with reasonable precision (Fig. 31). In view of the activation of the ortho and para positions, direct evaluation of the partial rate factors for the deactivated meta position is not always possible. Hence, indirect kinetic procedures were employed in several cases, halogenation and acylation, to estimate the values. Graphical analysis of the data shows that mfb is independent of the reagent selectivity. Deviations from the relationship are no greater than for the ordinary side-chain reactions. 

These procedures will provide a graphical representation of the rate of product formation. Such data can be analyzed visually or subjected to statistical analysis (see General References for details). In addition, data collected at several substrate concentrations can be used to obtain kinetic constants. Again, these data, collected by the HPLC method, can be manipulated by standardized methods (see General References). 

Again, the usual procedure for the graphical analysis of initial rate data would be to treat each substrate as the varied substrate at different fixed concentrations of another substrate, maintaining a fixed concentration of the third substrate. In this way, aU kinetic constants can be determined and, what is equally important, each mechanism can be identified unequivocally. 

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