Cornish-Bowden-Eisenthal Method

Cornish—Bowden—Eisenthal Method.9 This method is distinct from the previous three linear regression methods, in that each pair of (v, [S]) values is used to construct a separate line on a plot in which VW and Km form the y and x axes, respectively. Beginning with another version of the Michaelis-Menten equation, in which Vmax is the y value and Km is the x value as shown in Eq. 2.23, 

TABLE 2.3. Error-Free Michaelis-Menten Data for Method of Comparison 

The precisions and accuracies of the four methods described above for the determination of A m values were compared statistically by first generating an error-free data set of v and [S] data, and then introducing different types of error to the v values to generate a total of 100 individual data sets. The error-free data set was generated using Eq. 2.17 with Vm = Km = 1, and the seven individual values are given below in Table 2.3. 

Fifty data sets containing absolute errors were then generated by adding random numbers of mean zero and standard deviation 0.05 to each v value. Another 50 data sets were generated to contain relative error, by multiplying each v value by a random number of mean one and standard deviation 0.10. These 100 data sets were then analyzed individually by each of the four methods, to generate 100 Km values for each method. The average Km value and its uncertainty for each method and each error type are summarized in Table 2.4. 

The values summarized in Table 2.4 show that, while all four methods give accurate Km values (in all cases, Km = 1.00 is within the uncertainties reported), the 

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Four graphical methods may be used to establish Km and Vjn ,x values under given experimental conditions, called the Eadie-Hofstee, Hanes, Lineweaver-Burk, and Cornish-Bowden-Eisenthal methods. All four involve the measurement of initial rates of reaction as a function of initial substrate concentration, at constant enzyme concentration. 

Cornish-Bowden-Eisenthal method each of the v, v[S] points shown above gives the equation for a straight line, according to Vmax = v + ( 7[SJ)A m. The six equations are thus... 

Cornish-Bowden, A., Eisenthal, R. (1974) Statistical Considerations in the Estimation of Enzyme Kinetic Parameters by the Direct Linear Plot and other Methods, Biochem.J. 139, 721-730. 

Despite their appealing simplicity, these methods have serious limitations. The Lineweaver-Burk and Hanes plots are unreliable, e.g., the variation of the variance almost certainly results in an incorrect weighting, whereas in the Eadie-Hofstee plot Vo is present in both variables. The direct linear plot of Eisenthal and Cornish-Bowden (1974), for which the Michaelis-Menten equation is rearranged to relate to A , i.e., = Vo -f- Vo A ,/[S] is very simple but... 

A somewhat different method, also based on initial rate measurements, is the one proposed by Eisenthal and Cornish-Bowden (1974). The method is based on tracing straight lines joining the data points (0, —Si) and (vi,0) in a v versus s plot. Such lines intersect at a point whose coordinates are V and K, as can be easily demonstrated. Advantages of such method have been highlighted (Henderson 1978). 

A completely new method of determining enzyme kinetic parameters is one that may be called direct linearization. It is due to Eisenthal and Cornish-Bowden (1974) and is based on the direct dependence of on S, leading to the dependence of ax on in the form... 

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