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A plot of 1/n 0 against 1/[S] gives a straight line of slopeKm/Vmax, with an intercept on

the 1/ 0 axis of 1/Vmaxand an intercept on the 1/[S] axis of1/Km. Alternative plots

are based on theHanes equation:

½SŠ

 0

¼

Km

Vmax

þ

½SŠ

Vmax

ð 15 : 6 Þ

so that [S]/ 0 is plotted against [S], and on theEadie–Hofstee equation:

v 0

½SŠ¼

Vmax

Km 

v 0

Km ð^15 :^7 Þ

so that 0 /[S] is plotted againstv 0. The relative merits of the Lineweaver–Burk, Hanes

and Eadie–Hofstee equations for the determination ofKmandVmaxare illustrated in

Fig. 15.4 using the same set of experimental values of 0 for a series of substrate

concentrations (for further details, see Example 1).

It can be seen that the Lineweaver–Burk equation gives an unequal distribution of

points and greater emphasis to the points at low substrate concentration that are subject

to the greatest experimental error whilst the Eadie–Hofstee equation and the Hanes

equation give a better distribution of points. In the case of the Hanes plot, greater

emphasis is placed on the experimental data at higher substrate concentrations and on

balance it is the statistically preferred plot. In spite of their widespread use, these linear

transformations of enzyme kinetic data are subject to error. Specifically, they assume

that the scatter of points around the line follows a Gaussian distribution and that the

standard deviation of each point is the same. In practice this is rarely true. With the

advent of widely available non-linear regression software packages such as DynaFit

(www.biokin.com) and BRENDA (www.brenda-enzymes.info), there are now strong

arguments for their preferential use in cases where accurate kinetic data are required.

It is important to appreciate that whilstKmis a characteristic of an enzyme for its

substrate and is independent of the amount of enzyme used for its experimental

determination, this is not true ofVmax. It has no absolute value but varies with the

amount of enzyme used. This is illustrated in Fig. 15.3 and is discussed further in

Example 1. A valuable catalytic constant in addition toKmandVmaxis theturnover

number,kcat, defined as:

20

10 20 30 40

10

Lineweaver – Burk plot

1

2

43

65

7

1/

n^0

1/[S]

1.5

0.5

0.1 0.2 0.3 0.4

Hanes plot

123

4

56

7

[S]/

n^0

[S]

2.0

1.5

0.5

0.1 0.2 0.3

Eadie – Hofstee plot

(^1234)
(^56)
7
n^0
/[S]
n 0
1.0
Fig. 15.4Lineweaver–Burk, Hanes and Eadie–Hofstee plots for the same set of experimental data of the effect
of substrate concentration on the initial rate of an enzyme-catalysed reaction.
588 Enzymes