9780521516358book.pdf

Example 1(cont.)

Table B

[S] (mM) 0.03 0.06 0.09 0.12 0.18 0.24 0.36

v 0 (mmol min^1 ) 0.054 0.096 0.138 0.168 0.210 0.251 0.294

1/[S] (mM)^1 33.33 16.67 11.11 8.33 5.55 4.17 2.78

1/v 0 (mmol min^1 )^1 18.52 10.42 7.25 5.95 4.76 3.98 3.40

v 0 /[S] 103 (dm^3 min^1 ) 1.8 1.6 1.53 1.40 1.17 1.05 0.82

[S]/v 0  10 ^3 (min dm^3 ) 0.56 0.63 0.65 0.71 0.85 0.95 1.22

Data derived from the three linear plots are presented in Table C.

Table C

Plot

Regression

coefficient Slope Intercept Km(mM) Vmax(mmol min^1 )

Lineweaver–Burk 0.9997 0.499 1.91 0.26 0.52

Hanes 0.9970 1.990 0.489 0.25 0.50

Eadie–Hofstee 0.9930 3.99 2.030 0.25 0.51

The agreement between the three plots for the values ofKmandVmaxwas good but the

quality of the fitted regression line for the Lineweaver–Burk plot was noticeably better.

However, the distribution of the experimental points along the line is the poorest for this

plot (Fig. 15.6). The value forVmaxindicates the amount of product released per minute,

butofcoursethisisforthechosenamountofenzymeandisfor10cm^3 of reaction

mixture. For the value ofVmaxto have any absolute value, the amount of enzyme and

the volume of reaction mixture have to be taken into account. The volume can be

adjusted to 1 dm^3 givingVmaxof 51mmol min^1 dm^3 , but it is only possible to correct

for enzyme amount if it was pure and of known amount in molar terms. The enzyme is

known to have a molecular mass of 68 kDa so if there was 3mgofpureenzymeineach

10 cm^3 reaction mixture, its molar concentration would be 4.4 10 -3mM. This allows

the value of the turnover numberkcatto be calculated (see equation 15.8):

kcat¼Vmax=½EtŠ¼ 51 mM min^1 = 4 : 4  10 ^3 mM

¼ 11  103 min^1 or 1 : 8  102 s^1

kcatis a measure of the number of molecules of substrate (PNPG in this case) converted

to product per second by the enzyme under the defined experimental conditions. The

value of 180 is in the mid-range for the majority of enzymes. It is also possible to

calculate the specificity constant that is a measure of the efficiency with which the

enzyme converts substrate to product at low (Km) substrate concentrations:

kcat=Km¼ 1 : 8  102 s^1 = 0 : 25 mM¼ 7 : 2  102 mM^1 s^1 or 7 : 2  105 M^1 s^1

590 Enzymes