2009_Book_FoodChemistry

120 2 Enzymes
Table 2.9. Rate constants for some enzyme catalyzed
reactions
Enzyme Substrate k 1 K −1 k 0
(l· mol −1 s −1 )(s −1 ) (s −1 )
Fumarase Fumarate > 10 9 4.5 · 10 4 10 3
Acetylcho- Acetyl- 10 9 10 3
line choline
esterase
Alcohol NAD 5.3 · 10 5 74
dehydro- NADH 1.1 · 10 7 3.1
genase Ethanol > 1.2 · 10 4 > 74 10 3
(liver)
Catalase H 2 O 2 5 · 10 6 10 7
Peroxidase H 2 O 2 9 · 10 6 < 1.4 10 6
Hexokinase Glucose 3.7 · 10 6 1.5 · 10 3 10 3
Urease Urea > 5 · 10 6 10 4
Another special case to be considered is
if [A 0 ] ≪ K m , which occurs at about [A 0 ] <
0.05 K m . Here [A 0 ] in the denominator of
Equation 2.39 can be neglected:
υ 0 = k 2(E 0 )(A 0 )
(2.45)
K m
and, considering that k 2 [E 0 ]=V, it follows that:
υ 0 = V K m
(A 0 ) (2.46)
In this case the Michaelis–Menten equation reflects
a first-order reaction in which the rate of
substrate breakdown depends on substrate concentration.
In using a kinetic method for the determination
of substrate concentration (cf. 2.6.1.3),
the experimental conditions must be selected such
that Equation 2.46 is valid.
2.5.1.1.2 Determination of K m and V
In order to determine values of K m and V, the
catalytic activity of the enzyme preparation is
measured as a function of substrate concentration.
Very good results are obtained when [A 0 ] is in the
range of 0.1K m to10 K m .
A graphical evaluation of the result is obtained by
inserting the data into Equation 2.41. As can be
seen from a plot of the data in Fig. 2.22, the equation
corresponds to a rectangular hyperbola. This
graphical approach yields correct values for K m
Fig. 2.22. Determination of Michaelis constant, K m , according
to Equation (2.41)
only when the maximum velocity, V, can be accurately
determined.
For a more reliable extrapolation of V, Equation
2.41 is transformed into a straight-line equation.
Most frequently, the Lineweaver–Burk plot
is used which is the reciprocal form of Equation
2.41:
1
= K m
υ 0 V · 1
(A 0 ) + 1 (2.47)
V
Figure 2.23 graphically depicts a plot of 1/v 0 versus
1/[A 0 ]. The values V and K m are obtained
from the intercepts of the ordinate (1/V) and of
the abscissa (−1/K m ), respectively. If the data do
not fit a straight line, then the system deviates
from the required steady-state kinetics; e. g., there
is inhibition by excess substrate or the system
is influenced by allosteric effects (cf. 2.5.1.3; allosteric
enzymes do not obey Michaelis–Menten
kinetics).
A great disadvantage of the Lineweaver–Burk
plot is the possibility of departure from a straight
line since data taken in the region of saturating
substrate concentrations or at low substrate concentrations
can be slightly inflated. Thus, values
taken from the straight line may be somewhat
overestimated.
A procedure which yields a more uniform distribution
of the data on the straight line is that proposed
by Hofstee (the Eadie–Hofstee plot). In this
procedure the Michaelis–Menten equation, 2.41,
is algebraically rearranged into:
υ 0 (A 0 )+υ 0 K m = V · (A 0 )
(a)
υ 0 + υ 0
(A 0 ) · K m = V (b)