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> 109 4. 5 · 104103
Acetylcho- Acetyl- 10^9103
line choline
esterase
Alcohol NAD 5. 3 · 105 74
dehydro- NADH 1. 1 · 107 3.1
genase Ethanol > 1. 2 · 104 >74 10^3
(liver)
Catalase H 2 O 2 5 · 106 107
Peroxidase H 2 O 2 9 · 106 < 1. 4106
Hexokinase Glucose 3. 7 · 106 1. 5 · 103103
Urease Urea > 5 · 106 104Another special case to be considered is
if[A 0 ]Km, which occurs at about[A 0 ]<
0 .05 Km.Here[A 0 ] in the denominator of
Equation 2.39 can be neglected:
υ 0 =
k 2 (E 0 )(A 0 )
Km(2.45)and, considering that k 2 [E 0 ]=V, it follows that:
υ 0 =
V
Km(A 0 ) (2.46)In this case theMichaelis–Mentenequation re-
flects a first-order reaction in which the rate of
substrate breakdown depends on substrate con-
centration. In using a kinetic method for the deter-
mination 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 KmandV...............................
In order to determine values of Kmand 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 0.1Kmto10 Km.
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 equa-
tion corresponds to a rectangular hyperbola. This
graphical approach yields correct values for Km
Fig. 2.22.Determination ofMichaelisconstant, Km, ac-
cording to Equation (2.41)only when the maximum velocity, V, can be ac-
curately determined.
For a more reliable extrapolation of V, Equa-
tion 2.41 is transformed into a straight-line equa-
tion. Most frequently, theLineweaver–Burkplot
is used which is the reciprocal form of Equa-
tion 2.41:
1
υ 0=Km
V·1
(A 0 )+1
V(2.47)Figure 2.23 graphically depicts a plot of 1/v 0 ver-
sus 1/[A 0 ]. The values V and Kmare obtained
from the intercepts of the ordinate (1/V) and of
the abscissa (− 1 /Km), 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; al-
losteric enzymes do not obeyMichaelis–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 con-
centrations can be slightly inflated. Thus, values
taken from the straight line may be somewhat
overestimated.
A procedure which yields a more uniformdistri-
butionof the data on the straight line is that pro-
posed byHofstee(theEadie–Hofsteeplot). In this
procedure theMichaelis–Mentenequation, 2.41,
is algebraically rearranged into:υ 0 (A 0 )+υ 0 Km=V·(A 0 )(a)υ 0 +υ 0
(A 0 )·Km=V (b)