Industrial Biotransformations

5.2 Biocatalyst Kinetics
K M values usually range from 10 to 0.01 mM. A low K M value implies a high affinity between
the enzyme and the substrate. The function v =f(S) is shown in Fig. 5.4:
V
V max
½ V max
First order
kinetics:
V=
V max
K M
K M
·[S]
Michaelis-Menten
kinetics:
V=
Vmax KM Fig. 5.4 Typical Michaelis–Menten curve.
·[S]
+[S]
[S]
Zero order
kinetics:
V= Vmax Here, two borderline cases have to be discussed. If the substrate concentration [S] isa
long way below the K M value, a linear first-order kinetic results. The active sites of the
enzyme are almost all free and the substrate concentration is rate limiting. If the substrate
concentration is high, all active sites are saturated and zero-order kinetics results.
By the Michaelis–Menten equation given above, a one-substrate reaction can be
described. If a two-substrate reaction is to be addressed, two reaction rate terms are connected
by multiplication. For a simple two-substrate reaction of A + B the double substrate
kinetics for the forward reaction are:
‰AŠ ‰BŠ
vforward ˆ
…KMA ‡‰AŠ† …KMB ‡‰BŠ†
V forward
max
A corresponding equation for the reverse reaction can also be set up. The resulting
total reaction rate equals the difference between the forward and reverse reactions.
v ˆ d‰PŠ
dt ˆ v forward v reverse (21)
The easiest way to describe a double substrate reaction is by using the kinetics already
described [Eqs. (20 and 21)] derived from the single substrate Michaelis–Menten kinetics
[Eq. (18)]. The disadvantages of this approach are:
. no information about the mechanism is included;
. forward and reverse reactions are addressed as two totally independent reactions;
. no information about the equilibrium is included.
(20)
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