Industrial Biotransformations

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5 Basics of Bioreaction Engineering
Fig. 5.3 Determination of kinetic parameters.
The rate limiting step is the dissociation of the ES complex (k –1>>k 2). The reaction rate
is proportional to the rapid, “preceding equilibrium”. As a consequence of the latter
assumptions the following reaction rate equation is derived [Eq. (18)]:
v ˆ v max ‰SŠ
K‡‰SŠ
with : K ˆ K S ˆ k 1
k 1
where v = reaction rate (U mg –1 ); V max = maximum reaction rate (U mg –1 ); K = dissociation
constant of ES complex (mM); k x = reaction rate constant of reaction step x (min –1 );
and [S] = the substrate concentration (mM).
Here K is identical to the dissociation constant K S of the ES complex. Briggs and Haldane
extended this theory in 1925 [19]. They substituted the assumption of the “rapid
equilibrium” by a “steady state assumption”. This means that after starting the reaction
an almost steady state level of the ES complex is established in a very short time. The
concentration of the ES complex is constant with time (d[ES]/dt = 0). In this assumption,
the constant K has to be increased by k 2, resulting in the Michaelis–Menten constant K M.
K ˆ K M ˆ k 1 ‡k 2
k 1
where K M = Michaelis–Menten constant (mM).
The Michaelis–Menten constant does not now describe the dissociation, but rather it is
a kinetic constant. It denotes the special substrate concentration where half of the maximal
activity is reached. As the Michaelis–Menten constant approaches the dissociation
constant K S of the ES complex, it is valuable for estimating individual reaction kinetics.
(18)
(19)