194
Chapter 6
exponential function vanishes within milliseconds, before
s
has started to decrease from its initial value.
A much more serious criticism of both the Michaelis Menten and the Briggs Haldane mechanism lies in
the assumed irreversibility of the step 2 in (6.2). Since enzymes like other catalysts must in principle
enhance the rate of both the forward reaction and the reverse reaction (but certainly not to the same
degree - the product might not be able to dock on the enzyme) one must consider
—fi—>
E + S
ES
E + P
(2)
<
----
<
-----
*_2
rather than (6.2). Assuming pseudo- stationarity for
ES
yields
(« ) =
k^s
+
k_2p
k_t + k2 + kts + k_2p
(3)
r = k2
(
es
)
-k _ 2p- (e0 -
(as)) =
k {k2s -
k-ik-2 P
k-\
+
k2
+
+
k_2p
(4)
where
p
= 0 yields eq. (6.6).
An enzymatic assay is made with no
P
initially, and until
p
is built up equation (6.1) describes the rate of
substrate consumption quite accurately. The overall reaction
S
~*
P
may also be thermodynamically
favored which means that almost all
S
can be converted to
P
without any influence of the reverse
reaction
(k_2k,
~ 0), and as we have seen in Chapter 4 an enzymatic reaction in a pathway can convert
S
to
P
also when the reaction has a small negative or even a small positive AG°, if only
P
is sucked away
from the equilibrium by further reactions. Consequently, when using models for enzyme kinetics in
assays or in the analysis of pathway reactions the simple form (6.1) is usually adequate.
This is not necessarily so when studying the enzymatic conversion of substrate in an industrial
bioreactor. When glucose is converted to fructose in a commercial plug flow reactor using immobilized
glucose isomerase it is desired to approach the equilibrium conversion (about 50% at 40-60°C) quite
closely to obtain an adequate sweetening of the sugar solution. Calculation of the necessary amount of
catalyst will be wildly wrong if (6.1) rather than (4) is used (Gram
et al.,
1990)
Finally, one may raise the objection to (6.2) that most enzymatic reactions need a second substrate to
proceed. The cooperation of cofactors such as NAD+/NADPH, NADP7NADPH, ATP/ADP is seen in
many of the pathway reactions of Chapter 2. It is tacitly assumed that these cofactors are regenerated by
other cellular reactions and that their level is fixed through constraints on redox charge or energy charge.
But when planning to use a genetically engineered strain in which the balances between cofactors has
been artificially changed (an NADP' dependent enzyme may have been exchanged with an NAD'
dependent variant in a high flux pathway) the rate of the enzyme reaction may be significantly changed.
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