Enzyme Kinetics and Metabolic Control Analysis
197
which is the same as (6.8) except for the reduced rate constant. Here an increase of the
concentration of
S
will not alleviate the inhibitory effect of S,. If the nature of
St
is known it is
possible to study the inhibition process by repeating the experiment at different 5, levels, but
sadly one does not always know what the inhibitory substance is, and the so called
non-
competitive
enzyme inhibition may be difficult to detect in assays which probably do not contain
all the inhibitory substances that are present in the cell.
If the inhibitor attacks
ES
but not
E
the inhibitor is said to be
un-competitive
(for lack of a better
word).
With the enzyme balance
-(es)
+ —
— (es)
+
(es)s,
K eql
(6.15)
(
\
K.„ +
1
+ ^ -
V
J
(6.16)
and both the Michaelis constant and the rate constant decrease by a factor
+
K
eq
!
In either (6.10), (6.14) or (6.16) the inhibitor S, could be the substrate S in which case we have
substrate inhibition.
Unless the “dead-end” complex ES, is interpreted as an enzyme complex
between S and another form of E neither (6.10) nor (6.14) are of much help in interpretation of
substrate inhibition. It may, however well be that S complexes with ES to form ESS which is
now the “dead-end” complex. This is the mechanism of (6.16), and this rate expression (with s
used instead of s,) will also appear in Chapter 7 as a typical rate expression for substrate
inhibited cellular kinetics (Eq (7.21)).
Fig. 6.2 illustrates the difference (and similarity) between the different types of inhibition. In all
four cases
Mr
is shown as a function of 1/s which will give a linear plot of (6.1), (6.10), (6.14)
and (6.16). If in (6.16) s,=s then
Mr
is a hyperbolic function of 1/s with a vertical and an inclined
asymptote. Plots such as Fig. 6.2 (and similar linear plots found in textbooks on enzyme kinetics)
are excellent in a first phase of an experimental investigation of enzyme kinetics. They clearly
show what type of inhibition is present (if the nature of 5, is known!). When the experiment is
carried out at different levels of S, the parameters of the inhibition and thereafter the “true”
kinetic parameters
k
and
K m
of (6.1) can be obtained, possibly by extrapolation to the limit s, = 0
of data obtained from samples spiked with known concentrations of 5,
It is, however, not really good to determine kinetic parameters from any type of linear plot of the
variables
r
and s in a non-linear relation between the two. In Fig. 6.2 the error bars on
Mr
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