Enzyme Kinetics and Metabolic Control Analysis
195
6.2 More Complicated Enzyme Kinetics
Equation (6.1) derived by either eq. (6.3) or (6.7) has an almost exact analogue in Langmuirs
treatment during World War 1 of catalytic surfaces on which a reactant can adsorb on a finite
number of active sites and react in the adsorbed state, from which the product can finally be
desorbed. The presence of other species which could inhibit the overall reaction either reversibly
(the activity of the catalyst returns when the inhibitor is removed from the feed) or irreversibly
(it could be the permanent damage caused by sulfides or by sintering of the catalyst during a
temperature excursion) have been exhaustively studied both by chemists and by biochemists,
each in their own field.
Some of the most common inhibitory effects contributing to a reduction of the enzymatic activity
either through an action on
k
or on
K m
in (6.1) will be discussed in Section (6.2.1). In Section
6.2.2 we shall discuss certain rate expressions in which the dependence on .s is strong in a certain
s-interval and small outside this interval. Enzymes exhibiting this type of behavior are important
for the regulation of cell metabolism. The kinetics developed in Sections 6.2.1 and 6.2.2 below
both have apparent analogues in expressions for cell kinetics, but there they are used as pure data
fitters without any mechanistic foundation at all.
6.2.1 Variants of Michaelis-Menten Kinetics
Although enzymes are usually very specific catalysts there are important cases of interactions
between enzymes and substrate-analogues that practically impede the desired reaction. The
membrane bound transport enzymes for hexoses are typical examples. A specific example is the
membrane bound mannose-PTS system of lactic bacteria (Fig. 2.3C) that can transfer a number
of sugars from the medium to the cell where it arrives in phosphorylated form. Despite its name
the uptake of mannose by the enzyme is almost completely inhibited by the presence of glucose,
and also by the presence of glucose-analogues that are not even metabolized by the lactic bacteria
(Benthin
et al,
1993)
The free enzyme
E
is clearly removed from eq (6.2) by a competing reaction
- — >
E
+ S,
^
ES{
(6.9)
Following the derivation of the Michaelis Menten expression (6.8) one obtains
k2e0s
■ ^ , ( 1
v
)
^eq\
(
6
.
10
)
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