Enzyme Kinetics and Metabolic Control Analysis
191
Figure 6.1 Schematic representation of the rate of an enzymatic reaction. .s is the substrate concentration
(typical unit: g substrate (L medium)') and
r
is the rate of conversion of
5.
The shape of Fig. 1 with an initial near proportionality between
r
on .v and a final, maximum rate
of conversion is well correlated by the following expression:
r _
_ V o*
Ä
+
K m
s + K m
(
6
.
1
)
The substrate concentration s is in units of g (or mole) substrate(L medium)'1. The reaction rate r
can be specified in units of either g substrate(L medium h)'1
or in units of g substrate (g enzyme
preparation h ) 1. The last unit corresponds best with the standard used for catalytic reactions with
solid catalysts : g converted(g catalyst h)'1, and the use of the letter r for the rate would
correspond to that used for specific rates elsewhere in the text. But the whole literature on
enzyme kinetics is based on the first unit for r, and we shall follow this standard nomenclature.
Consequently k is in units of g substrate(L medium h)'1
, e0 : g enzyme preparation (L m edium )1
and k0 : g substrate(g enzyme preparation h)'. r/e0 is consequently the equivalent of the specific
rates used elsewhere in the book. In practical investigations of enzymatic reactions only
k
is
determined, and it signifies the maximum of r, or /
k„
and
e0
can not be determined separately,
but splitting
k
into two factors does show that an enzyme with a low activity per unit mass of
enzyme will lead to a low rate of conversion of the substrate. In the following derivation of some
classical enzyme kinetic models it will be convenient to describe r by the second expression in eq
(
6
.
1
).
In 1925 Briggs and Haldane derived the form of (6.1) by mechanistic modeling. They considered
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