204
Chapter 6
through the EMP pathway gives a high level of fructose 1,6 diphosphate. This activates the LDH
and strongly inhibits PFL. At low glucose flux (either because the concentration of glucose in the
medium is low or because a less easily fermented sugar such as lactose is used as feed) the
inhibition of PFL is immediately lifted (Melchiorsen
et al.,
2001)
Both in the relatively simple case of substrate cooperativity and in the case of cooperativity
between enzyme, substrate and effector the relationship between
r
and
s
(with the concentration
s, of the effector as a parameter) has the shape of Fig. 6.5. Enzymes which exhibit the property of
cooperativity are collectively named
allosteric enzymes.
Note 6.2
C om petition o f tw o substrates for the sam e enzym e
W hen tw o substrates
S
and 5', can be consum ed sim ultaneously on the sam e site o f an enzym e - e.g.
w hen m annose and glucose com pete for the sam e m em b ran e b o u n d PTS transport pro tein in lactic acid
bacteria - it becom es o f interest to calculate the relative u ptake rate o f the tw o substrates.
L et the rate o f conversion o f
S
and 5, be
r
and
respectively, and assum e a co m petitive inhibition o f
r
by 5, and o f
r
, by 5. In both cases the inhibition is described by eq. (6.10) w here the M ichaelis co n stan t is
denoted
Km
and
for
r
and r, respectively.
s + K.
(
\
1
+ ^
V
K,J
5,
+ K„
1 +
K
e q \
y
(
1
)
In
r
the equilibrium constant
Kcq
for the capture o f
E
by 5, to form the “dead-end “ com plex
ESt
is equal
to the M ichaelis constant
Kml
used in r, to d escribe the first step in the conversion o f
S,
by the enzym atic
reaction. Sim ilarly, in
r,
K ,q] is equal to
Km
C onsequently the tw o expressions in (1) h ave the sam e
denom inator and (1) can be rearranged to:
AT
K„
S
5 ,
---- + 1
+ —L
K„
s
I
.
5
+1 + -
(
2
)
AT.
K,
T he ratio o f the tw o rates o f conversion is consequently
''max
r _
U J
5
r
m a x
Km
l
and the value o f the
specificity constant
rm„
/
Km
determ ines the co m petitive edge o f one substrate
relative to the other.
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