Biomedical Engineering Reference
In-Depth Information
By following an analysis similar to that used previously, we eliminate the concentrations
of intermediates by using the equilibrium expressions, and write the reaction rate as
k Q ½
E
0 ½
A
½
B
r P ¼
(8.35)
K A K B K R þK B K R ½
A
þK R ½
A
½
B
Random-Order Reactions
In the case of random-order reactions, we must consider two parallel pathways for the
addition of substrates A and B to the enzyme. The resulting EAB complex then undergoes
reaction to form EPQ, and these products are then released in any order. The reaction
pathway is shown schematically below for the simplest case of rapid equilibrium between
all the ES complexes.
EA
k A
+
B
k -A
k B
k -B
A
k R
k Q
+
EAB
EPQ
EP + Q
(8.36)
E
k A
k -R
+
k P
k -A
B
A
k B
+
k -B
E + P
EB
Using the same method as before to eliminate the concentrations of the ES complexes apart
from EAB in the overall enzyme conservation equation, we can derive the following expres-
sion for the rate of reaction.
k Q ½
E
0 ½
A
½
B
r P ¼
(8.37)
K A K B þK A ½
A
þK B ½
B
þ½
A
½
B
The case of steady state existing among the ES complexes rather than equilibrium is consid-
erably more complex to analyze. We must consider the two possible routes for release of
products P and Q from the EPQ complex.
Enzyme-Substituted Reactions (the Ping-Pong Mechanism)
In enzyme-substituted or double-displacement mechanisms, both substrates need not be
bound together at the active site of the enzyme. No ternary intermediate is formed. This mech-
anismoccurs when, for example, a phosphate-transferring enzyme, such as phosphoglycerate
mutase, is phosphorylated. One substrate (A) reacts with the enzyme to give E* (e.g. a phos-
phorylenzyme) which then transfers the phosphoryl group to the second substrate B.
k P
E*B
E + P
k B
k -B
(8.38)
B
+
k A
k Q
E + A
EA
E* + Q
k -A
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