Enzymes - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 340

concepts we have developed to date can be applied to situations where one of the
substrates is held at a constant concentration; the kinetics then follow one of the forms
described earlier. Most types of multisubstrate reactions fall into one of two classes,
depending on the order of substrate binding and release of products. The description
of the reaction in these terms is referred to as the “formal kinetic mechanism.” In the first
case,whenallsubstratesareaddedtotheenzymepriortothereactionorconversion,
a complex ES intermediate exists. With two-substrate reactions, the mechanism is
referred to as a ternary complex mechanism. In the second case, when one product is
released before the second substrate is bound (for example, when a group is transferred
from one reactant to another), the mechanism is referred to as an enzyme-substituted
mechanism.
In the case of two-substrate enzyme-substituted systems, there is thus a required order
of substrate binding (i.e. a sequential mechanism). In the case of ternary complex mecha-
nisms, a number of possible binding orders arise. For example, binding of one substrate
may not be possible until a particular substrate is first bound, as this may result in a confor-
mational change in enzyme structure which then permits the binding of the second
substrate. This is referred to as compulsory order. When such order is not important, the
mechanism is known as random order. This is summarized in Table 8.3 for two-substrate
reactions.
We will consider the two main classes of mechanisms described above using the simplest
case, that of two-substrate reactions as an example. The reaction to be considered

A þ B P þ Q (8.17)

/

For situations where a ternary complex mechanism is involved, four possibilities can be
considered: either a compulsory order or randommechanismwith either pseudosteady-state
or rapid equilibrium assumptions being used to describe the behavior of the various ES
complexes formed. The enzyme-substituted mechanism (also referred to as a double-
displacement or ping-pong mechanism) is yet another possibility, distinct from the ternary
complex mechanism. In all of these situations, we shall see that the initial rates of reaction
can be written in the following form:

k 2 ½ E 0 ½ A ½ B

r P ¼ (8.18)

1þK 12 ½ A ½ B þK 1 ½ A þK 2 ½ B

We shall examine the various classes of two substrate reactions to determine detailed rate
equations which provide expressions for rate of reaction.

TABLE 8.3 Possible Mechanisms for Single-Site Enzyme with Two Substrates

Enzyme-substituted mechanism:
A binds and is released; group
transferred to B Ternary complex mechanism: (EAB) formed

Compulsory order Random order Compulsory binding order

A binds before B A or B can bind first (Sequential mechanism)