Biomedical Engineering Reference
In-Depth Information
where access to the enzyme's active site limits reaction. For example, considering the equilib-
rium adsorption of enzyme (E) onto substrate (S)
k ads
k des
S
E
þ
!
ES
(8.93)
If the total concentration of adsorption sites on the substrate surface is [S] 0 , expressed per
liquid volume, then we can write
½
S
0 ¼½
S
þ½
ES
(8.94)
and the equilibrium rate expression
0 ¼ r 1 ¼ k ads ½
E
½
S
k des ½
ES
(8.95)
The rate of reaction for the product formation is now assumed to be first order in [ES], with
a constant rate constant k 2 . Thus,
K eq þ½
r max ½
E
r P ¼
(8.96)
E
where
r max ¼ k 2 ½
S
0
(8.98)
and
k des
k ads
K eq ¼
(8.99)
The previous equation assumes slow binding of enzyme (i.e. [E]
[E] 0 ). S 0 is the number of
substrate bonds available initially for breakage, and k des and k ads refer to rates of enzyme
desorption and adsorption onto the insoluble matrix, respectively.
z
8.3. IMMOBILIZED ENZYME SYSTEMS
The restriction of enzyme mobility in a fixed space is known as enzyme immobilization. In
many applications, immobilization of enzymes provides important advantages, such as
enzyme reutilization and elimination of enzyme recovery and purification processes, and
may provide a better environment for enzyme activity. Since enzymes are expensive, catalyst
reuse is critical for many processes. Immobilized enzymes are typically macroscopic catalysts
that are retained in the reactor; therefore, continuous replacement of the enzyme is not neces-
sary, and separation of the enzyme from other components in the reaction mixture is simpli-
fied. Immobilized enzymes can be employed in a wide range of different reactor
configurations and, because high concentrations of catalyst can be obtained, correspondingly
high volumetric productivities are possible. Higher reactor productivities lead to lower
capital costs. Moreover, immobilized enzymes are often more stable than enzymes in solu-
tion. It is also important to note that the properties of the support, for example, its ionic
charge, can in some cases be exploited to modify the behavior of the enzyme. Since some
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