Enzymes - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 383

r 3 j r 1 ¼0;r 2 ¼0

r ¼ðr 1 þ r 2 þ r 3 Þ 1 z

(8.147c)

k 3 K C
k 1 C E 0 K P þ

k 3 K C
k c K P

1þ

Figure 8.28 shows the variations of free substrate and product concentrations with reaction
time comparing the full solutions with the approximate kinetics. One can observe that the
rescaled Michaelis e Menten approximation agrees with full solutions reasonably well.
Therefore, one can conclude that Michaelis e Menten equation can be applied to model
enzyme reactions after the initial “mixing” period without knowing if there is a rate-limiting
step. The rate constants: r max and K m are functions of the rate constants of all the steps
involved.

8.8. SUMMARY

Enzymes are protein, glycoprotein, or RNA molecules that catalyze biologically important
reactions. Enzymes are very effective, specific, and versatile biocatalysts. Enzymes bind
substrate molecules and reduce the activation energy of the reaction catalyzed, resulting in
significant increases in reaction rate. Some protein enzymes require a nonprotein group for
their activity as a cofactor.
The kinetics of enzyme-catalyzed reactions is usually modeled after FES: the catalytic reac-
tion step is the rate-limiting step while other steps are in equilibrium or their rates are zero.
The resulting rate expression is usually referred to as the Michaelis e Menten equation. The
rapid equilibrium assumption produces simplest rate expression and is easy to apply.
However, it has the limitation requiring other steps to be much faster. PSSH is more general,
and it puts reaction networks in direct analogy with electric circuit. The final rate expression
on the other hand, is quite similar to Michaelis e Menten equation when the kinetic parame-
ters are lumped together. Finally, the Michaelis e Menten rate expression can be employed to
correlate experimental data, without a true rate-limiting step.
The activity of some enzymes can be altered by inhibitory compounds, which bind the
enzyme molecule and reduce its activity. Enzyme inhibition may be competitive, noncompet-
itive, and uncompetitive. High substrate and product concentrations may be inhibitory, too.
Enzymes require optimal conditions (pH, temperature, ionic strength) for their maximum
activity. Enzymes with an ionizing group on their active site show a distinct optimal pH that
corresponds to the natural active form of the enzyme. The activation energy of enzyme-
catalyzed reactions is within 16 e 84 kJ/mol. Above the optimal temperature, enzymes lose
their activity, and the inactivation energy is on the order of 170 e 540 kJ/mol.
Enzymes can be used in suspension or in immobilized form. Enzymes can be immobilized
by entrapment in a porous matrix, by encapsulation in a semipermeable membrane capsule
or between membranes, such as in a hollow-fiber unit, or by adsorption onto a solid support
surface. Enzyme immobilization provides enzyme reutilization, eliminates costly enzyme
recovery and purification, and may result in increased activity by providing a more suitable
microenvironment for the enzyme. Enzyme immobilization may result in diffusion limita-
tions within the matrix. Immobilization may also cause enzyme instability, loss of activity,
and shift in optimal conditions (pH, ionic strength). To obtain maximum reaction rates, the