Enzymes - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 339

sample to sample. Hence a different approach must be adopted, and enzyme concentration is
reported in units of specific activity. A “unit” is defined as the amount of enzyme (e.g. micro-
gram) which gives a certain amount of catalytic activity under specified conditions (e.g.
producing 1.0

mol of product per minute in a solution containing a substrate concentration
sufficiently high to be in the “saturation” region, as shown in Fig. 8.9 where [ES] and [E] are
relatively invariant).
Thus different suppliers of enzymes may have preparations with different units of activity,
and care must be taken in analyzing kinetic data. Thus, a purified enzyme preparation will
have a higher specific activity than a crude preparation; often a protein is considered pure
when a constant specific activity is reached during the purification steps.

m

Activity
mg-protein ¼

mmol-product
mg-protein

Specific acivity ¼ (8.15)

min ml

The activity is given by the amount of product formed or substrate consumed in the reac-
tion mixture, under the conditions specified (temperature, pH, buffer type, substrate and
enzyme concentrations, etc.). If the molecular weight of the enzyme is known, the specific
activity can also be defined as:

Activity
mmol-protein ¼

mmol-product
mmol-protein

Specific acivity ¼ (8.16)

min ml

Example 8-1. To measure the amount of glucoamylase in a crude enzyme preparation, 1 mL
of the crude enzyme preparation containing 8-mg protein is added to 9 mL of a 4.44% starch
solution. One unit of activity of glucoamylase is defined as the amount of enzyme which
produces 1

mol of glucose/min in a 4% solution of Linter starch at pH 4.5 and at 60 C.
Initial rate experiments show that the reaction produces 0.6

m

m mol of glucose/(mL $ min).

What is the specific activity of the crude enzyme preparation?

Solution. The total amount of glucose made is 10 mL 0.6 m mol glucose/(mL $ min) or

6 m mol glucose/min. The specific activity is then:

6 units

Specific activity ¼

1 ml protein solution 8mg = ml

¼ 0:75 units = mg-protein

The maximum reaction rate r max must have units such as mol-product/(L min). Since
r max ¼ k 2 [E] 0 , the dimensions of k 2 must reflect the definition of units in [E] 0 . In the above

example, we had a concentration of enzyme of 8-mg protein/10-mL solution: 0.75 units/
mg-protein or 600 units/L. r max ¼ then k 2 ¼

If, for example, 1 mol/(L min), 1 mol/

(L min) O 600 units/L or k 2 ¼

m

1.67 mol/(unit min).

8.2.4. Models for More Complex Enzyme Kinetics
8.2.4.1. Kinetics of Multisubstrate Reactions
The majority of enzymes do not involve just one substrate; they usually involve two.
Often the second substrate is a cofactor, such as NAD þ in oxidoreductases. Many of the