Page 414 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.4 Enzymatic Reaction Fundamentals 385

Clearly, the greatest activity in the study of enzymes has been in relation
to bidogical reactions, because virtually every synthetic and degradation reac-
tion in all living cells has been shown to be controlled and catalyzed by spe-
cific e~ymes.'~ Many of these reactions are homogeneous in the liquid phase;
that is, they are type 111 reactions (soluble enzyme-soluble substrate). In the
following brief presentation we limit our discussion to type 111 reactions,
although the resulting equations have been found to be applicable to type I and
type I][ reactions in certain instances.
In developing some of the elementary principles of the lunetics of
enzyme reactions, we shall discuss an enzymatic reaction that has been sug-
gested by Levine and LaCourse as part of a system that would reduce the size
of an sdficial kidney.14 The desired result is the production of an artificial kid-
ney that could be worn by the patient and would incorporate a replaceable unit
for the elimination of the nitrogenous waste products such as uric acid and cre-
atinine. In the microencapsulation scheme proposed by Levine and LaComse,
the enzyme urease would be used in the removal of urea from the bloodstream.
Here, the catalytic action of urease would cause urea to decompose into
ammoilia and carbon dioxide. The mechanism of the reaction is believed to
proceed by the following sequence of elementary reactions:
1. The enzyme urease reacts with the substrate urea to form an
enzyme-substrate complex, E- S:
The reaction NH2CONH2 + urease kl > [NH2CONH2.urease]* (7-72)
mechanism
2. This complex can decompose back to urea and urease:
[NH2CONH2.urease]* k2 > urease + NH2CONH2 (7-73)

3. Or it can react with water to give ammonia, carbon dioxide, and urease:
+
[NH2CONH2-urease]* + H20 > ~NH, + CO~ urease (7-74)
We see that some of the enzyme added to the solution binds to the urea, and
some remains unbound. Although we can easily measure the total concentration
of enzyme, (Et), it is difficult to measure the concentration of free enzyme, (E).
Letting E, S, W, E-S, and P represent the enzyme, substrate, water, the
enzyme-substrate complex, and the reaction products, respectively, we can
write R.eactions (7-72), (7-73), and (7-74) symbolically in the forms

E+S > E-S (7-75)
E-S '' 3 E+S (7-76)

E*S+W " > P+E (7-77)

Here P = 2NH3 + COz.
I3R. G. Denkewalter and R. Hirschmann, Am. Sci., 57(4), 389 (1969).
14N. Levine and W. C. Lacourse, J. Biomed. Mater: Res., I, 275 (1967).