Page 291 - Introduction to chemical reaction engineering and kinetics

272 Chapter 10: Biochemical Reactions: Enzyme Kinetics

compounds with identical types of bonds. One example is lysozyme, which hydrolyzes
starch, a complex mucopolysaccharide. To illustrate the effect of multiple substrates
upon enzyme kinetics, we consider the reaction of two substrates (S, and S,) competing
for the same active site on a single enzyme (E). The substrates compete for E in forming
the complexes ES, and ES, en route to the final products Pi and P2 in the following
mechanism:

Sl + E+ES,
1
S, + E$ES,
2
k
ES, 2 E + P,
k
ES, 2 E + P2

The rates of production of P, and P2 may be determined by invoking the SSH for
both ES, and ES, in a procedure similar to that in Example 10-2. The resulting rate
laws are:

(10.4-4)

V max2CS2
rP2 =
Km2 + cs2 + Kn2K1ks1
where Vmaxl = krlcEo and Vmax2 = kr2cEo; Km, and Km2 are the Michaelis constants
(k-, + k,,)lk, and (kp2 + k,,)lk,, respectively.
The individual reaction rates in 10.4-4 and 10.4-5 are slower in the presence of both
substrates than in the presence of a single substrate. For example, if cs2 is zero, equation
10.4-4 simplifies to:

V mnxlCSl (10.4-6)
Ipl = Km1 + csl

which is identical in form to equation 10.2-9, the Michaelis-Menten equation. It is also
worth noting that the presence of other substrates can influence the results of studies
aimed at determining the kinetics parameters for a given enzyme process. If a detailed
compositional analysis is not performed, and S, is present, the predicted Michaelis con-
stant for S, is inaccurate; the effective (i.e., predicted) Michaelis constant is:

K wf f = &?ll[1 + (cs2mn2>1 (10.4-7)

In the absence of S,, the true Michaelis constant, Kml, is obtained. Consequently, the
values of K,,, ef f and V,,,,, determined in a kinetics study depend upon the composition
(csl and cs2) and total substrate concentration within the system.

10.4.2 External Inhibitors and Activators
Although substrates may enhance or inhibit their own conversion, as noted in Section
10.4.1, other species may also affect enzyme activity. Znhibitors are compounds that
decrease observable enzyme activity, and activators increase activity. The combination
of an inhibitor or activator with an enzyme may be irreversible, reversible, or partially