Food Chemistry

2.5 Kinetics of Enzyme-Catalyzed Reactions 125

indicative of positive cooperation. Each substrate
molecule, often called an effector, accelerates
the binding of succeeding substrate molecules,
thereby increasing the catalytic activity of the
enzyme (case b in Fig. 2.28). When Rs>81, the
system shows negative cooperation. The effector
(or allosteric inhibitor) decreases the binding of
the next substrate molecule (case c in Fig. 2.28).
Various models have been developed in or-
der to explain the allosteric effect. Only the
symmetry model proposed byMonod, Wyman
andChangeux(1965) will be described in its
simplified form: specifically, when the substrate
acts as a positive allosteric regulator or effec-
tor. Based on this model, the protomers of an
allosteric enzyme exist in two conformations,
one with a high affinity (R-form) and the other
with a low affinity (T-form) for the substrate.
These two forms are interconvertible. There is an
interaction between protomers. Thus, binding of
the allosteric regulator by one protomer induces
a conformational change of all the subunits and
greatly increases the activity of the enzyme.
Let us assume that the R- and T-forms of an en-
zyme consisting of four protomers are in an equi-
librium which lies completely on the side of the
T-form:

(2.64)

Addition of substrate, which here is synonymous
to the allosteric effector, shifts the equilibrium
from the low affinity T-form to the substantially
more catalytically active R-form. Since one sub-
strate molecule activates four catalytically active
sites, the steep rise in enzyme activity after only
a slight increase in substrate concentration is not
unexpected. In this model it is important that
the RT conformation is not permitted. All sub-
units must be in the same conformational state
at one time to conserve the symmetry of the pro-
tomers. The equation given byHillin 1913, de-
rived from the sigmoidal absorption of oxygen by
hemoglobin, is also suitable for a quantitative de-
scription of allosteric enzymes with sigmoidal be-
havior:

υ 0 =

V(A 0 )n

K′+(A 0 )n

(2.65)

Fig. 2.29.Linear presentation ofHill’sequation

The equation says that the catalytic rate increases

by the nth power of the substrate concentration

when[A 0 ]is small in comparison to K. TheHill

coefficient, n, is a measure of the sigmoidal char-

acter of the curve and, therefore, of the extent

of the enzyme’s cooperativity. For n=1 (Equa-

tion 2.65) the reaction rate is transformed into the

Michaelis–Mentenequation, i. e. in which no co-

operativity factor exists.

In order to assess the experimental data, Equa-

tion 2.65 is rearranged into an equation of

a straight line:

log=

υ 0

V−υ 0

=nlog(A 0 )−logK′ (2.66)

The slope of the straight line obtained by

plotting the substrate concentration as log[A 0 ]

versus log[v 0 /(V−v 0 )]is theHillcoefficient, n

(Fig. 2.29). The constant K incorporates all the

individual Kmvalues involved in all the steps of

substrate binding and transformation. The value

of Kmis obtained by using the substrate concen-

tration, denoted as[A 0 ] 0 .5v,atwhichv 0 = 0 .5V.

Under these conditions, the following is derived

from Equation 2.66):

log

0 .5V

0 .5V

= 0 =n·log(A 0 ) 0 .5V−logK′ (a)

K′=(A 0 )n 0 .5V (b)

(2.67)

2.5.2 EffectofInhibitors

The catalytic activity of an enzyme, in addition

to substrate concentration, is affected by the type