Page 138 - Thermodynamics of Biochemical Reactions

7.6 Effect of pH on Protein-Ligand Equilibria 135

of acid groups in the site is small, their pKs in the unoccupied and occupied site
can be calculated from the dependence of K' on pH. Thus the determination of
the pH dependence of K' can yield important information about the acid groups
in the binding site. If the effect of temperature on K' is studied, the standard
transformed enthalpies and entropies of the site can also be determined.
As an application of equation 7.6-5, consider the effect of pH on the inhibition
constants of fumarase, which have been determined for succinate, D-tartrate,
L-tartrate, and meso-tartrate inhibitors (Wigler and Alberty, 1960). The kinetics
of the conversion of fumarate to L-malate and the inhibition by these competitive
inhibitors indicate that there are two acid groups in the catalytic site that affect
the binding:

(7.6-6)

The binding by a competitive inhibitor can be represented by equation 7.6-5.
The binding polynomial for the unoccupied site in the protein is given by
p(p\,,c) = 1 + lO-PH+Phw + ~~-~PH+PKPSI+P~PS> (7.6-7)

The binding polynomial for the site when it is occupied by a competitive inhibitor
is given by

(7.6-8)
p(PL,,,,) = 1 + 10-pH+Phvi\l + ~~-~PH~P~PL~I~P~PLF~
Substituting equations 7.5-7 and 7.5-8 in equation 7.5-5 yields

1 + lQ-PH+Phm> + 10-2pH+~hw +Php\i
(7.6-9)
K' = Kref 1 + 10-pH+phrl\l + ~~-~PH+P~PLSI+PKPLI~
The pKs of the acid groups in the catalytic site of fumarase at 298 K and an
ionic strength of 0.01 M are given in Table 7.4 along with the equilibrium
constants for the reference reactions. More information on the experimental
determination of these parameters is available in Wigler and Alberty (1960). The
pKs for the two acid groups in the unoccupied catalytic site of fumarase are
pKPsl = 6.9 and pK,,, = 6.3. These two acid groups can be considered to be
identical and independent because their difference is 0.6 = log 4. The pKs for
site-L-tartrate are pK,,,, = 7.5 and pK,,,, = 7.4, indicating there is a cooperative
effect because they are closer than 0.6 pH units (see Section 1.2). The acid
dissociations of the ligands are ignored in these calculations because we are
primarily concerned with what happens in the neighborhood of pH 7. With these
values of the pKs, the pH dependence of the apparent equilibrium constant for

Table 7.4 pKs of Acid Groups in the Catalytic Site in
Fumarase at 298.15 K and an Ionic Strength of 0.01 M

Ligand PK, PK, Kref
Unoccupied 6.9 6.3
succinate 7.5 6.5 1.2 x 10-3
D-tartrate 7.8 6.9 2.5 x 10-
L-tartrate 7.5 7.4 4.1 10-3
ineso-tartrate 7.1 5.7 4.6

Source: With permission from P. W. Wigler and R. A. Alberty, J. Am.
Chem. SOC. 82, 5482 5488( 1960). Copyright 1960 American Chemical
Society.