Page 142 - Thermodynamics of Biochemical Reactions

7.7 Calculation of Standard Transformed Gibbs Energies of Formation 139

Table 7.5 Standard Transformed Gibbs Energies of Formation for the Catalytic Site
of Fumarase in kJ mo1-l at 25 C and Ionic Strength 0.01 M

PH 5 PH 6 PH 7 PH 8 PH 9

site - 18.39 - 7.96 - 1.66 -0.19 - 0.02
succinate - 576.28 - 553.45 - 530.62 - 507.78 - 484.95
site-succinate - 615.86 - 582.23 - 551.35 -525.15 - 501.70
D-tartrate 114.16 136.99 159.83 182.66 205.49
site-D - tartrate 72.45 106.43 138.75 166.52 190.48
L-tartrate 114.16 136.99 159.83 182.66 205.49
site-L-tartrate 72.56 106.71 140.02 168.21 191.78
meso- tart rate 114.16 136.99 159.83 182.66 205.49
site-meso-tartrate 101.51 133.36 161.52 186.15 209.24

Source: [With permission from R. A. Albcrty. J. PhJs. Chem. B 104,9929-9934 (2000). Copyright 2000
American Chemical Society.]
*This table is based on the convention that A[@ = 0 at 25‘C and zero ionic strength for the doubly
charged ions of D-tartrate. L-tartarate, and meso-lartratc. In addition, the convention is that A,G’” = 0
for the binding site at high pH.

The apparent dissociation constant of the fumarase site-succinate complex to
yield unoccupied site and succinate is represented by the following function of pH:

(7.7-2)

According to equation 7.1-19, this K’ is given by
- RTln K’ = A,G”(site) + A,G‘O(SUCC) A,G”(site-succ) (7.7-3)
~
The value of A,Go(succ2-) at 25°C and zero ionic strength is -690.44 kJ mol-’,
and the pH dependence of A,G’o(succ) is given by -690.44 - 4RTln (see
equation 4.4-lo), neglecting the effect of the binding hydrogen ions at lower pH
values. This value is independent of the ionic strength because 2; = NH(i).
A,G’”(site) is taken as zero in the limit of high pH by convention so that
A,G”(site) = -RTln(l + 106.y-pH + 1013.3-2pH 1 (7.7-4)

Equation 7.7-3 can be written as
RTln(1 + i06.9-pH + 1013.3-2pH )K‘
= -RTln - 960.44 - 4RTln(lOPPH) - A,G”(site-succ) (7.7-5)
Substituting equation 7.6-2 yields

A,G”(site-succ) = - 707.11 - 4RTlr1(10-~~)
~
~ ~ l + 107.5-p~ + 1014.0-~PH (7.7-6)
)
l
(
The values of A,G” for the catalytic site, succinate, and site-succinate calculated
in this way are shown in Table 7.5. Similar calculations have been made for
D-tartrate, L-tartrate, and meso-tartrate using data from Table 7.4. Since the AfGo
values for these three reactants are not known, the convention has been adopted
that they are equal to zero. Table 7.5 shows that standard transformed Gibbs
energies of formation at specified pH values can be calculated for an unoccupied
binding site and the binding site occupied by a ligand.