Page 129 - Thermodynamics of Biochemical Reactions

126 Chapter 7 Thermodynamics of the Binding of Ligands by Proteins

Table 7.1 Standard Transformed Gibbs Energy of Formation AfG'" and Standard Further Transformed Gibbs
Energies of Formation A,G"" of Hcinoglobin Tetramer at 21.5T, 1 bar, pH 7.4, [Cl-] = 0.2 M, and 0.2 M
Ionic Strength
A,G""/kJ mol

A,G'',kJ mol-' [Oz]=5 x 10-' M [O,]=lO-s M [O,]=~X 10-5M
~ ~~ ~~
T 0 0 0 0
PO,) - 10 092 2 3711 09 2 012 97 0 314 85
T(0,)2 - 17 045 5 10561 10 7 164 84 3 768 59
T(02)j - 32 5768 8833 13 3 738 77 - 1 355 60
~(0~4 -49 3213 5891 89 -0 900 59 - 7 693 07
A,G"J(TotT)/kJ mol ' -0736 51 - 0 73651 -2814 90 - 8 069 06

Sourti.. Ikprintcd from K. A. Alberty, Biop/i).s. C/iei?i. 62, 141 159 (1996), with permission from Elsevier Science
~
Norr: See Problem 7.1.
p"(T(O,),) = p"(T(O,),) = p"(T(0JJ. Therefore equation 7.2-5 can be written

dC" = -SdT+ VdP + p"(T)dnh(TotT) - n;(O,)dp'(O,) + RTln(lO)n,(H)dpH
(7.2-1 1)

This shows that the natural variables for the further transformed Gibbs energy G"
are 7: P, n:(T), p'(O,), and pH, and so the criterion for spontaneous change and
equilibrium is dC" < 0 at constant 7: P, nk(T), p"(02), pH. There are D" = 5
natural variables and F" = 4 independent intensive variables, the same as for G'.
The integrated form of equation 7.2-11 at constant values of the intensive
variables is

G" = p"(T)nk(TotT) (7.2- 12)
so this system behaves like a one-component system. Under these conditions the
entity TotT, which is made up of the various forms of the tetramer, has a set of
further transformed thermodynamic properties. As we have seen before, the
standard further transformed Gibbs energy of formation A,G""(TotT) of the
tetramer pseudoisomer group at a specified concentration of molecular oxygen
can be calculated by using equation 4.5-1 for an isomer group.
Derivations are carried out with chemical potentials, but calculations are
carried out with Gibbs energies of formation, and so equation 7.2-2 is used in the
form

Arc:" = AfCio + AJi(02)(AfCo(02) + RTln[O,]) (7.2- 13)
where A,G" values are given after equation 7.1-20. The values of A,C;" calculated
using equation 7.2-13 for the five forms at three [O,] are given in Table 7.1. The
ArGi") values for T are independent of [O,] because T does not contain 0,. The
other AfG;" values decrease as [O,] is raised because the oxygenated forms
become inore stable relative to T. The value of A,G""(TotT) is calculated using
the partition function in equation 4.5-1. A,G""(TotT) is more negative than A,G;"
for any of the pseudoisomers and becomes more negative as the concentration of
oxygen is increased. The entries in Table 7.1 were calculated with the Matlumut-
icu program calctgfT (Alberty, 1996b).
The equilibrium mole fractions of the various forms of the tetramer can be
calculated using the following analog of equation 4.5-2:
A,G""(TotT) - AfGa]
ri = exp (7.2- 1 4)

These equilibrium mole fractions are given in Table 7.2.