Page 130 - Thermodynamics of Biochemical Reactions

7.3 Partial Dissociation of Tetramers into Dimers 127

Table 7.2 Equilibrium Mole Fractions of Forms of the Tetramer at 21.4”C, 1 bar, pH
7.4, [Cl-] = 0.2 M, and 0.2 M Ionic Strength at [heme] = M

[O,] = xlO-‘M [OJ = 10 - 5 ~ [O,] = 2 x M

0.317 0.037
0.139 0.033
0.0 17 0.008
0.069 0.065
0.458 0.858

Nore: See Problem 7.1.

For these five forms of the tetramer, A,G”’(TotT) is the same as the binding
potential II defined by Wyman (1948,1964) as II = RTlnP, except for the
difference in sign. The binding polynomial P is defined as (see Section 1.3)

[MI + [ML] + [ML,] + ..
P= (7.2-15)
[MI
The binding polynomial for the binding of oxygen by the tetramer is given by
P, = 1 + Kkl[02] + KklK&2[02]2 + Kk1Kk2Kk3[O2l3

+ KkiKk2Kk3Kk,[OJ4
= 1 + Kk,CO,l(l + K&,CO,I(1 + Kk,CO,I(1 + Kk,Co,l)>) (7.2-16)
Binding potentials n become more positive with increasing stability, in contrast
to Gibbs energies of formation which become more negative. The values of Af G”’
and Fl agree for the tetramer because of the convention that AfG”(T) = 0. But
for the dimer D, these two physical quantities are not equal as shown in the next
section.
In this section we have seen that in addition to the Af G‘’ for the various forms
of the tetramer at a specified pH, the sum of various forms of the tetramer have
AfG”’ values that are function of [O,].

7.3 PARTIAL DISSOCIATION OF TETRAMERS
INTO DIMERS

The tetramer (a2P2) of hemoglobin is partially dissociated into dimers (2P). Mills,
Johnson, and Ackers (1976) give the following value for the apparent equilibrium
constant OK; (their symbol) for the association reaction in the absence of oxygen:

(7.3.1)

Therefore, since the standard transformed Gibbs energy of formation of T is taken
as zero, the standard transformed Gibbs energy of formation of D is 30.083 kJ
mol-’. The equilibrium constants for the dimer are given by

D + 0, = D(OJ K;, = cD(02)1 = 3.253 x lo6 (7.3-2)
CDICO2l

D(0,) + 0, = D(02)2 K;, = CD(02)21 = 8.155 x los (7.3-3)
CD(02)lCO21
Since A,G’’(D) = 30.08 kJ mol-’, A,G”O(D) is given by (Alberty, 1996b)

A,G”’(D) = 30.08 - R7ln P, (7.3-4)