Page 132 - Thermodynamics of Biochemical Reactions

7.4 Experimental Determination of Seven Apparent Equilibrium Constants 129

The values of A,G"'(TotT) in Table 7.1 and AfG"'(TotD) in Table 7.2 make
it possible to calculate the apparent equilibrium constant for the reaction
2TotD = TotT (7.3-7)
at three concentrations of molecular oxygen. The apparent equilibrium constant
K", which is a function of [O,], is defined by
[TotT]
K" = (7.3-8)
[Tot D]
This apparent equilibrium constant can be written in terms of the binding
polynomials of tetramer and dimer and "K';:

(7.3-9)

As [O,] approaches infinity, this apparent equilibrium constant approaches a
limiting value because the reaction becomes

2D(02)2 = T(02)4 (7.3- 10)
in the limit of infinite [O,]. The value of this apparent equilibrium constant at
very high oxygen concentrations is given by

(7.3-1 1)
Note that this equilibrium constant is 5 x lo4 times smaller than for 2D = T (see
Problem 7.3). This is not unexpected because of the cooperative effect in the
tetramer.

rn 7.4 EXPERIMENTAL DETERMINATION OF SEVEN
APPARENT EQUILIBRIUM CONSTANTS

The fractional saturation of tetramer Y, and the fractional saturation of dimer YD
are functions only of [O,] at specified 7; P, pH, etc., as shown by equations 7.1-18
and 7.3-6. However, since the tetramer form is partially dissociated into dimers,
the fractional saturation of heme Y is a function of both [O,] and [heme]. Ackers
and Halvorson (1974) derived an expression for the function Y([O,], [heme]).
When Legendre transforms are used, a simpler form of this function is obtained,
and it can be used to derive limiting forms at high and low [heme]. These limiting
forms are of interest because they show that if data can be obtained in regions
where Y is linear in some function of [heme], extrapolations can be made to
obtain Y, and Y,. These fractional saturations can be analyzed separately to
obtain the Adair constants for the tetramer and the dimmer (Alberty, 1997a).
When the tetramer and dimer are in equilibrium, the fractional saturation of
heme is given by

Y=fD% +fTYT (7.4-1)
where fD = 2[TotD]/[heme] is the fraction of the heme in the dimer and
fT = 4[TotT]/[heme] is the fraction of the heme in the tetramer. Since
fT = 1 - f,, equation 7.4-1 can be written
Y = YT + fD( YD - YT) (7.4-2)
The concentration of heme in the solution is given by

[heme] = 2[TotD] + 4[TotT] = 2[TotD] + 4K"[TotDI2 (7.4-3)
where equation 7.3-8 has been used in writing the last form. Applying the