Page 125 - Thermodynamics of Biochemical Reactions

122 Chapter 7 Thermodynamics of the Binding of Ligands by Proteins

The binding of oxygen by hemoglobin is discussed by Wyman and Gill (1 990)
and ligand-receptor energetics are discussed by Klotz (1997).

7.1 THE BINDING OF OXYGEN BY HEMOGLOBIN
TETRAMERS

Since a protein is a weak acid, its transformed thermodynamic properties are
functions of pH, and that is discussed specifically in Section 7.6. However, it is
not necessary to examine the pH dependence of the binding of a ligand first. This
is illustrated by the consideration of the binding of oxygen by hemoglobin at
specified pH. Since the pH is an independent variable, the criterion for equilib-
rium is provided by the transformed Gibbs energy G‘. Hemoglobin is more
complicated than a weak acid in that its binding properties are affected by
chloride ion and perhaps other ligands in the buffer used. If necessary, the
Legendre transform to define G’ at a specified pH can include specification of the
concentrations of chloride ions and other ligands that affect the binding of
molecular oxygen. Since the tetramers of hemoglobin (x2p2, represented here as
T) can combine with 1 to 4 molecules of oxygen, the fundamental equation for
the transformed Gibbs energy G’ for the binding by tetramer at a specified pH is
4
dG’ = -S’dT+ VdP + 1 p’(T(02)i)d/z’(T(02)i)
i=O
+ p’(02)dd(02) + RTln(lO)n,(H)dpH (7.1- 1)
where p’(T(02)J is the transformed chemical potential of the sum of various
protonated species binding i molecules of molecular oxygen and /I’(T(O~)~) is the
amount of species binding i molecules of molecular oxygen. When equation 7.1-1
is integrated at constant values of the intensive variables,

(7.1-2)
is obtained.
The biochemical equations for the binding reactions can be written in
different ways, but the usual way is

(7.1-3)

T(0,) + 0, = T(02), Kk2 = [T(O~)~l = 1.221 104 (7.1-4)
[IT(O,)lII021

T(O,), + 0, = T(02)“ Ki4 = cT(02)41 = 6.644 x los (7.1-6)
CT(O,),ICO21
where the values for the apparent equilibrium constants are those determined by
Mills, Johnson, and Ackers (1976) for human hemoglobin at 21.5 C, 1 bar, pH
7.4, [Cl-] = 0.2 M, and 0.2 M ionic strength. Molar concentrations are used. but
the apparent equilibrium constants are considered to be dimensionless.
The following equilibrium conditions for the four reactions (see 7.1-3 to 7.
can be derived using equation 7.1-1:
P‘(T) + p’(O2) = p’(TO2) (7.
P’(T(O2)) + 1402) = p’(T(Od2) (7.

p’(T(02)2) + p’(O2) = p’(T(02)3) (7.
p’(T(02)3) + LL’(02> = !L’(T(02)4) (7.1