Page 19 - Thermodynamics of Biochemical Reactions

12 Introduction to Apparent Equilibrium Constants

specified pH (and pMg) the biochemical reaction is written in terms of sums of
species:

ATP + H20 = ADP + PI (1.4-1)
Biochemical textbooks often add a H+ on the right-hand side, but this is
stoichiometrically incorrect when the pH is held constant, as we will see in the
next section. It is also wrong, in principle, as we will see in Chapter 4, since
hydrogen atoms are not balanced by biochemical reactions because the pH is held
constant. The statement that the pH is constant means that in principle acid or
alkali is added to the reaction system as the reaction occurs to hold the pH
constant. In practice, a buffer is used to hold the pH nearly constant. and the pH
is measured at equilibrium.
The expression for the apparent equilibrium constant K' for reaction 1.4-1 is

(1.4-2)

because the activity of water is taken as unity in dilute aqueous solutions at each
temperature. The apparent equilibrium constant K' is a function of 7; P, pH.
pMg, and ionic strength. In the neutral region in the absence of magnesium ions,
ATP, ADP, and Pi each consist of two species, and so
([ADP3-] + [HADP2-])([HPO~-] + [H2P0,])
K' =
[ATP4-] + [HATP3-]
- f [H+I/KIPi)
-- [ADP3-l[HPoi-I (l + [H+l/KIADP)(l
[ATP4-] (1 + ~H+I/K,ATP)

(1.4-3)

where Kref is the chemical equilibrium constant for the chemical reference reaction
ATP4- + H,O = ADP3- + HPOi- + H+ (1.4-4)
[ADP3 -][HPOi-] [H '1
Kref = (1.4-5)
[ATP4-]
Since the acid dissociation constants are known, the value of Kref can be
calculated from the value of K' at a pH in the neutral region in the absence of
metal ions by using equation 1.4-3. Values of Kref at zero ionic strength are given
in Table 1.2 for six reference reactions.
When magnesium ions or other metal ions are bound reversibly and a wider
range of pH is considered, equation 1.4-3 becomes more complicated. Therefore
it is convenient to use the nomenclature of binding polynomials introduced in
equation 1.3-8. The binding polynomial of ATP is given in equation 1.3-12, and
the binding potentials for ADP and PI are as follows:
PAD, = 1 + ~ CH'1 + W+I2

KIADP KlADPK2ADP
(1.4-7)

Thus the apparent equilibrium constant for the hydrolysis of ATP as a function of
[H'] and [Mg2+] is given by

K' = KrefPADPPPj
(1.4-8)
W+lPATP
Since the chemical equilibrium constants in this equation are known at zero ionic
strength at 298.15 K and are given in Table 1.2, K' can be calculated at any pH