Page 63 - Thermodynamics of Biochemical Reactions

58 Chapter 4 Thermodynamics of Biochemical Reactions at Specified pH

As shown in Chapter 1, it is convenient to discuss the thermodynamics of
biochemical reactions at specified pH in terms of reactants like ATP, which are
sums of species at equilibrium at the specified pH. The apparent equilibrium
constants K' for biochemical reactions in dilute aqueous solutions are functions
of 7; pH, and ionic strength. This chapter introduces the thermodynamics needed
to discuss biochemical reactions in terms of thermodynamic properties of reac-
tants (sums of species with different numbers of hydrogen atoms), the relations
between these properties, and the relations between the properties of species and
the properties of reactants. It also provides information on criteria for sponta-
neous change and equilibrium. An important issue in these calculations is the
number of intensive degrees of freedom and the total number of degrees of
freedom. The goal of this chapter is the production of functions of pH and ionic
strength that make it possible to calculate the apparent equilibrium constants and
transformed enthalpies of reaction of biochemical reactions at 298.15 K and
desired pHs in the range 5 to 9 and ionic stregths in the range zero to 0.35 M.
When the pH is specified, we enter into a whole new world of ther-
modynamics because there is a complete set of new thermodynamic properties,
called transformed properties, new fundamental equations, new Maxwell equa-
tions, new Gibbs-Helmholtz equations, and a new Gibbs-Duhem equation. These
new equations are similar to those in chemical thermodynamics, which were
discussed in the preceding chapter, but they deal with properties of reactants
(sums of species) rather than species. The fundamental equations for transformed
thermodynamic potentials include additional terms for hydrogen ions, and
perhaps metal ions. The transformed thermodynamic properties of reactants in
biochemical reactions are connected with the thermodynamic properties of species
in chemical reactions by equations given here.
The relationships between the thermodynamic properties of chemical reac-
tions and the transformed thermodynamic properties of biochemical reactions
have been treated in several reviews (Alberty, 1993a, 1994c, 1997b, 2001e).
Recommendations .for Nomenclature and Tables in Biochemical Thermodylzanzics
from an IUPAC-IUBMB Committee were published in 1994 and republished in
1996. This report is available on the Web: http:llivww chem.qmw. ac. uhlimbmbl
thermodl.
The treatment of pH as an independent variable can be extended to pMg or
the free concentrations of other cations that are bound reversibly by species of a
reactant.

4.1 FUNDAMENTAL EQUATION FOR A
BIOCHEMICAL REACTION SYSTEM AT
SPECIFIED pH

In a biochemical reaction one or more reactants may be weak acids or H+ may be
produced or consumed by the reaction. Therefore the specification of the pH
means that the concentration of a reacting species is held constant, and as a
consequence the equilibrium composition will be different at different pHs.
Actually the pH may drift during a biochemical reaction if the reaction produces
or consumes H', but the pH is measured at equilibrium and the experimental
value of K' corresponds with this pH. To find the criterion for equilibrium at
specified 7: P, and pH, it is necessary to use a Legendre transform (see Section 2.5)
to define a transformed Gibbs energy G' that has the chemical potential of H+ as a
natural variable (see Section 2.2). This transformed Gibbs energy provides the
criterion for equilibrium and spontaneous change at the specified pH. The
Legendre transform of the Gibbs energy for this purpose is (Alberty, 1992a. 1992c)
G' = G - n,(H)p(H+) (4.1 - 1)

where n,(H) is the total amount of the hydrogen component (see Section 3.3) and