Page 81 - Thermodynamics of Biochemical Reactions

76 Chapter 4 Thermodynamics of Biochemical Reactions at Specified pH

When the reactant of interest consists of two species with different numbers
of hydrogen atoms, the pK of the weak acid is needed to calculate A,G'"(I = 0)
of the two species, and the calculation is more complicated. The standard
transformed Gibbs energy of formation of a pseudoisomer group containing two
species is given by
1
A,G'" = AfCi0 - RTln(1 + 10yK1-pH (4.10- 10)
where pK, is the value at the experimental ionic strength at 298.15 K calculated
using
pK1(l) = pK,(I = 0) + 0.510651(C~,z~)1"~ (4.10-1 1)
1 + 1.6I1I2

Now equation 4.10-9 is used to adjust AfGlo(I) to ArGy(Z = 0). After A,GY(I = 0)
has been calculated, AfG:(I = 0) can be calculated using
A,G:(I = 0) = A,G:(Z = 0) - RTln(lO)pK,(I = 0) (4.10- 12)

A Mathematica program calcGef2sp has been written to produce output in
the form of equation 3.8-1 for a reactant made up of two species. It is given in the
package BasicBiochemData2. This output can be added to the database in
BasicBiochemData2 and can be used to calculate A,G" of the reactant at 298.15
K, pH 5 to 9. and ionic strengths 0 to 0.35 M.
When the reactant consists of three species with different numbers of
hydrogen atoms, equation 4.10-10 becomes
A,G'" = ArGP - RTln(1 + 1OpK1PH + 10pK1ipK2~2pH) (4.10-13)
Ar G;"(I = 0) can be calculated by using equation 4.10-9, and equation 4.10- 10 can
be used to calculate AfC?(I = 0). Then A,G',O(I = 0) can be calculated using
AfG:(Z = 0) = A,Gi(Z = 0) - RTln(lO)pK,(I = 0) (4.10-14)

A Mathematica program calcGef3sp has been written to produce output in the
form of equation 3.8-1, and it is given in BasicBiochemData2.
The species matrix for a reactant can be verified by use of the programs
calcdGmat and calckprime, which are also given in BasicBiochemData2. The
program calcdGmat yields the function of pH and ionic strength for A,G" of the
reactant. The program calckprime can then be used to calculate K' for the
reaction used at the experimental pH and ionic strength.
A good deal of work will have to be done to extract species information from
the apparent equilibrium constants that have been reported for about 500
reactions. Beyond that, use can be made of analogies with known reactions; for
example, the various ribonucleotide phosphates (AMP, GMP, CMP, UMP, and
dTMP) are believed to have the same hydrolysis constants and pKs. Beyond that,
the group additivity method (Alberty, 1998c) can be used to estimate ther-
modynamic properties.

4.11 TABLES OF STANDARD TRANSFORMED
THERMODYNAMIC PROPERTIES AT 298.15 K FOR
BIOCHEMICAL REACTANTS AT SPECIFIED pH
AND IONIC STRENGTH

Table 4.2 provides A,G" and ArHo for species of 131 biochemical reactants at
298.15 K in dilute aqueous solutions at zero ionic strength. These values are
available in the package BasicBiochemData2 (Alberty, 2002d), which is the first
item in the second part of this book. These values can be used to calculate ArG:"
and A, HI" for biochemical reactants at desired pHs in the range 5 to 9 and desired
ionic strengths in the range 0 to about 0.35 M, as described in this chapter.